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+Caustic spin wave beams in soft, thin ﬁlms: properties and classiﬁcation
+Alexis Wartelle,∗ Franz Vilsmeier, Takuya Taniguchi, and Christian H. Back
+Fakult¨at fur Physik, Technische Universit¨at M¨unchen, Garching, Germany
+(Dated: January 4, 2023)
+In the context of wave propagation, caustics are usually deﬁned as the envelope of a ﬁnite-extent
+wavefront; folds and cusps in a caustic result in enhanced wave amplitudes. Here, we tackle a related
+phenomenon, namely the existence of well-deﬁned beams originating solely from the geometric
+properties of the corresponding dispersion relation. This directional emission, termed caustic beam,
+is enabled by a stationary group velocity direction, and has been observed ﬁrst in the case of
+phonons. We propose an overview of this “focusing” eﬀect in the context of spin waves excited
+in soft, thin ferromagnetic ﬁlms. Based on an analytical dispersion relation, we provide tools for
+a systematic survey of caustic spin wave beams. Our theoretical approach is validated by time-
+resolved microscopy experiments using the magneto-optical Kerr eﬀect. Then, we identify two cases
+of particular interest both from fundamental and applicative perspectives. Indeed, both of them
+enable broadband excitations (in terms of wave vectors) to result in narrowband beams of low
+divergence.
+I.
+INTRODUCTION
+The collective motion of magnetic moments in a ma-
+terials, referred to as spin waves, has shown remarkable
+properties from a fundamental perspective.
+Examples
+range from anisotropic dispersion in thin ﬁlms [1], rel-
+evant for the ﬁeld of magnonics, to Bose-Einstein con-
+densation of magnons [2], through restricted-relativity-
+like bounded domain wall velocities [3].
+Applications
+of magnetization dynamics also abound, starting with
+the inﬁnite-wavelength ferromagnetic resonance (FMR)
+[4] and going all the way towards sub-micrometer wave-
+lengths, which are currently viewed as promising alterna-
+tive information carriers in the ﬁelds of magnonics [5]. In
+addition to the absence of Joule heating and the potential
+device downscaling (using small wavelengths), spin wave
+interference is an appealing prospect [6] as it allows logic
+operations through the design of the propagation lines.
+Several experimental techniques are readily available
+for the study of spin waves [1], especially in the case
+of thin ﬁlms or patterned elements thereof.
+Among
+them, micro-/phase-resolved Brillouin Light Scattering
+(BLS) [7], Time-Resolved Magneto-Optical Kerr Eﬀect
+(TR-MOKE) microscopy [8], and time-resolved Scan-
+ning Transmission X-ray Microscopy (TR-STXM) with
+magnetic sensitivity through X-ray Magnetic Circular
+Dichroism (XMCD [9]) [10] have demonstrated outstand-
+ing imaging capabilities. Nevertheless, the usually very
+small amplitudes of magnetization precession associated
+to spin waves as well as their attenuation lengths (typi-
+cally on the micrometer scale) pose a signiﬁcant challenge
+both for fundamental investigations and for applications.
+To be of practical use, spin waves must be harnessed
+via a power-eﬃcient strategy: some approaches like Win-
+ter’s magnons rely on channeling along domain walls [11],
+∗ alexis.wartelle@ens-lyon.org; Present address: Universit´e Greno-
+ble Alpes, CNRS, Grenoble INP, SIMaP, 38000 Grenoble, France
+others rely on careful control of spin wave scattering [12].
+Another possibility would take advantage of caustic spin
+wave beams (CSWBs), i.e.
+spin wave beams of well-
+deﬁned propagation direction, narrow angular width and
+higher power compared to e.g. Damon-Eshbach-type [13]
+spin waves.
+Furthermore, caustics in soft, thin ferro-
+magnetic ﬁlms can be very diﬀerent from the well-known
+acoustical or optical caustics, which originate from inho-
+mogeneous media [14–16], : here, spin wave caustics can
+arise in perfectly homogeneous ﬁlms in broad ranges of
+conditions solely because of suﬃcient anisotropies in their
+dispersion relation. The latter indeed allows the direc-
+tion of the group velocity to be stationary around some
+wave vectors, leading to well-deﬁned directions of wave
+propagation associated to signiﬁcantly stronger emission.
+In the context of phonon propagation, such phenomena
+have been referred to as “focussing” [17], and they have
+been observed and investigated since 1969 [17–21].
+By contrast, caustics in ferromagnetic ﬁlms were re-
+ported for the ﬁrst time ca. 30 years later [22]. There
+has been quite a few reports since then [23–31] but, to
+the best of our knowledge, there exists to date no sys-
+tematic survey of the properties of spin wave caustics,
+not even focusing on a certain type of systems e.g. ul-
+trathin ﬁlms with perpendicular anisotropy, or soft thin
+ﬁlms.
+In this work, we restrict ourselves to the latter
+and give an overview of caustics in soft thin ﬁlms, as well
+as tools to further investigate them. Moreover, we high-
+light two special cases which seem particularly appealing
+notably for application in magnonics.
+II.
+MODEL
+A.
+General considerations
+Our starting point is the model derived by Kalinikos
+and Slavin [32] for spin waves in soft ferromagnetic
+thin ﬁlms.
+These excitations correspond to a time-
+and space-dependent magnetization −→
+M(⃗r, t), yet its norm
+arXiv:2301.01220v1  [cond-mat.mes-hall]  3 Jan 2023
+
+2
+Ms = ||−→
+M(⃗r, t)|| the spontaneous magnetization is uni-
+form.
+As a result, it is simpler to consider the re-
+duced magnetization −→
+m(⃗r, t) = −→
+M(⃗r, t)/Ms with norm
+1.
+We focus on the linear regime i.e.
+the deviation
+δ−→
+m(⃗r, t) = −→
+m(⃗r, t) − −→
+m0(⃗r, t) from the equilibrium mag-
+netization (when no excitation is applied) −→
+m0 is such that
+||δ−→
+m|| ≪ 1. Under the assumption of negligible mode
+mixing and of a perfectly isotropic ferromagnetic mate-
+rial, one may write the dispersion relation of a thin ﬁlm
+as:
+ω2 =
+�
+γ0Ha + 2Aγ0
+µ0Ms
+k2��
+γ0
+�
+Ms + Ha
+�
++ 2Aγ0
+µ0Ms
+k2�
+−γ2
+0M 2
+s · ξ(kd)
+�
+1 − ξ(kd) + Ha
+Ms
++ 2Aγ0
+µ0M 2s
+k2�
+cos2 ϕ
++γ2
+0M 2
+s · ξ(kd) · [1 − ξ(kd)]
+(1)
+where ω is the spin wave angular frequency, γ0 = µ0|γ|
+with γ = qe/(2me) the electron’s gyromagnetic ratio
+(qe = −e and me being the electron’s charge and mass,
+respectively) and µ0 the permeability of vacuum, A is the
+micromagnetic exchange constant for the soft ferromag-
+netic material of interest, Ms its spontaneous magnetiza-
+tion, k the spin wave’s wavenumber corresponding to its
+wave vector −→k , Ha = ||−→
+Ha|| the strength of the externally
+applied magnetic ﬁeld −→
+Ha from which ϕ = angle
+�−→
+Ha, −→k
+�
+the wavefront angle is deﬁned, d the ﬁlm thickness, and
+ξ is the function whose values are deﬁned as:
+ξ(u) = 1 − 1 − e−u
+|u|
+.
+(2)
+As a consequence of the ferromagnetic material’s soft-
+ness, in the absence of excitation, the equilibrium mag-
+netization conﬁguration in our thin ﬁlm is the single-
+domain state, with a corresponding reduced magnetiza-
+tion −→
+m0 exactly along the applied ﬁeld. The orientations
+of −→
+m0, −→
+Ha, and −→k are illustrated in Fig. 1, which also
+highlights the natural wavelength λ0 = 2π/||−→k || of the
+spin wave as well as the unit vectors −→
+ex, −→
+ey and −→
+ez.
+Here, we focus on spin waves with no amplitude node
+across the ﬁlm thickness, i.e. we do not consider per-
+pendicular standing spin waves (PSSWs). However, we
+do note that the latter may play a role in experiments
+performed on suﬃciently thick ﬁlms where a realistic an-
+tenna for instance could excite them due to its inhomo-
+geneous magnetic ﬁeld.
+We introduce the following quantities:
+the Larmor
+angular frequencies associated to magnetization ωM =
+γ0Ms and to the applied magnetic ﬁeld ωH = γ0Ha, the
+material’s dipolar-exchange length lex =
+�
+2A/(µ0M 2s ).
+We then rewrite the equation as:
+−
+→
+ex
+−
+→
+k
+−→
+Ha
+−→
+m0
+φ
+λ0= 2π
+||−
+→
+k||
+= 2π
+k
+0
+δmz
+−
+→
+ez
+−
+→
+ey
+FIG. 1. Schematic representation of a spin plane wave prop-
+agating in a soft thin ﬁlm.
+The grey scale codes the local
+perpendicular component of the dynamic component of mag-
+netization, δmz.
+ω2
+ω2
+M
+=
+� ωH
+ωM
++ l2
+exk2
+� �
+1 + ωH
+ωM
++ l2
+exk2
+�
+−ξ(kd)
+�
+1 − ξ(kd) + ωH
+ωM
++ l2
+exk2�
+cos2 ϕ
++ξ(kd)
+�
+1 − ξ(kd)
+�
+(3)
+Introducing the reduced frequency ν = ω/ωM and ap-
+plied ﬁeld h = ωH/ωM = Ha/Ms, and normalizing both
+the dipolar-exchange length and wavenumber to the ﬁlm
+thickness d using η = lex/d and ˜k = kd, we arrive at:
+ν2 =
+�
+h + η2˜k2��
+1 + h + η2˜k2�
+−ξ(˜k)
+�
+1 − ξ(˜k) + h + η2˜k2�
+cos2 ϕ
++ξ(˜k)
+�
+1 − ξ(˜k)
+�
+(4)
+With this, it is clear that any given experiment of spin
+wave excitation corresponds to a speciﬁc value of the di-
+mensionless triplet (η, ν, h). In other words: they are
+the only independent parameters within this model.
+For a value of (η, ν, h), the solution to (4) is the pos-
+sibly empty set of accessible dimensionless wave vectors
+−→k d.
+The existence and properties of spin wave caus-
+tics depend on the geometrical characteristics of this set,
+which is why we are ﬁrst going to review several of its
+general properties.
+Keeping in mind that we focus on applied ﬁelds below
+the ferromagnetic resonance ﬁeld at the excitation fre-
+quency, we actually always have a non-empty solution,
+which is usually a closed curve winding around the ori-
+gin in wave-vector space. This is the so-called slowness
+curve, in reference to the fact that at ﬁxed frequency
+k ∝ 1/||−→
+vp|| where −→
+vp is the phase velocity [33], oriented
+of course along the wave vector. Considering the parity
+of the cosine function and its antisymmetry for the re-
+ﬂection ϕ → π − ϕ, we may restrict our analysis to only
+the quadrant ϕ ∈ [0, π/2] and deduce the others using
+mirror symmetries.
+
+3
+One can also parametrize the slowness curve using a
+curvilinear abscissa: we deﬁne it to be zero for the lowest
+dimensionless wavenumber ˜kmin at ϕ = π/2. One can in-
+deed show that the reduced wavenumber solving Eq. (4)
+at ϕ = π/2 (resp. 0) is minimum (resp. maximum) on
+the quadrant ϕ ∈ [0, π/2]. Thus, at the largest dimen-
+sionless wavenumber ˜kmax = ˜k(ϕ = 0), the correspond-
+ing curvilinear abscissa sM corresponds to the length of
+the slowness curve in the quadrant ϕ ∈ [0, π/2] i.e. one
+fourth of the whole length of this curve.
+Another important geometrical aspect of the slowness
+curve that is central to the present work is the local
+normal to it. Considering its deﬁnition as a constant-
+frequency intercept of the dispersion relation in wave-
+vector space, by nature, the frequency gradient −→
+∇−
+→
+k ω is
+perpendicular to the slowness curve. As a result, the di-
+rection of the group velocity of spin waves −→
+vg = −→
+∇−
+→
+k ω can
+be directly read from the direction of the local normal to
+the slowness curve. In our notations, we point out that:
+−→
+∇−
+→
+k ω ≡
+�
+β=x,y,z
+∂ω
+∂kβ
+· −→
+eβ
+where
+kβ = −→k · −→
+eβ.
+In the following,
+we will use the angle θV
+=
+angle(−→
+Ha, −→
+vg).
+We point out that in the present case,
+phase and group velocities need not be collinear:
+on
+the contrary, there can be diﬀerences between θV and
+ϕ much larger than in cases of light propagation through
+anisotropic media [34]. Fig. 2 illustrates this on the ex-
+ample of a slowness curve reconstructed for a vanishing
+reduced applied ﬁeld.
+B.
+Distinctive features of dispersion relation
+caustics
+Typically, caustics in inhomogeneous media occur
+when a wavefront folds onto itself; in this situation, there
+exists a surface (or a line in 2D wave propagation) such
+that across it the number of rays passing through a point
+in space changes by an even number [15, 16]: this is the
+caustic. Equivalently, it can be viewed as the set of the
+local extrema of positions on the ray bundle on the wave-
+front, for all the wavefronts along the wave propagation.
+It is this extremal nature that grants these caustics large
+and localized intensities compared to other points on the
+ray bundle.
+In a geometrical optics approach, the in-
+tensity diverges as an initially ﬁnite-sized portion of the
+wavefront shrinks to a vanishing area [15]. A wave op-
+tics treatment however reveals that the intensity remains
+ﬁnite due to interferences: illumination proﬁles across
+caustics can in principle be determined by taking into
+account the variations of phase as a function of distance
+to the caustic [14].
+Such an approach has been used by Schneider et al.
+[26] for spin wave caustics excited by the scattering of
+a spin wave travelling in a waveguide terminating into a
+θV
+φ0
+−
+→
+k0d
+a)
+b)
+c)
+FIG. 2.
+a) Exemplary slowness curve for (ν, h, η)
+=
+(0.2873, 10−20, 0.15). As can be clearly seen in the polar plot
+of kd = ˜k(ϕ), the direction (ϕ0 =32.00°) of the phase veloc-
+ity −→
+vp and that (θV =108.9°) of the group velocity −→
+vg at the
+point −→
+k0d are very diﬀerent.
+b) Radiation pattern (δmz is
+grey-coded) of a hypothetical source exciting only wavenum-
+bers very close to ||−→
+k0||d. c) Plane wave corresponding to the
+carrier wave vector −→
+k0d (red lines are guides to the eye).
+full permalloy (Ni80Fe20) ﬁlm. However, this is a very
+diﬀerent situation compared to the above. Indeed, the
+wavefront does not fold onto itself due to spatial varia-
+tions of medium properties, rather, its extent is deter-
+mined almost exclusively (owing to the sub-wavelength
+source size) by the characteristics of spin wave propaga-
+tion. The latter are determined by the anisotropic spin
+wave dispersion relation, which allows caustics to form
+thanks to the possibility of stationary group velocity di-
+rection i.e. a beam with a well-deﬁned propagation direc-
+tion yet comprising a range of wave vectors in the vicinity
+of a carrier. More precisely, caustics correspond to local
+extrema of the group velocity direction; in other words, a
+caustic spin wave beam implies the existence of a caustic
+point ˜kc on the slowness curve such that:
+dθV
+d˜k
+����˜kc
+= 0.
+(5)
+The CSWB has then a carrier wavenumber ˜kc, corre-
+sponding to a central wavefront angle ϕc = ϕ(˜kc) and a
+
+90
+75°
+.09
+45°
+30°
+Ug
+15°
+kd
+0°
+0.0
+0.5
+1.0
+1.5
+2.0
+2.5
+kd4
+beam direction θV,c = θV(˜kc).
+Coming back to the wavefront extent, rays from wave
+vectors not close enough to the carrier cannot play a role
+in the caustic wave amplitude simply because of diﬀer-
+ences in propagation direction.
+More speciﬁcally, the
+experimental data presented by Schneider et al.
+sug-
+gests that beam divergences of 2° or less can be obtained.
+Thus, there seems to be a contradiction between the cu-
+bic dispersion which is assumed to deﬁne the beam pro-
+ﬁle and the measurements. The question of the CSWB’s
+proﬁle goes however beyond the scope of this work. Nev-
+ertheless, it is clear from the low beam divergences ob-
+served in many experimental reports [23, 27, 35] that only
+small, almost straight parts of the slowness curve must
+contribute to CSWB.
+In fact, integrating the contribution of wave vectors all
+the way to inﬁnity as done in [26] neglects the geometric
+impossibility for them to create waves travelling from the
+point source to a far-away point on the caustic. To put it
+diﬀerently: for geometrical reasons, caustics originating
+solely from anisotropies in the dispersion relation and
+excited by a point-like source naturally restrict the range
+of relevant wave vectors, in contrast to the case of caustics
+due to inhomogeneities in the propagation medium.
+We wish to emphasize the above by reminding that in
+most cases [15, 36], caustics are treated on the basis of
+wave propagation in an isotropic or weakly anisotropic
+medium. One consequence is the fact that the ﬂow of
+power, i.e. the group velocity, is along the wave vector
+or close to parallel to it [14]. While this remains a rea-
+sonable approximation for slightly anisotropic media (as
+in usual crystal optics), in the case of perfectly soft but
+fully polarized thin ferromagnetic ﬁlms this collinearity
+may break down dramatically, as was illustrated in Fig.
+2. Therefore, even small changes in wave vector may re-
+sult in drastic changes in group velocity direction. By
+contrast, large changes in wave vectors do not necessar-
+ily lead to strong variations in the apparent wavelength
+λ which we deﬁne as:
+λ = 2π · ||−→
+vg||
+−→k · −→
+vg
+=
+2π
+−→k · −→
+eg
+=
+λ0(ϕ)
+cos (θV − ϕ),
+(6)
+where we have introduced −→
+eg as a unit vector along the
+group velocity. The apparent wavelength is simply the
+spatial period measured along the beam direction. Since
+large diﬀerences θV − ϕ can easily be obtained (cf. Fig.
+2, where cos (θV − ϕ0) ≃ 0.227), and more importantly
+since the projection ˜k(ϕ) cos (θV − ϕ) may remain almost
+constant over signiﬁcant portions of the slowness curve,
+one should consider notions such as propagation-induced
+phase or spectral breadth [37] of a spin wave beam care-
+fully.
+III.
+RESULTS AND DISCUSSION
+A.
+Limit of model applicability: thick ﬁlms
+We start by providing an example of situation where
+the model we use cannot be fully trusted, so as to high-
+light its limitations. In Fig. 3 we show a case where the
+reconstructed slowness curve splits into two separate con-
+nected components above a certain threshold frequency.
+˜k
+FIG. 3. Slowness curves for η = 0.015, h = 10−20, and ν =
+0.331 (dashed blue line) resp. ν = 0.333 (full red line).
+Such a behaviour has been described by Kreisel et al.
+[38]: the model chosen for spin wave dispersion predicts
+a local maximum in the ω(k, ϕ = π/2) vs. wavenumber
+curve, but this extremum is not reproduced by a formal
+approach not based on the thin-ﬁlm approximation [39],
+and designed to tackle the dipole-exchange regime. The
+maximum’s presence leads to an additional pair of so-
+lutions in terms of wavenumber in a certain frequency
+range, corresponding to a splitting of the slowness curve
+into two separate components.
+Clearly, results obtained within our approach about
+caustics deep in the dipole-exchange regime are not trust-
+worthy. Empirically, we see the slowness curve splitting
+into separate components for values of η up to ca. 0.075;
+for the sake of comparison, the thinnest ﬁlms investigated
+by Kreisel et al. feature η < 0.035 according to literature
+data on yttrium iron garnet (YIG) [40]. Nevertheless, the
+absence of this splitting is no proof that the reconstructed
+slowness curve is accurate, and we shall remain cautious
+in discussing results concerning CSWBs with wavenum-
+bers in the dipole-exchange regime. Finally, we note that
+promising theoretical developments such as the dipole-
+exchange dispersion relations recently derived by Harms
+and Duine [39] could eventually allow a more accurate
+treatment of caustics in the dipole-exchange regime.
+
+90°
+75°
+60°
+45°
+v =0.333
+v =0.331
+30°
+15°
+5
+10
+15
+20
+25
+30
+35
+0
+kd5
+B.
+General features
+Let us have a look at a ﬁrst example of frequency and
+ﬁeld map of caustic properties in Fig. 4. In the presented
+graphs, the red color means that either the corresponding
+(h, ν) point was not investigated because its reduced ﬁeld
+is above the reduced FMR ﬁeld hFMR, or because no
+caustic points were found there.
+First of all, one can see that there is indeed a portion
+of the (h, ν) plane where no caustic points exist. This
+occurs for frequencies above a certain νm(h, η). Then,
+going down in reduced frequency, there appears to be an
+oblique boundary between two regions of the map. Above
+it, ˜kc quickly enters the dipole-exchange regime, which we
+will only present but not discuss quantitatively as it cor-
+responds to a situation where our model is less reliable.
+Below the boundary, the reduced caustic wavenumber is
+much smaller than 1. Correspondingly, a boundary which
+we will label νb(h, η) appears at the same position on the
+plot of ϕc; this angle also seems close to constant over
+much of the region below the boundary. In both cases,
+its sharpness decreases towards low h, and at vanishing
+reduced ﬁeld the transitions in ˜kc or ϕc are both smooth.
+All these features are represented on a simpliﬁed repre-
+sentation of the map of ˜kc shown as inset on the ϕc map,
+including the point (hc, νc) at which the sharp boundary
+seems to end. A zoomed-in view on (hc,νc) is shown in
+the inset of Fig. 4.b).
+In the following, we will refer to the lowest reduced
+ﬁeld at which this boundary is sharp as hc and denote
+νc = νb(hc, η).
+As we shall see in more details, this
+abrupt boundary corresponds to a change in the num-
+ber of caustic points by two. The lowest point (hc, νc)
+is actually a cusp in the domain of existence of the two
+additional caustic points. We point out that for all re-
+duced ﬁelds and frequencies, the maps shown in Fig. 4
+displays the lowest caustic wavenumber respectively the
+associated wavefront angle.
+Before moving on to discussing the low-frequency
+pocket, its boundary and the existence of additional caus-
+tic points, and ﬁnally the threshold frequency for the ab-
+sence of caustic points, we stress that the behaviour of
+caustics strongly depends on η. As an example, we show
+in Fig. 5 ﬁeld and frequency maps for η = 0.09, 0.3, 0.6
+(from left to right). At the lowest value, the boundary
+νb extends all the way to h = 0, whereas the two other
+maps do not display such a sharp behaviour. In addition
+to the expected changes in range of values for ˜kc, one can
+see that the overall shape of the domain of existence of
+CSWBs also changes. From here on, we will call this area
+D. From η = 0.09 to 0.3, we see that D has expanded in
+the vertical direction at low h. In even thinner ﬁlms, for
+η = 0.6, the average slope of νm(h, η) has not changed
+much, yet νm(0, η) has decreased; as a result, D shrinks
+vertically.
+By contrast, even if the caustic group velocity direction
+displays a similar wealth of features as the caustic wave-
+front angle and reduced wavenumber, the jumps across
+the boundary νb are much less signiﬁcant when they ex-
+ist. An example of this is shown in Fig. 6, which shows
+maps for θV,c at the same values of η as in Fig. 5.
+In a certain range of reduced dipolar-exchange length,
+we ﬁnd that there may actually be more than one caustic
+point on the slowness curve. Empirically, we observe that
+the additional caustic points may exist for ˜kc < 1. When
+this inequality holds, the number of caustic points is ei-
+ther equal to one or to three; two being possible but only
+on a 1D curve in the ﬁeld and frequency plane; this curve
+includes the aforementioned boundary νb. Qualitatively,
+this is due to the fact that in the corresponding range
+of ﬁeld and frequency, when dθV/d˜k crosses 0, it does so
+with a local behaviour somewhat reminiscent of a poly-
+nomial of the type P(˜k; a, b) = (˜k − ˜kc)3 +a·(˜k − ˜kc)+b,
+where a and b are real parameters. If a > 0, there ex-
+ists only one root, whereas if a < 0 and |b| is suﬃciently
+small, there exists three distinct roots.
+The domain in the ﬁeld and frequency plane with these
+three roots will be referred to as D3 from now on, by
+contrast with D1 = D \ D3 in which there is only one
+caustic point instead of three. We will now describe D3
+using the P(˜k; a, b) approximant to dθV/d˜k for the sake
+of simplicity.
+Let us start with Fig. 7, which displays the same ﬁeld
+and frequency map for ˜kc as in Fig. 4 along with the
+maps for the two other reduced caustic wavenumbers.
+The two additional solutions can be shown to coincide on
+the rounded boundary of D3 to the lower left, which will
+be referred to as ∂D3,l. Entering D3 through this bound-
+ary by increasing ν corresponds to the situation where |b|
+becomes small enough to allow the two additional caustic
+points (with respect to the one with lowest ˜kc), thanks to
+a being negative enough. Increasing h on the other hand
+mostly decreases a: upon crossing ∂D3,l, a pair of caus-
+tic points with higher ˜kc’s appears. Of course, exactly on
+∂D3,l the two additional roots of dθ/d˜k are identical.
+Starting from inside D3, if one increases the reduced
+frequency, eventually the caustic point with the interme-
+diate value of ˜kc merges with the one featuring the small-
+est reduced wavenumber.
+This happens on the other
+boundary of D3, which we will call ∂D3,u from now on.
+This situation corresponds to ν = νb(h, η). Just above
+this boundary, the value of b is low enough so that only
+one root of dθ/d˜k remains. That is the reason for the dis-
+continuity in ˜kc in Fig. 4: the lowest caustic wavenumber
+jumps to what was the highest of the three ˜kc’s below
+νb. Experimentally, this could imply that SW excitation
+around this threshold wavenumber would have marked
+changes in intensity as a function of frequency.
+Based on the above, since the two boundaries other
+than ferromagnetic resonance each imply that a diﬀer-
+ent pair of caustic points coincide, we can infer that on
+the cusped intersection of ∂D3,l and ∂D3,u, there exists a
+single caustic point corresponding to three of them coin-
+ciding on the slowness curve. This is precisely the point
+(hc, νc) from the inset in Fig. 4.
+It is important to note that while a purely math-
+
+6
+φc (◦)
+˜kc
+0
+0.15
+0.31
+0.46 0.62
+h
+0.1
+0.2
+0.3
+0.4
+0.5
+0.6
+0.7
+0.8
+0.9
+1.0
+0
+0.15
+0.31
+0.46 0.62
+0.1
+0.2
+0.3
+0.4
+0.5
+0.6
+0.7
+0.8
+0.9
+1.0
+89.98
+83.40
+55.60
+34.37
+2.40
+4.66
+0
+0.19 0
+h
+0
+0.25
+0.48
+ν
+0.74
+1.5
+Low-
+frequency
+pocket
+νm(h, η)
+h
+ν
+0
+0.62
+νb(h, η)
+νc
+hc
+a)
+b)
+h
+1.0
+FIG. 4. Frequency and ﬁeld maps for a value of η = 0.12. For high enough ﬁelds, a sharp upturn in both properties can be seen
+for reduced frequencies above ca. 0.42. We remind the reader that ﬁelds above ferromagnetic resonance are not considered.
+Only few level curves are displayed for the sake of clarity. a) Caustic wavefront angle ϕc, with a schematic representation of
+the map’s distinctive features as inset. b) Normalized wavenumber ˜kc = kcd; a zoomed-in view on the area where the upturn’s
+sharpness drastically changes.
+0
+0.21
+0.41 0.62
+h
+0.1
+0.2
+0.3
+0.4
+0.5
+0.6
+0.7
+0.8
+0.9
+1.0
+˜kc
+0
+0.21
+0.41 0.62
+h
+0.1
+0.2
+0.3
+0.4
+0.5
+0.6
+0.7
+0.8
+0.9
+1.0
+0
+0.21
+0.41 0.62
+h
+0.1
+0.2
+0.3
+0.4
+0.5
+0.6
+0.7
+0.8
+0.9
+1.0
+1.25
+2.50
+3.75
+5.00
+6.19
+0
+˜kc
+0.350
+0.700
+1.05
+1.40
+1.69
+0
+˜kc
+0.125
+0.250
+0.375
+0.500
+0.611
+0
+a)
+b)
+c)
+η = 0.09
+η = 0.3
+η = 0.6
+FIG. 5. Examples of ﬁeld and frequency maps for a) η = 0.09, b) η = 0.3, and c) η = 0.6; only the reduced caustic wavenumber
+is shown.
+
+Caustic wavefront angles Φc vs. v and h
+89.98
+1.0000
+0.9000
+83.40
+0.8000
+0.7000
+0.6000
+0.5000
+0.4001
+55.60
+0.3001
+0.2001
+0.1001
+0.0001
+0.1547
+34.37
+0.0000
+0.3095
+0.4642
+0.6190
+hTNormalized wavenumber at Φc vs. v and h
+4.662
+1.0000
+0.9000
+0.8000
+0.7000
+0.6000
+2.400
+0.5000
+0.4001
+0.3001
+0.2001
+0.1001
+0.0001
+0.1547
+0.0000
+0.3095
+0.4642
+0.6190
+0.000
+h000
+0.0475
+0.0950
+0.1425
+0.1900
+7Normalized wavenumber at Φc vs. v and h
+0.9991
+1.688
+0.8992
+0.7993
+1.400
+0.6994
+1.050
+0.5995
+0.4996
+kc
+0.700
+0.3997
+0.2998
+0.350
+0.1999
+0.1000
+0.000
+0.0001
+0.0000
+0.2063
+0.4126
+0.6189
+hNormalized wavenumber at Φc vs. v and h
+0.9991
+0.6118
+0.8992
+0.7993
+0.5000
+0.6994
+0.5995
+0.3750
+0.4996
+kc
+0.2500
+0.3997
+0.2998
+0.1250
+0.1999
+0.1000
+0.0000
+0.0001
+0.0000
+0.2063
+0.4126
+0.6189
+hNormalized wavenumber at Φc vs. v and h
+0.9991
+6.189
+0.8992
+0.7993
+5.000
+0.6994
+0.5995
+3.750
+0.4996
+kc
+2.500
+0.3997
+0.2998
+1.250
+0.1999
+0.1000
+0.000
+0.0001
+0.0000
+0.2063
+0.4126
+0.6189
+h7
+ematical analysis yields well-deﬁned, separate caustic
+points, experimentally the distinction between close caus-
+tic points may well be impossible.
+In fact, there ex-
+ists no straightforward experimental signature of dθV/d˜k
+crossing 0, and portions of the slowness curve where this
+derivative is small but non-zero can behave similarly to
+an actual caustic point, as was noted by Gallardo et al.
+[41]. Nevertheless, the presence of more than one caustic
+point constrains a slowness curve to be almost straight in
+their vicinities; this should then favour marked caustics.
+C.
+Low-frequency pocket
+The low-frequency regime is important as it corre-
+sponds to a well established domain of validity of our
+theoretical model as well as wavelengths which can still
+be excited and detected reasonably easily in experiments.
+1.
+Analytics
+As could be seen in Fig.5, the shape or even the
+existence of the low-frequency pocket strongly depends
+on the chosen value of η.
+Nevertheless, we can in-
+vestigate the behaviour of caustics there by taking the
+limit ν → 0.
+In order to remain below ferromagnetic
+resonance, we also take the limit h → 0.
+Assum-
+ing h = 0 simpliﬁes the computation of the quantity
+tan θV = tan ϕ · [1 + f(˜k, ν, η)], where f is a function
+given in the Supplementary Materials. We can then dif-
+ferentiate this with respect to ˜k, take the limit ν → 0 and
+Taylor-expand the derivative; the details are provided in
+the Supplementary Materials. Eventually, we ﬁnd that:
+˜kc(ν → 0) = 3ν2 + O(ν4).
+(7)
+It was expected that the caustic wavenumber goes to
+zero; we can furthermore show that the lowest reduced
+wavenumber on the slowness curve (still in zero applied
+ﬁeld) i.e. the Damon-Eshbach wavenumber goes to zero
+as:
+˜kmin(ν → 0) = 2ν2 + O(ν4)
+(8)
+which proves that CSWBs exist down to vanishing re-
+duced frequencies, regardless of their values. In this limit,
+the associated caustic wavefront angle is such that:
+cos ϕc =
+1
+√
+3 + O(ν2).
+(9)
+From the latter, we also get the CSWB direction θV,c:
+tan θV (˜kc, h → 0, ν → 0) = −2
+√
+2 + O(ν2)
+(10)
+The strength of this result lies with its independence on
+η; this is not surprising as in the limit we are considering,
+the CSWB’s wavelength diverges which means it must
+be much larger than both the ﬁlm thickness d and the
+dipolar-exchange length lex, however large they may be.
+The numerical values for the limits of ϕc and θV,c are ca.
+54.74° and 109.5°, respectively.
+2.
+Comparison with literature
+We present in Table I a comparison between experi-
+mental reports on caustics and predictions we make for
+the same conditions, focusing on the CSWB direction.
+Whenever there are three caustic points, the indicated
+predicted value for θV,c is the closest found across all
+three caustic points.
+We ﬁnd a reasonable agreement in quite a few cases,
+generally for the larger values of η (i.e. for thinner ﬁlms)
+with the notable exception of the report by Sebastian et
+al. [28]. However, in this case, the theoretical dispersion
+relation that we use may not be accurate any more due
+to the strong lateral conﬁnement of spin waves.
+Furthermore, we ﬁnd much larger discrepancies in sev-
+eral cases. For instance, if we consider the excitation of a
+caustic-like beam by Gieniusz et al. [43] at 4.62 GHz and
+under an induction of 98 mT in a 4.5 µm thick YIG ﬁlm,
+our model predicts a caustic point at reduced wavenum-
+ber 13.2, with a beam direction 169°. However, the rele-
+vant reduced wavenumbers in this experiment are in the
+range of a few percents [43], and the measured beam di-
+rection is 128°. The origin of this strong disagreement is
+easily understood by observing the derivative dθV/d˜k in
+this case. As Fig. 8 reveals, there exists a local minimum
+at ˜k ≃ 0.0659 for dθV/d˜k deep in the dipolar-dominated
+regime. Moreover, the associated group velocity direc-
+tion is 128°, and past the next local maximum, similar
+values of dθV/d˜k are reached again only for ˜k ≃ 0.9.
+This illustrates the impossibility to distinguish a close-
+to-straight slowness curve from a true caustic point from
+measurements alone.
+Discrepancies may also arise due to the source’s non-
+ideal excitation eﬃciency, for instance if it is too direc-
+tional. This is illustrated by the excitation of caustic-
+like spin wave beams by K¨orner et al. [44]. One of the
+reported TR-MOKE measurements deals with a 60 nm
+thin permalloy ﬁlm driven at an excitation frequency of
+16.08 GHz, under 160 mT applied induction; the authors
+observe twin beams with a wavefront angle of 65°, a beam
+direction 114°, and a reduced wavenumber of 0.314. Yet,
+the expected caustic spin wave beams in these condi-
+tions should feature a reduced wavenumber of 1.7063, a
+beam direction 138.62°, not to mention a wavefront angle
+of 53.27°. In this case, it appears that the excited spin
+waves simply correspond to the rather narrow portion of
+the slowness curve that could be excited by the authors’
+tapered coplanar waveguide segments [45]. Indeed, at the
+measured wavefront angle of 65°, in the authors’ experi-
+
+8
+TABLE I. Comparison between reports on CSWBs and our predictions for the beam direction θV,c.
+Ref. Excitation method
+Material (thickness in nm) Predicted θV,c Measured θV,c
+h
+ν
+η
+[28] Edge modes of a waveg-
+uide and nonlinearities
+Co2Mn0.6Fe0.4Si (30)
+113°
+123°
+3.81·10−2 0.287
+0.15
+[42] Corners of slotline termi-
+nation and scattering oﬀ
+a defect
+YIG (235)
+123°
+124°, 122°
+0.126
+0.427 7.36·10−2
+[35] Corners
+of
+slotline
+termination
+YIG (245)
+119°
+118°
+0.126
+0.427 7.06·10−2
+[43] Spin wave scattering oﬀ
+antidots
+YIG (4.5·103)
+169°
+128°
+0.557
+0.939 3.84·10−3
+[27] Collapsing
+spin-wave
+bullet
+YIG (5·103)
+137°
+137°
+1.040
+1.442 3.46·10−3
+[22] Spin wave scattering oﬀ
+a defect
+YIG (7·103)
+139°
+135°
+2.47·10−3 1.616 2.47·10−3
+mental conditions, the expected reduced wavenumber is
+about 0.28 (which falls rather far from zeroes in the an-
+tenna’s expected excitation eﬃciency [46]), and the beam
+direction 120.2°. We do not have an explanation for the
+remaining deviation in beam direction, though.
+3.
+Experimental results
+We now present results from experiments we have
+carried out in order to validate our theoretical ap-
+proach. Our aim here is to measure CSWBs and compare
+their properties with our predictions.
+In order to ac-
+cess CSWBs experimentally, the reciprocal-space Fourier
+components of its magnetic ﬁeld must span a broad range
+of wave vectors. The ideal situation where all wave vec-
+tors are accessible corresponds to an unrealistic point
+source, which can obviously not correspond to any high-
+frequency antenna. As a result, we choose a compromise
+between ease of fabrication, and broad-band excitation
+eﬃciency, namely a half-ring shaped stripline antenna.
+This design allows for a spin wave excitation of the slow-
+ness curve within ϕ ∈ [0, π], i.e.
+twice the quadrant
+previously investigated. Of course, this excitation is not
+uniform because of the microwave antenna dimensions on
+the order of a micrometer.
+Our experiments were carried out using Time-Resolved
+Magneto-Optical Kerr Eﬀect (TR-MOKE) microscopy.
+Here, the dynamic out-of plane component of the mag-
+netization δmz is spatially mapped in the xy-plane at a
+ﬁxed phase between the microwave excitation frequency
+and the laser probing pulses. This enables direct imag-
+ing of the spin wave propagation in the magnetic ﬁlm.
+The wavenumber resolution of the set-up lies within the
+dipolar-dominated regime. Indeed, our spatial resolution
+r is about 0.29 µm (see Supplementary Materials), so that
+for a ﬁlm thickness t ∼100 nm, the largest accessible re-
+duced wavenumbers are 2π/(2r) · t ∼ 1.
+It shall be noted that the position of the microwave an-
+tenna in the resulting Kerr images is extracted from the
+topography image which is acquired simultaneously and
+is proportional to the reﬂectivity of the sample. Further
+information on TR-MOKE can be found in the Supple-
+mentary Materials. These experiments were performed
+on a 200 nm thick YIG ﬁlm grown on a gadolinium gal-
+lium garnet (GGG) substrate using liquid phase epitaxy.
+Considering this materials’ parameters [40], if not stated
+otherwise, η = 0.087 for all measurements. On top of
+the YIG ﬁlm the 2 µm to 3 µm wide microwave antenna
+was patterned by optical lithography with subsequent Ar-
+presputtering and electron-beam-induced evaporation of
+Cr(5 nm)/Au(100 nm to 220 nm). During the measure-
+ment the external bias ﬁeld −→
+Ha was always kept ﬁxed
+such that it aligned with the legs of the antenna structure
+along the x-direction. A sketch of the measurement ge-
+ometry can be found in Fig. 9. At this stage, we point out
+one complication resulting from this design. When driv-
+ing the antenna with a microwave ﬁeld, the legs them-
+selves excite spin waves in the Damon-Eshbach geometry
+[13]. These modes are not of interest for the generation
+of CSWBs, but due to the relatively long attenuation
+length in YIG [35] they may propagate to the tip of the
+antenna and interfere with the spin waves excited by the
+half-ring. In order to suppress this eﬀect, two diﬀerent
+approaches where applied. Either the length of the an-
+tenna was set to 50 µm and the YIG between the legs and
+tip was etched away, or the antenna was patterned to be
+1 mm long in the ﬁrst place.
+The ﬁrst Kerr image shown in Fig. 10.a) was ob-
+tained at a constant microwave frequency f =1.44 GHz
+and an external ﬁeld µ0Ha =5 mT.
+This corresponds
+to h = 0.028, ν = 0.292. The width of the waveguide
+was 2 µm and the distance between the legs and the tip
+was 1 mm. In the spatial map, two spin wave beams with
+well-deﬁned propagation directions are visible; moreover,
+the phase and group velocities are clearly non-collinear
+to each other. Here, beam II stems from the waveguide
+excitation in the quadrant ϕ ∈ [π/2, π]. The beam angles
+
+9
+0
+0.21 0.41 0.62
+0.1
+0.2
+0.3
+0.4
+0.5
+0.6
+0.7
+0.8
+0.9
+1.0
+a)
+b)
+c)
+0
+0.21 0.41 0.62
+0.1
+0.2
+0.3
+0.4
+0.5
+0.6
+0.7
+0.8
+0.9
+1.0
+0
+0.21 0.41 0.62
+0.1
+0.2
+0.3
+0.4
+0.5
+0.6
+0.7
+0.8
+0.9
+1.0
+η = 0.09
+η = 0.3
+η = 0.6
+θV,c (◦)
+90.00
+95.25
+111.1
+127.0
+142.9
+153.5
+90.00
+95.25
+104.8
+114.3
+123.8
+128.1
+90.00
+95.00
+104.5
+114.0
+123.5
+128.0
+θV,c (◦)
+θV,c (◦)
+θV,c (◦)
+h
+h
+h
+FIG. 6. Examples of ﬁeld and frequency maps for the CSWB direction θV,c, at a) η = 0.09, b) η = 0.3, and c) η = 0.6.
+0
+0.21
+0.41
+0.62
+0.1
+0.2
+0.3
+0.4
+0.5
+0.6
+0.7
+0.8
+0.9
+1.0
+˜kc
+a)
+b)
+c)
+0
+0.21
+0.41
+0.62
+0.1
+0.2
+0.3
+0.4
+0.5
+0.6
+0.7
+0.8
+0.9
+1.0
+0
+0.21
+0.41
+0.62
+0.1
+0.2
+0.3
+0.4
+0.5
+0.6
+0.7
+0.8
+0.9
+1.0
+0
+1.17
+2.35
+3.52
+4.66
+0.150
+0.300
+0.450
+0.555
+0
+0
+0.200
+0.400
+0.600
+0.800
+0.826
+˜kc
+˜kc
+h
+h
+h
+FIG. 7. Field and frequency maps for η = 0.12, looking at the three reduced caustic wavenumbers. Note the distinct grey
+scales for each graph. a) Lowest ˜kc in the presence of several caustic points, and single value for ˜kc otherwise. b) Intermediate
+value for ˜kc if several caustic points exist. c) Largest reduced caustic wavenumber.
+
+Caustic beam directions Avc vs. v and h
+0.9991
+153.49
+0.8992
+0.7993
+142.88
+0.6994
+0.5995
+127.00
+0.4996
+0.3997
+111.12
+0.2998
+0.1999
+95.25
+0.1000
+90.00
+0.0001
+0.0000
+0.2063
+0.4126
+0.6189
+hCaustic beam directions Oyc vs. v and h
+0.9991
+128.13
+0.8992
+123.83
+0.7993
+0.6994
+114.30
+0.5995
+0.4996
+0vc
+0.3997
+104.78
+0.2998
+0.1999
+95.25
+0.1000
+90.00
+0.0001
+0.0000
+0.2063
+0.4126
+0.6189
+hCaustic beam directions Oyc vs. v and h
+0.9991
+127.96
+0.8992
+123.50
+0.7993
+0.6994
+114.00
+0.5995
+0.4996
+0vc
+0.3997
+104.50
+0.2998
+0.1999
+95.00
+0.1000
+90.00
+0.0001
+0.0000
+0.2063
+0.4126
+0.6189
+hNormalized wavenumber at Φc vs. v and h
+1.0000
+4.662
+0.9000
+0.8000
+3.525
+0.7000
+0.6000
+0.5000
+2.350
+0.4001
+0.3001
+1.175
+0.2001
+0.1001
+0.000
+0.0001
+0.0000
+0.2063
+0.4127
+0.6190
+hNormalized wavenumber at Φc vs. v and h
+1.0000
+0.5552
+0.9000
+0.8000
+0.4500
+0.7000
+0.6000
+0.3000
+0.5000
+kc
+0.4001
+0.3001
+0.1500
+0.2001
+0.1001
+0.0000
+0.0001
+0.0000
+0.2063
+0.4127
+0.6190
+hNormalized wavenumber at Φc vs. v and h
+1.0000
+0.8256
+0.8000
+0.9000
+0.8000
+0.7000
+0.6000
+0.6000
+0.5000
+0.4000
+kc 
+0.4001
+0.3001
+0.2000
+0.2001
+0.1001
+0.0000
+0.0001
+0.0000
+0.2063
+0.4127
+0.6190
+h10
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+˜k
+0.0
+0.1
+0.2
+0.3
+0.4
+0.5
+0.6
+0.7
+dθV/d˜k
+FIG. 8. Calculated derivative of the group velocity direction
+with respect to the reduced wavenumber in the 4.62 GHz spin
+wave excitation described by Gieniusz et al. [43].
+YIG film
+2 µm
+−
+→
+k
+x
+y
+z
+−→
+Ha
+FIG. 9. Schematic of the measurement geometry. The half-
+ring shaped antenna excites spin wave propagation within a
+broad angular spectrum.
+of beams I and II with respect to the positive x direction
+are found to be 119.00◦ (beam I) and 64.28◦ (beam II)
+which results in eﬀective beam directions of θI = 119.00◦
+and θII = 180◦ − 64.28◦ = 115.72◦, respectively.
+The
+discrepancy between θI and θII simply originates from
+a small misalignment of the external ﬁeld with respect
+to the waveguide legs. Since −→
+Ha is not fully parallel to
+the x-axis, the slowness curve is rotated by a small an-
+gle αH = (θI − θII)/2 ≈ 1.64◦ in our frame of reference.
+Keeping this in mind, we extract an average beam direc-
+tion θV,e = 117.36◦, a wavefront angle ϕe = 50.66◦ and
+a reduced wavenumber ˜ke = 0.211. These experimental
+ﬁndings are in good agreement with our theoretical ap-
+proach; indeed, values of θV,c = 115.05◦, ϕc = 51.29◦ and
+˜kc = 0.223 are predicted for a CSWB in our experimental
+conditions.
+We can obtain further insight in reciprocal space with
+30
+20
+10
+10
+20
+30
+x (µm)
+y (µm)
+0
+0
+˜kx
+0
+0.2
+-0.2
+0
+˜ky
+|FT(δmz)|2
+(arb. u.)
+δmz (arb. u.)
+0
+0.4
+0.8
+-0.4
+-0.8
+a)
+b)
+FIG. 10. Measurement data obtained for η = 0.087, h = 0.028
+and ν = 0.292.
+a) Kerr image acquired from TR-MOKE.
+Two spin wave beams highlighted in yellow and red propa-
+gate from the tip of the antenna.
+b) Squared modulus of
+the Fourier transform (FT) of the Kerr image and expected
+slowness curve (blue).
+The yellow and red points and ar-
+rows indicate the expected caustic points and their respective
+group velocity directions. Caustic points I and II correspond
+to beams I and II in the Kerr image.
+the Fourier-transformed (FT) data shown in Fig. 10.b).
+Generally speaking, the FT data allows for a direct ob-
+servation of the slowness curve in ˜k-space. In order to re-
+duce spectral leakage, a Hanning windowing was applied;
+the latter provides a good trade-oﬀ between frequency
+and amplitude accuracy. We see that the chosen antenna
+structure indeed excites a wide range of wave vector di-
+rections. The gaps in the spectrum arise from the ﬁnite
+antenna dimensions, as previously mentioned. We ﬁnd a
+good agreement between the slowness curve (blue curve)
+derived from our model (and corrected by the external
+ﬁeld angle αH). More importantly, this graph conﬁrms
+that the antenna structure grants access to the expected
+caustic points (yellow and red points) since the Fourier
+magnitude is still suﬃciently large in that region. To con-
+clude, caustic points I and II can be assigned to beams I
+and II from the Kerr image.
+We may now turn to the additional caustic points pre-
+dicted by our model. The chosen triplet (η, h, ν) is an ele-
+ment of the D3 set, and we would expect two further caus-
+tic points θV,c,2 = 113.74◦, ϕc,2 = 33.00◦, ˜kc,2 = 0.662
+and θV,c,3 = 114.02◦, ϕc,3 = 28.78◦, ˜kc,3 = 1.227. These
+reduced wave vectors could actually be resolved by our
+experimental set-up where ˜kres ≈ 2.2.
+The reciprocal
+space image in Fig. 10.b), however, displays a very low
+amplitude for ˜k ≳ 0.55 meaning that the microwave an-
+tenna cannot excite the other caustic points very eﬃ-
+ciently.
+Hence, only the low frequency pocket can be
+accessed.
+Further Kerr images were taken for the same ν, but
+
+I
+II11
+for diﬀerent h values.
+The h values were chosen such
+that they lie beneath the expected FMR ﬁeld hFMR ≈
+0.078778. A selection of the resulting Kerr images is il-
+lustrated in the upper part of Fig. 11. In each of them,
+twin spin wave beams are apparent. An overview of all
+the beam properties for the corresponding h values is
+plotted in the lower part of Fig. 11. Here, the relevant pa-
+rameters from every individual beam are extracted with
+image processing and bootstrapping least squares regres-
+sion procedures. An example on how one set of experi-
+mental data points is obtained can be found in the Sup-
+plementary Materials. The reasonable, sometimes even
+very good agreement between predicted and experimen-
+tal values of θV,c and ˜kc strongly suggests true CSWBs.
+The deviation of the beam directions is mostly within the
+range of the external ﬁeld angle. The larger discrepancy
+between predicted and measured wavefront angles ϕc is
+attributed to the narrowness of the CSWB.
+b1)
+b2)
+b3)
+a1)
+a2)
+a3)
+h = 0.0341
+h = 0.0398
+h = 0.0511
+Theory
+Experiment
+θV,c (◦)
+φc (◦)
+˜kc
+30
+42
+54
+0.10
+0.18
+0.26
+110
+113
+116
+119
+122
+0.025
+0.030
+0.035
+0.040
+0.045
+0.050
+0.055
+0.060
+h
+30
+20
+10
+0
+10
+20
+30
+x (µm)
+y (µm)
+30
+20
+10
+0
+x (µm)
+30
+20
+10
+0
+x (µm)
+0
+0
+0
+0
+FIG. 11. Measurement data obtained for η = 0.087 and ν =
+0.292. Upper part: acquired Kerr images for reduced ﬁelds of
+a1) h = 0.0341, a2) h = 0.0398, and a3) h = 0.0511,. b1-3)
+comparison between experiment and theoretical predictions
+of caustic point properties θV,c, ˜kc, ϕc. The error bars are
+the standard deviations from a bootstrapping ﬁt procedure.
+Beam-like features which do not coincide with a caus-
+tic point were detected as well. This time, the measure-
+ments were conducted with the 50 µm antennna struc-
+ture and partially etched ﬁlm. The width of the antenna
+was 3 µm.
+The resulting Kerr map for f =1.84 GHz
+(ν = 0.372) and µ0Ha =5 mT (h = 0.028) is shown
+in the left upper half of Fig. 12.
+In this geometry, a
+Damon Eshbach-like mode propagating from the YIG
+edge could not be fully suppressed; it is visible as a
+plane wave background. Our procedure to analyze spin
+wave beams yields θV,e = 136.33◦, ϕe = 68.97◦ and
+˜ke = 0.522, whereas our model predicts a caustic point
+with θV,c = 121.39◦, ϕc = 35.84◦ and ˜kc = 1.564.
+The origin of the experimentally observed beams may
+be twofold.
+Firstly, a close-to-straight slowness curve
+similar to the case of Gieniusz et al. [43] is predicted to
+exist within relatively close distance to ˜ke. The dθV/d˜k
+plot in Fig. 12.b) displays almost a constant behaviour
+between 0.6 ≲ ˜k ≲ 1.2 (marked with green dashed lines).
+The proximity of the experimental caustic point to a
+straight-to-close slowness curve is also illustrated in the
+FT data in the lower part of Fig. 12. Here, the dashed
+green semicircle represents the lower bound of ˜k = 0.6
+and the extracted beam points are highlighted in yellow.
+For this portion of the slowness curve, group velocity
+directions of up to 121.39◦ are predicted. This beam di-
+rection, however, is still in stark contrast with the mea-
+surement result. Moreover, the calculated slowness curve
+(blue curve) deviates signiﬁcantly from the FT data. The
+diﬀerence between reciprocal space image and our model
+may show the limit of the model applicability, since a ﬁlm
+with η = 0.087 may not be considered a thin ﬁlm any-
+more. This results in predictions which are less reliable
+at higher ν values. A second possible origin of the beams
+is the excitation eﬃciency of the microwave antenna as
+there are many gaps in the FFT spectrum. The beams
+appear to be located close to some of them, and hence,
+may correspond to the excitation of only a small portion
+of the slowness curve within this region.
+|FT(δmz)|2
+(arb. u.)
+c)
+Theory
+Fit data
+˜kx
+0
+1.2
+0.8
+0
+˜ky
+0.8
+-0.8
+-1.6
+-1.6
+0.4
+30
+20
+10
+10
+20
+30
+y (µm)
+0
+0
+δmz (arb. u.)
+0
+a)
+b)
+dθV/d˜k
+0
+0
+0.2
+0.4
+0.6
+0.8
+1.6
+x (µm)
+˜k
+FIG. 12.
+a) Kerr image with twin beams obtained with
+η = 0.087 h = 0.028 and ν = 0.372. b) Calculated derivative
+of the group velocity direction with respect to the reduced
+wavenumber. Dashed green lines highlight close-to-straight
+slowness curve.
+c) FT of Kerr image.
+The experimentally
+observed beam parameters are depicted in yellow, the calcu-
+lated slowness curve in blue and the calculated caustic points
+in red. Dashed green semicircle illustrates lower limit of close-
+to-straight portion of slowness curve.
+
+12
+D.
+Caustic point of higher order
+Based on the conclusions from section III B, we know
+that the intersection of ∂D3,l and ∂D3,u there exists a sin-
+gle caustic point on the slowness curve; in the schematic
+discussion from the above based on the approximant
+P(˜k; a, b), it corresponds to a = 0 and b = 0, which
+means that dθV/d˜k ∼ (˜k − ˜kc)3 around this point. To
+put it diﬀerently: at this intersection, corresponding to
+the cusp seen in Fig. 7, the caustic point is not a simple
+extremum for θV on the slowness curve but an undulation
+point, in the vicinity of which θV − θV,c ∼ (˜k − ˜kc)4.
+The existence of such an undulation point is of par-
+ticular interest since the higher order in the dependence
+of θV on ˜k implies a ﬂatter extremum in group veloc-
+ity direction and therefore the possibility of larger por-
+tions of the slowness curve contributing to the CSWB.
+Moreover, as was discussed in Sec. II.II B, this does not
+necessarily mean an increase in spectral breadth of the
+CSWB since the latter depends on the apparent wave-
+length. In order to evidence this, we show in Fig. 13
+how the group velocity direction as well as the natural
+and apparent wavelengths vary around a caustic point
+very close to one of higher order, here the one such that
+its corresponding critical ﬁeld hc is zero. The considered
+slowness curve corresponds to h = h1 = 1.15 · 10−21,
+ν = ν1 = 0.315279504, η = η1 = 0.10253664614147.
+Let us brieﬂy outline how the coordinates νc,0 =
+νc(hc = 0) and ηc,0 = ηc(hc = 0) were found with a
+good accuracy. More details can be found in the Sup-
+plementary Materials. The starting point was a rough,
+hand-performed search for a value of η bringing the cusp
+of D3 to lie on the ordinate axis in a ﬁeld and fre-
+quency map. This yielded a starting point of η(0)
+c,0 = 0.10
+and ν(0)
+c,0 = 0.31.
+In these conditions, a caustic point
+was found for ˜k(0)
+c,0 ≃ 0.73.
+We then began an itera-
+tive procedure using appropriate Taylor expansions of
+the dispersion relation and of an exact expression for
+θV(h = 0, η, ν, ˜k, ϕ). Updating these at each step with
+the new solutions found by looking for the undulation
+point allows to converge to numerical values which we
+assimilate to the intersection of ∂D3,l and ∂D3,u.
+Over three iterations, the relative changes in the esti-
+mates steadily decrease in absolute value, from at most
+5% in the ﬁrst step to at most 5 · 10−6 in the last one,
+which provides the following guesses : ˜k(g)
+c,0 = 0.731717,
+η(g)
+c,0 = 0.1025366, ν(g)
+c,0 = 0.3152796. The latter can be
+compared with e.g. the hand-reﬁned values used for Fig.
+13: ν = ν1 = 0.315279504, η = η1 = 0.10253664614147,
+corresponding to ˜kc = 0.725904. It must be noted that
+the somewhat larger relative diﬀerence in terms of ˜kc,0 is
+due to the very steep dependence of ˜kc(ν, η, h → 0) on η.
+We do emphasize that the exact location (νc,0,ηc,0) is nec-
+essarily diﬀerent from (ν1, η1) but close enough to high-
+light the qualitatively diﬀerent behaviour of several char-
+acteristics of the slowness curve. Finally, we note that for
+˜k
+˜k
+˜k
+φ
+˜kc
+φc
+0
+1
+2
+3
+4
+0 ◦
+15 ◦
+30 ◦
+45 ◦
+60 ◦
+75 ◦
+90 ◦
+b)
+0.04
+0.02
+0
+-0.02
+-0.04
+−0.04
+0.5
+2.0
+0
+0.5
+1.5
+1.0
+2.0
+0.04
+θV/θV,c−1
+λ0/λ0,c−1
+λ/λc−1
+a)
+FIG. 13.
+a) Plots of the relative deviations from the fol-
+lowing caustic point properties as a function of ˜k: its group
+velocity direction θV, its natural wavelength λ0 = 2π/˜k
+and its apparent wavelength λ = 2π/[˜k cos (θV − ϕ)]. Main
+graph:
+h = h1 = 1.15 · 10−21, ν = ν1 = 0.315279504,
+η = η1 = 0.10253664614147, which are extremely close to
+the values of νc and η for which hc = 0. Inset: same h and
+η = η1, ν = 0.95 · ν1 = 0.2995155288. b) Slowness curve for
+ν1, η1 and h1; ˜kc ≃ 0.7259. The slowness curve at ν2 is not
+shown for clarity, as it is very similar to the other one.
+
+90°
+75°
+60°
+45°
+30°
+15°
+0
+2
+3
+1
+4
+kd13
+the parameters from Fig. 13, θV,c =118.36°, ϕc ≃42.75°,
+λ0,c = 84.41lex = 8.655d, and λc ≃ 339.7lex = 34.83d.
+We now examine the properties of the caustic point of
+higher order in more detail. From Fig. 13, the depen-
+dence of θV,c and the apparent wavelength λ on ˜k (in
+blue and green, respectively) clearly appears to be quar-
+tic rather than quadratic around the caustic point, which
+is where the deviations in natural wavelength (in red) go
+through 0. Its much steeper behaviour is easily under-
+stood by looking at the corresponding slowness curve in
+Fig. 13.b): around ˜kc it is not only almost straight but
+the angle γ between
+−→˜k and d
+−→˜k /ds is low, γ ≃14.38°.
+Hence, since d(˜k2)/ds is large, λ0 ∝ 1/˜k varies fast.
+By contrast, one can show that in the Taylor expansion
+of λ in (s−sc)/˜kc around λc, the ﬁrst coeﬃcient is always
+exactly zero at a caustic point. We stress again that this
+is caused by an unchanging projection of −→k on −→
+eg across
+the caustic point. If it is of higher order, it may be shown
+(see Supplementary Materials) that in this term, the con-
+tributions due to the second- and third-order variations
+of ϕ and to those of ˜k cancel out. To put it diﬀerently, the
+projection k · cos (θV − ϕ) is now constant up to fourth
+order in (s − sc)/˜kc. On the other hand, if the consid-
+ered caustic point is a regular extremum for θV, the term
+∝ (s − sc)2 will be non-zero.
+To summarize the above paragraph: for geometrical
+reasons, the caustic point of higher order suppresses the
+quadratic and cubic variations of the apparent wave-
+length around λc. Hence, λ has then a markedly quartic
+behaviour at a caustic point of higher order. Further-
+more, we point out that even a small oﬀset in frequency
+makes it display a clearly quadratic behaviour. This is
+shown in the inset of Fig. 13, showing the same relative
+variations for the slowness curve at h = h1 = 1.15·10−21,
+η = η1 = 0.10253664614147, but ν = 0.95 · ν1 =
+0.2995155288.
+We have thus shown that in a suﬃciently close vicin-
+ity of a higher-order caustic point, a broadband excita-
+tion in terms of wavenumber can result in a narrowband
+CSWB with a very well-deﬁned direction. As a result,
+this phenomenon is expected to be extremely favourable
+in experiments, since any realistic antenna cannot have
+an arbitrarily narrow excitation eﬃciency as a function
+of wavenumber. Provided that its design yields AC mag-
+netic ﬁelds with Fourier components in the (broad) range
+of interest and with phases in a given interval of width
+< π, all the corresponding spin waves will coherently add
+in a beam with very small spectral breadth.
+In other
+words: in such a situation, counter-intuitively, exciting
+additional wave vectors with diﬀerent wavenumbers does
+not average out the carrier wave’s amplitude but rather
+increase it. This naturally prompts the question of how
+much stronger the emission from a caustic point of higher
+order would be with respect to that of a regular caustic
+point, and more generally, of the spin wave amplitude
+enhancement due to the caustics. This, however, goes
+beyond the scope of the present manuscript.
+To conclude this section, we point out that the reduced
+ﬁeld hc(η) corresponding to the caustic point of higher
+order decreases as a function of reduced dipolar-exchange
+length. Thus, this feature is expected to exist only for
+η < ηc,0 ≃ 0.1025366.
+E.
+Merged caustic spin wave beams
+We now move on to the topic of the threshold fre-
+quency νm(h, η) corresponding to the upper boundary
+of D, i.e. above which there are no caustic points any
+more.
+As was shown in Fig.
+6, the CSWB direction
+θV,c goes to π/2 as ν → νm(h, η).
+This is illustrated
+in Fig. 14, where we show a slowness curve for η1, h1,
+and ν2 = 0.71836419052. We stress again that νm(h, η)
+is strictly speaking an inﬁnitely narrow boundary and
+therefore ν2 ̸= νm(h1, η1), but in these conditions, we
+ﬁnd a unique caustic point on the slowness curve, with
+π/2 − ϕc ≃0.32 µrad, and θV,c is equal to π/2 (within
+numerical precision). Moreover, at ν′
+2 = ν2 + δν, where
+δν = 1 · 10−11, we do not ﬁnd any caustic point on the
+slowness curve.
+As a result, we take the slowness curve at (ν2, h1, η1)
+to be assimilable to the one at (νm(h1, η1), h1, η1). Its
+very straight aspect around ϕ = π/2 is somewhat rem-
+iniscent of the one seen in the discussion of the caus-
+tic point of higher order. To illustrate this in more de-
+tail, Fig. 14.b) displays the relative deviations in group
+velocity direction θV, natural wavelength and apparent
+wavelength around the caustic point at ϕc.
+We point
+out that in the present case, the deviations are plotted
+against the curvilinear abscissa s normalized to the slow-
+ness curve’s length sM instead of ˜k as in Fig. 13. This
+choice is motivated by (i) the fact that in this case, to
+lowest order ˜k − ˜kc = O(s2) instead of O(s − sc) as be-
+fore, and (ii) the much smaller relative diﬀerence between
+the smallest and largest normalized wavenumbers ˜km re-
+spectively ˜kM: ˜km ≃ 5.17 and ˜kM ≃ 7.91, compared
+to ˜km ≃ 0.240 and ˜kM ≃ 5.66 before. (i) implies that
+for (ν2, h1, η1), ˜k cannot serve as a meaningful abscissa
+along the curve since d˜k/ds = 0, which was not the case
+for (ν1, h1, η1), while (ii) shows that the slowness curve
+for (ν2, h1, η1) is much closer to a fourth of a circle than
+that for (ν1, h1, η1); as a matter of fact, for (ν2, h1, η1),
+we ﬁnd that 1 − [π/2 · (˜km + ˜kM)/2]/sM = 3.7%. There-
+fore, s/sM provides a better feeling for how much of the
+slowness curve contributes to the CSWB.
+From the graph, it seems that the apparent wavelength
+has once more a quartic behaviour around the caustic
+point. We show in the Supplementary Materials that this
+is indeed the case: in the conditions where ν = νm(h, η),
+to the lowest non-zero order, θV(s → 0) − π/2 varies
+with an s3 dependence around s = 0, and the lowest-
+order variations in ˜k and ϕ (around ˜km and π/2) cancel
+each other out in the projection ˜k · cos (θV − ϕ).
+As a result, a caustic point at νm(h, η) is such that
+
+14
+0
+-0.02
+-0.04
+-0.06
+-0.08
+-0.10
+-0.12
+-0.14
+0
+0.1
+0.2
+0.3
+0.4
+s/sM
+φ
+0 ◦
+15 ◦
+30 ◦
+45 ◦
+60 ◦
+75 ◦
+90 ◦
+˜k
+0
+2
+4
+8
+6
+a)
+b)
+θV/θV,c−1
+λ0/λ0,c−1
+λ/λc−1
+FIG. 14. a) Slowness curve at (ν2 = 0.71836419052, h1, η1).
+b) Relative deviations in group velocity direction θV (blue),
+natural wavelength λ0 (red) and apparent wavelength λ
+(green), as a function of curvilinear abscissa along the slow-
+ness curve normalized by its total length sM.
+an excitation from a suitable, moderately directional an-
+tenna would be eﬀectively narrowband, and weakly di-
+vergent around the group velocity direction θV,c = π/2.
+This orientation is itself also advantageous in practice:
+as long as the used antenna can excite suﬃciently high
+wavenumbers, the CSWB direction becomes in this case
+simply perpendicular to the applied ﬁeld. Moreover, ow-
+ing to the symmetries of the dispersion relation, the
+CSWB beneﬁts from the part of the slowness curve at
+ϕ ≳ π/2, which also feature θV ≃ π/2. That is why large
+spin wave amplitudes can be expected, as eﬀectively two
+CSWB have merged at this particular frequency. We note
+that this merging phenomenon has already been observed
+in simulations by Kim et al. [29] in perpendicularly mag-
+netized ultrathin ﬁlms and by Gallardo et al. [41] in syn-
+thetic antiferromagnets. For the sake of completeness, let
+us comment on what happens from an analytical point of
+view when the two caustic points just below and above
+ϕ = π/2 coincide. It must be kept in mind that they
+respectively correspond to a maximum and a minimum
+for θV, temporarily considered for ϕ ∈ [0, π]. Thus, when
+they do coincide at ϕc = π/2, strictly speaking there is
+no caustic point any more.
+To put it diﬀerently: be-
+low νm(h, η), over ϕ ∈ [0, π], θV increases up to the ﬁrst
+caustic point where it reaches θV,c > π/2, decreases until
+the second one (for ϕ > π/2) where it reaches π − θV,c,
+then increases again to reach π when ϕ = π. Exactly
+at νm(h, η), it is monotonously increasing with an inﬂex-
+ion point, and above νm(h, η), it is strictly monotonously
+increasing.
+In order to go beyond the particular case presented
+here, we now investigate the evolution of νm(h → 0, η) =
+νm,0(η) as a function of reduced dipolar-exchange length
+η.
+Similarly to the caustic point of higher order, the
+evolutions as a function of reduced ﬁeld quickly become
+cumbersome. This is why we focus on the νm,0(η), which
+is both the lowest frequency at which CSWBs merge and
+a threshold frequency that is easier to reach in experi-
+ments owing to the vanishing applied ﬁeld, provided that
+the studied ﬁlm is soft enough.
+We do keep in mind that below a certain limit in terms
+of reduced dipolar-exchange length, the model we use
+loses its validity.
+However, it has been shown that at
+suﬃciently high frequency [38], the analytical dispersion
+relation derived by Kalinikos and Slavin describes spin
+waves once more with a good accuracy.
+Fig.
+15 displays the numerically determined depen-
+dence of νm0 on η, as well as that of λm/lex the wave-
+length of the corresponding CSWB, normalized by the
+dipolar-exchange length. The procedure to ﬁnd ﬁrst a
+coarse estimate of this curve (before reﬁning it with ac-
+tual ﬁeld and frequency maps) is described in the Supple-
+mentary Materials. We point out that in the case of the
+merged CSWBs, the apparent and natural wavelengths
+are equal since θV,c = ϕc = π/2. The minimum value
+of η in these graphs corresponds to the smallest one we
+used such that the slowness curve (in vanishing ﬁelds)
+has only one connected component. While we may not
+expect our ﬁndings to hold at the lowest η’s, we do expect
+their accuracy to improve as η increases; it should be suf-
+ﬁcient at least for η > 1 since in this case the considered
+ferromagnetic ﬁlm can truly be considered thin.
+If we think about searching for the merged CSWBs,
+Fig. 15.b) indicates that for realistic values of η = lex/d,
+the CSWBs’ apparent wavelengths λ are only about one
+order of magnitude larger than the material’s dipolar-
+exchange length, typically λ ≲ 25lex. This is in stark
+contrast with the case of the caustic point of higher
+order in vanishing ﬁeld, where the natural wavelength
+was λ0,HO ≃ 84lex, and the apparent wavelength λHO ≃
+334lex. As a result, it seems that while caustic points
+of higher order may readily be excited by antennas cre-
+ated with even conventional electron beam lithography,
+in the case of the merged CSWB achieving a suﬃcient
+excitation eﬃciency at the proper wavevectors should
+
+...15
+a)
+b)
+FIG. 15. a) νm,0(η) as a function of reduced dipolar-exchange
+length η.
+b) The corresponding reduced wavelength ˜λm =
+(2π/˜k)/η = λ/lex = λ0/lex. Here, natural and apparent wave-
+lengths coincide as phase and group velocities are collinear.
+prove quite challenging.
+For instance, even the low-
+magnetization, low-damping and rather soft ferrimagnet
+YIG features lex =17.3 nm [40], meaning that high-end
+antennas with a characteristic periodicity down to about
+200 nm would be required in this easiest of cases.
+IV.
+CONCLUSIONS
+We have focused on some properties displayed by spin
+wave caustics in soft, thin ferromagnetic ﬁlms. On the
+theoretical side, our approach relied on the analytical
+dispersion relation established by Kalinikos and Slavin.
+We could show that many reports on CSWBs in the lit-
+erature can be interpreted within this frame, although
+the absence of characteristic signs of a true CSWB may
+still cause some ambiguity. Following up on most stud-
+ies, we have performed time-resolved magneto-optical
+Kerr-eﬀect-based microscopy on samples designed for the
+study of CSWBs. Despite the large thickness of the fer-
+romagnetic material, our measurements are in very good
+agreement with our predictions, thus validating the ap-
+proach. Furthermore, we have speciﬁcally highlighted the
+large misalignment between phase and group velocities in
+this case, and succeeded in observing narrow CSWBs.
+Just at the boundary of the dipolar-dominated regime
+accessible in our experiments, we have predicted the ex-
+istence of a special caustic point. We refer to it as caustic
+point of higher order because it corresponds to an undu-
+lation point for the group velocity direction rather than
+a quadratic extremum.
+This conﬁguration was shown
+to be of particular interest because the apparent wave-
+length also featured a quartic behaviour, which implies
+a low spectral breadth for the CSWB even in the case
+of a broadband excitation. Although we focused on the
+special value ηc of reduced dipolar-exchange length such
+that the caustic point of higher order occurs at vanish-
+ing applied ﬁelds, we stress that this phenomenon would
+appear at non-zero ﬁelds for η < ηc, as long as the dis-
+persion relation we use is valid.
+Finally, we have investigated the merging of CSWBs.
+Once again, we have studied in detail the case of van-
+ishing applied ﬁelds, yet the merging may occur for any
+ﬁeld value, provided that the excitation frequency is large
+enough. In terms of model validity, it must be recalled
+that while vanishing values of η are problematic for the
+chosen dispersion relation, the merging always occurs
+at frequencies close to the exchange-dominated regime.
+The discrepancies between the actual spin wave disper-
+sion and the model by Kalinikos and Slavin decrease in
+this frequency range [39]. As a result, our claim is that
+the merging frequencies νm0 obtained for low η may be
+slightly inaccurate yet the phenomenology should remain
+the same as for larger η, where we expect our predictions
+to be more reliable. As the CSWBs merge, a very sig-
+niﬁcant portion of the slowness curve contributes to spin
+wave emission around θV = ϕ = π/2. Therefore, this
+conﬁguration appears promising in terms of channelling
+strong spin wave beams with short wavelengths, as low
+as ∼ 15lex.
+One of the most important questions remaining un-
+addressed so far concerns the quantiﬁcation and predic-
+tion of the enhancement of amplitude associated with
+CSWBs. More precisely, the crucial distinction between
+natural and apparent wavelength as well as the inad-
+equacy of the usual Huygens-Fresnel approach (due to
+the strong non-collinearity between phase and group ve-
+locities) in the construction of CSWBs calls for alterna-
+tive evaluations of their amplitudes. We intend to clar-
+ify these points and to go beyond the usually described
+amplitude divergence so as to reconcile the theoretically
+vanishing curvature (on the slowness curve) and experi-
+mentally ﬁnite amplitudes.
+[1] H. Yu, J. Xiao, and H. Schultheiss, Magnetic texture
+based magnonics, Physics Reports 905, 1 (2021).
+[2] B. Divinskiy, H. Merbouche, V. E. Demidov, K. O.
+Nikolaev, L. Soumah, D. Gou´er´e, R. Lebrun, V. Cros,
+J. Ben Youssef, P. Bortolotti, A. Anane, and S. O.
+Demokritov, Evidence for spin current driven bose-
+einstein condensation of magnons, Nature Communica-
+tions 12, 10.1038/s41467-021-26790-y (2021).
+[3] D. Bouzidi and H. Suhl, Motion of a bloch domain wall,
+Physical Review Letters 65, 2587 (1990).
+[4] D. D. Stancil and A. Prabhakar, Spin waves - Theory and
+applications (Springer New York, NY, 2009).
+[5] A.
+V.
+Chumak,
+Fundamentals
+of
+magnon-
+based
+computing,
+ArXiv
+e-prints
+(2019),
+arXiv:http://arxiv.org/abs/1901.08934v1.
+[6] D. Petti, S. Tacchi, and E. Albisetti, Review on magnon-
+ics with engineered spin textures, Journal of Physics D:
+Applied Physics 55, 293003 (2022).
+
+0.8
+-
+:
+:
+:
+:
+:
+.'.
+-
+0.6
+2
+:
+1
+-
+:
+-
+0.4
+:
+:
+-
+1
+-
+:
+--
+-
+0.2
+-
+-
+.'.
+.',
+-
+:
+1
+.
+1
+-
+-
+-
+I...
+:
+:
+-
+-
+-
+0.0
+i
+--
+0
+1
+2
+3
+n80
+70
+60
+50
+40
+uu
+30
+20
+10
+0
+-
+0
+1
+2
+3
+n16
+[7] D. Seo, S. Hwang, B. Kim, Y. Yang, S. Yoon, and
+B. K. Cho, Tunable asymmetric spin wave excitation and
+propagation in a magnetic system with two rectangular
+blocks, Scientiﬁc Reports 11, 10.1038/s41598-021-02967-
+9 (2021).
+[8] Y. Au, M. Dvornik, T. Davison, E. Ahmad, P. S. Keat-
+ley, A. Vansteenkiste, B. V. Waeyenberge, and V. V.
+Kruglyak, Direct excitation of propagating spin waves by
+focused ultrashort optical pulses, Physical Review Let-
+ters 110, 097201 (2013).
+[9] St¨ohr, J. and Siegmann, H. C., Magnetism: From Fun-
+damentals to Nanoscale Dynamics (Springer Berlin Hei-
+delberg, 2006).
+[10] V. Sluka, T. Schneider, R. A. Gallardo, A. K´akay,
+M. Weigand, T. Warnatz, R. Mattheis, A. Rold´an-
+Molina,
+P.
+Landeros,
+V.
+Tiberkevich,
+A.
+Slavin,
+G. Sch¨utz, A. Erbe, A. Deac, J. Lindner, J. Raabe,
+J. Fassbender, and S. Wintz, Emission and propaga-
+tion of 1d and 2d spin waves with nanoscale wavelengths
+in anisotropic spin textures, Nature Nanotechnology 14,
+328 (2019).
+[11] F. G. Aliev,
+A. A. Awad,
+D. Dieleman,
+A. Lara,
+V. Metlushko, and K. Y. Guslienko, Localized domain-
+wall excitations in patterned magnetic dots probed by
+broadband ferromagnetic resonance, Physical Review B
+84, 144406 (2011).
+[12] M. Golebiewski, P. Gruszecki, M. Krawczyk, and A. E.
+Serebryannikov, Spin-wave talbot eﬀect in thin ferromag-
+netic ﬁlm, Physical Review B 102 (2020).
+[13] R. W. Damon and J. R. Eshbach, Magnetostatic modes
+of a ferromagnet slab, Journal of Physics and Chemistry
+of Solids 19, 308 (1961).
+[14] Y. A. Kravtsov and Y. I. Orlov, Geometrical Optics of
+Inhomogeneous Media, Springer Series on Wave Phenom-
+ena, Vol. 6 (Springer-Verlag Berlin Heidelberg, 1990).
+[15] Y. A. Kravtsov and Y. I. Orlov, Caustics, Catastrophes
+and Wave Fields, Springer Series on Wave Phenomena,
+Vol. 15 (Springer, Berlin, Heidelberg, 1993).
+[16] T. Poston and I. Stewart, Catastrophe Theory and Its Ap-
+plications, Surveys and reference works in mathematics,
+Vol. 2 (Dover Publications, 1996).
+[17] G. A. Northrop and J. P. Wolfe, Ballistic phonon imaging
+in germanium, Physical Review B 22, 6196 (1980).
+[18] B. Taylor, H. J. Maris, and C. Elbaum, Phonon focusing
+in solids, Physical Review Letters 23, 416 (1969).
+[19] H. J. Maris, Enhancement of heat pulses in crystals due
+to elastic anisotropy, The Journal of the Acoustical So-
+ciety of America 50, 812 (1971).
+[20] A. G. Every, Eﬀects of ﬁrst-order spatial dispersion on
+phonon focusing: Application to quartz, Physical Review
+B 36, 1448 (1987).
+[21] H. J. Maris, Phonon focusing, in Nonequilibrium phonons
+in nonmetallic crystals, Modern Problems in Condensed
+Matter Sciences, Vol. 16, edited by W. Eisenmenger and
+A. A. Kaplyanskii (North Holland, 1986) pp. 51–90.
+[22] O. B¨uttner, M. Bauer, S. O. Demokritov, B. Hillebrands,
+Y. S. Kivshar, V. Grimalsky, Y. Rapoport, and A. N.
+Slavin, Linear and nonlinear diﬀraction of dipolar spin
+waves in yttrium iron garnet ﬁlms observed by space- and
+time-resolved brillouin light scattering, Physical Review
+B 61, 11576 (2000).
+[23] V. Veerakumar and R. E. Camley, Magnon focusing in
+thin ferromagnetic ﬁlms, Physical Review B 74, 214401
+(2006).
+[24] R. Khomeriki, Self-focusing magnetostatic beams in thin
+magnetic ﬁlms, The European Physical Journal B 41,
+219 (2004).
+[25] V. E. Demidov, S. O. Demokritov, D. Birt, B. O’Gorman,
+M. Tsoi, and X. Li, Radiation of spin waves from the open
+end of a microscopic magnetic-ﬁlm waveguide, Physical
+Review B 80, 10.1103/physrevb.80.014429 (2009).
+[26] T. Schneider, A. A. Serga, A. V. Chumak, C. W.
+Sandweg, S. Trudel, S. Wolﬀ, M. P. Kostylev, V. S.
+Tiberkevich, A. N. Slavin, and B. Hillebrands, Non-
+diﬀractive subwavelength wave beams in a medium with
+externally controlled anisotropy, Physical Review Letters
+104, 10.1103/physrevlett.104.197203 (2010).
+[27] M. P. Kostylev, A. A. Serga, and B. Hillebrands, Radi-
+ation of caustic beams from a collapsing bullet, Physi-
+cal Review Letters 106, 10.1103/physrevlett.106.134101
+(2011).
+[28] T. Sebastian, T. Br¨acher, P. Pirro, A. A. Serga, B. Hille-
+brands, T. Kubota, H. Naganuma, M. Oogane, and
+Y. Ando, Nonlinear Emission of Spin-Wave Caustics from
+an Edge Mode of a Microstructured Co2Mn0.6Fe0.4Si
+Waveguide, Physical Review Letters 110, 10.1103/phys-
+revlett.110.067201 (2013).
+[29] J.-V. Kim, R. L. Stamps, and R. E. Camley, Spin wave
+power ﬂow and caustics in ultrathin ferromagnets with
+the dzyaloshinskii-moriya interaction, Physical Review
+Letters 117, 10.1103/physrevlett.117.197204 (2016).
+[30] F. Heussner, A. A. Serga, T. Br¨acher, B. Hillebrands,
+and P. Pirro, A switchable spin-wave signal splitter for
+magnonic networks, Applied Physics Letters 111, 122401
+(2017).
+[31] S. Muralidhar, R. Khymyn, A. A. Awad, A. Alem´an,
+D. Hanstorp, and J. ˚Akerman, Femtosecond laser pulse
+driven caustic spin wave beams, Physical Review Letters
+126, 037204 (2021).
+[32] B. A. Kalinikos and A. N. Slavin, Theory of dipole-
+exchange spin wave spectrum for ferromagnetic ﬁlms
+with mixed exchange boundary conditions, Journal of
+Physics C: Solid State Physics 19, 7013 (1986).
+[33] M. Lax and V. Narayanamurti, Phonon magniﬁcation
+and the gaussian curvature of the slowness surface in
+anisotropic media: Detector shape eﬀects with applica-
+tion to GaAs, Physical Review B 22, 4876 (1980).
+[34] Even for markedly anisotropic dielectrics the diﬀerences
+in refractive indices lead to maximal angles between
+phase and group velocities below 10° [? ].
+[35] I. Bertelli, J. J. Carmiggelt, T. Yu, B. G. Simon, C. C.
+Pothoven, G. E. W. Bauer, Y. M. Blanter, J. Aarts, and
+T. van der Sar, Magnetic resonance imaging of spin-wave
+transport and interference in a magnetic insulator, Sci-
+ence Advances 6, eabd3556 (2020).
+[36] L. B. Felsen and N. Marcuvitz, Radiation and Scattering
+of Waves, IEEE Press Series on Electromagnetic Wave
+Theory (Wiley-IEEE Press, 1994).
+[37] We deﬁne the spectral breadth of a non-monochromatic
+beam with well-deﬁned propagation direction and negli-
+gible divergence as ∆λ/λcar., where λcar. is the carrier’s
+mean apparent wavelength, and ∆λ is the beam’s stan-
+dard deviation in apparent wavelength.
+[38] A. Kreisel, F. Sauli, L. Bartosch, and P. Kopietz, Mi-
+croscopic spin-wave theory for yttrium-iron garnet ﬁlms,
+The European Physical Journal B 71, 59 (2009).
+[39] J. S. Harms and R. A. Duine, Theory of the dipole-
+exchange spin wave spectrum in ferromagnetic ﬁlms with
+
+17
+in-plane magnetization revisited, Journal of Magnetism
+and Magnetic Materials 557, 169426 (2022).
+[40] S. Klingler, A. V. Chumak, T. Mewes, B. Khodadadi,
+C. Mewes, C. Dubs, O. Surzhenko, B. Hillebrands, and
+A. Conca, Measurements of the exchange stiﬀness of
+YIG ﬁlms using broadband ferromagnetic resonance tech-
+niques, Journal of Physics D: Applied Physics 48, 015001
+(2014).
+[41] R. A. Gallardo, P. Alvarado-Seguel, A. K´akay, J. Lind-
+ner, and P. Landeros, Spin-wave focusing induced by
+dipole-dipole interaction in synthetic antiferromagnets,
+Physical Review B 104, 174417 (2021).
+[42] I. Bertelli, B. G. Simon, T. Yu, J. Aarts, G. E. W.
+Bauer, Y. M. Blanter, and T. van der Sar, Imaging spin-
+wave damping underneath metals using electron spins in
+diamond, Advanced Quantum Technologies 4, 2100094
+(2021).
+[43] R. Gieniusz, H. Ulrichs, V. D. Bessonov, U. Guzowska,
+A. I. Stognii, and A. Maziewski, Single antidot as a pas-
+sive way to create caustic spin-wave beams in yttrium
+iron garnet ﬁlms, Applied Physics Letters 102, 102409
+(2013).
+[44] H. S. K¨orner, J. Stigloher, and C. H. Back, Excitation
+and tailoring of diﬀractive spin-wave beams in NiFe using
+nonuniform microwave antennas, Physical Review B 96,
+10.1103/physrevb.96.100401 (2017).
+[45] We point out that the segment perpendicular to the ta-
+pered waveguide segments was at an angle of about 60°
+with respect to the applied ﬁeld in these experiments [46].
+[46] H. S. K¨orner, Time-resolved Kerr microscopy of spin
+waves propagating in magnetic nanostructures, Ph.D.
+thesis, Universit¨at Regensburg (2019).
+
diff --git a/2NAzT4oBgHgl3EQfRvtg/content/tmp_files/load_file.txt b/2NAzT4oBgHgl3EQfRvtg/content/tmp_files/load_file.txt
new file mode 100644
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+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf,len=1615
+page_content='Caustic spin wave beams in soft, thin ﬁlms: properties and classiﬁcation  Alexis Wartelle,∗ Franz Vilsmeier, Takuya Taniguchi, and Christian H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Back  Fakult¨at fur Physik, Technische Universit¨at M¨unchen, Garching, Germany  (Dated: January 4, 2023)  In the context of wave propagation, caustics are usually deﬁned as the envelope of a ﬁnite-extent  wavefront;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' folds and cusps in a caustic result in enhanced wave amplitudes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Here, we tackle a related  phenomenon, namely the existence of well-deﬁned beams originating solely from the geometric  properties of the corresponding dispersion relation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' This directional emission, termed caustic beam,  is enabled by a stationary group velocity direction, and has been observed ﬁrst in the case of  phonons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' We propose an overview of this “focusing” eﬀect in the context of spin waves excited  in soft, thin ferromagnetic ﬁlms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Based on an analytical dispersion relation, we provide tools for  a systematic survey of caustic spin wave beams.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Our theoretical approach is validated by time-  resolved microscopy experiments using the magneto-optical Kerr eﬀect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Then, we identify two cases  of particular interest both from fundamental and applicative perspectives.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Indeed, both of them  enable broadband excitations (in terms of wave vectors) to result in narrowband beams of low  divergence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  INTRODUCTION  The collective motion of magnetic moments in a ma-  terials, referred to as spin waves, has shown remarkable  properties from a fundamental perspective.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  Examples  range from anisotropic dispersion in thin ﬁlms [1], rel-  evant for the ﬁeld of magnonics, to Bose-Einstein con-  densation of magnons [2], through restricted-relativity-  like bounded domain wall velocities [3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  Applications  of magnetization dynamics also abound, starting with  the inﬁnite-wavelength ferromagnetic resonance (FMR)  [4] and going all the way towards sub-micrometer wave-  lengths, which are currently viewed as promising alterna-  tive information carriers in the ﬁelds of magnonics [5].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' In  addition to the absence of Joule heating and the potential  device downscaling (using small wavelengths), spin wave  interference is an appealing prospect [6] as it allows logic  operations through the design of the propagation lines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  Several experimental techniques are readily available  for the study of spin waves [1], especially in the case  of thin ﬁlms or patterned elements thereof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  Among  them, micro-/phase-resolved Brillouin Light Scattering  (BLS) [7], Time-Resolved Magneto-Optical Kerr Eﬀect  (TR-MOKE) microscopy [8], and time-resolved Scan-  ning Transmission X-ray Microscopy (TR-STXM) with  magnetic sensitivity through X-ray Magnetic Circular  Dichroism (XMCD [9]) [10] have demonstrated outstand-  ing imaging capabilities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Nevertheless, the usually very  small amplitudes of magnetization precession associated  to spin waves as well as their attenuation lengths (typi-  cally on the micrometer scale) pose a signiﬁcant challenge  both for fundamental investigations and for applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  To be of practical use, spin waves must be harnessed  via a power-eﬃcient strategy: some approaches like Win-  ter’s magnons rely on channeling along domain walls [11],  ∗ alexis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='wartelle@ens-lyon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='org;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Present address: Universit´e Greno-  ble Alpes, CNRS, Grenoble INP, SIMaP, 38000 Grenoble, France  others rely on careful control of spin wave scattering [12].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  Another possibility would take advantage of caustic spin  wave beams (CSWBs), i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  spin wave beams of well-  deﬁned propagation direction, narrow angular width and  higher power compared to e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Damon-Eshbach-type [13]  spin waves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  Furthermore, caustics in soft, thin ferro-  magnetic ﬁlms can be very diﬀerent from the well-known  acoustical or optical caustics, which originate from inho-  mogeneous media [14–16], : here, spin wave caustics can  arise in perfectly homogeneous ﬁlms in broad ranges of  conditions solely because of suﬃcient anisotropies in their  dispersion relation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' The latter indeed allows the direc-  tion of the group velocity to be stationary around some  wave vectors, leading to well-deﬁned directions of wave  propagation associated to signiﬁcantly stronger emission.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  In the context of phonon propagation, such phenomena  have been referred to as “focussing” [17], and they have  been observed and investigated since 1969 [17–21].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  By contrast, caustics in ferromagnetic ﬁlms were re-  ported for the ﬁrst time ca.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' 30 years later [22].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' There  has been quite a few reports since then [23–31] but, to  the best of our knowledge, there exists to date no sys-  tematic survey of the properties of spin wave caustics,  not even focusing on a certain type of systems e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' ul-  trathin ﬁlms with perpendicular anisotropy, or soft thin  ﬁlms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  In this work, we restrict ourselves to the latter  and give an overview of caustics in soft thin ﬁlms, as well  as tools to further investigate them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Moreover, we high-  light two special cases which seem particularly appealing  notably for application in magnonics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  MODEL  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  General considerations  Our starting point is the model derived by Kalinikos  and Slavin [32] for spin waves in soft ferromagnetic  thin ﬁlms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  These excitations correspond to a time-  and space-dependent magnetization −→  M(⃗r, t), yet its norm  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='01220v1  [cond-mat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='mes-hall]  3 Jan 2023  2  Ms = ||−→  M(⃗r, t)|| the spontaneous magnetization is uni-  form.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  As a result, it is simpler to consider the re-  duced magnetization −→  m(⃗r, t) = −→  M(⃗r, t)/Ms with norm  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  We focus on the linear regime i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  the deviation  δ−→  m(⃗r, t) = −→  m(⃗r, t) − −→  m0(⃗r, t) from the equilibrium mag-  netization (when no excitation is applied) −→  m0 is such that  ||δ−→  m|| ≪ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Under the assumption of negligible mode  mixing and of a perfectly isotropic ferromagnetic mate-  rial,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' one may write the dispersion relation of a thin ﬁlm  as:  ω2 =  �  γ0Ha + 2Aγ0  µ0Ms  k2��  γ0  �  Ms + Ha  �  + 2Aγ0  µ0Ms  k2�  −γ2  0M 2  s · ξ(kd)  �  1 − ξ(kd) + Ha  Ms  + 2Aγ0  µ0M 2s  k2�  cos2 ϕ  +γ2  0M 2  s · ξ(kd) · [1 − ξ(kd)]  (1)  where ω is the spin wave angular frequency,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' γ0 = µ0|γ|  with γ = qe/(2me) the electron’s gyromagnetic ratio  (qe = −e and me being the electron’s charge and mass,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  respectively) and µ0 the permeability of vacuum,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' A is the  micromagnetic exchange constant for the soft ferromag-  netic material of interest,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Ms its spontaneous magnetiza-  tion,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' k the spin wave’s wavenumber corresponding to its  wave vector −→k ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Ha = ||−→  Ha|| the strength of the externally  applied magnetic ﬁeld −→  Ha from which ϕ = angle  �−→  Ha,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' −→k  �  the wavefront angle is deﬁned,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' d the ﬁlm thickness,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' and  ξ is the function whose values are deﬁned as:  ξ(u) = 1 − 1 − e−u  |u|  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  (2)  As a consequence of the ferromagnetic material’s soft-  ness, in the absence of excitation, the equilibrium mag-  netization conﬁguration in our thin ﬁlm is the single-  domain state, with a corresponding reduced magnetiza-  tion −→  m0 exactly along the applied ﬁeld.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' The orientations  of −→  m0, −→  Ha, and −→k are illustrated in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' 1, which also  highlights the natural wavelength λ0 = 2π/||−→k || of the  spin wave as well as the unit vectors −→  ex, −→  ey and −→  ez.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  Here, we focus on spin waves with no amplitude node  across the ﬁlm thickness, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' we do not consider per-  pendicular standing spin waves (PSSWs).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' However, we  do note that the latter may play a role in experiments  performed on suﬃciently thick ﬁlms where a realistic an-  tenna for instance could excite them due to its inhomo-  geneous magnetic ﬁeld.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  We introduce the following quantities:  the Larmor  angular frequencies associated to magnetization ωM =  γ0Ms and to the applied magnetic ﬁeld ωH = γ0Ha, the  material’s dipolar-exchange length lex =  �  2A/(µ0M 2s ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  We then rewrite the equation as:  −  →  ex  −  →  k  −→  Ha  −→  m0  φ  λ0= 2π  ||−  →  k||  = 2π  k  0  δmz  −  →  ez  −  →  ey  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Schematic representation of a spin plane wave prop-  agating in a soft thin ﬁlm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  The grey scale codes the local  perpendicular component of the dynamic component of mag-  netization, δmz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  ω2  ω2  M  =  � ωH  ωM  + l2  exk2  � �  1 + ωH  ωM  + l2  exk2  �  −ξ(kd)  �  1 − ξ(kd) + ωH  ωM  + l2  exk2�  cos2 ϕ  +ξ(kd)  �  1 − ξ(kd)  �  (3)  Introducing the reduced frequency ν = ω/ωM and ap-  plied ﬁeld h = ωH/ωM = Ha/Ms,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' and normalizing both  the dipolar-exchange length and wavenumber to the ﬁlm  thickness d using η = lex/d and ˜k = kd,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' we arrive at:  ν2 =  �  h + η2˜k2��  1 + h + η2˜k2�  −ξ(˜k)  �  1 − ξ(˜k) + h + η2˜k2�  cos2 ϕ  +ξ(˜k)  �  1 − ξ(˜k)  �  (4)  With this,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' it is clear that any given experiment of spin  wave excitation corresponds to a speciﬁc value of the di-  mensionless triplet (η,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' ν,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' h).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' In other words: they are  the only independent parameters within this model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  For a value of (η, ν, h), the solution to (4) is the pos-  sibly empty set of accessible dimensionless wave vectors  −→k d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  The existence and properties of spin wave caus-  tics depend on the geometrical characteristics of this set,  which is why we are ﬁrst going to review several of its  general properties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  Keeping in mind that we focus on applied ﬁelds below  the ferromagnetic resonance ﬁeld at the excitation fre-  quency, we actually always have a non-empty solution,  which is usually a closed curve winding around the ori-  gin in wave-vector space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' This is the so-called slowness  curve, in reference to the fact that at ﬁxed frequency  k ∝ 1/||−→  vp|| where −→  vp is the phase velocity [33], oriented  of course along the wave vector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Considering the parity  of the cosine function and its antisymmetry for the re-  ﬂection ϕ → π − ϕ, we may restrict our analysis to only  the quadrant ϕ ∈ [0, π/2] and deduce the others using  mirror symmetries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  3  One can also parametrize the slowness curve using a  curvilinear abscissa: we deﬁne it to be zero for the lowest  dimensionless wavenumber ˜kmin at ϕ = π/2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' One can in-  deed show that the reduced wavenumber solving Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' (4)  at ϕ = π/2 (resp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' 0) is minimum (resp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' maximum) on  the quadrant ϕ ∈ [0, π/2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Thus, at the largest dimen-  sionless wavenumber ˜kmax = ˜k(ϕ = 0), the correspond-  ing curvilinear abscissa sM corresponds to the length of  the slowness curve in the quadrant ϕ ∈ [0, π/2] i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' one  fourth of the whole length of this curve.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  Another important geometrical aspect of the slowness  curve that is central to the present work is the local  normal to it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Considering its deﬁnition as a constant-  frequency intercept of the dispersion relation in wave-  vector space, by nature, the frequency gradient −→  ∇−  →  k ω is  perpendicular to the slowness curve.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' As a result, the di-  rection of the group velocity of spin waves −→  vg = −→  ∇−  →  k ω can  be directly read from the direction of the local normal to  the slowness curve.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' In our notations, we point out that:  −→  ∇−  →  k ω ≡  �  β=x,y,z  ∂ω  ∂kβ  −→  eβ  where  kβ = −→k · −→  eβ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  In the following,  we will use the angle θV  =  angle(−→  Ha, −→  vg).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  We point out that in the present case,  phase and group velocities need not be collinear:  on  the contrary, there can be diﬀerences between θV and  ϕ much larger than in cases of light propagation through  anisotropic media [34].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' 2 illustrates this on the ex-  ample of a slowness curve reconstructed for a vanishing  reduced applied ﬁeld.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  Distinctive features of dispersion relation  caustics  Typically, caustics in inhomogeneous media occur  when a wavefront folds onto itself;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' in this situation, there  exists a surface (or a line in 2D wave propagation) such  that across it the number of rays passing through a point  in space changes by an even number [15, 16]: this is the  caustic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Equivalently, it can be viewed as the set of the  local extrema of positions on the ray bundle on the wave-  front, for all the wavefronts along the wave propagation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  It is this extremal nature that grants these caustics large  and localized intensities compared to other points on the  ray bundle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  In a geometrical optics approach, the in-  tensity diverges as an initially ﬁnite-sized portion of the  wavefront shrinks to a vanishing area [15].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' A wave op-  tics treatment however reveals that the intensity remains  ﬁnite due to interferences: illumination proﬁles across  caustics can in principle be determined by taking into  account the variations of phase as a function of distance  to the caustic [14].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  Such an approach has been used by Schneider et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  [26] for spin wave caustics excited by the scattering of  a spin wave travelling in a waveguide terminating into a  θV  φ0  −  →  k0d  a)  b)  c)  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  a) Exemplary slowness curve for (ν, h, η)  =  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='2873, 10−20, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='15).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' As can be clearly seen in the polar plot  of kd = ˜k(ϕ), the direction (ϕ0 =32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='00°) of the phase veloc-  ity −→  vp and that (θV =108.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='9°) of the group velocity −→  vg at the  point −→  k0d are very diﬀerent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  b) Radiation pattern (δmz is  grey-coded) of a hypothetical source exciting only wavenum-  bers very close to ||−→  k0||d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' c) Plane wave corresponding to the  carrier wave vector −→  k0d (red lines are guides to the eye).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  full permalloy (Ni80Fe20) ﬁlm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' However, this is a very  diﬀerent situation compared to the above.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Indeed, the  wavefront does not fold onto itself due to spatial varia-  tions of medium properties, rather, its extent is deter-  mined almost exclusively (owing to the sub-wavelength  source size) by the characteristics of spin wave propaga-  tion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' The latter are determined by the anisotropic spin  wave dispersion relation, which allows caustics to form  thanks to the possibility of stationary group velocity di-  rection i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' a beam with a well-deﬁned propagation direc-  tion yet comprising a range of wave vectors in the vicinity  of a carrier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' More precisely, caustics correspond to local  extrema of the group velocity direction;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' in other words, a  caustic spin wave beam implies the existence of a caustic  point ˜kc on the slowness curve such that:  dθV  d˜k  ����˜kc  = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  (5)  The CSWB has then a carrier wavenumber ˜kc, corre-  sponding to a central wavefront angle ϕc = ϕ(˜kc) and a  90  75°  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='09  45°  30°  Ug  15°  kd  0°  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='5  kd4  beam direction θV,c = θV(˜kc).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  Coming back to the wavefront extent, rays from wave  vectors not close enough to the carrier cannot play a role  in the caustic wave amplitude simply because of diﬀer-  ences in propagation direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  More speciﬁcally, the  experimental data presented by Schneider et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  sug-  gests that beam divergences of 2° or less can be obtained.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  Thus, there seems to be a contradiction between the cu-  bic dispersion which is assumed to deﬁne the beam pro-  ﬁle and the measurements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' The question of the CSWB’s  proﬁle goes however beyond the scope of this work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Nev-  ertheless, it is clear from the low beam divergences ob-  served in many experimental reports [23, 27, 35] that only  small, almost straight parts of the slowness curve must  contribute to CSWB.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  In fact, integrating the contribution of wave vectors all  the way to inﬁnity as done in [26] neglects the geometric  impossibility for them to create waves travelling from the  point source to a far-away point on the caustic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' To put it  diﬀerently: for geometrical reasons, caustics originating  solely from anisotropies in the dispersion relation and  excited by a point-like source naturally restrict the range  of relevant wave vectors, in contrast to the case of caustics  due to inhomogeneities in the propagation medium.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  We wish to emphasize the above by reminding that in  most cases [15, 36], caustics are treated on the basis of  wave propagation in an isotropic or weakly anisotropic  medium.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' One consequence is the fact that the ﬂow of  power, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' the group velocity, is along the wave vector  or close to parallel to it [14].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' While this remains a rea-  sonable approximation for slightly anisotropic media (as  in usual crystal optics), in the case of perfectly soft but  fully polarized thin ferromagnetic ﬁlms this collinearity  may break down dramatically, as was illustrated in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Therefore, even small changes in wave vector may re-  sult in drastic changes in group velocity direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' By  contrast, large changes in wave vectors do not necessar-  ily lead to strong variations in the apparent wavelength  λ which we deﬁne as:  λ = 2π · ||−→  vg||  −→k · −→  vg  =  2π  −→k · −→  eg  =  λ0(ϕ)  cos (θV − ϕ),  (6)  where we have introduced −→  eg as a unit vector along the  group velocity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' The apparent wavelength is simply the  spatial period measured along the beam direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Since  large diﬀerences θV − ϕ can easily be obtained (cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  2, where cos (θV − ϕ0) ≃ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='227), and more importantly  since the projection ˜k(ϕ) cos (θV − ϕ) may remain almost  constant over signiﬁcant portions of the slowness curve,  one should consider notions such as propagation-induced  phase or spectral breadth [37] of a spin wave beam care-  fully.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  RESULTS AND DISCUSSION  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  Limit of model applicability: thick ﬁlms  We start by providing an example of situation where  the model we use cannot be fully trusted, so as to high-  light its limitations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' 3 we show a case where the  reconstructed slowness curve splits into two separate con-  nected components above a certain threshold frequency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  ˜k  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Slowness curves for η = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='015, h = 10−20, and ν =  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='331 (dashed blue line) resp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' ν = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='333 (full red line).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  Such a behaviour has been described by Kreisel et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  [38]: the model chosen for spin wave dispersion predicts  a local maximum in the ω(k, ϕ = π/2) vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' wavenumber  curve, but this extremum is not reproduced by a formal  approach not based on the thin-ﬁlm approximation [39],  and designed to tackle the dipole-exchange regime.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' The  maximum’s presence leads to an additional pair of so-  lutions in terms of wavenumber in a certain frequency  range, corresponding to a splitting of the slowness curve  into two separate components.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  Clearly, results obtained within our approach about  caustics deep in the dipole-exchange regime are not trust-  worthy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Empirically, we see the slowness curve splitting  into separate components for values of η up to ca.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='075;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  for the sake of comparison, the thinnest ﬁlms investigated  by Kreisel et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' feature η < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='035 according to literature  data on yttrium iron garnet (YIG) [40].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Nevertheless, the  absence of this splitting is no proof that the reconstructed  slowness curve is accurate, and we shall remain cautious  in discussing results concerning CSWBs with wavenum-  bers in the dipole-exchange regime.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Finally, we note that  promising theoretical developments such as the dipole-  exchange dispersion relations recently derived by Harms  and Duine [39] could eventually allow a more accurate  treatment of caustics in the dipole-exchange regime.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  90°  75°  60°  45°  v =0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='333  v =0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='331  30°  15°  5  10  15  20  25  30  35  0  kd5  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  General features  Let us have a look at a ﬁrst example of frequency and  ﬁeld map of caustic properties in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' In the presented  graphs, the red color means that either the corresponding  (h, ν) point was not investigated because its reduced ﬁeld  is above the reduced FMR ﬁeld hFMR, or because no  caustic points were found there.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  First of all, one can see that there is indeed a portion  of the (h, ν) plane where no caustic points exist.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' This  occurs for frequencies above a certain νm(h, η).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Then,  going down in reduced frequency, there appears to be an  oblique boundary between two regions of the map.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Above  it, ˜kc quickly enters the dipole-exchange regime, which we  will only present but not discuss quantitatively as it cor-  responds to a situation where our model is less reliable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  Below the boundary, the reduced caustic wavenumber is  much smaller than 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Correspondingly, a boundary which  we will label νb(h, η) appears at the same position on the  plot of ϕc;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' this angle also seems close to constant over  much of the region below the boundary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' In both cases,  its sharpness decreases towards low h, and at vanishing  reduced ﬁeld the transitions in ˜kc or ϕc are both smooth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  All these features are represented on a simpliﬁed repre-  sentation of the map of ˜kc shown as inset on the ϕc map,  including the point (hc, νc) at which the sharp boundary  seems to end.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' A zoomed-in view on (hc,νc) is shown in  the inset of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  In the following, we will refer to the lowest reduced  ﬁeld at which this boundary is sharp as hc and denote  νc = νb(hc, η).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  As we shall see in more details, this  abrupt boundary corresponds to a change in the num-  ber of caustic points by two.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' The lowest point (hc, νc)  is actually a cusp in the domain of existence of the two  additional caustic points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' We point out that for all re-  duced ﬁelds and frequencies, the maps shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' 4  displays the lowest caustic wavenumber respectively the  associated wavefront angle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  Before moving on to discussing the low-frequency  pocket, its boundary and the existence of additional caus-  tic points, and ﬁnally the threshold frequency for the ab-  sence of caustic points, we stress that the behaviour of  caustics strongly depends on η.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' As an example, we show  in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' 5 ﬁeld and frequency maps for η = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='09, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='3, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='6  (from left to right).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' At the lowest value, the boundary  νb extends all the way to h = 0, whereas the two other  maps do not display such a sharp behaviour.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' In addition  to the expected changes in range of values for ˜kc, one can  see that the overall shape of the domain of existence of  CSWBs also changes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' From here on, we will call this area  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' From η = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='09 to 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='3, we see that D has expanded in  the vertical direction at low h.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' In even thinner ﬁlms, for  η = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='6, the average slope of νm(h, η) has not changed  much, yet νm(0, η) has decreased;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' as a result, D shrinks  vertically.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  By contrast, even if the caustic group velocity direction  displays a similar wealth of features as the caustic wave-  front angle and reduced wavenumber, the jumps across  the boundary νb are much less signiﬁcant when they ex-  ist.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' An example of this is shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' 6, which shows  maps for θV,c at the same values of η as in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  In a certain range of reduced dipolar-exchange length,  we ﬁnd that there may actually be more than one caustic  point on the slowness curve.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Empirically, we observe that  the additional caustic points may exist for ˜kc < 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' When  this inequality holds, the number of caustic points is ei-  ther equal to one or to three;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' two being possible but only  on a 1D curve in the ﬁeld and frequency plane;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' this curve  includes the aforementioned boundary νb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Qualitatively,  this is due to the fact that in the corresponding range  of ﬁeld and frequency, when dθV/d˜k crosses 0, it does so  with a local behaviour somewhat reminiscent of a poly-  nomial of the type P(˜k;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' a, b) = (˜k − ˜kc)3 +a·(˜k − ˜kc)+b,  where a and b are real parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' If a > 0, there ex-  ists only one root, whereas if a < 0 and |b| is suﬃciently  small, there exists three distinct roots.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  The domain in the ﬁeld and frequency plane with these  three roots will be referred to as D3 from now on, by  contrast with D1 = D \\ D3 in which there is only one  caustic point instead of three.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' We will now describe D3  using the P(˜k;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' a, b) approximant to dθV/d˜k for the sake  of simplicity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  Let us start with Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' 7, which displays the same ﬁeld  and frequency map for ˜kc as in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' 4 along with the  maps for the two other reduced caustic wavenumbers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  The two additional solutions can be shown to coincide on  the rounded boundary of D3 to the lower left, which will  be referred to as ∂D3,l.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Entering D3 through this bound-  ary by increasing ν corresponds to the situation where |b|  becomes small enough to allow the two additional caustic  points (with respect to the one with lowest ˜kc), thanks to  a being negative enough.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Increasing h on the other hand  mostly decreases a: upon crossing ∂D3,l, a pair of caus-  tic points with higher ˜kc’s appears.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Of course, exactly on  ∂D3,l the two additional roots of dθ/d˜k are identical.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  Starting from inside D3, if one increases the reduced  frequency, eventually the caustic point with the interme-  diate value of ˜kc merges with the one featuring the small-  est reduced wavenumber.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  This happens on the other  boundary of D3, which we will call ∂D3,u from now on.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  This situation corresponds to ν = νb(h, η).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Just above  this boundary, the value of b is low enough so that only  one root of dθ/d˜k remains.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' That is the reason for the dis-  continuity in ˜kc in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' 4: the lowest caustic wavenumber  jumps to what was the highest of the three ˜kc’s below  νb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Experimentally, this could imply that SW excitation  around this threshold wavenumber would have marked  changes in intensity as a function of frequency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  Based on the above, since the two boundaries other  than ferromagnetic resonance each imply that a diﬀer-  ent pair of caustic points coincide, we can infer that on  the cusped intersection of ∂D3,l and ∂D3,u, there exists a  single caustic point corresponding to three of them coin-  ciding on the slowness curve.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' This is precisely the point  (hc, νc) from the inset in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  It is important to note that while a purely math-  6  φc (◦)  ˜kc  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
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+page_content='19 0  h  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
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+page_content='48  ν  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='74  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='5  Low-  frequency  pocket  νm(h, η)  h  ν  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='62  νb(h, η)  νc  hc  a)  b)  h  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='0  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Frequency and ﬁeld maps for a value of η = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' For high enough ﬁelds, a sharp upturn in both properties can be seen  for reduced frequencies above ca.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
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+page_content=' We remind the reader that ﬁelds above ferromagnetic resonance are not considered.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  Only few level curves are displayed for the sake of clarity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' a) Caustic wavefront angle ϕc, with a schematic representation of  the map’s distinctive features as inset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' b) Normalized wavenumber ˜kc = kcd;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' a zoomed-in view on the area where the upturn’s  sharpness drastically changes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
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+page_content='250  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='1999  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='1000  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='000  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='0001  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='0000  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='2063  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='4126  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='6189  h7  ematical analysis yields well-deﬁned, separate caustic  points, experimentally the distinction between close caus-  tic points may well be impossible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  In fact, there ex-  ists no straightforward experimental signature of dθV/d˜k  crossing 0, and portions of the slowness curve where this  derivative is small but non-zero can behave similarly to  an actual caustic point, as was noted by Gallardo et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  [41].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Nevertheless, the presence of more than one caustic  point constrains a slowness curve to be almost straight in  their vicinities;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' this should then favour marked caustics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  Low-frequency pocket  The low-frequency regime is important as it corre-  sponds to a well established domain of validity of our  theoretical model as well as wavelengths which can still  be excited and detected reasonably easily in experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  Analytics  As could be seen in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='5, the shape or even the  existence of the low-frequency pocket strongly depends  on the chosen value of η.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  Nevertheless, we can in-  vestigate the behaviour of caustics there by taking the  limit ν → 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  In order to remain below ferromagnetic  resonance, we also take the limit h → 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  Assum-  ing h = 0 simpliﬁes the computation of the quantity  tan θV = tan ϕ · [1 + f(˜k, ν, η)], where f is a function  given in the Supplementary Materials.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' We can then dif-  ferentiate this with respect to ˜k, take the limit ν → 0 and  Taylor-expand the derivative;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' the details are provided in  the Supplementary Materials.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Eventually, we ﬁnd that:  ˜kc(ν → 0) = 3ν2 + O(ν4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  (7)  It was expected that the caustic wavenumber goes to  zero;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' we can furthermore show that the lowest reduced  wavenumber on the slowness curve (still in zero applied  ﬁeld) i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' the Damon-Eshbach wavenumber goes to zero  as:  ˜kmin(ν → 0) = 2ν2 + O(ν4)  (8)  which proves that CSWBs exist down to vanishing re-  duced frequencies, regardless of their values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' In this limit,  the associated caustic wavefront angle is such that:  cos ϕc =  1  √  3 + O(ν2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  (9)  From the latter, we also get the CSWB direction θV,c:  tan θV (˜kc, h → 0, ν → 0) = −2  √  2 + O(ν2)  (10)  The strength of this result lies with its independence on  η;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' this is not surprising as in the limit we are considering,  the CSWB’s wavelength diverges which means it must  be much larger than both the ﬁlm thickness d and the  dipolar-exchange length lex, however large they may be.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  The numerical values for the limits of ϕc and θV,c are ca.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  54.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='74° and 109.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='5°, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  Comparison with literature  We present in Table I a comparison between experi-  mental reports on caustics and predictions we make for  the same conditions, focusing on the CSWB direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  Whenever there are three caustic points, the indicated  predicted value for θV,c is the closest found across all  three caustic points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  We ﬁnd a reasonable agreement in quite a few cases,  generally for the larger values of η (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' for thinner ﬁlms)  with the notable exception of the report by Sebastian et  al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' [28].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' However, in this case, the theoretical dispersion  relation that we use may not be accurate any more due  to the strong lateral conﬁnement of spin waves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  Furthermore, we ﬁnd much larger discrepancies in sev-  eral cases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' For instance, if we consider the excitation of a  caustic-like beam by Gieniusz et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' [43] at 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='62 GHz and  under an induction of 98 mT in a 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='5 µm thick YIG ﬁlm,  our model predicts a caustic point at reduced wavenum-  ber 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='2, with a beam direction 169°.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' However, the rele-  vant reduced wavenumbers in this experiment are in the  range of a few percents [43], and the measured beam di-  rection is 128°.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' The origin of this strong disagreement is  easily understood by observing the derivative dθV/d˜k in  this case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' As Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' 8 reveals, there exists a local minimum  at ˜k ≃ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='0659 for dθV/d˜k deep in the dipolar-dominated  regime.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Moreover, the associated group velocity direc-  tion is 128°, and past the next local maximum, similar  values of dθV/d˜k are reached again only for ˜k ≃ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  This illustrates the impossibility to distinguish a close-  to-straight slowness curve from a true caustic point from  measurements alone.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  Discrepancies may also arise due to the source’s non-  ideal excitation eﬃciency, for instance if it is too direc-  tional.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' This is illustrated by the excitation of caustic-  like spin wave beams by K¨orner et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' [44].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' One of the  reported TR-MOKE measurements deals with a 60 nm  thin permalloy ﬁlm driven at an excitation frequency of  16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='08 GHz, under 160 mT applied induction;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' the authors  observe twin beams with a wavefront angle of 65°, a beam  direction 114°, and a reduced wavenumber of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='314.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Yet,  the expected caustic spin wave beams in these condi-  tions should feature a reduced wavenumber of 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='7063, a  beam direction 138.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='62°, not to mention a wavefront angle  of 53.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='27°.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' In this case, it appears that the excited spin  waves simply correspond to the rather narrow portion of  the slowness curve that could be excited by the authors’  tapered coplanar waveguide segments [45].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Indeed, at the  measured wavefront angle of 65°, in the authors’ experi-  8  TABLE I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Comparison between reports on CSWBs and our predictions for the beam direction θV,c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Excitation method  Material (thickness in nm) Predicted θV,c Measured θV,c  h  ν  η  [28] Edge modes of a waveg-  uide and nonlinearities  Co2Mn0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='6Fe0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='4Si (30)  113°  123°  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='81·10−2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='287  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='15  [42] Corners of slotline termi-  nation and scattering oﬀ  a defect  YIG (235)  123°  124°, 122°  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='126  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='427 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='36·10−2  [35] Corners  of  slotline  termination  YIG (245)  119°  118°  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='126  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='427 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='06·10−2  [43] Spin wave scattering oﬀ  antidots  YIG (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='5·103)  169°  128°  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='557  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='939 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='84·10−3  [27] Collapsing  spin-wave  bullet  YIG (5·103)  137°  137°  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='040  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='442 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='46·10−3  [22] Spin wave scattering oﬀ  a defect  YIG (7·103)  139°  135°  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='47·10−3 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='616 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='47·10−3  mental conditions, the expected reduced wavenumber is  about 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='28 (which falls rather far from zeroes in the an-  tenna’s expected excitation eﬃciency [46]), and the beam  direction 120.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='2°.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' We do not have an explanation for the  remaining deviation in beam direction, though.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  Experimental results  We now present results from experiments we have  carried out in order to validate our theoretical ap-  proach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Our aim here is to measure CSWBs and compare  their properties with our predictions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  In order to ac-  cess CSWBs experimentally, the reciprocal-space Fourier  components of its magnetic ﬁeld must span a broad range  of wave vectors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' The ideal situation where all wave vec-  tors are accessible corresponds to an unrealistic point  source, which can obviously not correspond to any high-  frequency antenna.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' As a result, we choose a compromise  between ease of fabrication, and broad-band excitation  eﬃciency, namely a half-ring shaped stripline antenna.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  This design allows for a spin wave excitation of the slow-  ness curve within ϕ ∈ [0, π], i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  twice the quadrant  previously investigated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Of course, this excitation is not  uniform because of the microwave antenna dimensions on  the order of a micrometer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  Our experiments were carried out using Time-Resolved  Magneto-Optical Kerr Eﬀect (TR-MOKE) microscopy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  Here, the dynamic out-of plane component of the mag-  netization δmz is spatially mapped in the xy-plane at a  ﬁxed phase between the microwave excitation frequency  and the laser probing pulses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' This enables direct imag-  ing of the spin wave propagation in the magnetic ﬁlm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  The wavenumber resolution of the set-up lies within the  dipolar-dominated regime.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Indeed, our spatial resolution  r is about 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='29 µm (see Supplementary Materials), so that  for a ﬁlm thickness t ∼100 nm, the largest accessible re-  duced wavenumbers are 2π/(2r) · t ∼ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  It shall be noted that the position of the microwave an-  tenna in the resulting Kerr images is extracted from the  topography image which is acquired simultaneously and  is proportional to the reﬂectivity of the sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Further  information on TR-MOKE can be found in the Supple-  mentary Materials.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' These experiments were performed  on a 200 nm thick YIG ﬁlm grown on a gadolinium gal-  lium garnet (GGG) substrate using liquid phase epitaxy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  Considering this materials’ parameters [40], if not stated  otherwise, η = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='087 for all measurements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' On top of  the YIG ﬁlm the 2 µm to 3 µm wide microwave antenna  was patterned by optical lithography with subsequent Ar-  presputtering and electron-beam-induced evaporation of  Cr(5 nm)/Au(100 nm to 220 nm).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' During the measure-  ment the external bias ﬁeld −→  Ha was always kept ﬁxed  such that it aligned with the legs of the antenna structure  along the x-direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' A sketch of the measurement ge-  ometry can be found in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' At this stage, we point out  one complication resulting from this design.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' When driv-  ing the antenna with a microwave ﬁeld, the legs them-  selves excite spin waves in the Damon-Eshbach geometry  [13].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' These modes are not of interest for the generation  of CSWBs, but due to the relatively long attenuation  length in YIG [35] they may propagate to the tip of the  antenna and interfere with the spin waves excited by the  half-ring.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' In order to suppress this eﬀect, two diﬀerent  approaches where applied.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Either the length of the an-  tenna was set to 50 µm and the YIG between the legs and  tip was etched away, or the antenna was patterned to be  1 mm long in the ﬁrst place.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  The ﬁrst Kerr image shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='a) was ob-  tained at a constant microwave frequency f =1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='44 GHz  and an external ﬁeld µ0Ha =5 mT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  This corresponds  to h = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='028, ν = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='292.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' The width of the waveguide  was 2 µm and the distance between the legs and the tip  was 1 mm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' In the spatial map, two spin wave beams with  well-deﬁned propagation directions are visible;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' moreover,  the phase and group velocities are clearly non-collinear  to each other.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Here, beam II stems from the waveguide  excitation in the quadrant ϕ ∈ [π/2, π].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
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+page_content=' 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Calculated derivative of the group velocity direction  with respect to the reduced wavenumber in the 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='62 GHz spin  wave excitation described by Gieniusz et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' [43].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  YIG film  2 µm  −  →  k  x  y  z  −→  Ha  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Schematic of the measurement geometry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' The half-  ring shaped antenna excites spin wave propagation within a  broad angular spectrum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  of beams I and II with respect to the positive x direction  are found to be 119.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='00◦ (beam I) and 64.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='28◦ (beam II)  which results in eﬀective beam directions of θI = 119.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='00◦  and θII = 180◦ − 64.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='28◦ = 115.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='72◦, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  The  discrepancy between θI and θII simply originates from  a small misalignment of the external ﬁeld with respect  to the waveguide legs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Since −→  Ha is not fully parallel to  the x-axis, the slowness curve is rotated by a small an-  gle αH = (θI − θII)/2 ≈ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='64◦ in our frame of reference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  Keeping this in mind, we extract an average beam direc-  tion θV,e = 117.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='36◦, a wavefront angle ϕe = 50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='66◦ and  a reduced wavenumber ˜ke = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
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+page_content=' These experimental  ﬁndings are in good agreement with our theoretical ap-  proach;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' indeed, values of θV,c = 115.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='05◦, ϕc = 51.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='29◦ and  ˜kc = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='223 are predicted for a CSWB in our experimental  conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  We can obtain further insight in reciprocal space with  30  20  10  10  20  30  x (µm)  y (µm)  0  0  ˜kx  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
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+page_content=')  δmz (arb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
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+page_content='8  a)  b)  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Measurement data obtained for η = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='087, h = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='028  and ν = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='292.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  a) Kerr image acquired from TR-MOKE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  Two spin wave beams highlighted in yellow and red propa-  gate from the tip of the antenna.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  b) Squared modulus of  the Fourier transform (FT) of the Kerr image and expected  slowness curve (blue).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  The yellow and red points and ar-  rows indicate the expected caustic points and their respective  group velocity directions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Caustic points I and II correspond  to beams I and II in the Kerr image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  the Fourier-transformed (FT) data shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  Generally speaking, the FT data allows for a direct ob-  servation of the slowness curve in ˜k-space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' In order to re-  duce spectral leakage, a Hanning windowing was applied;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  the latter provides a good trade-oﬀ between frequency  and amplitude accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' We see that the chosen antenna  structure indeed excites a wide range of wave vector di-  rections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' The gaps in the spectrum arise from the ﬁnite  antenna dimensions, as previously mentioned.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' We ﬁnd a  good agreement between the slowness curve (blue curve)  derived from our model (and corrected by the external  ﬁeld angle αH).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' More importantly, this graph conﬁrms  that the antenna structure grants access to the expected  caustic points (yellow and red points) since the Fourier  magnitude is still suﬃciently large in that region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' To con-  clude, caustic points I and II can be assigned to beams I  and II from the Kerr image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  We may now turn to the additional caustic points pre-  dicted by our model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' The chosen triplet (η, h, ν) is an ele-  ment of the D3 set, and we would expect two further caus-  tic points θV,c,2 = 113.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='74◦, ϕc,2 = 33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='00◦, ˜kc,2 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='662  and θV,c,3 = 114.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='02◦, ϕc,3 = 28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='78◦, ˜kc,3 = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='227.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' These  reduced wave vectors could actually be resolved by our  experimental set-up where ˜kres ≈ 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  The reciprocal  space image in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='b), however, displays a very low  amplitude for ˜k ≳ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='55 meaning that the microwave an-  tenna cannot excite the other caustic points very eﬃ-  ciently.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  Hence, only the low frequency pocket can be  accessed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  Further Kerr images were taken for the same ν, but  I  II11  for diﬀerent h values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  The h values were chosen such  that they lie beneath the expected FMR ﬁeld hFMR ≈  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='078778.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' A selection of the resulting Kerr images is il-  lustrated in the upper part of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' In each of them,  twin spin wave beams are apparent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' An overview of all  the beam properties for the corresponding h values is  plotted in the lower part of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Here, the relevant pa-  rameters from every individual beam are extracted with  image processing and bootstrapping least squares regres-  sion procedures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' An example on how one set of experi-  mental data points is obtained can be found in the Sup-  plementary Materials.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' The reasonable, sometimes even  very good agreement between predicted and experimen-  tal values of θV,c and ˜kc strongly suggests true CSWBs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  The deviation of the beam directions is mostly within the  range of the external ﬁeld angle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' The larger discrepancy  between predicted and measured wavefront angles ϕc is  attributed to the narrowness of the CSWB.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  b1)  b2)  b3)  a1)  a2)  a3)  h = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='0341  h = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='0398  h = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='0511  Theory  Experiment  θV,c (◦)  φc (◦)  ˜kc  30  42  54  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='18  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='26  110  113  116  119  122  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='025  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='030  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='035  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='040  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='045  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='050  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='055  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='060  h  30  20  10  0  10  20  30  x (µm)  y (µm)  30  20  10  0  x (µm)  30  20  10  0  x (µm)  0  0  0  0  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Measurement data obtained for η = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='087 and ν =  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='292.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Upper part: acquired Kerr images for reduced ﬁelds of  a1) h = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='0341, a2) h = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='0398, and a3) h = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='0511,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' b1-3)  comparison between experiment and theoretical predictions  of caustic point properties θV,c, ˜kc, ϕc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' The error bars are  the standard deviations from a bootstrapping ﬁt procedure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  Beam-like features which do not coincide with a caus-  tic point were detected as well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' This time, the measure-  ments were conducted with the 50 µm antennna struc-  ture and partially etched ﬁlm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' The width of the antenna  was 3 µm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  The resulting Kerr map for f =1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='84 GHz  (ν = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='372) and µ0Ha =5 mT (h = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='028) is shown  in the left upper half of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  In this geometry, a  Damon Eshbach-like mode propagating from the YIG  edge could not be fully suppressed;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' it is visible as a  plane wave background.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Our procedure to analyze spin  wave beams yields θV,e = 136.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='33◦, ϕe = 68.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='97◦ and  ˜ke = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='522, whereas our model predicts a caustic point  with θV,c = 121.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='39◦, ϕc = 35.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='84◦ and ˜kc = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='564.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  The origin of the experimentally observed beams may  be twofold.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  Firstly, a close-to-straight slowness curve  similar to the case of Gieniusz et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' [43] is predicted to  exist within relatively close distance to ˜ke.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' The dθV/d˜k  plot in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='b) displays almost a constant behaviour  between 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='6 ≲ ˜k ≲ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='2 (marked with green dashed lines).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  The proximity of the experimental caustic point to a  straight-to-close slowness curve is also illustrated in the  FT data in the lower part of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Here, the dashed  green semicircle represents the lower bound of ˜k = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='6  and the extracted beam points are highlighted in yellow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  For this portion of the slowness curve, group velocity  directions of up to 121.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='39◦ are predicted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' This beam di-  rection, however, is still in stark contrast with the mea-  surement result.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Moreover, the calculated slowness curve  (blue curve) deviates signiﬁcantly from the FT data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' The  diﬀerence between reciprocal space image and our model  may show the limit of the model applicability, since a ﬁlm  with η = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='087 may not be considered a thin ﬁlm any-  more.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' This results in predictions which are less reliable  at higher ν values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' A second possible origin of the beams  is the excitation eﬃciency of the microwave antenna as  there are many gaps in the FFT spectrum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' The beams  appear to be located close to some of them, and hence,  may correspond to the excitation of only a small portion  of the slowness curve within this region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  |FT(δmz)|2  (arb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=')  c)  Theory  Fit data  ˜kx  0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='8  0  ˜ky  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='6  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='4  30  20  10  10  20  30  y (µm)  0  0  δmz (arb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=')  0  a)  b)  dθV/d˜k  0  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='6  x (µm)  ˜k  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  a) Kerr image with twin beams obtained with  η = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='087 h = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='028 and ν = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='372.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' b) Calculated derivative  of the group velocity direction with respect to the reduced  wavenumber.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Dashed green lines highlight close-to-straight  slowness curve.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  c) FT of Kerr image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  The experimentally  observed beam parameters are depicted in yellow, the calcu-  lated slowness curve in blue and the calculated caustic points  in red.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Dashed green semicircle illustrates lower limit of close-  to-straight portion of slowness curve.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  12  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  Caustic point of higher order  Based on the conclusions from section III B, we know  that the intersection of ∂D3,l and ∂D3,u there exists a sin-  gle caustic point on the slowness curve;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' in the schematic  discussion from the above based on the approximant  P(˜k;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' a, b), it corresponds to a = 0 and b = 0, which  means that dθV/d˜k ∼ (˜k − ˜kc)3 around this point.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' To  put it diﬀerently: at this intersection, corresponding to  the cusp seen in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' 7, the caustic point is not a simple  extremum for θV on the slowness curve but an undulation  point, in the vicinity of which θV − θV,c ∼ (˜k − ˜kc)4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  The existence of such an undulation point is of par-  ticular interest since the higher order in the dependence  of θV on ˜k implies a ﬂatter extremum in group veloc-  ity direction and therefore the possibility of larger por-  tions of the slowness curve contributing to the CSWB.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  Moreover, as was discussed in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='II B, this does not  necessarily mean an increase in spectral breadth of the  CSWB since the latter depends on the apparent wave-  length.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' In order to evidence this, we show in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' 13  how the group velocity direction as well as the natural  and apparent wavelengths vary around a caustic point  very close to one of higher order, here the one such that  its corresponding critical ﬁeld hc is zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' The considered  slowness curve corresponds to h = h1 = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='15 · 10−21,  ν = ν1 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='315279504, η = η1 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='10253664614147.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  Let us brieﬂy outline how the coordinates νc,0 =  νc(hc = 0) and ηc,0 = ηc(hc = 0) were found with a  good accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' More details can be found in the Sup-  plementary Materials.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' The starting point was a rough,  hand-performed search for a value of η bringing the cusp  of D3 to lie on the ordinate axis in a ﬁeld and fre-  quency map.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' This yielded a starting point of η(0)  c,0 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='10  and ν(0)  c,0 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  In these conditions, a caustic point  was found for ˜k(0)  c,0 ≃ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='73.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  We then began an itera-  tive procedure using appropriate Taylor expansions of  the dispersion relation and of an exact expression for  θV(h = 0, η, ν, ˜k, ϕ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Updating these at each step with  the new solutions found by looking for the undulation  point allows to converge to numerical values which we  assimilate to the intersection of ∂D3,l and ∂D3,u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  Over three iterations, the relative changes in the esti-  mates steadily decrease in absolute value, from at most  5% in the ﬁrst step to at most 5 · 10−6 in the last one,  which provides the following guesses : ˜k(g)  c,0 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='731717,  η(g)  c,0 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='1025366, ν(g)  c,0 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='3152796.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' The latter can be  compared with e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' the hand-reﬁned values used for Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  13: ν = ν1 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='315279504, η = η1 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='10253664614147,  corresponding to ˜kc = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='725904.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' It must be noted that  the somewhat larger relative diﬀerence in terms of ˜kc,0 is  due to the very steep dependence of ˜kc(ν, η, h → 0) on η.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  We do emphasize that the exact location (νc,0,ηc,0) is nec-  essarily diﬀerent from (ν1, η1) but close enough to high-  light the qualitatively diﬀerent behaviour of several char-  acteristics of the slowness curve.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Finally, we note that for  ˜k  ˜k  ˜k  φ  ˜kc  φc  0  1  2  3  4  0 ◦  15 ◦  30 ◦  45 ◦  60 ◦  75 ◦  90 ◦  b)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='04  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='02  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='04  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='04  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='0  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='04  θV/θV,c−1  λ0/λ0,c−1  λ/λc−1  a)  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  a) Plots of the relative deviations from the fol-  lowing caustic point properties as a function of ˜k: its group  velocity direction θV, its natural wavelength λ0 = 2π/˜k  and its apparent wavelength λ = 2π/[˜k cos (θV − ϕ)].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Main  graph:  h = h1 = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='15 · 10−21, ν = ν1 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='315279504,  η = η1 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='10253664614147, which are extremely close to  the values of νc and η for which hc = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Inset: same h and  η = η1, ν = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='95 · ν1 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='2995155288.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' b) Slowness curve for  ν1, η1 and h1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' ˜kc ≃ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='7259.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' The slowness curve at ν2 is not  shown for clarity, as it is very similar to the other one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  90°  75°  60°  45°  30°  15°  0  2  3  1  4  kd13  the parameters from Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' 13, θV,c =118.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='36°, ϕc ≃42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='75°,  λ0,c = 84.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='41lex = 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='655d, and λc ≃ 339.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='7lex = 34.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='83d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  We now examine the properties of the caustic point of  higher order in more detail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' From Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' 13, the depen-  dence of θV,c and the apparent wavelength λ on ˜k (in  blue and green, respectively) clearly appears to be quar-  tic rather than quadratic around the caustic point, which  is where the deviations in natural wavelength (in red) go  through 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Its much steeper behaviour is easily under-  stood by looking at the corresponding slowness curve in  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='b): around ˜kc it is not only almost straight but  the angle γ between  −→˜k and d  −→˜k /ds is low, γ ≃14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='38°.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  Hence, since d(˜k2)/ds is large, λ0 ∝ 1/˜k varies fast.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  By contrast, one can show that in the Taylor expansion  of λ in (s−sc)/˜kc around λc, the ﬁrst coeﬃcient is always  exactly zero at a caustic point.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' We stress again that this  is caused by an unchanging projection of −→k on −→  eg across  the caustic point.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' If it is of higher order, it may be shown  (see Supplementary Materials) that in this term, the con-  tributions due to the second- and third-order variations  of ϕ and to those of ˜k cancel out.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' To put it diﬀerently, the  projection k · cos (θV − ϕ) is now constant up to fourth  order in (s − sc)/˜kc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' On the other hand, if the consid-  ered caustic point is a regular extremum for θV, the term  ∝ (s − sc)2 will be non-zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  To summarize the above paragraph: for geometrical  reasons, the caustic point of higher order suppresses the  quadratic and cubic variations of the apparent wave-  length around λc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Hence, λ has then a markedly quartic  behaviour at a caustic point of higher order.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Further-  more, we point out that even a small oﬀset in frequency  makes it display a clearly quadratic behaviour.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' This is  shown in the inset of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' 13, showing the same relative  variations for the slowness curve at h = h1 = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='15·10−21,  η = η1 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='10253664614147, but ν = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='95 · ν1 =  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='2995155288.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  We have thus shown that in a suﬃciently close vicin-  ity of a higher-order caustic point, a broadband excita-  tion in terms of wavenumber can result in a narrowband  CSWB with a very well-deﬁned direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' As a result,  this phenomenon is expected to be extremely favourable  in experiments, since any realistic antenna cannot have  an arbitrarily narrow excitation eﬃciency as a function  of wavenumber.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Provided that its design yields AC mag-  netic ﬁelds with Fourier components in the (broad) range  of interest and with phases in a given interval of width  < π, all the corresponding spin waves will coherently add  in a beam with very small spectral breadth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  In other  words: in such a situation, counter-intuitively, exciting  additional wave vectors with diﬀerent wavenumbers does  not average out the carrier wave’s amplitude but rather  increase it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' This naturally prompts the question of how  much stronger the emission from a caustic point of higher  order would be with respect to that of a regular caustic  point, and more generally, of the spin wave amplitude  enhancement due to the caustics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' This, however, goes  beyond the scope of the present manuscript.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  To conclude this section, we point out that the reduced  ﬁeld hc(η) corresponding to the caustic point of higher  order decreases as a function of reduced dipolar-exchange  length.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Thus, this feature is expected to exist only for  η < ηc,0 ≃ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='1025366.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  Merged caustic spin wave beams  We now move on to the topic of the threshold fre-  quency νm(h, η) corresponding to the upper boundary  of D, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' above which there are no caustic points any  more.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  As was shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  6, the CSWB direction  θV,c goes to π/2 as ν → νm(h, η).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  This is illustrated  in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' 14, where we show a slowness curve for η1, h1,  and ν2 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='71836419052.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' We stress again that νm(h, η)  is strictly speaking an inﬁnitely narrow boundary and  therefore ν2 ̸= νm(h1, η1), but in these conditions, we  ﬁnd a unique caustic point on the slowness curve, with  π/2 − ϕc ≃0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='32 µrad, and θV,c is equal to π/2 (within  numerical precision).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Moreover, at ν′  2 = ν2 + δν, where  δν = 1 · 10−11, we do not ﬁnd any caustic point on the  slowness curve.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  As a result, we take the slowness curve at (ν2, h1, η1)  to be assimilable to the one at (νm(h1, η1), h1, η1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Its  very straight aspect around ϕ = π/2 is somewhat rem-  iniscent of the one seen in the discussion of the caus-  tic point of higher order.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' To illustrate this in more de-  tail, Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='b) displays the relative deviations in group  velocity direction θV, natural wavelength and apparent  wavelength around the caustic point at ϕc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  We point  out that in the present case, the deviations are plotted  against the curvilinear abscissa s normalized to the slow-  ness curve’s length sM instead of ˜k as in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' This  choice is motivated by (i) the fact that in this case, to  lowest order ˜k − ˜kc = O(s2) instead of O(s − sc) as be-  fore, and (ii) the much smaller relative diﬀerence between  the smallest and largest normalized wavenumbers ˜km re-  spectively ˜kM: ˜km ≃ 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='17 and ˜kM ≃ 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='91, compared  to ˜km ≃ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='240 and ˜kM ≃ 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='66 before.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' (i) implies that  for (ν2, h1, η1), ˜k cannot serve as a meaningful abscissa  along the curve since d˜k/ds = 0, which was not the case  for (ν1, h1, η1), while (ii) shows that the slowness curve  for (ν2, h1, η1) is much closer to a fourth of a circle than  that for (ν1, h1, η1);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' as a matter of fact, for (ν2, h1, η1),  we ﬁnd that 1 − [π/2 · (˜km + ˜kM)/2]/sM = 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='7%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' There-  fore, s/sM provides a better feeling for how much of the  slowness curve contributes to the CSWB.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  From the graph, it seems that the apparent wavelength  has once more a quartic behaviour around the caustic  point.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' We show in the Supplementary Materials that this  is indeed the case: in the conditions where ν = νm(h, η),  to the lowest non-zero order, θV(s → 0) − π/2 varies  with an s3 dependence around s = 0, and the lowest-  order variations in ˜k and ϕ (around ˜km and π/2) cancel  each other out in the projection ˜k · cos (θV − ϕ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  As a result, a caustic point at νm(h, η) is such that  14  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='04  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='06  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='08  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='12  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='14  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='4  s/sM  φ  0 ◦  15 ◦  30 ◦  45 ◦  60 ◦  75 ◦  90 ◦  ˜k  0  2  4  8  6  a)  b)  θV/θV,c−1  λ0/λ0,c−1  λ/λc−1  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' a) Slowness curve at (ν2 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='71836419052, h1, η1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  b) Relative deviations in group velocity direction θV (blue),  natural wavelength λ0 (red) and apparent wavelength λ  (green), as a function of curvilinear abscissa along the slow-  ness curve normalized by its total length sM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  an excitation from a suitable, moderately directional an-  tenna would be eﬀectively narrowband, and weakly di-  vergent around the group velocity direction θV,c = π/2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  This orientation is itself also advantageous in practice:  as long as the used antenna can excite suﬃciently high  wavenumbers, the CSWB direction becomes in this case  simply perpendicular to the applied ﬁeld.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Moreover, ow-  ing to the symmetries of the dispersion relation, the  CSWB beneﬁts from the part of the slowness curve at  ϕ ≳ π/2, which also feature θV ≃ π/2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' That is why large  spin wave amplitudes can be expected, as eﬀectively two  CSWB have merged at this particular frequency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' We note  that this merging phenomenon has already been observed  in simulations by Kim et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' [29] in perpendicularly mag-  netized ultrathin ﬁlms and by Gallardo et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' [41] in syn-  thetic antiferromagnets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' For the sake of completeness, let  us comment on what happens from an analytical point of  view when the two caustic points just below and above  ϕ = π/2 coincide.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' It must be kept in mind that they  respectively correspond to a maximum and a minimum  for θV, temporarily considered for ϕ ∈ [0, π].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Thus, when  they do coincide at ϕc = π/2, strictly speaking there is  no caustic point any more.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  To put it diﬀerently: be-  low νm(h, η), over ϕ ∈ [0, π], θV increases up to the ﬁrst  caustic point where it reaches θV,c > π/2, decreases until  the second one (for ϕ > π/2) where it reaches π − θV,c,  then increases again to reach π when ϕ = π.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Exactly  at νm(h, η), it is monotonously increasing with an inﬂex-  ion point, and above νm(h, η), it is strictly monotonously  increasing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  In order to go beyond the particular case presented  here, we now investigate the evolution of νm(h → 0, η) =  νm,0(η) as a function of reduced dipolar-exchange length  η.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  Similarly to the caustic point of higher order, the  evolutions as a function of reduced ﬁeld quickly become  cumbersome.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' This is why we focus on the νm,0(η), which  is both the lowest frequency at which CSWBs merge and  a threshold frequency that is easier to reach in experi-  ments owing to the vanishing applied ﬁeld, provided that  the studied ﬁlm is soft enough.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  We do keep in mind that below a certain limit in terms  of reduced dipolar-exchange length, the model we use  loses its validity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  However, it has been shown that at  suﬃciently high frequency [38], the analytical dispersion  relation derived by Kalinikos and Slavin describes spin  waves once more with a good accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  15 displays the numerically determined depen-  dence of νm0 on η, as well as that of λm/lex the wave-  length of the corresponding CSWB, normalized by the  dipolar-exchange length.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' The procedure to ﬁnd ﬁrst a  coarse estimate of this curve (before reﬁning it with ac-  tual ﬁeld and frequency maps) is described in the Supple-  mentary Materials.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' We point out that in the case of the  merged CSWBs, the apparent and natural wavelengths  are equal since θV,c = ϕc = π/2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' The minimum value  of η in these graphs corresponds to the smallest one we  used such that the slowness curve (in vanishing ﬁelds)  has only one connected component.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' While we may not  expect our ﬁndings to hold at the lowest η’s, we do expect  their accuracy to improve as η increases;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' it should be suf-  ﬁcient at least for η > 1 since in this case the considered  ferromagnetic ﬁlm can truly be considered thin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  If we think about searching for the merged CSWBs,  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='b) indicates that for realistic values of η = lex/d,  the CSWBs’ apparent wavelengths λ are only about one  order of magnitude larger than the material’s dipolar-  exchange length, typically λ ≲ 25lex.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' This is in stark  contrast with the case of the caustic point of higher  order in vanishing ﬁeld, where the natural wavelength  was λ0,HO ≃ 84lex, and the apparent wavelength λHO ≃  334lex.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' As a result, it seems that while caustic points  of higher order may readily be excited by antennas cre-  ated with even conventional electron beam lithography,  in the case of the merged CSWB achieving a suﬃcient  excitation eﬃciency at the proper wavevectors should  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='15  a)  b)  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' a) νm,0(η) as a function of reduced dipolar-exchange  length η.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  b) The corresponding reduced wavelength ˜λm =  (2π/˜k)/η = λ/lex = λ0/lex.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Here, natural and apparent wave-  lengths coincide as phase and group velocities are collinear.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  prove quite challenging.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  For instance, even the low-  magnetization, low-damping and rather soft ferrimagnet  YIG features lex =17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='3 nm [40], meaning that high-end  antennas with a characteristic periodicity down to about  200 nm would be required in this easiest of cases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  CONCLUSIONS  We have focused on some properties displayed by spin  wave caustics in soft, thin ferromagnetic ﬁlms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' On the  theoretical side, our approach relied on the analytical  dispersion relation established by Kalinikos and Slavin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  We could show that many reports on CSWBs in the lit-  erature can be interpreted within this frame, although  the absence of characteristic signs of a true CSWB may  still cause some ambiguity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Following up on most stud-  ies, we have performed time-resolved magneto-optical  Kerr-eﬀect-based microscopy on samples designed for the  study of CSWBs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Despite the large thickness of the fer-  romagnetic material, our measurements are in very good  agreement with our predictions, thus validating the ap-  proach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Furthermore, we have speciﬁcally highlighted the  large misalignment between phase and group velocities in  this case, and succeeded in observing narrow CSWBs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  Just at the boundary of the dipolar-dominated regime  accessible in our experiments, we have predicted the ex-  istence of a special caustic point.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' We refer to it as caustic  point of higher order because it corresponds to an undu-  lation point for the group velocity direction rather than  a quadratic extremum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  This conﬁguration was shown  to be of particular interest because the apparent wave-  length also featured a quartic behaviour, which implies  a low spectral breadth for the CSWB even in the case  of a broadband excitation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Although we focused on the  special value ηc of reduced dipolar-exchange length such  that the caustic point of higher order occurs at vanish-  ing applied ﬁelds, we stress that this phenomenon would  appear at non-zero ﬁelds for η < ηc, as long as the dis-  persion relation we use is valid.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  Finally, we have investigated the merging of CSWBs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  Once again, we have studied in detail the case of van-  ishing applied ﬁelds, yet the merging may occur for any  ﬁeld value, provided that the excitation frequency is large  enough.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' In terms of model validity, it must be recalled  that while vanishing values of η are problematic for the  chosen dispersion relation, the merging always occurs  at frequencies close to the exchange-dominated regime.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  The discrepancies between the actual spin wave disper-  sion and the model by Kalinikos and Slavin decrease in  this frequency range [39].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' As a result, our claim is that  the merging frequencies νm0 obtained for low η may be  slightly inaccurate yet the phenomenology should remain  the same as for larger η, where we expect our predictions  to be more reliable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' As the CSWBs merge, a very sig-  niﬁcant portion of the slowness curve contributes to spin  wave emission around θV = ϕ = π/2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Therefore, this  conﬁguration appears promising in terms of channelling  strong spin wave beams with short wavelengths, as low  as ∼ 15lex.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  One of the most important questions remaining un-  addressed so far concerns the quantiﬁcation and predic-  tion of the enhancement of amplitude associated with  CSWBs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' More precisely, the crucial distinction between  natural and apparent wavelength as well as the inad-  equacy of the usual Huygens-Fresnel approach (due to  the strong non-collinearity between phase and group ve-  locities) in the construction of CSWBs calls for alterna-  tive evaluations of their amplitudes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' We intend to clar-  ify these points and to go beyond the usually described  amplitude divergence so as to reconcile the theoretically  vanishing curvature (on the slowness curve) and experi-  mentally ﬁnite amplitudes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  [1] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Yu, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Xiao, and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Schultheiss, Magnetic texture  based magnonics, Physics Reports 905, 1 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  [2] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Divinskiy, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Merbouche, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Demidov, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  Nikolaev, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Soumah, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Gou´er´e, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Lebrun, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Cros,  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Ben Youssef, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Bortolotti, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Anane, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  Demokritov, Evidence for spin current driven bose-  einstein condensation of magnons, Nature Communica-  tions 12, 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='1038/s41467-021-26790-y (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  [3] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Bouzidi and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Suhl, Motion of a bloch domain wall,  Physical Review Letters 65, 2587 (1990).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  [4] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Stancil and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Prabhakar, Spin waves - Theory and  applications (Springer New York, NY, 2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  [5] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  Chumak,  Fundamentals  of  magnon-  based  computing,  ArXiv  e-prints  (2019),  arXiv:http://arxiv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='org/abs/1901.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='08934v1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  [6] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Petti, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Tacchi, and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Albisetti, Review on magnon-  ics with engineered spin textures, Journal of Physics D:  Applied Physics 55, 293003 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='8 :  :  :  :  :  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=" '." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='6  2  :  1 : 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='4  :  : 1 :  -- 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=" '." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=" ', :  1  ." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  1 I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  :  : 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='0  i  --  0  1  2  3  n80  70  60  50  40  uu  30  20  10  0 0  1  2  3  n16  [7] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Seo, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Hwang, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Kim, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Yang, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Yoon, and  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Cho, Tunable asymmetric spin wave excitation and  propagation in a magnetic system with two rectangular  blocks, Scientiﬁc Reports 11, 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='1038/s41598-021-02967-  9 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  [8] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Au, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Dvornik, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Davison, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Ahmad, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Keat-  ley, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Vansteenkiste, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Waeyenberge, and V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  Kruglyak, Direct excitation of propagating spin waves by  focused ultrashort optical pulses, Physical Review Let-  ters 110, 097201 (2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  [9] St¨ohr, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' and Siegmann, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=', Magnetism: From Fun-  damentals to Nanoscale Dynamics (Springer Berlin Hei-  delberg, 2006).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  [10] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Sluka, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Schneider, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Gallardo, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' K´akay,  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Weigand, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Warnatz, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Mattheis, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Rold´an-  Molina,  P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  Landeros,  V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  Tiberkevich,  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  Slavin,  G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Sch¨utz, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Erbe, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Deac, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Lindner, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Raabe,  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Fassbender, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Wintz, Emission and propaga-  tion of 1d and 2d spin waves with nanoscale wavelengths  in anisotropic spin textures, Nature Nanotechnology 14,  328 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  [11] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Aliev,  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Awad,  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Dieleman,  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Lara,  V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Metlushko, and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Guslienko, Localized domain-  wall excitations in patterned magnetic dots probed by  broadband ferromagnetic resonance, Physical Review B  84, 144406 (2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  [12] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Golebiewski, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Gruszecki, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Krawczyk, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  Serebryannikov, Spin-wave talbot eﬀect in thin ferromag-  netic ﬁlm, Physical Review B 102 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  [13] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Damon and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Eshbach, Magnetostatic modes  of a ferromagnet slab, Journal of Physics and Chemistry  of Solids 19, 308 (1961).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  [14] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Kravtsov and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Orlov, Geometrical Optics of  Inhomogeneous Media, Springer Series on Wave Phenom-  ena, Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' 6 (Springer-Verlag Berlin Heidelberg, 1990).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  [15] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Kravtsov and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Orlov, Caustics, Catastrophes  and Wave Fields, Springer Series on Wave Phenomena,  Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' 15 (Springer, Berlin, Heidelberg, 1993).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  [16] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Poston and I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Stewart, Catastrophe Theory and Its Ap-  plications, Surveys and reference works in mathematics,  Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' 2 (Dover Publications, 1996).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  [17] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Northrop and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Wolfe, Ballistic phonon imaging  in germanium, Physical Review B 22, 6196 (1980).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  [18] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Taylor, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Maris, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Elbaum, Phonon focusing  in solids, Physical Review Letters 23, 416 (1969).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  [19] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Maris, Enhancement of heat pulses in crystals due  to elastic anisotropy, The Journal of the Acoustical So-  ciety of America 50, 812 (1971).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  [20] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Every, Eﬀects of ﬁrst-order spatial dispersion on  phonon focusing: Application to quartz, Physical Review  B 36, 1448 (1987).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  [21] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Maris, Phonon focusing, in Nonequilibrium phonons  in nonmetallic crystals, Modern Problems in Condensed  Matter Sciences, Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' 16, edited by W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Eisenmenger and  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Kaplyanskii (North Holland, 1986) pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' 51–90.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  [22] O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' B¨uttner, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Bauer, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Demokritov, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Hillebrands,  Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Kivshar, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Grimalsky, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Rapoport, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  Slavin, Linear and nonlinear diﬀraction of dipolar spin  waves in yttrium iron garnet ﬁlms observed by space- and  time-resolved brillouin light scattering, Physical Review  B 61, 11576 (2000).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  [23] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Veerakumar and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Camley, Magnon focusing in  thin ferromagnetic ﬁlms, Physical Review B 74, 214401  (2006).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  [24] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Khomeriki, Self-focusing magnetostatic beams in thin  magnetic ﬁlms, The European Physical Journal B 41,  219 (2004).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  [25] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Demidov, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Demokritov, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Birt, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' O’Gorman,  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Tsoi, and X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Li, Radiation of spin waves from the open  end of a microscopic magnetic-ﬁlm waveguide, Physical  Review B 80, 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='1103/physrevb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='80.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='014429 (2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  [26] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Schneider, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Serga, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Chumak, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  Sandweg, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Trudel, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Wolﬀ, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Kostylev, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  Tiberkevich, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Slavin, and B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Hillebrands, Non-  diﬀractive subwavelength wave beams in a medium with  externally controlled anisotropy, Physical Review Letters  104, 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='1103/physrevlett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='104.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='197203 (2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  [27] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Kostylev, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Serga, and B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Hillebrands, Radi-  ation of caustic beams from a collapsing bullet, Physi-  cal Review Letters 106, 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='1103/physrevlett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='106.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='134101  (2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  [28] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Sebastian, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Br¨acher, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Pirro, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Serga, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Hille-  brands, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Kubota, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Naganuma, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Oogane, and  Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Ando, Nonlinear Emission of Spin-Wave Caustics from  an Edge Mode of a Microstructured Co2Mn0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='6Fe0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='4Si  Waveguide, Physical Review Letters 110, 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='1103/phys-  revlett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='110.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='067201 (2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  [29] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='-V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Kim, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Stamps, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Camley, Spin wave  power ﬂow and caustics in ultrathin ferromagnets with  the dzyaloshinskii-moriya interaction, Physical Review  Letters 117, 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='1103/physrevlett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='117.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='197204 (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  [30] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Heussner, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Serga, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Br¨acher, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Hillebrands,  and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Pirro, A switchable spin-wave signal splitter for  magnonic networks, Applied Physics Letters 111, 122401  (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  [31] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Muralidhar, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Khymyn, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Awad, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Alem´an,  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Hanstorp, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' ˚Akerman, Femtosecond laser pulse  driven caustic spin wave beams, Physical Review Letters  126, 037204 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  [32] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Kalinikos and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Slavin, Theory of dipole-  exchange spin wave spectrum for ferromagnetic ﬁlms  with mixed exchange boundary conditions, Journal of  Physics C: Solid State Physics 19, 7013 (1986).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  [33] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Lax and V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Narayanamurti, Phonon magniﬁcation  and the gaussian curvature of the slowness surface in  anisotropic media: Detector shape eﬀects with applica-  tion to GaAs, Physical Review B 22, 4876 (1980).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  [34] Even for markedly anisotropic dielectrics the diﬀerences  in refractive indices lead to maximal angles between  phase and group velocities below 10° [?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' ].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  [35] I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Bertelli, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Carmiggelt, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Yu, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Simon, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  Pothoven, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Bauer, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Blanter, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Aarts, and  T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' van der Sar, Magnetic resonance imaging of spin-wave  transport and interference in a magnetic insulator, Sci-  ence Advances 6, eabd3556 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  [36] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Felsen and N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Marcuvitz, Radiation and Scattering  of Waves, IEEE Press Series on Electromagnetic Wave  Theory (Wiley-IEEE Press, 1994).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  [37] We deﬁne the spectral breadth of a non-monochromatic  beam with well-deﬁned propagation direction and negli-  gible divergence as ∆λ/λcar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=', where λcar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' is the carrier’s  mean apparent wavelength, and ∆λ is the beam’s stan-  dard deviation in apparent wavelength.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  [38] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Kreisel, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Sauli, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Bartosch, and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Kopietz, Mi-  croscopic spin-wave theory for yttrium-iron garnet ﬁlms,  The European Physical Journal B 71, 59 (2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  [39] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Harms and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Duine, Theory of the dipole-  exchange spin wave spectrum in ferromagnetic ﬁlms with  17  in-plane magnetization revisited, Journal of Magnetism  and Magnetic Materials 557, 169426 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  [40] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Klingler, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Chumak, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Mewes, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Khodadadi,  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Mewes, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Dubs, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Surzhenko, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Hillebrands, and  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Conca, Measurements of the exchange stiﬀness of  YIG ﬁlms using broadband ferromagnetic resonance tech-  niques, Journal of Physics D: Applied Physics 48, 015001  (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  [41] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Gallardo, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Alvarado-Seguel, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' K´akay, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Lind-  ner, and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Landeros, Spin-wave focusing induced by  dipole-dipole interaction in synthetic antiferromagnets,  Physical Review B 104, 174417 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  [42] I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Bertelli, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Simon, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Yu, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Aarts, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  Bauer, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Blanter, and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' van der Sar, Imaging spin-  wave damping underneath metals using electron spins in  diamond, Advanced Quantum Technologies 4, 2100094  (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  [43] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Gieniusz, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Ulrichs, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Bessonov, U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Guzowska,  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Stognii, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Maziewski, Single antidot as a pas-  sive way to create caustic spin-wave beams in yttrium  iron garnet ﬁlms, Applied Physics Letters 102, 102409  (2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  [44] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' K¨orner, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Stigloher, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' Back, Excitation  and tailoring of diﬀractive spin-wave beams in NiFe using  nonuniform microwave antennas, Physical Review B 96,  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='1103/physrevb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='96.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='100401 (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  [45] We point out that the segment perpendicular to the ta-  pered waveguide segments was at an angle of about 60°  with respect to the applied ﬁeld in these experiments [46].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  [46] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content=' K¨orner, Time-resolved Kerr microscopy of spin  waves propagating in magnetic nanostructures, Ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
+page_content='  thesis, Universit¨at Regensburg (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NAzT4oBgHgl3EQfRvtg/content/2301.01220v1.pdf'}
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+Impact of electron correlations on the k-resolved electronic structure of PdCrO2 revealed by
+Compton scattering
+A. D. N. James,1 D. Billington,2 and S. B. Dugdale1
+1H. H. Wills Physics Laboratory, University of Bristol, Tyndall Avenue, Bristol, BS8 1TL, United Kingdom
+2School of Physics and Astronomy, Cardiff University, Queen’s Building, The Parade, Cardiff, CF24 3AA, United Kingdom
+(Dated: January 6, 2023)
+Delafossite PdCrO2 is an intriguing material which displays nearly-free electron and Mott insulating be-
+haviour in different layers. Both angle-resolved photoemission spectroscopy (ARPES) and Compton scattering
+measurements have established a hexagonal Fermi surface in the material’s paramagnetic phase. However, the
+Compton experiment detected an additional structure in the projected occupancy which was originally inter-
+preted as an additional Fermi surface feature not seen by ARPES. Here, we revisit this interpretation of the
+Compton data. State-of-the-art density functional theory (DFT) with dynamical mean ﬁeld theory (DMFT), the
+so-called DFT+DMFT method, predicts the Mott insulating state along with a single hexagonal Fermi surface in
+excellent agreement with ARPES and Compton. However, DFT+DMFT fails to predict the intensity of the ad-
+ditional spectral weight feature observed in the Compton data. We infer that this discrepancy may arise from the
+DFT+DMFT not being able to correctly predict certain features in the shape and dispersion of the unoccupied
+quasiparticle band near the Fermi level. Therefore, a theoretical description beyond our DFT+DMFT model
+is needed to incorporate vital electron interactions, such as inter-layer electron coupling interactions which for
+PdCrO2 gives rise to the Kondo-like so-called intertwined excitation.
+I.
+INTRODUCTION
+Interest has grown over the last few decades in layered
+triangular-lattice delafossite materials with chemical formula
+ABO2 (A = Pt, Pd, Ag or Cu, and B = Cr, Co, Fe, Rh,
+Al, Ga, Sc, In or Tl). This interest in metallic delafossites
+was sparked by reports from Tanaka et al. [1, 2] of strongly
+anisotropic conductivity in their PdCoO2 and PtCoO2 single
+crystals. Previous measurements of PtCoO2 displayed an ex-
+tremely low in-plane room temperature resistivity of 3 µΩcm,
+a value comparable to elemental Cu [3, 4]. This led to the
+emergence of a new ﬁeld of research into these materials [4].
+The PdCrO2 compound also has the anticipated anisotropic
+conductivity [5], but displays an antiferromagnetic phase be-
+low its N´eel temperature, TN = 37.5 K, above which the lo-
+cal Cr3+ (S = 3/2) electron spins in the CrO2 layers are
+frustrated. Within the antiferromagnetic phase this frustration
+is relieved, resulting in the local spins ordering with a rota-
+tion of 120◦ between adjacent sites [5–8]. The observation of
+this ordered state offers an opportunity to study the coupling
+between nearly-free electrons and (frustrated) local electron
+spins in a frustrated antiferromagnet. This interest in PdCrO2
+has led to further experimental characterisation of this mate-
+rial, leading to the discovery of an unconventional anomalous
+Hall effect [7, 9], and a reconstructed Fermi surface within the
+(smaller) antiferromagnetic Brillouin zone, measured by both
+angle resolved photoemission spectroscopy (ARPES) [10–12]
+and quantum oscillations [13, 14]. For PdCrO2, it has been
+implicitly assumed that electron correlations are the driving
+force for the antiferromagnetic state, and hence why the be-
+haviour of the CrO2 layer has been described with the concept
+of local moments [4].
+Within the paramagnetic phase, both ARPES [10, 11] and
+Compton scattering [8] measurements were performed to de-
+termine the Fermi surface geometry. ARPES measures the
+energies of the emitted photoelectrons from the sample sur-
+face together with their angle of emission such that the quasi-
+particle energy and its dispersion with (crystal) momentum
+up to and including the Fermi energy can be extracted. The
+ARPES spectra show both the ground and excited states of
+the electronic structure and measurements are sensitive to the
+surface and matrix element effects [15]. Compton scattering
+experiments probe the bulk ground-state electronic structure
+through its electron momentum distribution [16] by measur-
+ing so-called Compton proﬁles which are the doubly projected
+electron momentum densities (EMDs) [17]. The EMD is the
+electron density distribution in real momentum, p, which can
+be directly related to the electron occupancy by folding the
+EMD back into the ﬁrst Brillouin zone (the Lock-Crisp-West
+(LCW) theorem [18]) to recover the full translational sym-
+metry of the reciprocal lattice. This folded EMD is now a
+function of the crystal momentum, k. Electron occupancy in
+k-space is inﬂuenced by temperature, site disorder, and many-
+body electron correlations.
+The step changes in the occu-
+pancy can be used to determine the Fermi wave-vectors (and
+hence Fermi surface) even in materials which are either inac-
+cessible by or challenging for other techniques. Such mate-
+rials include highly chemically-disordered alloys [19] which
+have short electronic mean-free paths. Evidently, ARPES and
+Compton scattering probe different aspects of the electronic
+structure. The Fermi surface may be extracted from either the
+k-resolved photoelectron dispersion around the Fermi energy
+measured by ARPES, or the changes in the occupation derived
+from the Compton data.
+Both ARPES and Compton scattering conﬁrmed the pres-
+ence of the hexagonal Fermi surface, but the Compton ex-
+periments clearly showed an additional contribution to the
+projected electron occupancy around the corners of the (pro-
+jected) Brillouin zone. In an effort to understand their re-
+sult, Billington et al. [8] performed density functional theory
+(DFT) calculations from which they concluded that at least
+two Fermi surface sheets were required to describe all the fea-
+tures in the k-space occupancy. This led to speculation by
+arXiv:2301.02143v1  [cond-mat.str-el]  5 Jan 2023
+
+2
+Billington et al. that what appeared to be an additional Fermi
+surface sheet observed in the bulk-sensitive Compton exper-
+iments but not in the ARPES might be due to some combi-
+nation of the surface not being representative of the bulk or
+unfavourable matrix elements. Although Ong et al. [20] had
+shown that the DFT magnetic structure of PdCrO2 was three
+dimensional, at the time of the study by Billington et al. there
+were no published DFT calculations of non-magnetic PdCrO2
+in opposition to their two Fermi surface model.
+This interpretation of the Compton data was subsequently
+critically examined by Mackenzie [4] who argued that it did
+not take into account the existence of the Mott insulating state
+in the CrO2 layers (the existence of which is supported by
+several experiments). However, these arguments do not ex-
+plain the extra features in the occupation number measured by
+the Compton scattering. Recent calculations combining DFT
+with dynamical mean ﬁeld theory (DFT+DMFT) [12, 21, 22]
+showed that the Mott insulating state in the CrO2 layers is a
+natural consequence of the inclusion of the local dynamical
+electron correlations. Also, DFT+DMFT naturally includes
+paramagnetic electron correlations within the DMFT part [23]
+which is vital for this frustrated antiferromagnetic material.
+Therefore, the interpretation of the results from the Compton
+experiment warrants further investigation in order to reconcile
+it with the picture of local moments within the Mott insulating
+CrO2 layers and to help resolve the inconsistent conclusions
+about the Fermiology from the different measurements.
+In light of the recent PdCrO2 DFT+DMFT calculations, it
+is necessary to ﬁrst reproduce them in order to then deter-
+mine the DFT+DMFT EMD using the recent technique im-
+plemented by James et al. [24]. From such calculations, a
+comparison with the Compton scattering experiment, primar-
+ily the projected occupation, could be made. With respect to
+a non-interacting prediction, the inclusion of many-body cor-
+relations (such as that predicted by Fermi liquid theory [25])
+generally leads to a redistribution and apparent smearing in
+k-space of the occupation around the Fermi wave-vector. The
+presence of the Mott insulating CrO2 layers in the previous
+DFT+DMFT predictions lead to signiﬁcant changes to the
+shape and dispersion of the quasiparticle bands which also
+means that there would be signiﬁcant changes to the occupa-
+tion, which the Compton scattering will be sensitive to. Hence
+it is important to use DFT+DMFT to determine whether the
+predicted electronic structure with these Mott insulating CrO2
+layers are compatible with the electron occupancy as mea-
+sured by Compton scattering.
+In this study, we revisit the interpretation of the Compton
+scattering experimental results and compare them with the
+corresponding quantities calculated from the non-magnetic
+DFT and paramagnetic DFT+DMFT methods.
+Here, we
+see that the size and shape of the predicted DFT+DMFT
+hexagonal Fermi surface is in excellent agreement with the
+ARPES [10–12], quantum oscillations [13, 14], and Comp-
+ton measurements [8].
+However, there are still discrep-
+ancies between the experimental Compton data and the
+DFT+DMFT calculations around the corners of the Brillouin
+zone.
+These discrepancies can be reduced (but not elimi-
+nated) in the DFT+DMFT calculation by artiﬁcially (and un-
+physical) broadening the unoccupied quasiparticle band just
+above the Fermi level around the corners of the Brillouin
+zone. This suggests that changes to both the shape and disper-
+sion of that quasiparticle band are required, most likely driven
+by certain electron correlation effects which theories beyond
+our DFT+DMFT would possibly capture, such as inter-layer
+electron coupling interactions which gives rise to the previ-
+ously observed (Kondo-like) so-called intertwined excitation
+in Ref. [12] which is a convolution of the charge spectrum of
+the metallic layer and the spin susceptibility of the Mott insu-
+lating layer.
+II.
+METHODS
+We have used the full potential augmented plane-wave
+plus local orbitals (APW+lo) ELK code [26] in combina-
+tion with the toolbox for research on interacting quantum
+systems (TRIQS) library [27]. This so-called ELK+TRIQS
+DFT+DMFT framework is described in Ref. [28]. Further
+discussion of interfacing the APW+lo DFT basis with the
+DMFT Anderson’s impurity model is found in Ref. [29]. The
+PdCrO2 delafossite structure is shown in Fig. 1 (a) and the
+lattice parameters of the conventional (hexagonal) unit cell
+are a = 2.929 ˚A, c = 18.093 ˚A [7] with the Pd–O distance,
+dPd−O = 0.11c.
+The DFT calculation used the Perdew-
+Burke-Ernzerhof (PBE) generalized gradient approximation
+(GGA) for the exchange-correlation functional [30] and was
+converged on a 32 × 32 × 16 Monkhorst-Pack k-mesh of
+2601 irreducible k-points in the irreducible Brillouin zone.
+We used the all-electron full-potential APW+lo DFT method
+instead of the pseudo-potential plane-wave approach used in
+Refs. [21, 22].
+The DFT outputs were interfaced to the
+TRIQS/DFTTools application of the TRIQS library [31] by
+constructing Wannier projectors, as described in Ref. [28],
+for all the Cr 3d-states within a correlated energy window of
+[−8.5, 3] eV relative to the Fermi level.
+The paramagnetic DMFT part of the DFT+DMFT calcu-
+lation was implemented using the continuous-time quantum
+Monte Carlo (CT-QMC) solver within the TRIQS/CTHYB
+application [32] with the Slater interaction Hamiltonian pa-
+rameterised by the Hubbard interaction U = 3.0 eV and Hund
+exchange interaction J = 0.7 eV, unless otherwise speciﬁed.
+These U and J values are similar to those used in previous
+calculations of PdCrO2 [12, 21, 22], and other CrO2 com-
+pounds [22, 33]. We approximated the double counting in the
+fully localised limit in line with the previous DFT+DMFT cal-
+culations [12, 21, 22]. Our DFT+DMFT approach slightly dif-
+fers from previous DFT+DMFT calculations where different
+correlated energy windows were used and either the Hubbard-
+Kanamori interaction Hamiltonian [21, 22] or the Hubbard I
+approximation for the impurity solver [12] were chosen. We
+note that our DFT+DMFT calculations are paramagnetic with
+no overall ordered moment. The Cr 3d orbitals were diag-
+onalised from the complex spherical harmonic basis into the
+diagonal trigonal basis (obtained by diagonalising the orbital
+density matrix) resulting in the three sets of non-degenerate
+orbitals, namely the two doubly degenerate e′
+g and eg or-
+
+3
+Pd
+CrO2
+(a)
+(c)
+(b)
+(d)
+FIG. 1. (a) The PdCrO2 delafossite structure showing the triangular-lattice Pd and CrO2 layers. (b) The logarithm of the DFT+DMFT spectral
+spectral function A(k, ω) overlaid with the DFT band structure (blue solid lines). These have been evaluated along a path connecting points
+within the kz = 0 plane of the Brillouin zone of PdCrO2. The points Γ and K are high-symmetry points, with K on the Brillouin zone
+boundary of the primitive rhombohedral cell. While M is not a high-symmetry point in that Brillouin zone, it is used here with reference to the
+equivalent point in a simple hexagonal Brillouin zone, as in previous work [12, 21, 22]. Here, the changes to the Fermi surface between these
+theoretical methods are most prominent. (c) The three DFT Fermi surface sheets in the rhombohedral Brillouin zone and (d) the DFT+DMFT
+hexagonal Fermi surface (given by the spectral function evaluated at the Fermi level where ω = 0 eV) in the same kz plane as described in
+(b). Note that there is distinguishable spectral weight at K with respect to the Γ and M points.
+bitals along with the single a1g orbital, in agreement with
+Ref. [21]. We used the fully-charge-self-consistent (FCSC)
+DFT+DMFT method with a total of 8.4 × 107 Monte Carlo
+sweeps within the impurity solver for each DMFT cycle. An
+inverse temperature β = 40 eV−1 (∼ 290 K) was used which
+is similar to the (room) temperature of the Compton scattering
+experiments. The spectral functions were calculated by ana-
+lytically continuing the DMFT self-energy obtained from the
+LineFitAnalyzer technique of the maximum entropy analytic
+continuation method implemented within the TRIQS/Maxent
+application [34].
+For the DFT and DFT+DMFT EMD calculations, we
+used the method of Ernsting et al. [35] together with the
+DFT+DMFT L¨owdin-type basis electron wave functions and
+occupation numbers determined by the method described in
+Ref. [24]. A maximum momentum cut-off of 16.0 a.u. was
+used. We emphasise that the EMD related results do not use
+analytic continuation so they do not suffer from its associ-
+ated complications. We concentrate on the projected EMD
+for comparisons with the experimental Compton data.
+To
+compare with the experimental 2D occupancy in Ref. [8],
+which directly relates to the electron occupation, the calcu-
+lated EMDs were ﬁrst projected along the kz-axis (parallel to
+the c-axis of the conventional unit cell) and this projected 2D
+EMD was then convoluted with a 2D Gaussian function with a
+full-width-at-half-maximum of 0.106 a.u. approximating the
+effect of the ﬁnite Compton scattering experimental momen-
+tum resolution [8]. These convoluted EMDs are subsequently
+folded back into the ﬁrst Brillouin zone, via the LCW theo-
+rem, producing the theoretical 2D projected occupancy. The
+Compton proﬁles, J(pz), which are double-projections of the
+EMD, were evaluated along the experimental scattering vec-
+tors (which for convenience are conventionally referred to as
+being along pz in the local coordinate system),
+J(pz) =
+��
+ρ(p)dpxdpy,
+(1)
+where ρ(p) is the 3D EMD. The so-called directional differ-
+ences, which are the differences between Compton proﬁles
+resolved along different crystallographic directions, were cal-
+culated so that they could be compared to the experimental
+ones.
+III.
+RESULTS
+Fig. 1 (b) shows the DFT band structure and DFT+DMFT
+spectral function plotted along the high symmetry directions
+in the kz = 0 plane.
+The DFT and DFT+DMFT results
+show good agreement with previous studies [12, 21, 22]. We
+note that our spin-orbit coupling DFT calculation differs to
+that presented in Ref. [8], even though those previously pub-
+lished results are reproducible with the same version (2.2.9)
+of ELK. The lack of reproducibility of the Ref. [8] ground
+state with the current version of ELK suggests that there was
+some problem with that calculation in version 2.2.9 (which
+has been ﬁxed in later versions) which coincidentally gave
+convincing agreement between the reported electronic struc-
+ture and experimental Compton data. In agreement with the
+other previously reported DFT and DFT+DMFT predictions,
+the hybridised Pd 4d and Cr 3d DFT bands which lie around
+the Fermi level and which contribute to the DFT Fermi sur-
+face shown in Fig. 1 (c) drastically redistribute, with the Cr
+3d dominant bands now insulating in DFT+DMFT due to the
+
+4
+FIG. 2. The DFT+DMFT (ﬁxed U = 3.0 eV and J = 0.7 eV)
+spectral function A(k, ω) plotted in the style of ARPES energy dis-
+tribution curves (EDCs). This shows the spectral function dispersion
+around the Fermi level along a portion of the path of Fig. 1 (b) fo-
+cusing on the Pd quasiparticle conduction band crossing the Fermi
+level (ω = 0 eV). The inset reveals structure in the spectral func-
+tion evaluated at a k-point between M to Γ which is highlighted in
+red in the EDCs. The axes of the inset are the same as the main ﬁg-
+ure. The Pd quasiparticle conduction band centre is just above the
+Fermi level, but there is spectral weight from this Lorentzian-like
+quasiparticle band spectral function crossing the Fermi level and this
+occupied spectral weight will contribute to the occupation distribu-
+tion. This occupied weight is referred to as spectral weight spillage
+across the Fermi level.
+formation of a Mott insulating state within the CrO2 layers
+which arises from the strong local electron correlations on the
+Cr site. The remaining quasiparticle band which crosses the
+Fermi level in DFT+DMFT A(k, ω) is now predominantly Pd
+4d in character and forms the hexagonal Fermi surface sheet
+shown in Fig. 1 (d), in excellent agreement with that observed
+in the paramagnetic ARPES [11] measurements. There are
+also incoherent, non-dispersive Hubbard-like bands, shown in
+Fig. 1 (b) centred around ±1.5 eV, which arise from the Mott
+insulating Cr states. We note that the DFT+DMFT spectral
+function in Fig. 1 (d) shows signiﬁcant spectral weight around
+the K point which is also seen in previous DFT+DMFT cal-
+culations by Lechermann [21].
+To help illustrate certain concepts which link the spectral
+function to the occupation distribution (required for subse-
+quent discussions), we have included the DFT+DMFT spec-
+tral function around the Fermi level in Fig. 2, plotted in the
+style of ARPES energy distribution curves (EDCs). The spec-
+tral function of the Pd dominant quasiparticle conduction band
+is seen to be broader and have a smaller amount of spectral
+weight than the inverted parabolic quasiparticle band around
+M which peaks at about −0.5 eV (which is also shown in the
+inset of Fig. 2). The inset shows that at a particular k-point
+between M and Γ the Pd quasiparticle conduction band cen-
+tre is just above the Fermi level which of course means that
+there is no Fermi surface at this wave-vector. However, owing
+to the ﬁnite width of the spectral function around the quasi-
+particle peaks (which arises from the ﬁnite lifetime linked to
+the imaginary part of the DMFT self-energy), there is a por-
+tion of the spectral function tail which crosses the Fermi level
+and is consequently occupied. This occupied portion of the
+Pd quasiparticle conduction band contributes to the EMD and
+will be seen in the electron occupancy measured by Comp-
+ton scattering. Conversely, if the band centre (quasiparticle
+peak) were below the Fermi level, but the higher energy tail
+crosses the Fermi level, then that quasiparticle band will have
+a reduced contribution to the occupation at that k-point with
+respect to a fully occupied quasiparticle band. We refer to the
+spectral weight from the quasiparticle band tails crossing the
+Fermi level as spectral weight spillage. The spectral weight
+spillage will be dependent on factors which inﬂuence the ﬁ-
+nite width (inverse lifetime) of the (quasiparticle) peaks in
+the spectral function. In the DFT picture within the Green’s
+function formalism, the typical DFT spectral function would
+be a series of Lorentzian-like functions corresponding to the
+DFT bands and most likely have small widths relating to the
+temperature used in the calculation. The corresponding oc-
+cupation distribution will therefore have contributions from
+the fully occupied spectral function below the Fermi level and
+from spectral weight spillage. The common consequence of
+spectral weight spillage contribution in DFT is the apparent
+smearing of the occupation distribution in (crystal) momen-
+tum around the Fermi wave-vector (which is temperature de-
+pendent because of the temperature dependence of the spectral
+weight spillage). The effects of spectral weight spillages on
+the occupation distribution are often less prominent in DFT
+but have been seen for DFT bands grazing the Fermi level
+such as in ZrZn2 [36] and in highly compositionally disor-
+dered systems [19].
+The 2D projected occupancy (along the projected bulk high
+symmetry path used in Ref. [8]) determined from the DFT
+and DFT+DMFT calculated EMDs, together with the the ex-
+perimental 2D occupancy, are shown in Fig. 3. Here, we see
+that the agreement in the DFT+DMFT (U = 3.0 eV, J = 0.7
+eV) 2D projected occupancy signiﬁcantly improves along the
+Γ to M direction compared to the DFT results, with there
+being a single step along this direction in the DFT+DMFT
+compared to the smoothed shoulder predicted by the DFT.
+The location of this single step along Γ to M gives the Fermi
+wave-vector of the hexagonal Fermi surface sheet along this
+direction. We can also extract the Fermi wave-vector of the
+hexagonal Fermi surface sheet along the Γ to K from the lo-
+cation of the largest change in the projected occupation. The
+DFT+DMFT projected occupation which relates to hexago-
+nal Fermi surface sheet along with the region it encompasses
+(see Fig. 4) is in excellent agreement with the Compton data.
+We ﬁnd the occupied fraction of the Brillouin zone associ-
+ated with DFT+DMFT hexagonal Fermi surface is approxi-
+mately equal to one half, which is in excellent agreement with
+both the occupation fraction expected from the Fermi surface
+of a monovalent metal and the experimental fractions deter-
+mined from Compton [8], ARPES [10], and quantum oscilla-
+tions [13].
+The DFT projected occupancy has some similarities to the
+experiment around K.
+This feature in the DFT relates to
+
+5
+M
+K
+M
+K
+min
+max
+occupancy
+DFT
+J=0.25 eV
+J=0.30 eV
+J=0.50 eV
+J=0.70 eV
+experiment
+FIG. 3. The 2D occupancy (projected along the kz-axis) plotted along the projected bulk high-symmetry directions (denoted with overlines)
+for DFT and DFT+DMFT with different values of the Hund exchange J at ﬁxed Hubbard U = 3.0 eV. The theoretical projected EMDs were
+convoluted with a two dimensional Gaussian (full-width-at-half-maximum = 0.106 a.u.) to approximate the effect of the ﬁnite experimental
+momentum resolution prior to calculating the occupancy. The experimental data are from Ref. [8]. Varying J explores the changes to the
+electronic structure passing through the Mott transition of the Cr states, with the Mott insulating state occurring for J > 0.25 eV.
+the Cr DFT band crossing the Fermi level near K (and the
+corresponding points along the kz-axis) resulting in an elec-
+tron Fermi surface pocket around K (see Fig. 1 (b) and (c)).
+However, the agreement at K signiﬁcantly worsens in the
+DFT+DMFT (at J = 0.7 eV) as there is no contribution from
+the Cr band as it is now below the Fermi level and hence fully
+occupied (insulating). Interestingly, however, there is a small
+contribution at K in the DFT+DMFT (J = 0.7 eV) projected
+occupations which arises from the spectral weight of the Pd
+quasiparticle conduction band spilling across the Fermi level
+(such as that seen around K in Fig. 1 (d)) which then becomes
+occupied, similar to that seen in Refs. [19, 36] as discussed
+previously. This additional spectral weight is small relative
+to the background (i.e., relative to the Γ point) which would
+likely mean that this feature might be difﬁcult for the ARPES
+to distinguish within the experimental and statistical error. It
+should be noted that the projected occupation from Compton
+presented here relates to the energy integral of the occupied
+part of the spectral function which is then integrated along
+the kz-axis. Consequently, the accumulation of this feature
+around K seen in the spectral function in Fig. 1 (d) becomes
+more prominent in the projected occupation at K. This is seen
+in the DFT+DMFT (J = 0.7 eV) projected occupation fea-
+ture around K in Fig. 3. We note that the DFT+DMFT spec-
+tral plot along the same in-plane path as Fig. 1 (b) but with a
+shift of 0.5 reciprocal lattice units along the kz-axis shows a
+similar dispersion to kz = 0 plane which is expected for this
+quasi-2D system. Therefore, this DFT+DMFT feature at K
+will have contributions from all the spectral weight spillage
+along the kz-axis centred at K owing to the projected nature
+of the Compton occupation data.
+Also shown in Fig. 3 are several DFT+DMFT calculations
+of the 2D projected occupancy plotted for different J but with
+U ﬁxed to 3.0 eV. These show the evolution of the 2D pro-
+jected occupancy (and by inference, the electronic structure)
+as a function of the size of the Hund exchange interaction J as
+the CrO2 layer transitions from the metallic (low J) to Mott
+insulating state (high J), where the Mott insulating state oc-
+curs for J > 0.25 eV. The result of increasing J causes the
+smoothed double-step feature prominent in the DFT projected
+occupancy along Γ to M to transform into a single step due to
+the spectral weight from the previously conducting Cr quasi-
+particle bands shifting below the Fermi level and becoming
+fully occupied. On the other hand, increasing J suppresses
+the 2D occupancy contribution around K as the Cr quasipar-
+ticle bands transition into being Mott insulating. There are no
+optimal DFT+DMFT U and J parameters which are able to
+simultaneously capture the 2D projected occupancy features
+from Γ to K and the single step along Γ to M. The hexagonal
+Fermi surface sheet is a robust feature in all the Fermi surface
+measurements and is clearly captured by the DFT+DMFT pre-
+dictions with Mott insulating CrO2 layers.
+To get a better perspective of the agreement between the
+different calculations with the experimental data, Fig. 4 shows
+
+6
+DFT
+experiment
+DFT+DMFT
+K
+M
+min
+max
+occupancy
+FIG. 4. The 2D (projected along the kz-axis) occupancy in the 2D
+hexagonal Brillouin zone. The left hand side shows the experimental
+data, whereas each quadrant on the right hand side represents a differ-
+ent calculation, as indicated. The theoretical two dimensional EMDs
+were convoluted as described in the Fig. 3 caption. The DFT quan-
+drant includes the Brillouin zone boundary as well as the projected
+2D high symmetry points (denoted with overlines). The experimen-
+tal data are from Ref. [8].
+the 2D projected occupancy of the different calculations and
+experiment. The DFT results give good agreement in cer-
+tain regions, but is overall worse than the DFT+DMFT as ex-
+pected. The size of DFT+DMFT hexagonal occupancy weight
+around Γ is in excellent agreement with the experimental 2D
+projected occupancy, as previously established. However, it
+is clear that the DFT+DMFT is unable to predict the signiﬁ-
+cant additional occupation feature surrounding the hexagonal
+region which gives rise to elongated black ellipsoidal region
+centred around M, with the major axis of this ellipsoid along
+the M—K path. Next, we present the comparison of the di-
+rectional differences along the different measured (crystallo-
+graphic) directions in Fig. 5 for the DFT, DFT+DMFT and the
+experimental data. It is clear that the DFT+DMFT results are
+superior in agreement with the experiment compared with the
+DFT.
+Thus far, the origin of the features measured in the ex-
+perimental techniques has been discussed from a theoretical
+perspective. However, the discrepancy between experimen-
+tally measured features by ARPES and Compton still needs to
+be addressed. Both of these experiments were performed at
+different temperatures with the Compton being at room tem-
+perature, whereas the ARPES was measured at 100 K. There
+have been no reported signatures which could be related to
+a temperature-dependent Lifshitz transition in the transport
+measurements [5] which could have explained this extra fea-
+ture in the Compton data at K being related to the Fermi sur-
+face. However, it should be noted that the spectral weight of
+the Pd quasiparticle conduction band would be more broadly
+distributed in energy in the room temperature Compton data
+than the 100 K ARPES data meaning more spectral weight
+0.2
+0.1
+0.0
+0.1
+0.2
+J(pz) (a. u.
+1)
+M 
+ K
+DFT
+DFT+DMFT
+experiment
+0.2
+0.1
+0.0
+0.1
+0.2
+J(pz) (a. u.
+1)
+M 
+ 22.5
+0.2
+0.1
+0.0
+0.1
+0.2
+J(pz) (a. u.
+1)
+M 
+ 15
+0
+1
+2
+3
+4
+5
+6
+pz (a.u.)
+0.2
+0.1
+0.0
+0.1
+0.2
+J(pz) (a. u.
+1)
+M 
+ 7.5
+FIG. 5.
+The directional differences ∆J(pz) (i.e., the difference
+between two Compton proﬁles measured along different crystallo-
+graphic directions) as speciﬁed at the bottom right of each panel
+where the angle refers to the rotation away from the ΓM direc-
+tion towards ΓK. These differences are of the DFT, DFT+DMFT,
+and the experiment. The theoretical Compton proﬁles were convo-
+luted with a one dimensional (1D) Gaussian of full-width-at-half-
+maximum = 0.106 a.u. to represent the experimental momentum
+resolution. The experimental data are from Ref. [8].
+from the tail of that quasiparticle band would likely be oc-
+cupied.
+It would be strange if the ARPES spectra would
+miss a Fermi surface feature at K due to cross-section ef-
+fects as it is very unlikely for ARPES not measure the same
+band in different regions of the Brillouin zone. It is also un-
+likely that the ARPES matrix elements effects are suppressing
+a Fermi surface feature originating from the Pd quasiparticle
+band, although ARPES matrix elements effects do cause some
+changes in the measured intensity [12]. The reduced dimen-
+sionality at the surface may enhance the electron correlation
+effects within the Mott insulating CrO2 layers at the surface,
+similar to that seen in SrVO3 [37–42]. On the other hand,
+there is unlikely any notable contribution from surface states
+in the ARPES as these would give additional features [10], not
+remove some.
+Returning to the experimental feature at K, one possible ex-
+planation is that this may actually arise from the DFT+DMFT
+Pd conduction quasiparticle band at K (and the positions dis-
+
+7
+0.5
+0.0
+0.5
+1.0
+ (eV)
+(a)
+K
+M
+min
+max
+occupancy
+(b)
+ = 0.0 eV
+ = 0.1 eV
+ = 1.0 eV
+ = 5.0 eV
+FIG. 6. (a) The logarithm of DFT+DMFT spectral function with an
+additional artiﬁcial broadening term (in energy) along the same path
+and colour scale as in Fig. 1 (b). This broadening is only applied
+to the Pd quasiparticle conduction band centred around K up to the
+dashed boundaries. This broadening term varies quadratically from
+zero at the dashed boundaries to a maximum of δ (here it is equal to
+1 eV) at K. There is no physical signiﬁcance to the relation between
+the additional broadening and its k-dependence, it just ensures a con-
+tinuous change in the broadening. (b) The occupancy along this path
+obtained from integrating the artiﬁcially broadened spectral function
+up to the Fermi level for different maximum δ values given in the
+legend. Both panels help to show how the spectral function (mea-
+sured by ARPES) and occupancy (measured by Compton scattering)
+are related to each other, along with the different features of the elec-
+tronic structure ARPES and Compton scattering would probe.
+placed along kz) being broader and/or closer to the Fermi level
+than predicted in the DFT+DMFT with the feature arising
+from the spectral weight spillage. A computationally inexpen-
+sive way to gain some insight into the contribution that this
+part of the quasiparticle band would make to the occupancy
+is to add an artiﬁcial (and arbitrary) broadening term (in en-
+ergy) to this DFT+DMFT Pd quasiparticle conduction band
+around the K point as shown in Fig. 6 (a). It is clear how dis-
+persive this makes the quasiparticle band around K resulting
+in additional spectral weight spillage crossing the Fermi level
+which gives rise to a more prominent occupancy feature at K
+in Fig. 6 (b). The occupancy in Fig. 6 (b) is calculated by
+integrating the real-frequency-dependent broadened spectral
+function up to the Fermi level. This feature grows as a func-
+tion of increasing δ, which is the maximum of the additional
+broadening as explained in Fig. 6 (b), until exceeding δ = 5
+eV. The occupation for the unbroadened (δ = 0.0 eV) spectral
+function is very similar to the DFT+DMFT (J = 0.7 eV) 2D
+projected occupancy in Fig. 3, with the additional smearing in
+that occupancy coming from the convolution with the exper-
+imental momentum resolution function. This similarity is to
+be expected as this is a quasi-2D electronic structure. We note
+that the additional occupation from this broadening violates
+charge conservation and as such, the Fermi level would need
+to move to compensate for this.
+This broadened spectral function serves to illustrate how
+the feature at K in the experimental Compton data may arise
+from this quasiparticle band. However, even with the unphys-
+ical arbitrary broadening, it is still not enough to fully agree
+with the experimental Compton data. This would suggest that
+the shape of this quasiparticle band may need to change with
+the dip around K likely being closer to the Fermi level, but its
+band centre must remain above the Fermi level to agree with
+the established single hexagonal Fermi surface. We emphasise
+Fig. 6 illustrates how ARPES and Compton probe the elec-
+tronic structure differently, in this case around K. For δ = 1
+eV, Compton scattering would probe a distinct occupation fea-
+ture around K, but the spectral function at the Fermi level
+around K is relatively small in magnitude which may make
+it difﬁcult to distinguish in ARPES. We note that Lecher-
+mann [21] showed that the introduction of relatively large
+(electron) doping results in a downward shift in energy of the
+Pd quasiparticle band around K. This will likely give a more
+prominent feature in the occupancy feature around K, for the
+reasons previously discussed. However, the PdCrO2 single-
+crystal sample measured by Billington et al. were grown by
+H. Takatsu as described in Ref. [43] and were of similar high
+purity and quality to those measured by ARPES [10–12] and
+quantum oscillations [13, 14]. Therefore, it is highly unlikely
+that the measured feature at K in the projected occupation
+comes solely from naturally occurring doping effects, but their
+contributions cannot be fully ruled out.
+The Cr 3d DMFT self-energy signiﬁcantly inﬂuences the
+Pd quasiparticle conduction band around K due to coupling
+between the layers of the localised Cr and itinerant Pd elec-
+trons, as discussed in detail by Lechermann [21]. This type of
+coupling is similar to the Kondo effect, but here the localised
+spins in PdCrO2 originate from a Mott mechanism which sup-
+presses the electron hopping between sites. The inclusion of
+the DMFT self-energy brings the Pd quasiparticle conduction
+band closer to the Fermi level around K and redistributes a
+signiﬁcant amount of the Cr 3d contribution to the spectral
+function away from this quasiparticle band peak and into the
+Hubbard-like bands. The disagreement in the occupancy may
+stem from inadequacies in the description of the hybridisation
+between the Cr 3d and Pd 4d states (which relates to the inter-
+layer electron coupling) at the DFT level. This can be very
+sensitive to the exchange-correlation functional used at the
+DFT level, as seen for group V and VI elements [44]. Con-
+sidering that the Pd states are primarily treated on the DFT
+level, higher order electron correlation contributions may in-
+ﬂuence the Pd conduction quasiparticle band dispersion and
+impact the inter-layer electron coupling. The correct descrip-
+tion of this inter-layer coupling may cause the shape and
+broadening of the Pd quasiparticle band to change to give the
+(2D projected) occupancy feature at K revealed by Comp-
+ton scattering while also being potentially difﬁcult to distin-
+guish in ARPES. We note that the reduced dimensionality at
+the surface could inﬂuence the inter-layer electron coupling
+(and other electron correlation effects), which may alter the
+Pd quasiparticle conduction band shape and dispersion which
+ARPES (potentially) would measure in comparison to what
+the Compton scattering bulk-probe measures. The results of
+DFT+DMFT calculations performed with an additional im-
+purity site for the Pd 4d orbitals (with the Cr and Pd DMFT
+impurities are treated independently) do not signiﬁcantly alter
+
+8
+the presented DFT+DMFT results which suggests that the lo-
+cal Pd electron correlations are insigniﬁcant when it comes to
+explaining the origin of the missing feature around K in the
+projected occupations.
+There is increasing amount of experimental evidence show-
+ing signiﬁcant inter-layer electron coupling. Transport mea-
+surements in Ref. [5] show that the frustrated Cr spins affect
+the out-of-plane and in-plane motion of the conduction elec-
+trons in the Pd layer. The interpretation of the magnetother-
+mopower measurements in Ref. [45] also point to there being
+signiﬁcant coupling between the itinerant Pd electrons with
+the short-range electron spin-correlations of the Cr electron
+spins well above TN. The short-range electron spin correla-
+tions which persisted above TN were also measured by single-
+crystal neutron scattering in Ref. [8]. Further transport mea-
+surements have shown the effect of the short-range order on
+the Hall and Nernst effects [46]. Raman and electron spin res-
+onance (ESR) measurements [47] have also shown evidence
+for inter-layer hoppings along the c-axis and a reconstruction
+of electronic bands on approaching TN. Recent ARPES [12]
+measurements in the antiferromagnetic phase showed that the
+measured spectra can be explained by an intertwined excita-
+tion consisting of a convolution of the charge spectrum of the
+metallic Pd layer and the spin susceptibility of the Mott insu-
+lating CrO2 layer. This excitation arises from an inter-layer
+Kondo-like coupling. The authors of Ref. [12] draw parallels
+with the results of the doping calculations of the Mott layer
+calculated in Ref. [21] which, as already discussed, signiﬁ-
+cantly affects the shape and dispersion of the Pd quasiparti-
+cle band at K. They emphasise that the results of their mea-
+surements and the doped DFT+DMFT calculations reﬂect the
+fact that in a coupled Mott-itinerant system, the itinerant layer
+will support charge excitations [12]. As the short-range elec-
+tron spin correlations persist beyond TN, our interpretation of
+the Compton results with respect to the Pd quasiparticle band
+ties in with the experimental evidence of the inter-layer elec-
+tron coupling, and may be linked to the intertwined excitation.
+Therefore, electron correlation effects which contribute to the
+inter-layer electron coupling, such as those in the models used
+in Refs. [12, 48], beyond those included in our DFT+DMFT
+calculations, seem to be signiﬁcant. To conﬁrm that the Pd
+conduction quasiparticle band is indeed broader and closer
+to the Fermi level than that predicted, the experimental k-
+resolved dispersion of that band could, for example, be mea-
+sured by pump-probe ARPES or k-resolved inverse photoe-
+mission spectroscopy (KRIPES) experiments which can probe
+the unoccupied part of the band structure.
+IV.
+CONCLUSION
+We have shown that the paramagnetic DFT+DMFT theo-
+retical description of the electronic structure of PdCrO2 is su-
+perior to DFT as it gives excellent agreement with the features
+relating to the hexagonal Fermi surface sheet measurement by
+all the Fermi surface experimental data, all of which agrees
+with the picture of the Mott insulating CrO2 layers [4]. How-
+ever, there are still discrepancies between the paramagnetic
+DFT+DMFT results and the Compton data measured within
+the paramagnetic phase. We found that there is no combina-
+tion of U and J around the Mott insulator transition (in the
+CrO2 layers) in DFT+DMFT which agrees with the presence
+of both the hexagonal Fermi surface and the feature around K
+as measured by the Compton. By adding an unphysical broad-
+ening term (in energy) to the DFT+DMFT the Pd quasiparti-
+cle conduction band around K, more spectral weight spills
+across the Fermi level which gives rise to a more prominent
+feature in the occupancy. However, this is still not enough to
+agree with the measured projected occupancy feature in the
+Compton data, so a change in both the broadening and shape
+of this quasiparticle band is needed while keeping its band
+centre above the Fermi level to avoid any changes to the es-
+tablished Fermi surface topology. Overall, our DFT+DMFT
+results help to clarify the origin of features in the Compton
+data.
+From the available experimental and theoretical evidence
+thus far, the feature in the projected electron occupancy mea-
+sured at K by Compton scattering is likely from the spectral
+weight of the Pd conduction quasiparticle band spilling across
+the Fermi level and becoming occupied. The ARPES may not
+measure this proposed spectral weight spillage if the Pd quasi-
+particle band is very dispersive around K (and the positions
+displaced along kz) and if the surface inﬂuences the electron
+correlation effects, such as the inter-layer electron coupling,
+which may then alter the quasiparticle band shape and disper-
+sion. As the DFT+DMFT model used does not predict the
+measured projected occupation feature at K, theories beyond
+our DFT+DMFT are required to establish the exact origin of
+this feature, which likely relates to the inter-layer electron
+coupling between the Pd and CrO2 layers which gives rise
+to new Kondo-like physics such as the previously observed
+intertwined excitation [12]. The discrepancy with the Comp-
+ton data gives motivation to experimentally measure the dis-
+persion of the unoccupied part of the Pd quasiparticle con-
+duction band to determine if it is indeed closer to the Fermi
+level and much more smeared in energy than predicted by our
+DFT+DMFT calculations. Evidently, Compton scattering is a
+powerful probe of many-body electron correlation effects.
+V.
+ACKNOWLEDGEMENTS
+A.D.N.J. acknowledges the Doctoral Prize Fellowship
+funding and support from the Engineering and Physical Sci-
+ences Research Council (EPSRC). We are grateful for the use-
+ful discussions with J. Laverock, M. Favaro-Bedford, Wenhan
+Chen, and C. Mackellar. Calculations were performed using
+the computational facilities of the Advanced Computing Re-
+search Centre, University of Bristol (http://bris.ac.uk/acrc/).
+The VESTA package (https://jp-minerals.org/vesta/en/) has
+been used in the preparation of some ﬁgures.
+
+9
+[1] M. Tanaka,
+M. Hasegawa, and H. Takei, Growth and
+Anisotropic Physical Properties of PdCoO2 Single Crystals,
+Journal of the Physical Society of Japan 65, 3973 (1996).
+[2] M. Tanaka, M. Hasegawa, and H. Takei, Crystal growth of
+PdCoO2, PtCoO2 and their solid-solution with delafossite
+structure, Journal of Crystal Growth 173, 440 (1997).
+[3] R. D. Shannon, D. B. Rogers, and C. T. Prewitt, Chemistry of
+noble metal oxides. I. Syntheses and properties of ABO2 de-
+lafossite compounds, Inorganic Chemistry 10, 713 (1971).
+[4] A. P. Mackenzie, The properties of ultrapure delafossite metals,
+Reports on Progress in Physics 80, 032501 (2017).
+[5] H. Takatsu, S. Yonezawa, C. Michioka, K. Yoshimura, and
+Y. Maeno, Anisotropy in the magnetization and resistivity of the
+metallic triangular-lattice magnet PdCrO2, Journal of Physics:
+Conference Series 200, 012198 (2010).
+[6] H. Takatsu, H. Yoshizawa, S. Yonezawa, and Y. Maeno, Critical
+behavior of the metallic triangular-lattice Heisenberg antiferro-
+magnet PdCrO2, Phys. Rev. B 79, 104424 (2009).
+[7] H. Takatsu, G. N´enert, H. Kadowaki, H. Yoshizawa, M. En-
+derle, S. Yonezawa, Y. Maeno, J. Kim, N. Tsuji, M. Takata,
+Y. Zhao, M. Green, and C. Broholm, Magnetic structure of the
+conductive triangular-lattice antiferromagnet PdCrO2, Phys.
+Rev. B 89, 104408 (2014).
+[8] D. Billington, D. Ernsting, T. E. Millichamp, C. Lester, S. B.
+Dugdale, D. Kersh, J. A. Duffy, S. R. Giblin, J. W. Taylor,
+P. Manuel, et al., Magnetic frustration, short-range correlations
+and the role of the paramagnetic Fermi surface of PdCrO2, Sci-
+entiﬁc reports 5, 12428 (2015).
+[9] H. Takatsu, S. Yonezawa, S. Fujimoto, and Y. Maeno, Uncon-
+ventional Anomalous Hall Effect in the Metallic Triangular-
+Lattice Magnet PdCrO2, Phys. Rev. Lett. 105, 137201 (2010).
+[10] J. A. Sobota, K. Kim, H. Takatsu, M. Hashimoto, S.-K. Mo,
+Z. Hussain, T. Oguchi, T. Shishidou, Y. Maeno, B. I. Min, and
+Z.-X. Shen, Electronic structure of the metallic antiferromag-
+net PdCrO2 measured by angle-resolved photoemission spec-
+troscopy, Phys. Rev. B 88, 125109 (2013).
+[11] H.-J. Noh, J. Jeong, B. Chang, D. Jeong, H. S. Moon, E.-J.
+Cho, J. M. Ok, J. S. Kim, K. Kim, B. I. Min, H.-K. Lee, J.-
+Y. Kim, B.-G. Park, H.-D. Kim, and S. Lee, Direct Observa-
+tion of Localized Spin Antiferromagnetic Transition in PdCrO2
+by Angle-Resolved Photoemission Spectroscopy, Scientiﬁc Re-
+ports 4, 3680 (2014).
+[12] V. Sunko, F. Mazzola, S. Kitamura, S. Khim, P. Kushwaha, O. J.
+Clark, M. D. Watson, I. Markovi´c, D. Biswas, L. Pourovskii,
+T. K. Kim, T.-L. Lee, P. K. Thakur, H. Rosner, A. Georges,
+R. Moessner, T. Oka, A. P. Mackenzie, and P. D. C. King, Prob-
+ing spin correlations using angle-resolved photoemission in a
+coupled metallic/Mott insulator system, Science Advances 6,
+eaaz0611 (2020).
+[13] J. M. Ok, Y. J. Jo, K. Kim, T. Shishidou, E. S. Choi, H.-J.
+Noh, T. Oguchi, B. I. Min, and J. S. Kim, Quantum Oscillations
+of the Metallic Triangular-Lattice Antiferromagnet PdCrO2,
+Phys. Rev. Lett. 111, 176405 (2013).
+[14] C. W. Hicks, A. S. Gibbs, L. Zhao, P. Kushwaha, H. Borrmann,
+A. P. Mackenzie, H. Takatsu, S. Yonezawa, Y. Maeno, and E. A.
+Yelland, Quantum oscillations and magnetic reconstruction in
+the delafossite PdCrO2, Phys. Rev. B 92, 014425 (2015).
+[15] A. Bansil, R. Markiewicz, C. Kusko, M. Lindroos, and
+S. Sahrakorpi, Matrix element and strong electron correlation
+effects in ARPES from cuprates, Journal of Physics and Chem-
+istry of Solids 65, 1417 (2004).
+[16] B. Barbiellini, High-temperature cuprate superconductors stud-
+ied by x-ray Compton scattering and positron annihilation spec-
+troscopies, Journal of Physics: Conference Series 443, 012009
+(2013).
+[17] S. B. Dugdale, Probing the Fermi surface by positron annihila-
+tion and Compton scattering, Low Temperature Physics 40, 328
+(2014).
+[18] D. G. Lock, V. H. C. Crisp, and R. N. West, Positron annihi-
+lation and Fermi surface studies: a new approach, Journal of
+Physics F: Metal Physics 3, 561 (1973).
+[19] H. C. Robarts, T. E. Millichamp, D. A. Lagos, J. Laverock,
+D. Billington, J. A. Duffy, D. O’Neill, S. R. Giblin, J. W. Tay-
+lor, G. Kontrym-Sznajd, M. Samsel-Czekała, H. Bei, S. Mu,
+G. D. Samolyuk, G. M. Stocks, and S. B. Dugdale, Extreme
+fermi surface smearing in a maximally disordered concentrated
+solid solution, Phys. Rev. Lett. 124, 046402 (2020).
+[20] K. P. Ong and D. J. Singh, Three-dimensional magnetism and
+coupling to the conduction electrons in PdCrO2, Phys. Rev. B
+85, 134403 (2012).
+[21] F. Lechermann, Hidden Mott insulator in metallic PdCrO2,
+Phys. Rev. Materials 2, 085004 (2018).
+[22] F. Lechermann, From basic properties to the Mott design of cor-
+related delafossites, npj Computational Materials 7, 120 (2021).
+[23] I. Abrikosov, A. Ponomareva, P. Steneteg, S. Barannikova, and
+B. Alling, Recent progress in simulations of the paramagnetic
+state of magnetic materials, Current Opinion in Solid State and
+Materials Science 20, 85 (2016).
+[24] A. D. N. James, M. Sekania, S. B. Dugdale, and L. Chioncel,
+Magnetic Compton proﬁles of Ni beyond the one-particle pic-
+ture: Numerically exact and perturbative solvers of dynamical
+mean-ﬁeld theory, Phys. Rev. B 103, 115144 (2021).
+[25] G. Giuliani and G. Vignale, The normal Fermi liquid, in Quan-
+tum Theory of the Electron Liquid (Cambridge University Press,
+2005) p. 405–500.
+[26] J. K. Dewhurst, S. Sharma, L. Nordstr¨om, F. Cricchio,
+O. Granas, and E. K. U. Gross, http://elk.sourceforge.net/.
+[27] O. Parcollet, M. Ferrero, T. Ayral, H. Hafermann, I. Krivenko,
+L. Messio, and P. Seth, TRIQS: A toolbox for research on in-
+teracting quantum systems, Comp. Phys. Commun. 196, 398
+(2015).
+[28] A. D. N. James, E. I. Harris-Lee, A. Hampel, M. Aichhorn,
+and S. B. Dugdale, Wave functions, electronic localization, and
+bonding properties for correlated materials beyond the Kohn-
+Sham formalism, Phys. Rev. B 103, 035106 (2021).
+[29] M. Aichhorn, L. Pourovskii, V. Vildosola, M. Ferrero, O. Par-
+collet, T. Miyake, A. Georges, and S. Biermann, Dynamical
+mean-ﬁeld theory within an augmented plane-wave framework:
+Assessing electronic correlations in the iron pnictide LaFeAsO,
+Phys. Rev. B 80, 085101 (2009).
+[30] J. P. Perdew, K. Burke, and M. Ernzerhof, Generalized gradient
+approximation made simple, Phys. Rev. Lett. 77, 3865 (1996).
+[31] M. Aichhorn, L. Pourovskii, P. Seth, V. Vildosola, M. Zingl,
+O. E. Peil, X. Deng, J. Mravlje, G. J. Kraberger, C. Martins,
+M. Ferrero, and O. Parcollet, TRIQS/DFTTools: A TRIQS
+application for ab initio calculations of correlated materials,
+Comp. Phys. Commun. 204, 200 (2016).
+[32] P.
+Seth,
+I.
+Krivenko,
+M.
+Ferrero,
+and
+O.
+Parcollet,
+TRIQS/CTHYB: A continuous-time quantum Monte Carlo hy-
+bridisation expansion solver for quantum impurity problems,
+Comp. Phys. Commun. 200, 274 (2016).
+
+10
+[33] M. A. Korotin, V. I. Anisimov, D. I. Khomskii, and G. A.
+Sawatzky, CrO2: A Self-Doped Double Exchange Ferromag-
+net, Phys. Rev. Lett. 80, 4305 (1998).
+[34] G. J. Kraberger, R. Triebl, M. Zingl, and M. Aichhorn, Maxi-
+mum entropy formalism for the analytic continuation of matrix-
+valued Green’s functions, Phys. Rev. B 96, 155128 (2017).
+[35] D. Ernsting, D. Billington, T. Haynes, T. Millichamp, J. Taylor,
+J. Duffy, S. Giblin, J. Dewhurst, and S. Dugdale, Calculating
+electron momentum densities and Compton proﬁles using the
+linear tetrahedron method, Journal of Physics: Condensed Mat-
+ter 26, 495501 (2014).
+[36] Wenhan Chen, A. D. N. James, and S. B. Dugdale, Local elec-
+tron correlation effects on the fermiology of the weak itinerant
+ferromagnet ZrZn2, Electronic Structure 4, 045002 (2022).
+[37] K. Maiti, D. D. Sarma, M. J. Rozenberg, I. H. Inoue, H. Makino,
+O. Goto, M. Pedio, and R. Cimino, Electronic structure of
+Ca1−xSrxVO3: A tale of two energy scales, Europhysics Let-
+ters 10, 246 (2001).
+[38] A. Liebsch, Surface versus Bulk Coulomb Correlations in Pho-
+toemission Spectra of SrVO3 and CaVO3, Phys. Rev. Lett. 90,
+096401 (2003).
+[39] J. Laverock, J. Kuyyalil, B. Chen, R. P. Singh, B. Karlin, J. C.
+Woicik, G. Balakrishnan, and K. E. Smith, Enhanced electron
+correlations at the SrxCa1−xVO3 surface, Phys. Rev. B 91,
+165123 (2015).
+[40] H. Ishida, D. Wortmann, and A. Liebsch, Electronic structure of
+SrVO3(001) surfaces: A local-density approximation plus dy-
+namical mean-ﬁeld theory calculation, Phys. Rev. B 73, 245421
+(2006).
+[41] K. Yoshimatsu, T. Okabe, H. Kumigashira, S. Okamoto,
+S. Aizaki,
+A. Fujimori, and M. Oshima, Dimensional-
+crossover-driven metal-insulator transition in SrVO3 ultrathin
+ﬁlms, Phys. Rev. Lett. 104, 147601 (2010).
+[42] Z. Zhong, M. Wallerberger, J. M. Tomczak, C. Taranto, N. Par-
+ragh, A. Toschi, G. Sangiovanni, and K. Held, Electronics with
+Correlated Oxides: SrVO3/SrTiO3 as a Mott Transistor, Phys.
+Rev. Lett. 114, 246401 (2015).
+[43] H. Takatsu and Y. Maeno, Single crystal growth of the metal-
+lic triangular-lattice antiferromagnet PdCrO2, Journal of Crys-
+tal Growth 312, 3461 (2010).
+[44] E. I. Harris-Lee, A. D. N. James, and S. B. Dugdale, Sensitivity
+of the Fermi surface to the treatment of exchange and correla-
+tion, Phys. Rev. B 103, 235144 (2021).
+[45] S. Arsenijevi´c, J. M. Ok, P. Robinson, S. Ghannadzadeh, M. I.
+Katsnelson, J. S. Kim, and N. E. Hussey, Anomalous magne-
+tothermopower in a metallic frustrated antiferromagnet, Phys.
+Rev. Lett. 116, 087202 (2016).
+[46] R. Daou, R. Fr´esard, S. H´ebert, and A. Maignan, Impact
+of short-range order on transport properties of the two-
+dimensional metal PdCrO2, Phys. Rev. B 92, 245115 (2015).
+[47] A. Glamazda, W.-J. Lee, S.-H. Do, K.-Y. Choi, P. Lemmens,
+J. van Tol, J. Jeong, and H.-J. Noh, Collective excitations in the
+metallic triangular antiferromagnet PdCrO2, Phys. Rev. B 90,
+045122 (2014).
+[48] A. J. McRoberts, J. F. Mendez-Valderrama, R. Moessner, and
+D. Chowdhury, An intermediate-scale theory for electrons cou-
+pled to frustrated local-moments 10.48550/ARXIV.2207.10087
+(2022).
+
diff --git a/3NA0T4oBgHgl3EQfNP9P/content/tmp_files/load_file.txt b/3NA0T4oBgHgl3EQfNP9P/content/tmp_files/load_file.txt
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@@ -0,0 +1,899 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf,len=898
+page_content='Impact of electron correlations on the k-resolved electronic structure of PdCrO2 revealed by  Compton scattering  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' James,1 D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Billington,2 and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Dugdale1  1H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Wills Physics Laboratory, University of Bristol, Tyndall Avenue, Bristol, BS8 1TL, United Kingdom  2School of Physics and Astronomy, Cardiff University, Queen’s Building, The Parade, Cardiff, CF24 3AA, United Kingdom  (Dated: January 6, 2023)  Delafossite PdCrO2 is an intriguing material which displays nearly-free electron and Mott insulating be-  haviour in different layers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Both angle-resolved photoemission spectroscopy (ARPES) and Compton scattering  measurements have established a hexagonal Fermi surface in the material’s paramagnetic phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' However, the  Compton experiment detected an additional structure in the projected occupancy which was originally inter-  preted as an additional Fermi surface feature not seen by ARPES.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Here, we revisit this interpretation of the  Compton data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' State-of-the-art density functional theory (DFT) with dynamical mean ﬁeld theory (DMFT), the  so-called DFT+DMFT method, predicts the Mott insulating state along with a single hexagonal Fermi surface in  excellent agreement with ARPES and Compton.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' However, DFT+DMFT fails to predict the intensity of the ad-  ditional spectral weight feature observed in the Compton data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' We infer that this discrepancy may arise from the  DFT+DMFT not being able to correctly predict certain features in the shape and dispersion of the unoccupied  quasiparticle band near the Fermi level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Therefore, a theoretical description beyond our DFT+DMFT model  is needed to incorporate vital electron interactions, such as inter-layer electron coupling interactions which for  PdCrO2 gives rise to the Kondo-like so-called intertwined excitation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='  I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='  INTRODUCTION  Interest has grown over the last few decades in layered  triangular-lattice delafossite materials with chemical formula  ABO2 (A = Pt, Pd, Ag or Cu, and B = Cr, Co, Fe, Rh,  Al, Ga, Sc, In or Tl).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' This interest in metallic delafossites  was sparked by reports from Tanaka et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' [1, 2] of strongly  anisotropic conductivity in their PdCoO2 and PtCoO2 single  crystals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Previous measurements of PtCoO2 displayed an ex-  tremely low in-plane room temperature resistivity of 3 µΩcm,  a value comparable to elemental Cu [3, 4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' This led to the  emergence of a new ﬁeld of research into these materials [4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='  The PdCrO2 compound also has the anticipated anisotropic  conductivity [5], but displays an antiferromagnetic phase be-  low its N´eel temperature, TN = 37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='5 K, above which the lo-  cal Cr3+ (S = 3/2) electron spins in the CrO2 layers are  frustrated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Within the antiferromagnetic phase this frustration  is relieved, resulting in the local spins ordering with a rota-  tion of 120◦ between adjacent sites [5–8].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' The observation of  this ordered state offers an opportunity to study the coupling  between nearly-free electrons and (frustrated) local electron  spins in a frustrated antiferromagnet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' This interest in PdCrO2  has led to further experimental characterisation of this mate-  rial, leading to the discovery of an unconventional anomalous  Hall effect [7, 9], and a reconstructed Fermi surface within the  (smaller) antiferromagnetic Brillouin zone, measured by both  angle resolved photoemission spectroscopy (ARPES) [10–12]  and quantum oscillations [13, 14].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' For PdCrO2, it has been  implicitly assumed that electron correlations are the driving  force for the antiferromagnetic state, and hence why the be-  haviour of the CrO2 layer has been described with the concept  of local moments [4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='  Within the paramagnetic phase, both ARPES [10, 11] and  Compton scattering [8] measurements were performed to de-  termine the Fermi surface geometry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' ARPES measures the  energies of the emitted photoelectrons from the sample sur-  face together with their angle of emission such that the quasi-  particle energy and its dispersion with (crystal) momentum  up to and including the Fermi energy can be extracted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' The  ARPES spectra show both the ground and excited states of  the electronic structure and measurements are sensitive to the  surface and matrix element effects [15].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Compton scattering  experiments probe the bulk ground-state electronic structure  through its electron momentum distribution [16] by measur-  ing so-called Compton proﬁles which are the doubly projected  electron momentum densities (EMDs) [17].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' The EMD is the  electron density distribution in real momentum, p, which can  be directly related to the electron occupancy by folding the  EMD back into the ﬁrst Brillouin zone (the Lock-Crisp-West  (LCW) theorem [18]) to recover the full translational sym-  metry of the reciprocal lattice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' This folded EMD is now a  function of the crystal momentum, k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Electron occupancy in  k-space is inﬂuenced by temperature, site disorder, and many-  body electron correlations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='  The step changes in the occu-  pancy can be used to determine the Fermi wave-vectors (and  hence Fermi surface) even in materials which are either inac-  cessible by or challenging for other techniques.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Such mate-  rials include highly chemically-disordered alloys [19] which  have short electronic mean-free paths.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Evidently, ARPES and  Compton scattering probe different aspects of the electronic  structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' The Fermi surface may be extracted from either the  k-resolved photoelectron dispersion around the Fermi energy  measured by ARPES, or the changes in the occupation derived  from the Compton data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='  Both ARPES and Compton scattering conﬁrmed the pres-  ence of the hexagonal Fermi surface, but the Compton ex-  periments clearly showed an additional contribution to the  projected electron occupancy around the corners of the (pro-  jected) Brillouin zone.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' In an effort to understand their re-  sult, Billington et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' [8] performed density functional theory  (DFT) calculations from which they concluded that at least  two Fermi surface sheets were required to describe all the fea-  tures in the k-space occupancy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' This led to speculation by  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='02143v1  [cond-mat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='str-el]  5 Jan 2023  2  Billington et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' that what appeared to be an additional Fermi  surface sheet observed in the bulk-sensitive Compton exper-  iments but not in the ARPES might be due to some combi-  nation of the surface not being representative of the bulk or  unfavourable matrix elements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Although Ong et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' [20] had  shown that the DFT magnetic structure of PdCrO2 was three  dimensional, at the time of the study by Billington et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' there  were no published DFT calculations of non-magnetic PdCrO2  in opposition to their two Fermi surface model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='  This interpretation of the Compton data was subsequently  critically examined by Mackenzie [4] who argued that it did  not take into account the existence of the Mott insulating state  in the CrO2 layers (the existence of which is supported by  several experiments).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' However, these arguments do not ex-  plain the extra features in the occupation number measured by  the Compton scattering.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Recent calculations combining DFT  with dynamical mean ﬁeld theory (DFT+DMFT) [12, 21, 22]  showed that the Mott insulating state in the CrO2 layers is a  natural consequence of the inclusion of the local dynamical  electron correlations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Also, DFT+DMFT naturally includes  paramagnetic electron correlations within the DMFT part [23]  which is vital for this frustrated antiferromagnetic material.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='  Therefore, the interpretation of the results from the Compton  experiment warrants further investigation in order to reconcile  it with the picture of local moments within the Mott insulating  CrO2 layers and to help resolve the inconsistent conclusions  about the Fermiology from the different measurements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='  In light of the recent PdCrO2 DFT+DMFT calculations, it  is necessary to ﬁrst reproduce them in order to then deter-  mine the DFT+DMFT EMD using the recent technique im-  plemented by James et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' [24].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' From such calculations, a  comparison with the Compton scattering experiment, primar-  ily the projected occupation, could be made.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' With respect to  a non-interacting prediction, the inclusion of many-body cor-  relations (such as that predicted by Fermi liquid theory [25])  generally leads to a redistribution and apparent smearing in  k-space of the occupation around the Fermi wave-vector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' The  presence of the Mott insulating CrO2 layers in the previous  DFT+DMFT predictions lead to signiﬁcant changes to the  shape and dispersion of the quasiparticle bands which also  means that there would be signiﬁcant changes to the occupa-  tion, which the Compton scattering will be sensitive to.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Hence  it is important to use DFT+DMFT to determine whether the  predicted electronic structure with these Mott insulating CrO2  layers are compatible with the electron occupancy as mea-  sured by Compton scattering.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='  In this study, we revisit the interpretation of the Compton  scattering experimental results and compare them with the  corresponding quantities calculated from the non-magnetic  DFT and paramagnetic DFT+DMFT methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='  Here, we  see that the size and shape of the predicted DFT+DMFT  hexagonal Fermi surface is in excellent agreement with the  ARPES [10–12], quantum oscillations [13, 14], and Comp-  ton measurements [8].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='  However, there are still discrep-  ancies between the experimental Compton data and the  DFT+DMFT calculations around the corners of the Brillouin  zone.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='  These discrepancies can be reduced (but not elimi-  nated) in the DFT+DMFT calculation by artiﬁcially (and un-  physical) broadening the unoccupied quasiparticle band just  above the Fermi level around the corners of the Brillouin  zone.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' This suggests that changes to both the shape and disper-  sion of that quasiparticle band are required, most likely driven  by certain electron correlation effects which theories beyond  our DFT+DMFT would possibly capture, such as inter-layer  electron coupling interactions which gives rise to the previ-  ously observed (Kondo-like) so-called intertwined excitation  in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' [12] which is a convolution of the charge spectrum of  the metallic layer and the spin susceptibility of the Mott insu-  lating layer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='  II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='  METHODS  We have used the full potential augmented plane-wave  plus local orbitals (APW+lo) ELK code [26] in combina-  tion with the toolbox for research on interacting quantum  systems (TRIQS) library [27].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' This so-called ELK+TRIQS  DFT+DMFT framework is described in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' [28].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Further  discussion of interfacing the APW+lo DFT basis with the  DMFT Anderson’s impurity model is found in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' [29].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' The  PdCrO2 delafossite structure is shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' 1 (a) and the  lattice parameters of the conventional (hexagonal) unit cell  are a = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='929 ˚A, c = 18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='093 ˚A [7] with the Pd–O distance,  dPd−O = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='11c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='  The DFT calculation used the Perdew-  Burke-Ernzerhof (PBE) generalized gradient approximation  (GGA) for the exchange-correlation functional [30] and was  converged on a 32 × 32 × 16 Monkhorst-Pack k-mesh of  2601 irreducible k-points in the irreducible Brillouin zone.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='  We used the all-electron full-potential APW+lo DFT method  instead of the pseudo-potential plane-wave approach used in  Refs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' [21, 22].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='  The DFT outputs were interfaced to the  TRIQS/DFTTools application of the TRIQS library [31] by  constructing Wannier projectors, as described in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' [28],  for all the Cr 3d-states within a correlated energy window of  [−8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='5, 3] eV relative to the Fermi level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='  The paramagnetic DMFT part of the DFT+DMFT calcu-  lation was implemented using the continuous-time quantum  Monte Carlo (CT-QMC) solver within the TRIQS/CTHYB  application [32] with the Slater interaction Hamiltonian pa-  rameterised by the Hubbard interaction U = 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='0 eV and Hund  exchange interaction J = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='7 eV, unless otherwise speciﬁed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='  These U and J values are similar to those used in previous  calculations of PdCrO2 [12, 21, 22], and other CrO2 com-  pounds [22, 33].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' We approximated the double counting in the  fully localised limit in line with the previous DFT+DMFT cal-  culations [12, 21, 22].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Our DFT+DMFT approach slightly dif-  fers from previous DFT+DMFT calculations where different  correlated energy windows were used and either the Hubbard-  Kanamori interaction Hamiltonian [21, 22] or the Hubbard I  approximation for the impurity solver [12] were chosen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' We  note that our DFT+DMFT calculations are paramagnetic with  no overall ordered moment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' The Cr 3d orbitals were diag-  onalised from the complex spherical harmonic basis into the  diagonal trigonal basis (obtained by diagonalising the orbital  density matrix) resulting in the three sets of non-degenerate  orbitals, namely the two doubly degenerate e′  g and eg or-  3  Pd  CrO2  (a)  (c)  (b)  (d)  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' (a) The PdCrO2 delafossite structure showing the triangular-lattice Pd and CrO2 layers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' (b) The logarithm of the DFT+DMFT spectral  spectral function A(k, ω) overlaid with the DFT band structure (blue solid lines).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' These have been evaluated along a path connecting points  within the kz = 0 plane of the Brillouin zone of PdCrO2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' The points Γ and K are high-symmetry points, with K on the Brillouin zone  boundary of the primitive rhombohedral cell.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' While M is not a high-symmetry point in that Brillouin zone, it is used here with reference to the  equivalent point in a simple hexagonal Brillouin zone, as in previous work [12, 21, 22].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Here, the changes to the Fermi surface between these  theoretical methods are most prominent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' (c) The three DFT Fermi surface sheets in the rhombohedral Brillouin zone and (d) the DFT+DMFT  hexagonal Fermi surface (given by the spectral function evaluated at the Fermi level where ω = 0 eV) in the same kz plane as described in  (b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Note that there is distinguishable spectral weight at K with respect to the Γ and M points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='  bitals along with the single a1g orbital, in agreement with  Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' [21].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' We used the fully-charge-self-consistent (FCSC)  DFT+DMFT method with a total of 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='4 × 107 Monte Carlo  sweeps within the impurity solver for each DMFT cycle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' An  inverse temperature β = 40 eV−1 (∼ 290 K) was used which  is similar to the (room) temperature of the Compton scattering  experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' The spectral functions were calculated by ana-  lytically continuing the DMFT self-energy obtained from the  LineFitAnalyzer technique of the maximum entropy analytic  continuation method implemented within the TRIQS/Maxent  application [34].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='  For the DFT and DFT+DMFT EMD calculations, we  used the method of Ernsting et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' [35] together with the  DFT+DMFT L¨owdin-type basis electron wave functions and  occupation numbers determined by the method described in  Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' [24].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' A maximum momentum cut-off of 16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='0 a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' was  used.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' We emphasise that the EMD related results do not use  analytic continuation so they do not suffer from its associ-  ated complications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' We concentrate on the projected EMD  for comparisons with the experimental Compton data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='  To  compare with the experimental 2D occupancy in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' [8],  which directly relates to the electron occupation, the calcu-  lated EMDs were ﬁrst projected along the kz-axis (parallel to  the c-axis of the conventional unit cell) and this projected 2D  EMD was then convoluted with a 2D Gaussian function with a  full-width-at-half-maximum of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='106 a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' approximating the  effect of the ﬁnite Compton scattering experimental momen-  tum resolution [8].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' These convoluted EMDs are subsequently  folded back into the ﬁrst Brillouin zone, via the LCW theo-  rem, producing the theoretical 2D projected occupancy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' The  Compton proﬁles, J(pz), which are double-projections of the  EMD, were evaluated along the experimental scattering vec-  tors (which for convenience are conventionally referred to as  being along pz in the local coordinate system),  J(pz) =  ��  ρ(p)dpxdpy,  (1)  where ρ(p) is the 3D EMD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' The so-called directional differ-  ences, which are the differences between Compton proﬁles  resolved along different crystallographic directions, were cal-  culated so that they could be compared to the experimental  ones.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='  III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='  RESULTS  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' 1 (b) shows the DFT band structure and DFT+DMFT  spectral function plotted along the high symmetry directions  in the kz = 0 plane.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='  The DFT and DFT+DMFT results  show good agreement with previous studies [12, 21, 22].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' We  note that our spin-orbit coupling DFT calculation differs to  that presented in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' [8], even though those previously pub-  lished results are reproducible with the same version (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='9)  of ELK.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' The lack of reproducibility of the Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' [8] ground  state with the current version of ELK suggests that there was  some problem with that calculation in version 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='9 (which  has been ﬁxed in later versions) which coincidentally gave  convincing agreement between the reported electronic struc-  ture and experimental Compton data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' In agreement with the  other previously reported DFT and DFT+DMFT predictions,  the hybridised Pd 4d and Cr 3d DFT bands which lie around  the Fermi level and which contribute to the DFT Fermi sur-  face shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' 1 (c) drastically redistribute, with the Cr  3d dominant bands now insulating in DFT+DMFT due to the  4  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' The DFT+DMFT (ﬁxed U = 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='0 eV and J = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='7 eV)  spectral function A(k, ω) plotted in the style of ARPES energy dis-  tribution curves (EDCs).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' This shows the spectral function dispersion  around the Fermi level along a portion of the path of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' 1 (b) fo-  cusing on the Pd quasiparticle conduction band crossing the Fermi  level (ω = 0 eV).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' The inset reveals structure in the spectral func-  tion evaluated at a k-point between M to Γ which is highlighted in  red in the EDCs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' The axes of the inset are the same as the main ﬁg-  ure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' The Pd quasiparticle conduction band centre is just above the  Fermi level, but there is spectral weight from this Lorentzian-like  quasiparticle band spectral function crossing the Fermi level and this  occupied spectral weight will contribute to the occupation distribu-  tion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' This occupied weight is referred to as spectral weight spillage  across the Fermi level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='  formation of a Mott insulating state within the CrO2 layers  which arises from the strong local electron correlations on the  Cr site.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' The remaining quasiparticle band which crosses the  Fermi level in DFT+DMFT A(k, ω) is now predominantly Pd  4d in character and forms the hexagonal Fermi surface sheet  shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' 1 (d), in excellent agreement with that observed  in the paramagnetic ARPES [11] measurements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' There are  also incoherent, non-dispersive Hubbard-like bands, shown in  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' 1 (b) centred around ±1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='5 eV, which arise from the Mott  insulating Cr states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' We note that the DFT+DMFT spectral  function in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' 1 (d) shows signiﬁcant spectral weight around  the K point which is also seen in previous DFT+DMFT cal-  culations by Lechermann [21].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='  To help illustrate certain concepts which link the spectral  function to the occupation distribution (required for subse-  quent discussions), we have included the DFT+DMFT spec-  tral function around the Fermi level in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' 2, plotted in the  style of ARPES energy distribution curves (EDCs).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' The spec-  tral function of the Pd dominant quasiparticle conduction band  is seen to be broader and have a smaller amount of spectral  weight than the inverted parabolic quasiparticle band around  M which peaks at about −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='5 eV (which is also shown in the  inset of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' 2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' The inset shows that at a particular k-point  between M and Γ the Pd quasiparticle conduction band cen-  tre is just above the Fermi level which of course means that  there is no Fermi surface at this wave-vector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' However, owing  to the ﬁnite width of the spectral function around the quasi-  particle peaks (which arises from the ﬁnite lifetime linked to  the imaginary part of the DMFT self-energy), there is a por-  tion of the spectral function tail which crosses the Fermi level  and is consequently occupied.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' This occupied portion of the  Pd quasiparticle conduction band contributes to the EMD and  will be seen in the electron occupancy measured by Comp-  ton scattering.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Conversely, if the band centre (quasiparticle  peak) were below the Fermi level, but the higher energy tail  crosses the Fermi level, then that quasiparticle band will have  a reduced contribution to the occupation at that k-point with  respect to a fully occupied quasiparticle band.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' We refer to the  spectral weight from the quasiparticle band tails crossing the  Fermi level as spectral weight spillage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' The spectral weight  spillage will be dependent on factors which inﬂuence the ﬁ-  nite width (inverse lifetime) of the (quasiparticle) peaks in  the spectral function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' In the DFT picture within the Green’s  function formalism, the typical DFT spectral function would  be a series of Lorentzian-like functions corresponding to the  DFT bands and most likely have small widths relating to the  temperature used in the calculation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' The corresponding oc-  cupation distribution will therefore have contributions from  the fully occupied spectral function below the Fermi level and  from spectral weight spillage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' The common consequence of  spectral weight spillage contribution in DFT is the apparent  smearing of the occupation distribution in (crystal) momen-  tum around the Fermi wave-vector (which is temperature de-  pendent because of the temperature dependence of the spectral  weight spillage).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' The effects of spectral weight spillages on  the occupation distribution are often less prominent in DFT  but have been seen for DFT bands grazing the Fermi level  such as in ZrZn2 [36] and in highly compositionally disor-  dered systems [19].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='  The 2D projected occupancy (along the projected bulk high  symmetry path used in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' [8]) determined from the DFT  and DFT+DMFT calculated EMDs, together with the the ex-  perimental 2D occupancy, are shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Here, we see  that the agreement in the DFT+DMFT (U = 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='0 eV, J = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='7  eV) 2D projected occupancy signiﬁcantly improves along the  Γ to M direction compared to the DFT results, with there  being a single step along this direction in the DFT+DMFT  compared to the smoothed shoulder predicted by the DFT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='  The location of this single step along Γ to M gives the Fermi  wave-vector of the hexagonal Fermi surface sheet along this  direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' We can also extract the Fermi wave-vector of the  hexagonal Fermi surface sheet along the Γ to K from the lo-  cation of the largest change in the projected occupation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' The  DFT+DMFT projected occupation which relates to hexago-  nal Fermi surface sheet along with the region it encompasses  (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' 4) is in excellent agreement with the Compton data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='  We ﬁnd the occupied fraction of the Brillouin zone associ-  ated with DFT+DMFT hexagonal Fermi surface is approxi-  mately equal to one half, which is in excellent agreement with  both the occupation fraction expected from the Fermi surface  of a monovalent metal and the experimental fractions deter-  mined from Compton [8], ARPES [10], and quantum oscilla-  tions [13].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='  The DFT projected occupancy has some similarities to the  experiment around K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='  This feature in the DFT relates to  5  M  K  M  K  min  max  occupancy  DFT  J=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='25 eV  J=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='30 eV  J=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='50 eV  J=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='70 eV  experiment  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' The 2D occupancy (projected along the kz-axis) plotted along the projected bulk high-symmetry directions (denoted with overlines)  for DFT and DFT+DMFT with different values of the Hund exchange J at ﬁxed Hubbard U = 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='0 eV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' The theoretical projected EMDs were  convoluted with a two dimensional Gaussian (full-width-at-half-maximum = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='106 a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=') to approximate the effect of the ﬁnite experimental  momentum resolution prior to calculating the occupancy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' The experimental data are from Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' [8].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Varying J explores the changes to the  electronic structure passing through the Mott transition of the Cr states, with the Mott insulating state occurring for J > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='25 eV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='  the Cr DFT band crossing the Fermi level near K (and the  corresponding points along the kz-axis) resulting in an elec-  tron Fermi surface pocket around K (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' 1 (b) and (c)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='  However, the agreement at K signiﬁcantly worsens in the  DFT+DMFT (at J = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='7 eV) as there is no contribution from  the Cr band as it is now below the Fermi level and hence fully  occupied (insulating).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Interestingly, however, there is a small  contribution at K in the DFT+DMFT (J = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='7 eV) projected  occupations which arises from the spectral weight of the Pd  quasiparticle conduction band spilling across the Fermi level  (such as that seen around K in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' 1 (d)) which then becomes  occupied, similar to that seen in Refs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' [19, 36] as discussed  previously.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' This additional spectral weight is small relative  to the background (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=', relative to the Γ point) which would  likely mean that this feature might be difﬁcult for the ARPES  to distinguish within the experimental and statistical error.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' It  should be noted that the projected occupation from Compton  presented here relates to the energy integral of the occupied  part of the spectral function which is then integrated along  the kz-axis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Consequently, the accumulation of this feature  around K seen in the spectral function in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' 1 (d) becomes  more prominent in the projected occupation at K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' This is seen  in the DFT+DMFT (J = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='7 eV) projected occupation fea-  ture around K in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' We note that the DFT+DMFT spec-  tral plot along the same in-plane path as Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' 1 (b) but with a  shift of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='5 reciprocal lattice units along the kz-axis shows a  similar dispersion to kz = 0 plane which is expected for this  quasi-2D system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Therefore, this DFT+DMFT feature at K  will have contributions from all the spectral weight spillage  along the kz-axis centred at K owing to the projected nature  of the Compton occupation data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='  Also shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' 3 are several DFT+DMFT calculations  of the 2D projected occupancy plotted for different J but with  U ﬁxed to 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='0 eV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' These show the evolution of the 2D pro-  jected occupancy (and by inference, the electronic structure)  as a function of the size of the Hund exchange interaction J as  the CrO2 layer transitions from the metallic (low J) to Mott  insulating state (high J), where the Mott insulating state oc-  curs for J > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='25 eV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' The result of increasing J causes the  smoothed double-step feature prominent in the DFT projected  occupancy along Γ to M to transform into a single step due to  the spectral weight from the previously conducting Cr quasi-  particle bands shifting below the Fermi level and becoming  fully occupied.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' On the other hand, increasing J suppresses  the 2D occupancy contribution around K as the Cr quasipar-  ticle bands transition into being Mott insulating.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' There are no  optimal DFT+DMFT U and J parameters which are able to  simultaneously capture the 2D projected occupancy features  from Γ to K and the single step along Γ to M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' The hexagonal  Fermi surface sheet is a robust feature in all the Fermi surface  measurements and is clearly captured by the DFT+DMFT pre-  dictions with Mott insulating CrO2 layers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='  To get a better perspective of the agreement between the  different calculations with the experimental data, Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' 4 shows  6  DFT  experiment  DFT+DMFT  K  M  min  max  occupancy  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' The 2D (projected along the kz-axis) occupancy in the 2D  hexagonal Brillouin zone.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' The left hand side shows the experimental  data, whereas each quadrant on the right hand side represents a differ-  ent calculation, as indicated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' The theoretical two dimensional EMDs  were convoluted as described in the Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' 3 caption.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' The DFT quan-  drant includes the Brillouin zone boundary as well as the projected  2D high symmetry points (denoted with overlines).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' The experimen-  tal data are from Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' [8].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='  the 2D projected occupancy of the different calculations and  experiment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' The DFT results give good agreement in cer-  tain regions, but is overall worse than the DFT+DMFT as ex-  pected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' The size of DFT+DMFT hexagonal occupancy weight  around Γ is in excellent agreement with the experimental 2D  projected occupancy, as previously established.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' However, it  is clear that the DFT+DMFT is unable to predict the signiﬁ-  cant additional occupation feature surrounding the hexagonal  region which gives rise to elongated black ellipsoidal region  centred around M, with the major axis of this ellipsoid along  the M—K path.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Next, we present the comparison of the di-  rectional differences along the different measured (crystallo-  graphic) directions in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' 5 for the DFT, DFT+DMFT and the  experimental data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' It is clear that the DFT+DMFT results are  superior in agreement with the experiment compared with the  DFT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='  Thus far, the origin of the features measured in the ex-  perimental techniques has been discussed from a theoretical  perspective.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' However, the discrepancy between experimen-  tally measured features by ARPES and Compton still needs to  be addressed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Both of these experiments were performed at  different temperatures with the Compton being at room tem-  perature, whereas the ARPES was measured at 100 K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' There  have been no reported signatures which could be related to  a temperature-dependent Lifshitz transition in the transport  measurements [5] which could have explained this extra fea-  ture in the Compton data at K being related to the Fermi sur-  face.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' However, it should be noted that the spectral weight of  the Pd quasiparticle conduction band would be more broadly  distributed in energy in the room temperature Compton data  than the 100 K ARPES data meaning more spectral weight  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='2  J(pz) (a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='  1)  M  K  DFT  DFT+DMFT  experiment  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='2  J(pz) (a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='  1)  M  22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='2  J(pz) (a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='  1)  M  15  0  1  2  3  4  5  6  pz (a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=')  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='2  J(pz) (a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='  1)  M  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='5  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='  The directional differences ∆J(pz) (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=', the difference  between two Compton proﬁles measured along different crystallo-  graphic directions) as speciﬁed at the bottom right of each panel  where the angle refers to the rotation away from the ΓM direc-  tion towards ΓK.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' These differences are of the DFT, DFT+DMFT,  and the experiment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' The theoretical Compton proﬁles were convo-  luted with a one dimensional (1D) Gaussian of full-width-at-half-  maximum = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='106 a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' to represent the experimental momentum  resolution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' The experimental data are from Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' [8].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='  from the tail of that quasiparticle band would likely be oc-  cupied.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='  It would be strange if the ARPES spectra would  miss a Fermi surface feature at K due to cross-section ef-  fects as it is very unlikely for ARPES not measure the same  band in different regions of the Brillouin zone.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' It is also un-  likely that the ARPES matrix elements effects are suppressing  a Fermi surface feature originating from the Pd quasiparticle  band, although ARPES matrix elements effects do cause some  changes in the measured intensity [12].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' The reduced dimen-  sionality at the surface may enhance the electron correlation  effects within the Mott insulating CrO2 layers at the surface,  similar to that seen in SrVO3 [37–42].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' On the other hand,  there is unlikely any notable contribution from surface states  in the ARPES as these would give additional features [10], not  remove some.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='  Returning to the experimental feature at K, one possible ex-  planation is that this may actually arise from the DFT+DMFT  Pd conduction quasiparticle band at K (and the positions dis-  7  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='0  (eV)  (a)  K  M  min  max  occupancy  (b)  = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='0 eV  = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='1 eV  = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='0 eV  = 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='0 eV  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' (a) The logarithm of DFT+DMFT spectral function with an  additional artiﬁcial broadening term (in energy) along the same path  and colour scale as in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' 1 (b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' This broadening is only applied  to the Pd quasiparticle conduction band centred around K up to the  dashed boundaries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' This broadening term varies quadratically from  zero at the dashed boundaries to a maximum of δ (here it is equal to  1 eV) at K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' There is no physical signiﬁcance to the relation between  the additional broadening and its k-dependence, it just ensures a con-  tinuous change in the broadening.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' (b) The occupancy along this path  obtained from integrating the artiﬁcially broadened spectral function  up to the Fermi level for different maximum δ values given in the  legend.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Both panels help to show how the spectral function (mea-  sured by ARPES) and occupancy (measured by Compton scattering)  are related to each other, along with the different features of the elec-  tronic structure ARPES and Compton scattering would probe.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='  placed along kz) being broader and/or closer to the Fermi level  than predicted in the DFT+DMFT with the feature arising  from the spectral weight spillage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' A computationally inexpen-  sive way to gain some insight into the contribution that this  part of the quasiparticle band would make to the occupancy  is to add an artiﬁcial (and arbitrary) broadening term (in en-  ergy) to this DFT+DMFT Pd quasiparticle conduction band  around the K point as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' 6 (a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' It is clear how dis-  persive this makes the quasiparticle band around K resulting  in additional spectral weight spillage crossing the Fermi level  which gives rise to a more prominent occupancy feature at K  in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' 6 (b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' The occupancy in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' 6 (b) is calculated by  integrating the real-frequency-dependent broadened spectral  function up to the Fermi level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' This feature grows as a func-  tion of increasing δ, which is the maximum of the additional  broadening as explained in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' 6 (b), until exceeding δ = 5  eV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' The occupation for the unbroadened (δ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='0 eV) spectral  function is very similar to the DFT+DMFT (J = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='7 eV) 2D  projected occupancy in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' 3, with the additional smearing in  that occupancy coming from the convolution with the exper-  imental momentum resolution function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' This similarity is to  be expected as this is a quasi-2D electronic structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' We note  that the additional occupation from this broadening violates  charge conservation and as such, the Fermi level would need  to move to compensate for this.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='  This broadened spectral function serves to illustrate how  the feature at K in the experimental Compton data may arise  from this quasiparticle band.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' However, even with the unphys-  ical arbitrary broadening, it is still not enough to fully agree  with the experimental Compton data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' This would suggest that  the shape of this quasiparticle band may need to change with  the dip around K likely being closer to the Fermi level, but its  band centre must remain above the Fermi level to agree with  the established single hexagonal Fermi surface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' We emphasise  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' 6 illustrates how ARPES and Compton probe the elec-  tronic structure differently, in this case around K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' For δ = 1  eV, Compton scattering would probe a distinct occupation fea-  ture around K, but the spectral function at the Fermi level  around K is relatively small in magnitude which may make  it difﬁcult to distinguish in ARPES.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' We note that Lecher-  mann [21] showed that the introduction of relatively large  (electron) doping results in a downward shift in energy of the  Pd quasiparticle band around K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' This will likely give a more  prominent feature in the occupancy feature around K, for the  reasons previously discussed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' However, the PdCrO2 single-  crystal sample measured by Billington et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' were grown by  H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Takatsu as described in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' [43] and were of similar high  purity and quality to those measured by ARPES [10–12] and  quantum oscillations [13, 14].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Therefore, it is highly unlikely  that the measured feature at K in the projected occupation  comes solely from naturally occurring doping effects, but their  contributions cannot be fully ruled out.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='  The Cr 3d DMFT self-energy signiﬁcantly inﬂuences the  Pd quasiparticle conduction band around K due to coupling  between the layers of the localised Cr and itinerant Pd elec-  trons, as discussed in detail by Lechermann [21].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' This type of  coupling is similar to the Kondo effect, but here the localised  spins in PdCrO2 originate from a Mott mechanism which sup-  presses the electron hopping between sites.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' The inclusion of  the DMFT self-energy brings the Pd quasiparticle conduction  band closer to the Fermi level around K and redistributes a  signiﬁcant amount of the Cr 3d contribution to the spectral  function away from this quasiparticle band peak and into the  Hubbard-like bands.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' The disagreement in the occupancy may  stem from inadequacies in the description of the hybridisation  between the Cr 3d and Pd 4d states (which relates to the inter-  layer electron coupling) at the DFT level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' This can be very  sensitive to the exchange-correlation functional used at the  DFT level, as seen for group V and VI elements [44].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Con-  sidering that the Pd states are primarily treated on the DFT  level, higher order electron correlation contributions may in-  ﬂuence the Pd conduction quasiparticle band dispersion and  impact the inter-layer electron coupling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' The correct descrip-  tion of this inter-layer coupling may cause the shape and  broadening of the Pd quasiparticle band to change to give the  (2D projected) occupancy feature at K revealed by Comp-  ton scattering while also being potentially difﬁcult to distin-  guish in ARPES.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' We note that the reduced dimensionality at  the surface could inﬂuence the inter-layer electron coupling  (and other electron correlation effects), which may alter the  Pd quasiparticle conduction band shape and dispersion which  ARPES (potentially) would measure in comparison to what  the Compton scattering bulk-probe measures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' The results of  DFT+DMFT calculations performed with an additional im-  purity site for the Pd 4d orbitals (with the Cr and Pd DMFT  impurities are treated independently) do not signiﬁcantly alter  8  the presented DFT+DMFT results which suggests that the lo-  cal Pd electron correlations are insigniﬁcant when it comes to  explaining the origin of the missing feature around K in the  projected occupations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='  There is increasing amount of experimental evidence show-  ing signiﬁcant inter-layer electron coupling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Transport mea-  surements in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' [5] show that the frustrated Cr spins affect  the out-of-plane and in-plane motion of the conduction elec-  trons in the Pd layer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' The interpretation of the magnetother-  mopower measurements in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' [45] also point to there being  signiﬁcant coupling between the itinerant Pd electrons with  the short-range electron spin-correlations of the Cr electron  spins well above TN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' The short-range electron spin correla-  tions which persisted above TN were also measured by single-  crystal neutron scattering in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' [8].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Further transport mea-  surements have shown the effect of the short-range order on  the Hall and Nernst effects [46].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Raman and electron spin res-  onance (ESR) measurements [47] have also shown evidence  for inter-layer hoppings along the c-axis and a reconstruction  of electronic bands on approaching TN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Recent ARPES [12]  measurements in the antiferromagnetic phase showed that the  measured spectra can be explained by an intertwined excita-  tion consisting of a convolution of the charge spectrum of the  metallic Pd layer and the spin susceptibility of the Mott insu-  lating CrO2 layer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' This excitation arises from an inter-layer  Kondo-like coupling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' The authors of Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' [12] draw parallels  with the results of the doping calculations of the Mott layer  calculated in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' [21] which, as already discussed, signiﬁ-  cantly affects the shape and dispersion of the Pd quasiparti-  cle band at K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' They emphasise that the results of their mea-  surements and the doped DFT+DMFT calculations reﬂect the  fact that in a coupled Mott-itinerant system, the itinerant layer  will support charge excitations [12].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' As the short-range elec-  tron spin correlations persist beyond TN, our interpretation of  the Compton results with respect to the Pd quasiparticle band  ties in with the experimental evidence of the inter-layer elec-  tron coupling, and may be linked to the intertwined excitation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='  Therefore, electron correlation effects which contribute to the  inter-layer electron coupling, such as those in the models used  in Refs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' [12, 48], beyond those included in our DFT+DMFT  calculations, seem to be signiﬁcant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' To conﬁrm that the Pd  conduction quasiparticle band is indeed broader and closer  to the Fermi level than that predicted, the experimental k-  resolved dispersion of that band could, for example, be mea-  sured by pump-probe ARPES or k-resolved inverse photoe-  mission spectroscopy (KRIPES) experiments which can probe  the unoccupied part of the band structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='  IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='  CONCLUSION  We have shown that the paramagnetic DFT+DMFT theo-  retical description of the electronic structure of PdCrO2 is su-  perior to DFT as it gives excellent agreement with the features  relating to the hexagonal Fermi surface sheet measurement by  all the Fermi surface experimental data, all of which agrees  with the picture of the Mott insulating CrO2 layers [4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' How-  ever, there are still discrepancies between the paramagnetic  DFT+DMFT results and the Compton data measured within  the paramagnetic phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' We found that there is no combina-  tion of U and J around the Mott insulator transition (in the  CrO2 layers) in DFT+DMFT which agrees with the presence  of both the hexagonal Fermi surface and the feature around K  as measured by the Compton.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' By adding an unphysical broad-  ening term (in energy) to the DFT+DMFT the Pd quasiparti-  cle conduction band around K, more spectral weight spills  across the Fermi level which gives rise to a more prominent  feature in the occupancy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' However, this is still not enough to  agree with the measured projected occupancy feature in the  Compton data, so a change in both the broadening and shape  of this quasiparticle band is needed while keeping its band  centre above the Fermi level to avoid any changes to the es-  tablished Fermi surface topology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Overall, our DFT+DMFT  results help to clarify the origin of features in the Compton  data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='  From the available experimental and theoretical evidence  thus far, the feature in the projected electron occupancy mea-  sured at K by Compton scattering is likely from the spectral  weight of the Pd conduction quasiparticle band spilling across  the Fermi level and becoming occupied.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' The ARPES may not  measure this proposed spectral weight spillage if the Pd quasi-  particle band is very dispersive around K (and the positions  displaced along kz) and if the surface inﬂuences the electron  correlation effects, such as the inter-layer electron coupling,  which may then alter the quasiparticle band shape and disper-  sion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' As the DFT+DMFT model used does not predict the  measured projected occupation feature at K, theories beyond  our DFT+DMFT are required to establish the exact origin of  this feature, which likely relates to the inter-layer electron  coupling between the Pd and CrO2 layers which gives rise  to new Kondo-like physics such as the previously observed  intertwined excitation [12].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' The discrepancy with the Comp-  ton data gives motivation to experimentally measure the dis-  persion of the unoccupied part of the Pd quasiparticle con-  duction band to determine if it is indeed closer to the Fermi  level and much more smeared in energy than predicted by our  DFT+DMFT calculations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Evidently, Compton scattering is a  powerful probe of many-body electron correlation effects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='  V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='  ACKNOWLEDGEMENTS  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' acknowledges the Doctoral Prize Fellowship  funding and support from the Engineering and Physical Sci-  ences Research Council (EPSRC).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' We are grateful for the use-  ful discussions with J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Laverock, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Favaro-Bedford, Wenhan  Chen, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Mackellar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Calculations were performed using  the computational facilities of the Advanced Computing Re-  search Centre, University of Bristol (http://bris.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='ac.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='uk/acrc/).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='  The VESTA package (https://jp-minerals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='org/vesta/en/) has  been used in the preparation of some ﬁgures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='  9  [1] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Tanaka,  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Hasegawa, and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Takei, Growth and  Anisotropic Physical Properties of PdCoO2 Single Crystals,  Journal of the Physical Society of Japan 65, 3973 (1996).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='  [2] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Tanaka, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Hasegawa, and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Takei, Crystal growth of  PdCoO2, PtCoO2 and their solid-solution with delafossite  structure, Journal of Crystal Growth 173, 440 (1997).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='  [3] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Shannon, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Rogers, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Prewitt, Chemistry of  noble metal oxides.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Syntheses and properties of ABO2 de-  lafossite compounds, Inorganic Chemistry 10, 713 (1971).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='  [4] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Mackenzie, The properties of ultrapure delafossite metals,  Reports on Progress in Physics 80, 032501 (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='  [5] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Takatsu, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Yonezawa, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Michioka, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Yoshimura, and  Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Maeno, Anisotropy in the magnetization and resistivity of the  metallic triangular-lattice magnet PdCrO2, Journal of Physics:  Conference Series 200, 012198 (2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='  [6] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Takatsu, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Yoshizawa, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Yonezawa, and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Maeno, Critical  behavior of the metallic triangular-lattice Heisenberg antiferro-  magnet PdCrO2, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' B 79, 104424 (2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='  [7] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Takatsu, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' N´enert, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Kadowaki, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Yoshizawa, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' En-  derle, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Yonezawa, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Maeno, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Kim, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Tsuji, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Takata,  Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Zhao, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Green, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Broholm, Magnetic structure of the  conductive triangular-lattice antiferromagnet PdCrO2, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='  Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' B 89, 104408 (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='  [8] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Billington, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Ernsting, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Millichamp, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Lester, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='  Dugdale, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Kersh, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Duffy, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Giblin, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Taylor,  P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Manuel, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=', Magnetic frustration, short-range correlations  and the role of the paramagnetic Fermi surface of PdCrO2, Sci-  entiﬁc reports 5, 12428 (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='  [9] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Takatsu, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Yonezawa, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Fujimoto, and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Maeno, Uncon-  ventional Anomalous Hall Effect in the Metallic Triangular-  Lattice Magnet PdCrO2, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' 105, 137201 (2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='  [10] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Sobota, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Kim, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Takatsu, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Hashimoto, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='-K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Mo,  Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Hussain, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Oguchi, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Shishidou, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Maeno, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Min, and  Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='-X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Shen, Electronic structure of the metallic antiferromag-  net PdCrO2 measured by angle-resolved photoemission spec-  troscopy, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' B 88, 125109 (2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='  [11] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='-J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Noh, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Jeong, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Chang, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Jeong, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Moon, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='-J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='  Cho, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Ok, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Kim, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Kim, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Min, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='-K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Lee, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='-  Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Kim, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='-G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Park, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='-D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Kim, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Lee, Direct Observa-  tion of Localized Spin Antiferromagnetic Transition in PdCrO2  by Angle-Resolved Photoemission Spectroscopy, Scientiﬁc Re-  ports 4, 3680 (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='  [12] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Sunko, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Mazzola, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Kitamura, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Khim, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Kushwaha, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='  Clark, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Watson, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Markovi´c, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Biswas, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Pourovskii,  T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Kim, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='-L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Lee, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Thakur, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Rosner, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Georges,  R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Moessner, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Oka, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Mackenzie, and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' King, Prob-  ing spin correlations using angle-resolved photoemission in a  coupled metallic/Mott insulator system, Science Advances 6,  eaaz0611 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='  [13] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Ok, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Jo, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Kim, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Shishidou, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Choi, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='-J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='  Noh, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Oguchi, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Min, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Kim, Quantum Oscillations  of the Metallic Triangular-Lattice Antiferromagnet PdCrO2,  Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' 111, 176405 (2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='  [14] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Hicks, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Gibbs, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Zhao, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Kushwaha, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Borrmann,  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Mackenzie, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Takatsu, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Yonezawa, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Maeno, and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='  Yelland, Quantum oscillations and magnetic reconstruction in  the delafossite PdCrO2, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' B 92, 014425 (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='  [15] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Bansil, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Markiewicz, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Kusko, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Lindroos, and  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Sahrakorpi, Matrix element and strong electron correlation  effects in ARPES from cuprates, Journal of Physics and Chem-  istry of Solids 65, 1417 (2004).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='  [16] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Barbiellini, High-temperature cuprate superconductors stud-  ied by x-ray Compton scattering and positron annihilation spec-  troscopies, Journal of Physics: Conference Series 443, 012009  (2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='  [17] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Dugdale, Probing the Fermi surface by positron annihila-  tion and Compton scattering, Low Temperature Physics 40, 328  (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='  [18] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Lock, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Crisp, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' West, Positron annihi-  lation and Fermi surface studies: a new approach, Journal of  Physics F: Metal Physics 3, 561 (1973).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='  [19] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Robarts, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Millichamp, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Lagos, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Laverock,  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Billington, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Duffy, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' O’Neill, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Giblin, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Tay-  lor, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Kontrym-Sznajd, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Samsel-Czekała, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Bei, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Mu,  G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Samolyuk, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Stocks, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Dugdale, Extreme  fermi surface smearing in a maximally disordered concentrated  solid solution, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' 124, 046402 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='  [20] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Ong and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Singh, Three-dimensional magnetism and  coupling to the conduction electrons in PdCrO2, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' B  85, 134403 (2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='  [21] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Lechermann, Hidden Mott insulator in metallic PdCrO2,  Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Materials 2, 085004 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='  [22] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Lechermann, From basic properties to the Mott design of cor-  related delafossites, npj Computational Materials 7, 120 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='  [23] I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Abrikosov, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Ponomareva, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Steneteg, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Barannikova, and  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Alling, Recent progress in simulations of the paramagnetic  state of magnetic materials, Current Opinion in Solid State and  Materials Science 20, 85 (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='  [24] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' James, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Sekania, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Dugdale, and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Chioncel,  Magnetic Compton proﬁles of Ni beyond the one-particle pic-  ture: Numerically exact and perturbative solvers of dynamical  mean-ﬁeld theory, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' B 103, 115144 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='  [25] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Giuliani and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Vignale, The normal Fermi liquid, in Quan-  tum Theory of the Electron Liquid (Cambridge University Press,  2005) p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' 405–500.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='  [26] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Dewhurst, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Sharma, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Nordstr¨om, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Cricchio,  O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Granas, and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Gross, http://elk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='sourceforge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='net/.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='  [27] O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Parcollet, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Ferrero, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Ayral, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Hafermann, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Krivenko,  L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Messio, and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Seth, TRIQS: A toolbox for research on in-  teracting quantum systems, Comp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' 196, 398  (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='  [28] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' James, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Harris-Lee, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Hampel, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Aichhorn,  and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Dugdale, Wave functions, electronic localization, and  bonding properties for correlated materials beyond the Kohn-  Sham formalism, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' B 103, 035106 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='  [29] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Aichhorn, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Pourovskii, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Vildosola, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Ferrero, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Par-  collet, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Miyake, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Georges, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Biermann, Dynamical  mean-ﬁeld theory within an augmented plane-wave framework:  Assessing electronic correlations in the iron pnictide LaFeAsO,  Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' B 80, 085101 (2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='  [30] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Perdew, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Burke, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Ernzerhof, Generalized gradient  approximation made simple, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' 77, 3865 (1996).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='  [31] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Aichhorn, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Pourovskii, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Seth, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Vildosola, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Zingl,  O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Peil, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Deng, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Mravlje, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Kraberger, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Martins,  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Ferrero, and O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Parcollet, TRIQS/DFTTools: A TRIQS  application for ab initio calculations of correlated materials,  Comp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' 204, 200 (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='  [32] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='  Seth,  I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='  Krivenko,  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='  Ferrero,  and  O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='  Parcollet,  TRIQS/CTHYB: A continuous-time quantum Monte Carlo hy-  bridisation expansion solver for quantum impurity problems,  Comp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' 200, 274 (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='  10  [33] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Korotin, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Anisimov, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Khomskii, and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='  Sawatzky, CrO2: A Self-Doped Double Exchange Ferromag-  net, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' 80, 4305 (1998).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='  [34] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Kraberger, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Triebl, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Zingl, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Aichhorn, Maxi-  mum entropy formalism for the analytic continuation of matrix-  valued Green’s functions, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' B 96, 155128 (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='  [35] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Ernsting, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Billington, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Haynes, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Millichamp, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Taylor,  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Duffy, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Giblin, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Dewhurst, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Dugdale, Calculating  electron momentum densities and Compton proﬁles using the  linear tetrahedron method, Journal of Physics: Condensed Mat-  ter 26, 495501 (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='  [36] Wenhan Chen, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' James, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Dugdale, Local elec-  tron correlation effects on the fermiology of the weak itinerant  ferromagnet ZrZn2, Electronic Structure 4, 045002 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='  [37] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Maiti, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Sarma, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Rozenberg, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Inoue, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Makino,  O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Goto, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Pedio, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Cimino, Electronic structure of  Ca1−xSrxVO3: A tale of two energy scales, Europhysics Let-  ters 10, 246 (2001).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='  [38] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Liebsch, Surface versus Bulk Coulomb Correlations in Pho-  toemission Spectra of SrVO3 and CaVO3, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' 90,  096401 (2003).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='  [39] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Laverock, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Kuyyalil, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Chen, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Singh, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Karlin, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='  Woicik, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Balakrishnan, and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Smith, Enhanced electron  correlations at the SrxCa1−xVO3 surface, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' B 91,  165123 (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='  [40] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Ishida, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Wortmann, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Liebsch, Electronic structure of  SrVO3(001) surfaces: A local-density approximation plus dy-  namical mean-ﬁeld theory calculation, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' B 73, 245421  (2006).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='  [41] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Yoshimatsu, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Okabe, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Kumigashira, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Okamoto,  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Aizaki,  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Fujimori, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Oshima, Dimensional-  crossover-driven metal-insulator transition in SrVO3 ultrathin  ﬁlms, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' 104, 147601 (2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='  [42] Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Zhong, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Wallerberger, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Tomczak, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Taranto, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Par-  ragh, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Toschi, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Sangiovanni, and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Held, Electronics with  Correlated Oxides: SrVO3/SrTiO3 as a Mott Transistor, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='  Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' 114, 246401 (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='  [43] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Takatsu and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Maeno, Single crystal growth of the metal-  lic triangular-lattice antiferromagnet PdCrO2, Journal of Crys-  tal Growth 312, 3461 (2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='  [44] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Harris-Lee, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' James, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Dugdale, Sensitivity  of the Fermi surface to the treatment of exchange and correla-  tion, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' B 103, 235144 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='  [45] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Arsenijevi´c, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Ok, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Robinson, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Ghannadzadeh, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='  Katsnelson, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Kim, and N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Hussey, Anomalous magne-  tothermopower in a metallic frustrated antiferromagnet, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='  Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' 116, 087202 (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='  [46] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Daou, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Fr´esard, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' H´ebert, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Maignan, Impact  of short-range order on transport properties of the two-  dimensional metal PdCrO2, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' B 92, 245115 (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='  [47] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Glamazda, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='-J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Lee, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='-H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Do, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='-Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Choi, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Lemmens,  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' van Tol, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Jeong, and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='-J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Noh, Collective excitations in the  metallic triangular antiferromagnet PdCrO2, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' B 90,  045122 (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='  [48] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' McRoberts, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Mendez-Valderrama, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Moessner, and  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content=' Chowdhury, An intermediate-scale theory for electrons cou-  pled to frustrated local-moments 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='48550/ARXIV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='2207.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
+page_content='10087  (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NA0T4oBgHgl3EQfNP9P/content/2301.02143v1.pdf'}
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+Scalable Quantum Error Correction for Surface Codes using FPGA
+Namitha Liyanage, Yue Wu, Alexander Deters and Lin Zhong
+Department of Computer Science, Yale University, New Haven, CT
+Abstract
+A fault-tolerant quantum computer must decode and correct
+errors faster than they appear. The faster errors can be cor-
+rected, the more time the computer can do useful work. The
+Union-Find (UF) decoder is promising with an average time
+complexity slightly higher than O(d3). We report a distributed
+version of the UF decoder that exploits parallel computing re-
+sources for further speedup. Using an FPGA-based implemen-
+tation, we empirically show that this distributed UF decoder
+has a sublinear average time complexity with regard to d,
+given O(d3) parallel computing resources. The decoding time
+per measurement round decreases as d increases, a ﬁrst time
+for a quantum error decoder. The implementation employs
+a scalable architecture called Helios that organizes parallel
+computing resources into a hybrid tree-grid structure. Using
+Xilinx’s cycle-accurate simulator, we present cycle-accurate
+decoding time for d up to 15, with the phenomenological
+noise model with p = 0.1%. We are able to implement d
+up to 7 with a Xilinx ZC106 FPGA, for which an average
+decoding time is 120 ns per measurement round. Since the
+decoding time per measurement round of Helios decreases
+with d, Helios can decode a surface code of arbitrarily large
+d without a growing backlog.
+1
+Introduction
+The high error rates of quantum devices pose a signiﬁcant ob-
+stacle to the realization of a practical quantum computer. As a
+result, the development of effective quantum error correction
+(QEC) mechanisms is crucial for the successful implementa-
+tion of a fault-tolerant quantum computer.
+One promising approach for implementing QEC is the use
+of surface codes [1–3] in which information of a single qubit
+(called a logical qubit) is redundantly encoded across many
+physical data qubits, with a set of ancillary qubits interacting
+with the data qubits. By periodically measuring the ancillary
+qubits, one can detect and potentially correct errors in physical
+qubits.
+Once the presence of errors has been detected through
+the measurement of ancillary qubits, a classical algorithm, or
+decoder, guesses the underlying error pattern based on the
+measurement results. The faster errors can be corrected, the
+more time a quantum computer can spend on useful work.
+Due to the error rate of the state of the art qubits, very large
+surface codes (d > 25) are necessary to achieve fault-tolerant
+quantum computing [2, 4, 5]. See §2 for more background.
+As surveyed in §3, previously reported decoders capable
+of decoding errors as fast as measured, or backlog-free, either
+exploit limited parallelism [6, 7], or sacriﬁce accuracy [8, 9].
+The largest d reported for any backlog-free implementations
+is 5 [6], based on a design that is physically infeasible beyond
+d = 5.
+In this paper we report a distributed Union-Find (UF) de-
+coder (§4) and its FPGA implementation called Helios (§5).
+Given O(d3) parallel resources, our decoder achieves sublin-
+ear average time complexity according to empirical results
+for d up to 15, the ﬁrst to the best of our knowledge. No-
+tably, adding more parallel resources will not reduce the time
+complexity of the decoder, due to the inherent nature of error
+patterns. Our decoder is a distributed design of and logically
+equivalent to the UF decoder ﬁrst proposed in [10]. We im-
+plement the distributed UF decoder with Helios, a scalable
+architecture for organizing the parallel computation units.
+Helios is the ﬁrst architecture of its kind that can scale to
+arbitrarily large surface codes by exploiting parallelism at
+the vertex level of the model graph. In §6, we report experi-
+mental validations of the distributed UF decoder and Helios
+with a ZCU106 FPGA board [11] which is capable of run-
+ning surface codes up to d = 7. For d = 7 the decoder has
+an average decoding time of 120 ns per measurement round,
+faster than any existing decoder. We validate our design for
+surface codes of d > 7 by using Xilinx Vivado cycle accurate
+simulator [12]. These validations successfully demonstrate,
+for the ﬁrst time, a decoder design with decreasing average
+time per measurement round when d increases. This shows
+evidence that the decoder can scale to arbitrarily large surface
+codes without a growing backlog.
+arXiv:2301.08419v1  [quant-ph]  20 Jan 2023
+
+2
+Background
+2.1
+Qubit and Errors
+Qubit is the basic unit of quantum computing which is rep-
+resented as |ψ⟩ = α|0⟩ + β|1⟩. Here α and β are complex
+numbers such that |α|2 + |β|2 = 1 and |0⟩ and |1⟩ are the
+basis states of a qubit.
+Unlike classical bits, qubits are highly susceptible to er-
+rors. A qubit can unintentionally interact with its surrounding
+resulting in a change of its quantum state. Even the latest
+quantum computers still have an error rate of 10−3 [4] which
+is signiﬁcantly worse than classical computers which have
+error rates lower than 10−18. In contrast a useful quantum
+application requires an error rate of 10−15 or below necessi-
+tating error correction. Errors in qubits can be modeled as
+bit ﬂip errors and phase ﬂip errors. A bit ﬂip is marked by
+the X operator, i.e., X|ψ⟩ = β|0⟩+α|1⟩, while a phase ﬂip is
+marked by Z operator, i.e., Z|ψ⟩ = α|0⟩−β|1⟩ .
+2.2
+Error Correction and Surface Code
+Quantum Error Correction (QEC) is more challenging than
+classical error correction due to the nature of Quantum bits.
+First, qubits cannot be copied to achieve redundancy due to
+the no-cloning theorem. Second, the value of the qubits cannot
+be directly measured as measurements perturb the state of
+qubits. Therefore QEC is achieved by encoding the logical
+state of a qubit, as a highly entangled state of many physical
+qubits. Such an encoded qubit is called a logical qubit.
+The surface code is the widely used error correction code
+for quantum computing due to its high error correction capa-
+bility and the ease of implementation due to only requiring
+connectivity between adjacent qubits. A distance d surface
+code is a topological code made out of a (2d −1)×(2d −1)
+array of qubits as shown in Figure 1. A key feature of surface
+codes is that a larger d can exponentially reduce the rate of
+logical errors making them advantageous. For example, even
+if the physical error rate is 10 times below the threshold, d
+should be greater than 17 to achieve a logical error rate below
+10−10 [2].
+A surface code contains two types of qubits, namely data
+qubits and ancilla qubits. The data qubits collectively encode
+the logical state of the qubit. The ancilla qubits (called X-type
+and Z-type) entangle with the data qubits and by periodically
+measuring the ancilla qubits, physical errors in all qubits can
+be discovered and corrected. An X error occurring in a data
+qubit will ﬂip the measurement outcome of Z ancilla qubits
+connected with the data qubit and Z error will ﬂip the X ancilla
+qubits likewise. Such a measurement outcome is called non-
+trivial measurement value. Because ancilla qubits themselves
+could also suffer from physical qubit errors, multiple rounds
+of measurements are necessary. Figure 2 shows some example
+physical qubit errors occurring in a surface code and how
+Z
+Z
+Z
+Z
+Z
+Z
+X
+X
+X
+X
+X
+X
+X
+X
+X
+X
+Z
+Z
+Z
+Z
+Z
+Z
+Z
+Z
+X
+X
+X
+X
+X
+X
+X
+X
+X
+X
+Z
+Z
+Z
+Z
+Z
+Z
+d = 3
+d = 3
+(a)
+Z
+Z
+Z
+Z
+S
+A
+B
+C
+D
+A
+B
+C
+D
+S
+|0
+Z
+(b)
+X
+X
+X
+X
+S
+A
+B
+C
+D
+A
+B
+C
+D
+S
+|+
+X
+(c)
+Figure 1: (a) : CSS surface code (d = 3), a commonly used type of surface
+code. The white circles are data qubits and the black the Z-type and X-type
+ancillas. (b) and (c) : Measurement circuit of Z-type and X-type ancillas.
+Excluding the ancillas in the border, each Z-type and X-type ancilla interacts
+with 4 adjacent data qubits.
+X
+(a)
+Z
+(b)
+X
+X
+X
+(c)
+X
+X
+X
+(d)
+Round 1
+Round 2
+Round 3
+X
+X
+M
+M
+time
+(e)
+(f)
+Figure 2: (a) to (d) : Various error patterns on d = 3 surface code. X and Z
+mark the corresponding physical qubit errors. Ancillas reporting non trivial
+measurements are shown in red. The red lines are to visualize error chains.
+(a) isolated X error (b) isolated Z error (c) error chain of three X errors (d)
+error chain introducing a logical error which has no non-trivial measurements.
+Note that even though (a) and (c) are different error patterns, they produce
+the same syndrome. (e) Error patterns spread across multiple measurement
+rounds. Here single X and Z errors can also spread across two rounds and
+error chains can include measurement errors (indicated by ‘M’) as well. (f)
+Decoding graph with vertices with nontrivial measurement marked red for
+the error pattern in (e).
+they are detected by ancilla qubits. We show X and Z errors
+separately because they can be independently dealt with in
+the same way. The outcomes from these multiple rounds of
+measurements of ancilla qubits constitute a syndrome.
+A syndrome can be conveniently represented by a graph
+called decoding graph in which a vertex represents a measure-
+ment outcome of an ancilla and an edge a data qubit. Vertices
+of nontrivial measurement outcome are specially marked. The
+weight of edge is determined by the probability of error in
+the corresponding data qubit or measurement. For distance
+d surface code, there are d ×(d −1) vertices. This decoding
+graph can be extended to three dimensional in which multi-
+ple identical planar layers are stacked on each other. Each
+layer represents a round of measurement. The total number of
+rounds is usually the same as the distance of the surface code.
+Corresponding vertices in adjacent layers are connected by
+edges which represent the probability of measurement error
+of the corresponding ancilla. That is, there are d ×d ×(d −1)
+vertices in this three-dimensional graph. Figure 2f shows the
+decoding graph for a syndrome from d = 3 surface code.
+2
+
+2.3
+Error Decoders
+Given a syndrome, an error decoder identiﬁes the underlying
+error pattern, which will be used to generate a correction
+pattern. As multiple error patterns can generate the same
+syndrome, the decoder has to make a probabilistic guess of
+the underlying physical error. The objective is that when the
+correction pattern is applied, the chance of the surface code
+entering a different logical state (i.e a logical error) will be
+minimized.
+Metrics
+The two important aspects of decoders are accu-
+racy and speed. A decoder must correct errors faster than
+syndromes are produced to avoid a backlog. A faster decoder
+also allows more time for the quantum hardware to do actual
+useful work. The average decoding time per measurement
+round is a widely used criteria for speed.
+A decoder must make careful tradeoff between speed and
+accuracy. A faster decoder with lower accuracy requires a
+larger d to achieve any given logical error rate, which may
+require more computation overall.
+Union-Find (UF) Decoder
+The UF decoder is a fast sur-
+face code decoder design ﬁrst described by Delfosse and
+Nickerson [10]. According to [13], it can be viewed as an
+approximation to the blossom algorithm that solves minimum-
+weight perfect matching (MWPM) problems. It has a worst
+case time complexity of O(d3α(d)), where α is the inverse
+of Ackermann’s function, a slow growing function that is less
+than three for any practical code distances. Based on our anal-
+ysis, it has an average case time complexity slightly higher
+than O(d3).
+algorithm 1 describes the UF decoder. It takes a decoding
+graph G(V,E) as input. Each edge e ∈ E has a weight and a
+growth, denoted by e.w and e.g, respectively. e.g is initialized
+with 0 and the decoder may grow e.g until it reaches e.w.
+When that happens, we say the edge is fully grown.
+The decoder maintains a set of odd clusters, denoted by
+L. L is initialized to include all {v} that v ∈ V is non-trivial
+(L81). Each cluster C keeps track of whether its cardinality is
+odd or even as well as its root element.
+The UF decoder iterates over growing and merging the
+odd cluster list until there are no more odd clusters (inside
+the while loop of algorithm 1). Each iteration has two stages:
+Growing and Merging. In the Growing stage, each odd cluster
+“grows” by increasing the growth of the edges incidental to its
+boundary. This process creates a set of fully grown edges F
+(L86 to L95). The Growing stage is the more time-consuming
+step as it requires traversing all the edges in the boundary of
+all the odd clusters and updating the global edge table. Since
+the number of edges is O(d3), the UF decoder is not scalable
+for surface codes with large d.
+In the Merging stage, the decoder goes through each fully-
+grown edge to merge the two clusters connected by the edge.
+Algorithm 1: Union Find Decoder
+input :A decoding graph G(V,E) with X (or Z) syndrome
+output :A correction pattern
+77 % Initialization
+78 for each v ∈ V do
+79
+if v is non-trivial then
+80
+Create a cluster {v}
+81
+end
+82 end
+83 while there is an odd cluster do
+84
+% Growing
+85
+F ← /0
+86
+for each odd cluster C do
+87
+for each e =< u,v >, u ∈ C,v ̸∈ C do
+88
+if e.growth < e.w then
+89
+e.growth ← e.growth+1
+90
+if e.growth = e.w then
+91
+F ← F ∪{e}
+92
+end
+93
+end
+94
+end
+95
+end
+96
+% Merging
+97
+for each e =< u,v >∈ F do
+98
+UNION(u, v)
+99
+end
+100 end
+101 Build correction within each cluster
+When two clusters merge, the new cluster may become even.
+When there is no more odd cluster, the decoder ﬁnds a
+correction within each cluster and combines them to produce
+the correction pattern (L101).
+3
+Related Work
+There is a large body of literature on fast QEC decoding, e.g.,
+[14–16]. The most related are solutions that leverage parallel
+compute resources.
+Fowler [17] describes a method for decoding at the rate of
+measurement (O(d)). The proposed design divides the decod-
+ing graph among specialized hardware units arranged in a grid.
+Each unit contains a subset of vertices and can independently
+decode error chains contained within it. The design is based
+on the observation that large error patterns spanning multiple
+units are exponentially rare, so inter-unit communication is
+not frequently required. It, however, paradoxically assumes
+that the number of vertices per unit is “sufﬁcient large” and
+a unit can ﬁnd an MWPM for its vertices within half the
+measurement time on average. Not surprisingly, to date, no
+implementation or empirical data have been reported for this
+work. Our approach distributes computation to a vertex-level
+and leverages the same observation that communication be-
+tween distant vertices is infrequent.
+NISQ+[8] and QECOOL[9] parallelize computation at the
+ancilla level, where all vertices in the decoding graph repre-
+senting measurements of one ancilla are handled by a single
+3
+
+compute unit. This results in an increase in decoding time
+per measurement round as d increases. In contrast we allo-
+cate a processing element per each vertex, which results in
+decreasing decoding time per measurement round with d at
+the expense of number of parallel units growing O(d3). Fur-
+thermore, they both implement the same greedy decoding
+algorithm that has much lower accuracy than the UF decoder
+used in this work. QECOOL has an accuracy that is approx-
+imately four orders of magnitude lower than that of a UF
+decoder [7] and NISQ+ ignores measurement errors further
+lowering its accuracy than QECOOL.
+Skoric et al. [18] propose a method of using measurement
+round-level parallelism, in which a decoder waits for a large
+number of measurement rounds to be completed and then
+decodes multiple blocks of measurement rounds in parallel.
+By using sufﬁcient parallel resources this method can achieve
+a rate of decoding faster than the rate of measurement. How-
+ever, the latency of this approach grows with the number of
+measurement rounds the decoder needs to batch to achieve
+a throughput equal to the rate of measurement. In contrast,
+our approach exploits vertex-level parallelism and completes
+decoding of every d rounds of measurements with an average
+latency that grows sublinearly with d.
+Pipelining can be considered a special form of using com-
+pute resources in parallel, i.e., in different pipeline stages.
+AFS [7] is a UF decoder architected in three pipeline stages.
+The authors estimate the decoder will have a 42 ns latency
+for d = 11 surface code, which is three times lower than what
+we report based on implementation and measurement. The
+authors assume a specialized hardware that is capable of run-
+ning at 4 GHz and as a result, the decoding latency will be
+dominated by memory access. However, no implementation
+or cycle-accurate simulation is known for this decoder. Im-
+portantly, pipelining is limited in how much parallelism it can
+leverage: the number of pipeline stages. In contrast, paral-
+lelism of our decoder grows along d3, which enables us to
+achieve a sublinear average case latency.
+LILLIPUT [6] is a three stage look-up-table based decoder
+similar to AFS. Look-up-table based decoders can achieve
+fast decoding but are not scalable beyond d = 5 as the size
+of the look-up table grows O(2d3). For d = 7 surface code
+with 7 measurement rounds, it would require a memory of
+2168 Bytes, which is infeasible in any foreseeable future.
+4
+Distributed UF Decoder Design
+Our goal to build a QEC decoder is scalability to the number
+of qubits. As surface codes can exponentially reduce logical
+error rate with respect to d, larger surface codes with hundreds
+or even thousands of qubits are necessary for fault-tolerant
+quantum computing. Therefore, the average decoding time
+per measurement round should not grow with d, to avoid
+exponential backlog for any larger d.
+We choose the UF decoder for two reasons. First, it has
+much lower time complexity than the MWPM algorithm. Al-
+though in general the UF decoder achieve lower decoding
+accuracy than MWPM decoders, it is as accurate in many
+interesting surface codes and noise models [13]. Second, the
+UF decoder maintains much less intermediate states, which
+makes it easier to implement in a distributed manner. We
+observe that growing stage from L86 to L95 in algorithm 1
+operates on each vertex independently without dependencies
+from other vertices. A vertex requires only the parity of the
+cluster it is a part of for the growing stage. Second, during
+the merging stage, a vertex only needs to interact with its
+immediate neighbors (L98).
+Like the original UF decoder, our distributed UF decoder
+is also based on the decoding graph. Logically, the distributed
+decoder associates a processing element (PE) with each ver-
+tex in the decoding graph. Therefore, When describing the
+distributed decoder, we often use PE and vertex in an inter-
+exchangeable manner. PEs operate with the same algorithm,
+speciﬁed by algorithm 2. The PE algorithm iterates over three
+stages.
+4.1
+PE States
+A PE has direct read access to its local states and some states
+of incident PEs. A PE can only modify its local states.
+Thanks to the decoding graph, a PE has immediate access
+to the following objects.
+• v, the vertex it is associated with.
+• v.E, the set of edges incident to v.
+• v.U, the set of vertices that are incident to any e ∈ v.E. We
+say these vertices are adjacent to v.
+The algorithm augments the data structures of vertex and
+edge of the decoding graph, according to the UF decoder
+design [10]. For each vertex v ∈ V, the following information
+is added
+• id : a unique identity number which ranges from 1 to n
+where n = |V|. id is statically assigned and never changes.
+• m is a binary indicating whether the measurement outcome
+is trivial (false) or not (true). m is initialized according
+to the syndrome.
+• cid: a unique integer identiﬁer for the cluster to which v
+belongs to, and is equal to the lowest id of all the vertices
+inside the cluster. The vertex with this lowest id is called
+the cluster root. v.cid is initialized to be v.id. That is, each
+vertex starts with its own single-vertex cluster. When cid =
+id, the vertex is a root of a cluster.
+• odd is a binary indicating whether the cluster is odd. odd
+is initialized to be m.
+• codd is a copy of odd.
+• stage indicates the stage the PE currently operates in
+4
+
+• busyis a binary indicating whether the PE has any pending
+operations.
+For each edge e ∈ E, the decoder maintains e.growth, which
+indicates the growth of the edge, in addition to e.w, the weight.
+e.growth is initialized as 0. The decoder grows e.growth
+until it reaches e.w and e becomes fully grown.
+For clarity of exposition, we introduce a mathematical
+shorthand v.nb, the set of vertices connected with v by full-
+grown edges, i.e., v.nb={u|e = ⟨v,u⟩ ∈ v.E & e.growth=
+e.w}. We call these vertices the neighbors of v. Note neigh-
+bors are always adjacent but not all adjacent vertices are neigh-
+bors.
+4.2
+Shared memory based communication
+We use coherent shared memory for shared state that has a
+single writer. For all shared memories, given the coherence,
+a read always returns the most recently written value. Like
+ordinary memory, we also assume both read and write are
+atomic.
+• memory read/write for PE (v) and read-only for adjacent
+PEs, i.e., ∀u ∈ v.U. v.cid and v.odd reside in this memory
+(S1).
+• memory read/write for PE (v) and read-only for the con-
+troller. The PE local states, v.codd, v.stage and v.busy
+reside in this memory (S2).
+• memory for e.growth, which can be written by incident
+PEs (S3).
+• memory read/write for the controller and read-only for all
+PEs. The controller state global_stage is stored in this
+memory (S4).
+4.3
+Message based communication
+Only instance in our decoder where a PE needs to commu-
+nicate with a distant PE is when a PE needs to notify the
+root when joining a new cluster (L32). Implementing this
+using shared memory is costly because the PE is not neces-
+sarily adjacent to the root. As there is one type of message in
+our decoder, each message M contains only the destination of
+the message. The destination take value from 1 to n, which
+represents the vertex identiﬁer.
+For the correctness of the decoder we only assume guaran-
+teed delivery of messages and do not assume a time bound
+for message delivery.
+4.4
+PE Algorithm
+All PEs iterate over three stages of operation. Within each
+stage, they operate independently but transit from one stage to
+the next when the controller updates global_stage. When a
+PE enters a stage, it sets v.stage accordingly and keep v.busy
+Algorithm 2: Algorithm for vertex v in the distributed
+UF decoder.
+1 v.cid ← v.id; v.odd ← v.m
+2 while true do
+3
+if global_stage =terminate then
+4
+return
+5
+end
+6
+growing(v)
+7
+merging(v)
+8
+syncing(v)
+9 end
+as true until it ﬁnishes all work in the stage. The controller
+uses these two pieces of information from all PEs to determine
+if a stage has started and completed, respectively (See §4.5).
+We next describe the three stages of the PE algorithm.
+In the Growing stage, vertices at the boundary of an odd
+cluster increase e.growth for boundary edges (L16). As PEs
+perform Growing simultaneously, two adjacent PEs may com-
+pare e.w and e.growth and update e.growth for the same e.
+Such compare-and-update operations must be atomic to avoid
+data race.
+In the Merging stage, two clusters connected through a
+fully-grown edge merge by adopting the lower cluster id (cid)
+of theirs. To achieve this each PE compares its cid with PEs
+connected through fully-grown edges (L31). If the other in-
+cident vertex of a fully grown edge has a lower cid the PE
+adopts the lower cid as its own (L31). Merging process con-
+tinues until every PE in the cluster have the same cid which
+is the lowest v.id of the cluster. This procedure is related to
+leader election in a distributed systems: vertices in a newly
+formed cluster must adopt the lowest id. The Merging stage
+also calculates the parity of the cluster. Each PE representing
+a non-trivial measurement (m is true) messages the root of
+the cluster it joins (L32). Likewise, the root updates its parity
+when it receives a message from a PE (L38).
+In the Syncing stage, a root broadcasts its v.odd to all PEs
+in its cluster, which is necessary for the next Growing stage.
+We achieve this using a modiﬁed version of the ﬂooding
+algorithm, which uses shared memory instead of message
+passing. Every non-root node initially set its v.odd as false
+and continues comparing v.odd with PEs with fully connected
+edges. If any of the PEs connected with a fully grown edge has
+v.odd as true the PE set its v.odd as true (L53). If a cluster
+has v.odd as truein the root, this results in propagating true
+to all vertices in the cluster similar to a ﬂooding algorithm.
+4.5
+Controller Algorithm
+The controller moves all PEs and itself along the three stages.
+In each stage, it checks for v.busy signals and in addition
+in merging stage it checks for outstanding messages. The
+controller determines completion of a stage when all PEs
+have v.busy as false and there are no outstanding messages.
+5
+
+Algorithm 3: Vertex growing algorithm
+10 function growing(vertex v)
+11
+Wait until global_stage=growing
+12
+v.busy← true; v.stage← growing
+13
+if v.odd then
+14
+for each e = ⟨u,v⟩ ∈ v.E atomic do
+15
+if e.growth< e.w and u.cid ̸= v.cid then
+16
+e.growth← e.growth+1
+17
+end
+18
+end
+19
+end
+20
+v.busy← false;
+21 end
+Algorithm 4: Vertex merging algorithm
+22 function merging(vertex v)
+23
+Wait until global_stage=merging
+24
+v.busy← true; v.stage← merging
+25
+26
+while true do
+27
+if global_stage ̸=merging then return
+28
+29
+if ∃u ∈ v.nb s.t. u.cid < v.cid then
+30
+v.busy← true
+31
+v.cid ← MIN(u.cid|u ∈ v.nb)
+32
+if v.m then send M(v.cid)
+33
+else if ∀u ∈ v.nb,u.cid = v.cid then
+34
+v.busy← false
+35
+end
+36
+37
+for each received message M do
+38
+v.odd ← ¬v.odd
+39
+end
+40
+end
+41 end
+Algorithm 5: Vertex syncing algorithm
+42 function syncing(vertex v)
+43
+v.busy← true; v.stage← syncing
+44
+if v.cid ̸= v.id then v.odd ← false
+45
+v.codd ← v.odd
+46
+47
+while true do
+48
+if global_stage ̸=syncing then return
+49
+50
+if ∀u ∈ v.nb,u.odd = v.odd then
+51
+v.busy← false
+52
+else
+53
+v.odd ← true
+54
+v.busy← true
+55
+end
+56
+end
+57 end
+Upon completion, the controller updates the global_stage
+variable to move to the next stage and the PEs acknowledge
+this update by updating their own v.stage variable.
+The controller also calculates the presence of odd clusters.
+At the end of the syncing stage, it reads the v.odd value of
+Algorithm 6: The controller coordinates all PEs along
+stages and detects the presence of odd clusters.
+58 while true do
+59
+global_stage← growing
+60
+wait until ∀v ∈ V,v.stage= growing
+61
+wait until ∀v ∈ V,v.busy= false
+62
+63
+global_stage← merging
+64
+wait until ∀v ∈ V,v.stage= merging
+65
+wait until ∀v ∈ V,v.busy= false
+66
+wait until no outstanding messages in the system
+67
+68
+global_stage← syncing
+69
+wait until ∀v ∈ V,v.syncing= growing
+70
+wait until ∀v ∈ V,v.busy= false
+71
+72
+if ∀v ∈ V,v.codd = false then
+73
+global_stage← terminate
+74
+return
+75
+end
+76 end
+each vertex. If any vertex has v.odd = true, the controller
+updates the global stage variable to Growing to continue the
+algorithm. Otherwise, it updates it to Terminate to end the
+algorithm.
+4.6
+Time Complexity Analysis
+The worst case time complexity of our distributed UF decoder
+is O(d3). The worst case occurs when parallelism is maxi-
+mally lost in the system; all vertices are non-trivial and merge
+into a single cluster and the root must process all incoming
+messages from all other vertices (L38). However, the occur-
+rence of the worst case scenario is extremely rare as larger
+clusters are exponentially unlikely to occur. Empirical results
+reported in §6 show that average time grows sublinearly with
+d.
+The time complexity of the controller depends on the im-
+plementation of the shared memory for v.busy and checking
+for outstanding messages in the system. As both checks are
+logical OR operators of individual PE information, the most
+efﬁcient implementation is a logical tree of OR operations
+which results in a time complexity of O(log(d)). Thus, the
+overhead of coordination is signiﬁcantly smaller than the
+worst case time complexity.
+PE Communication Complexity
+The communication
+complexity of the shared memory based communication is
+O(d3). The leader election in the Merging stage and the broad-
+casting of v.odd in the Syncing stage are implemented using a
+shared memory based ﬂooding algorithm. The time complex-
+ity of a ﬂooding operation is O(D), where D is the diameter of
+the cluster. Therefore, in the worst case the time complexity
+of ﬂooding messages is O(d3).
+6
+
+The communication complexity of the message based com-
+munication is O(d6). Messages from each trivial measure-
+ment to the root of the cluster is proportional to the number
+of trivial vertices in the cluster and number of changes of cid
+of each vertex. Thus in the worst case there would be O(d6)
+messages and the time complexity will be O(d3).
+5
+Helios Architecture and Implementation
+We next describe Helios, the architecture for the distributed
+UF decoder.
+5.1
+Overview
+Helios organizes PEs and controller in a custom topology that
+combines a 3-D grid and a B+ tree as illustrated by Figure 3
+and explained below.
+• PEs are organized according to the position of vertices
+they represent in the model graph. We assign v.id sequen-
+tially, starting with 1 from bottom left corner and continuing
+in row-major order for each measurement round. Shared
+memory S1 (v.cid and v.odd) and S2 (v.codd, v.stage, and
+v.busy) are added alongside each PE.
+• Shared memory S3 (e.growth) is added to the incident PE
+with the lower id.
+• A link between every two adjacent PEs to read from each
+other’s S1 and for the one with the higher id to read the
+other’s S4. This results in a network of links in a 3-D grid
+topology. As a PE represents a vertex in the model graph,
+a link represents an edge. Broad pink lines in Figure 3
+represent these links.
+• A directional link between two adjacent PEs and between
+PEs with consecutive v.id values for message passing (L32).
+These links are directed from the PE with higher v.id to the
+other and are buffered. They are represented by blue arrows
+in Figure 3.
+• The controller, realized as a tree of control nodes (§5.3).
+The leaf control nodes of the tree contain shared memory
+S4.
+• A link between each PE and the controller for the controller
+to read from S2 and for the PEs to read from S4. Dashed
+orange lines in Figure 3 represent these links.
+5.2
+Message-passing between PEs
+To implement the vertex merging algorithm (algorithm 4), a
+PE may send and receive messages from another PE, which
+is not necessarily adjacent. Helios implements this with the
+directional links and allows a PE to forward messages over
+directional links. The forward logic is trivially simple because
+PE 5
+PE 1
+PE 2
+PE 6
+PE 13
+PE 17
+Control 
+node 
+Control 
+node
+Root 
+control 
+node 
+Control 
+node 
+Controller
+PE 3
+PE 4
+PE 9
+PE 11
+PE 15
+PE 14
+PE 18
+PE 16
+PE 8
+PE 12
+PE 10
+PE 7
+Figure 3: Helios architecture for d=3 surface code for 3 measurement rounds.
+As d=3 surface code has 6 (3 by 2) ancilla qubits, Helios contains of a 3x2x3
+PE array. PE n indicates PE with v.id = n.
+S3
+growth
+grow
+logic_busy
+S3
+mem
+logic
+ PE 1 
+ FIFO 
+growth
+grow
+logic_busy
+S3
+growth
+grow
+logic_busy
+S2
+stage
+codd
+busy
+mem
+logic
+ FIFO 
+mem
+logic
+ FIFO 
+ nonempty 
+growth, odd, cid
+odd, cid
+growth 
+odd 
+cid
+odd 
+cid
+ PE 2 
+odd, cid
+growth, odd, cid
+nonempty
+nonempty
+To/from controller
+ PE 3 
+ PE 7 
+codd 
+busy
+stage
+Figure 4: The bottom left corner of the PE array shown in Figure 3. Only part
+of the logic and memory inside PE 1 is shown : growth (S3) is per edge and
+is stored in the PE with lower id. grow logic (in pink) calculates the updated
+growth value (Figure 5). logic_busy(in green) (Figure 6) is per adjacent PE
+and is used to calculate the busy signal.
+(1) a PE only messages another PE with a lower id per al-
+gorithm 4 and (2) the links are directional from a PE with a
+higher id to that with a lower one.
+We note that the directional links consist of the 3-D grid
+structure, from the edges of the model graph, and additional
+links between PEs with consecutive v.id values, i.e., the “di-
+agonal” ones in Figure 3. The 3-D grid topology is optimal
+for exchanging messages between nearby PEs, which is fre-
+quent. The additional “diagonal” links prevent deadlocks by
+breaking potential circular dependency amongst several PEs,
+e.g., PE 1 to PE 4 in Figure 3.
+7
+
+The directional links between PEs are buffered because a
+PE can receive multiple messages at a time. Because these
+buffers have a ﬁnite size, the sending PE can stall if a buffer
+is full. In §6.2, we show empirical evidence that stall rarely
+happens.
+5.3
+Controller
+Helios implements the controller as a tree of nodes to avoid
+the scalability bottleneck. The controller requires four pieces
+of information from each PE: v.codd, v.stage, v.busy and
+the presence of outstanding messages of the system. Each
+leaf node of the tree is directly connected with a subset of
+PEs. We can consider these PEs as the children of the leaf
+node. Each node in the tree gathers vertex information from
+its children and reports it to the parent. With information
+from all vertices, the root node runs algorithm 6 and decides
+whether to advance the stage.
+We leave height, branching factor and the subset of PEs
+connected to each leaf node as implementation choices. The
+necessary requirement is that the controller should not slow
+down the overall design.
+5.4
+FPGA Implementation
+We next describe an implementation of Helios targeting a
+single FPGA. We choose FPGA for two reasons. It supports
+massively parallel logic, which is essential as the number of
+PEs grows proportional to d3 in our distributed UF design.
+Moreover, it allows deterministic latency for each operation,
+which facilitates synchronizing all the PEs.
+Figure 4 shows a minimal diagram of a PE and a controller
+in the FPGA implementation.
+Controller: Since we only use a single FPGA and evaluate
+with d below 20, a single node controller sufﬁces.
+Directional links: We implement the directional links as
+ﬁrst-in-ﬁst-out (FIFO) buffers, which are mapped by Xilinx
+Vivado to LUT based RAMs. We choose the buffer size of four
+because our evaluations in §6.2 show that increasing the buffer
+size beyond four does not improve decoding time. Reducing
+the buffer size below four slightly increases decoding time
+(by 0.01%) while using the same number of LUTs as memory
+as a buffer of size four (up to 32).
+Shared memory:
+We implement all shared memories as
+FPGA registers, i.e., reg in Verilog. FPGA registers by de-
+sign guarantee that a read returns the last written value. In
+order to ensure that the S4 memory has a single writer, we
+modify the PE logic as shown in Figure 5. Compare and up-
+date operation (L15) is implemented in the PE that the S3
+memory resides in, and the PE increases e.growth by two if
+both endpoints of the edge have v.odd as true.
+Detecting outstanding messages:
+Each PE updates its
+busy state based on pending messages in addition to condi-
+tions in L33 and L50 as shown in the code snippet in Figure 6.
+Adder
+odd[0]
+odd[1]
+Min
+w
+2x1 
+Mux
+==
+stage
+growing
+ grow 
+D
+Q
+Q
+growth
+clk
+reg growth;
+always@(posedge clk)
+if(stage == growing)
+growth <= ‘MIN(growth
++ odd[0] + odd[1], w);
+Figure 5: Circuit diagram of grow sub-module and Verilog implementation.
+This implements the atomic compare and update operation in L15 as part
+of the PE module. odd[0] and odd[1] represents the odd state of the two
+incident PEs of the edge.
+==
+w
+==
+cid[0]
+u∈nb
+cid[i]
+==
+stage
+merging
+==
+odd[0]
+odd[i]
+==
+stage
+syncing
+growth[i]
+assign logic_busy[i] =
+(growth[i] == w &&
+stage == merging
+&& cid[i] != cid[0]) ||
+(growth[i] == w &&
+stage == syncing
+&& odd[i] != odd[0]);
+Figure 6: Circuit diagram of logic_busy sub-module and Verilog imple-
+mentation. The sub-module is implemented per each adjacent PE which are
+indexed from 1 to the number of edges. The variables odd[0] and cid[0]
+represent the odd and cid of the PE, while odd[i], cid[i] and growth[i]
+represent the corresponding values for the ith adjacent PE and the edge
+connecting them.
+The sub-circuit logic_busychecks for the conditions in L33
+and L50 for each incident edge. In our FPGA implementation
+of FIFO buffers, when a value is written to a FIFO (using
+the we signal), nonempty state of the FIFO will be true in
+the next cycle. This results in at least one PE having busy
+as true when there are outstanding messages in the system.
+The controller reads busy every clock cycle to identify the
+completion of a stage.
+In total, our implementation contains approximately 6000
+lines of Verilog code. The code is available at [19].
+On the ZCU106 FPGA development board [11], we are
+able to support the distributed UF decoder with d up to 7,
+due to resource limits. Table 1 shows the resource usage for
+various d. While the numbers of vertices and edges grow
+by O(d3), the resource usage grows faster for the following
+reasons. First, resource usage by a PE grows due to the in-
+crease of bitwidth required for v.id, and v.cid. A PE for d = 7
+with six adjacent PEs requires 182 LUTs and a similar PE for
+d = 3 requires only 127 LUTs. Second, PEs on the surface
+of the three-dimensional array as shown in Figure 3 use less
+resources than those inside because the latter have more in-
+cident edges. When d increases a higher portion of PEs are
+inside the array.
+We ﬁnd that LUTs are the most critical resource in the
+FPGA for our design. It may be possible to run a design with
+d = 15 on a Xilinx VU19 FPGA [20], which currently has
+the highest number of LUTs among commercially available
+FPGAs at the time of this writing.
+Existing commercial FPGAs like ZCU106 often dedicate
+a lot of silicon to digital signal processing (DSP) units and
+block RAMs (BRAMs). However, our design does not use
+8
+
+Table 1: Resource usage of Helios on ZCU106 FPGA board for various code
+distances
+d
+# of LUTs
+# of
+registers
+as logic
+as memory (FIFOs)
+3
+2419
+608
+1187
+5
+18655
+3236
+7189
+7
+61793
+12636
+27664
+any DSPs because it only requires comparison operators and
+ﬁxed point additions. Our design does not use any BRAMs
+because the FIFOs have a depth of four and can be efﬁciently
+implemented using LUTs. Each BRAM tile in Xilinx has a
+default size of 18 Kbits and using BRAM for FIFOs would re-
+sult in signiﬁcant unused space in each BRAM tile. Therefore,
+an ideal FPGA designed to run our distributed UF decoder
+would be simpler than current large FPGAs, as it would only
+need a large number of LUTs, no DSP units and a limited
+amount of BRAM.
+6
+Evaluation
+The main objective of our evaluation is to assess the scalability
+of our distributed UF implementation. To that end, we ﬁrst
+describe our methodology and then show that the latency of
+our implementation grows sub-linearly with respect to the
+surface code size d.
+6.1
+Methodology
+For speed, we measure the number of cycles required to de-
+code a syndrome. To evaluate correctness, we compare the
+result of clustering generated by our distributed UF decoder
+with the clustering generated by the original UF decoder. We
+compare clusters because the original UF decoder and ours
+only differ in the clustering process. This shows that both
+decoders generate identical clusters in all cases tested, con-
+ﬁrming the correctness of our decoder. In the rest of our
+evaluation, we will focus only on the speed of the distributed
+UF decoder and not on the accuracy of its results.
+Experimental Setup
+We use two setups to evaluate our
+FPGA implementation. The primary setup is a Xilinx
+ZCU106 FPGA development board [11], which is capable
+of handling surface codes with d up to 7. As an alternative
+setup, we run our implementation on the Xilinx Vivado simu-
+lator [12], which emulates the behavior of FPGA in a cycle-
+accurate manner, allowing us to evaluate the performance of
+our implementation for surface codes of any size. We simu-
+lated up to d = 15 as this is the upper bound of d possible in
+the largest FPGA currently available [20].
+We also compare the results obtained from the Vivado
+simulator with those obtained from the FPGA development
+board for surface code sizes 7 and smaller, to gain conﬁdence
+in the correctness of the simulator itself.
+Noise Model
+We use the phenomenological noise model [1]
+that accounts for errors in both data and ancilla qubits. As
+decoding for X-errors and Z-errors are independent and iden-
+tical, we only focus on decoding X-errors in the evaluation.
+To emulate noise, we independently ﬂip each qubit with
+a probability of p (the physical error rate) between every
+two measurement rounds. This is a widely used approach
+by prior QEC decoders [7, 8, 18]. We then generate the
+syndrome from the physical errors and provides it as input to
+our decoder.
+For most of our experiments, we use as default p = 0.001,
+like other works [7]. This value is reasonable for surface
+codes, as p should be sufﬁciently below the threshold (at least
+ten times lower) to exponentially reduce errors. We note that
+the UF decoder has a threshold of p = 0.026, calculated by
+Delfosse and Nickerson [10].
+6.2
+Decoding Time
+We experimentally show how average time for decoding
+grows with the size of the surface code. Additionally, we
+show the effect of noise and buffer size on the average time.
+Average time
+To demonstrate the scalability of our algo-
+rithm with respect to the size of the surface code, we plot
+the average time for decoding against the size of the surface
+code. In Figure 7 (left) the y-axis shows the average FPGA
+clock cycle count and the x-axis shows the distance (d) of the
+surface code. We obtained these values from running the dis-
+tributed UF decoder on the Vivado simulator where each data
+point represents the average of 1000 trials. We see that for all
+3 physical error rates we tested, average decoding time grows
+sub-linearly with respect to the surface code size, which sat-
+isﬁes the scalability criteria to avoid an exponential backlog.
+This implies that the average time to decode a measurement
+round reduces with increasing d as shown in Figure 7 (right).
+Distribution of decoding time
+To understand the growth
+of decoding time with respect to the code distance, in Fig-
+ure 8a we plot the distribution of decoding time for different
+code distances. The y-axis shows the FPGA clock cycle count
+and the x-axis shows the distance (d) of the surface code. We
+ran both our test setups for this experiment and the distribu-
+tion of FPGA clock cycle count for each surface code size is
+shown in green, while the distribution of clock cycle count
+on the Vivado simulator is shown in gray. The average cycle
+count is indicated with ×.
+Due to resource limitations on the ZCU106 FPGA, we
+are unable to run surface codes with d > 7 on the FPGA.
+9
+
+ 40
+ 60
+ 80
+ 100
+ 120
+ 140
+ 160
+ 180
+ 200
+ 220
+ 240
+ 1
+ 3
+ 5
+ 7
+ 9
+ 11
+ 13
+ 15
+ 17
+decoding time
+code distance (d)
+ p = 0.0005
+p = 0.001
+p = 0.005
+ 6
+ 8
+ 10
+ 12
+ 14
+ 16
+ 18
+ 20
+ 22
+ 1
+ 3
+ 5
+ 7
+ 9
+ 11
+ 13
+ 15
+ 17
+time per measurement round
+code distance (d)
+ p = 0.0005
+p = 0.001
+p = 0.005
+Figure 7: Average decoding time scales sub-linearly with d. We measure the average decoding time for 3 different noise levels using the Vivado simulator.
+(Left) The average decoding time in FPGA clock cycles. (Right) The average decoding time per measurement round in FPGA clock cycles. Average time per
+measurement round reducing continuously justiﬁes that our decoder is scalable for large surface codes. We show the distributions separately in Figure 8a
+For d = 3,5 and 7, the results from the FPGA and those
+from the Vivado simulator agree. The statistical parameters
+such as mean, median, and percentile values(P25, P75, P90)
+differ between running on the FPGA and using the simulator
+by less than 1%. Only noticeable difference is the higher
+maximum observed value on the FPGA, which is caused
+by exponentially unlikely long error chains appearing when
+running for 108 trials in the FPGA. This justiﬁes the use of
+the Vivado simulator to obtain results for large surface codes
+that cannot be mapped to the ZCU 106 FPGA board due to
+resource limitations.
+The key factor determining the decoding time is the number
+of iterations of growing, merging and syncing the distributed
+UF decoder requires. The peaks in the probability distribution
+for each distance in Figure 8a correspond to the number of
+iterations. The variation around each peak is caused by the
+delay due to routing messages. The number of iterations is
+related to the size of the largest cluster, which in turn corre-
+lates with the size of the longest error chain in the syndrome.
+As the size of the surface code increases, the probability of a
+longer error chain also increases, resulting in the probability
+distribution shifting to the right.
+Furthermore, as seen in Figure 8a, the distribution for each
+surface code size is right-skewed. For example, for d = 7,
+90% of trials required two iterations or fewer, which were
+completed within 140 cycles. In the same test, 99.99% of
+trials were completed within 237 cycles. Only a very small
+number of error patterns require long decoding times, corre-
+sponding to syndromes with long error chains. Since such
+syndromes occur rarely and have poor decoding accuracy
+even if the decoding time is bounded, the impact on accuracy
+will be minimal.
+Effect of physical error rate
+To understand the effect of
+the physical error rate on decoding time, in Figure 8b we plot
+the distribution of latency for three different noise levels. We
+obtained this distribution by running on the ZCU106 FPGA
+with 108 trials. The y-axis shows the FPGA clock cycle count
+and the x-axis shows the physical error rate.
+As the noise level increases, the probability distribution
+of latency shifts to the right. This is caused by the increased
+probability of a longer error chain when the physical error rate
+increases, which in turn requires more iterations to decode. As
+a result, the average decoding time increases with the physical
+error rate.
+Effect of buffer size
+To measure the impact of the buffer
+size on decoding time, we varied the buffer size and analyzed
+the latency distribution. In Figure 8c, the x-axis shows the cy-
+cle count and the y-axis shows the cumulative distribution of
+the latency. We varied the buffer size from 1 to 32. Our results
+showed that there was no noticeable difference in latency with
+respect to the buffer size. The obtained results were identical
+for all buffer sizes above 4 and showed a slowdown of less
+than 0.01% for buffer sizes of 1 and 2. This indicates that
+the communication overhead in our design is minimal for the
+average case
+We can explain this result using statistics on the number of
+messages generated. For example, when the physical error rate
+is 0.001 and d = 7, 97.7% of trials are statistically unaffected
+by the buffer size. This includes 46% of trials resulting in
+fully non-trivial syndromes, 47.6% of trials resulting in a
+single qubit error in each cluster, and 4.1% of trials resulting
+in a chain of two qubit errors. In all of these cases, at most a
+single message is generated in each cluster, making the buffer
+size irrelevant. In the remaining 2.3% of trials, the buffer size
+will only affect the results if error chains occur close to each
+other and share a common link in their message paths. In our
+experiments, such congestion occurred in less than 0.1% of
+runs. Therefore, the buffer size can be reduced without any
+signiﬁcant impact on average decoding time.
+10
+
+ 0
+ 50
+ 100
+ 150
+ 200
+ 250
+ 300
+ 350
+ 400
+ 1
+ 3
+ 5
+ 7
+ 9
+ 11
+ 13
+ 15
+ 17
+decoding time
+distance (d)
+(a) Simulator and implementation results agree
+ 0
+ 100
+ 200
+ 300
+ 400
+ 500
+ 600
+ 700
+0.0005
+0.001
+0.005
+decoding time
+physical error rate (p)
+(b) Decoding time grows with physical error rate.
+ 0
+ 50
+ 100
+ 150
+ 200
+ 250
+ 300
+ 350
+ 400
+1
+2
+4
+8
+16
+decoding time
+buﬀer size
+(c) Buffer size does not matter for decoding time.
+Figure 8: Distribution of decoding time with the average marked with ×. For
+each error rate we ran 108 trials. Results from implementation with Xilinx
+ZCU 106 FPGA are in green; those from Xilinx Vivado simulator gray. By
+default d = 7, p = 0.001.
+6.3
+Comparison with related work
+Our empirical results as shown in Figure 8a suggest that He-
+lios has a lower asymptotic complexity than any existing
+MWPM or UF implementation for which asymptotic com-
+plexities are available, e.g., [10, 17]. Indeed, the empirical
+results suggest that our decoder has a sub-linear time complex-
+ity: the decoding time per round decreases with the number
+of measurement rounds, which has never been achieved be-
+fore. This implies that Helios can support arbitrarily large
+d as rate of decoding will always be faster than the rate of
+measurement.
+Das et al [7] calculate an average latency for their AFS de-
+coder based on memory access cycles and assuming a design
+running at 4 GHz. As the number of memory access cycles
+grows quadratically with d, the average decoding time per
+measurement round of AFS grows O(d2). Similarly, Ueno et
+al [9] estimate the decoding time of QECOOL from d = 5
+to d = 13 based on SPICE-level simulations with a clock
+frequency of 5 GHz. For the given range of d the decoding
+time per measurement round increases quadratically with d.
+In comparison, the decoding time of Helios decreases per
+measurement round.
+We should like to point out that AFS and QECOOL assume
+very high clock frequencies, which is key to their estimated
+low latency. For example, for d = 11, AFS and QECOOL
+respectively report latencies of 42 ns and 8.32 ns per measure-
+ment round. Helios, in contrast, requires 107 ns per measure-
+ment round with a 100 MHz clock. In terms of clock cycles,
+Helios requires on average 10.7 cycles for d = 11 surface
+code, lower than both AFS (168 cycles) and QECOOL (41
+cycles).
+To the best of our knowledge, LILLIPUT [6] is the only
+hardware decoder in literature that provides implementation-
+based results, for d = 5. The decoder has an average time of
+21 ns per measurement round, which is shorter than that of
+Helios for d = 5, i.e., 126 ns. However, as analyzed in §3,
+LILLIPUT is not scalable for d > 5. Our work, in contrast,
+has successfully demonstrated the implementation of a d = 7
+surface code on a ZCU106 FPGA with 120 ns per measure-
+ment round. The architecture of Helios can potentially support
+larger d using a larger FPGA, for example d = 15 for Xilinx
+VU19P [20], and even larger d using a network of FPGAs.
+7
+Conclusion
+We describe a distributed design of the Union Find decoder for
+quantum error-correcting surface codes and present Helios, a
+system architecture for realizing it. We report an FPGA-based
+implementation Helios. Using Xilinx Vivaldo cycle-accurate
+simulator, we demonstrate empirically that the average decod-
+ing time of Helios grows sub-linearly with d. Using a ZCU106
+FPGA, we implement the fastest decoding of distance 7 sur-
+face codes, which achieves 120ns average decoding time per
+measurement round. Helios is faster and more scalable than
+any reported implementation of surface code decoder. Our
+results suggest that by leveraging parallel hardware resources,
+Helios can avoid a growing backlog of syndrome measure-
+ments for arbitrarily large surface codes.
+Acknowledgments
+This work was supported in part by Yale University and NSF
+MRI Award #2216030.
+11
+
+References
+[1] E. Dennis, A. Kitaev, A. Landahl, and J. Preskill, “Topological quantum
+memory,” Journal of Mathematical Physics, vol. 43, no. 9, pp. 4452–
+4505, 2002.
+[2] A. G. Fowler, M. Mariantoni, J. M. Martinis, and A. N. Cleland, “Sur-
+face codes: Towards practical large-scale quantum computation,” Phys-
+ical Review A, vol. 86, no. 3, p. 032324, 2012.
+[3] J. P. Bonilla-Ataides, D. K. Tuckett, S. D. Bartlett, S. T. Flammia, and
+B. J. Brown, “The XZZX surface code,” arXiv e-prints, pp. arXiv–2009,
+2020.
+[4] Z. Chen, K. J. Satzinger, J. Atalaya, A. N. Korotkov, A. Dunsworth,
+D. Sank, C. Quintana, M. McEwen, R. Barends, P. V. Klimov, S. Hong,
+C. Jones, A. Petukhov, D. Kafri, S. Demura, B. Burkett, C. Gidney,
+A. G. Fowler, H. Putterman, I. Aleiner, F. Arute, K. Arya, R. Babbush,
+J. C. Bardin, A. Bengtsson, A. Bourassa, M. Broughton, B. B. Buckley,
+D. A. Buell, N. Bushnell, B. Chiaro, R. Collins, W. Courtney, A. R.
+Derk, D. Eppens, C. Erickson, E. Farhi, B. Foxen, M. Giustina,
+J. A. Gross, M. P. Harrigan, S. D. Harrington, J. Hilton, A. Ho,
+T. Huang, W. J. Huggins, L. B. Ioffe, S. V. Isakov, E. Jeffrey, Z. Jiang,
+K. Kechedzhi, S. Kim, F. Kostritsa, D. Landhuis, P. Laptev, E. Lucero,
+O. Martin, J. R. McClean, T. McCourt, X. Mi, K. C. Miao, M. Mohseni,
+W. Mruczkiewicz, J. Mutus, O. Naaman, M. Neeley, C. Neill,
+M. Newman, M. Y. Niu, T. E. O’Brien, A. Opremcak, E. Ostby,
+B. Pató, N. Redd, P. Roushan, N. C. Rubin, V. Shvarts, D. Strain,
+M. Szalay, M. D. Trevithick, B. Villalonga, T. White, Z. J. Yao, P. Yeh,
+A. Zalcman, H. Neven, S. Boixo, V. Smelyanskiy, Y. Chen, A. Megrant,
+and J. Kelly, “Exponential suppression of bit or phase errors with cyclic
+error correction,” Nature, vol. 595, no. 7867, pp. 383–387, Jul 2021.
+[Online]. Available: https://doi.org/10.1038/s41586-021-03588-y
+[5] C. Gidney and M. Ekerå, “How to factor 2048 bit rsa integers in 8 hours
+using 20 million noisy qubits,” Quantum, vol. 5, p. 433, Apr 2021.
+[Online]. Available: http://dx.doi.org/10.22331/q-2021-04-15-433
+[6] P. Das, A. Locharla, and C. Jones, “LILLIPUT: A lightweight
+low-latency lookup-table based decoder for near-term quantum error
+correction,” 2021. [Online]. Available: https://arxiv.org/abs/2108.065
+69
+[7] P. Das, C. A. Pattison, S. Manne, D. Carmean, K. Svore, M. Qureshi, and
+N. Delfosse, “A scalable decoder micro-architecture for fault-tolerant
+quantum computing,” arXiv preprint arXiv:2001.06598, 2020.
+[8] A. Holmes, M. R. Jokar, G. Pasandi, Y. Ding, M. Pedram, and
+F. T. Chong, “NISQ+: Boosting quantum computing power by
+approximating quantum error correction,” 2020. [Online]. Available:
+https://arxiv.org/abs/2004.04794
+[9] Y. Ueno, M. Kondo, M. Tanaka, Y. Suzuki, and Y. Tabuchi, “QECOOL:
+On-line quantum error correction with a superconducting decoder for
+surface code,” in Proc. ACM/IEEE Design Automation Conference
+(DAC), 2021.
+[10] N. Delfosse and N. H. Nickerson, “Almost-linear time decoding algo-
+rithm for topological codes,” arXiv preprint arXiv:1709.06218, 2017.
+[11] Xilinx, “Zynq UltraScale+ RFSoC ZCU106 evaluation kit,” https://ww
+w.xilinx.com/products/boards-and-kits/zcu106.html.
+[12] Vivado
+Design
+Suite
+User
+Guide:
+Logic
+Sim-
+ulation,
+Xilinx
+Inc.,
+04
+2022.
+[Online].
+Avail-
+able: https://www.xilinx.com/content/dam/xilinx/support/document
+s/sw_manuals/xilinx2022_1/ug900-vivado-logic-simulation.pdf
+[13] Y. Wu, N. Liyanage, and L. Zhong, “An interpretation of union-
+ﬁnd decoder on weighted graphs,” 2022. [Online]. Available:
+https://arxiv.org/abs/2211.03288
+[14] B. M. Terhal, “Quantum error correction for quantum memories,”
+Reviews of Modern Physics, vol. 87, no. 2, pp. 307–346, apr 2015.
+[Online]. Available: https://doi.org/10.1103%2Frevmodphys.87.307
+[15] D. Gottesman, “An introduction to quantum error correction and
+fault-tolerant quantum computation,” 2009. [Online]. Available:
+https://arxiv.org/abs/0904.2557
+[16] H. Bombín, Topological codes.
+Cambridge University Press, 2013, p.
+455–481.
+[17] A. G. Fowler, “Minimum weight perfect matching of fault-tolerant
+topological quantum error correction in average O(1) parallel time,”
+2014.
+[18] L. Skoric, D. E. Browne, K. M. Barnes, N. I. Gillespie, and
+E. T. Campbell, “Parallel window decoding enables scalable
+fault tolerant quantum computation,” 2022. [Online]. Available:
+https://arxiv.org/abs/2209.08552
+[19] “Distributed UF on FPGA,” https://github.com/NamiLiy/qec_fpga,
+2022.
+[20] Xilinx, “Virtex UltraScale+ VU19P FPGA,” https://www.xilinx.com
+/content/dam/xilinx/publications/product-briefs/virtex-ultrascale-plu
+s-vu19p-product-brief.pdf.
+12
+
diff --git a/3NFAT4oBgHgl3EQfEBxO/content/tmp_files/load_file.txt b/3NFAT4oBgHgl3EQfEBxO/content/tmp_files/load_file.txt
new file mode 100644
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@@ -0,0 +1,887 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf,len=886
+page_content='Scalable Quantum Error Correction for Surface Codes using FPGA  Namitha Liyanage, Yue Wu, Alexander Deters and Lin Zhong  Department of Computer Science, Yale University, New Haven, CT  Abstract  A fault-tolerant quantum computer must decode and correct  errors faster than they appear.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' The faster errors can be cor-  rected, the more time the computer can do useful work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' The  Union-Find (UF) decoder is promising with an average time  complexity slightly higher than O(d3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' We report a distributed  version of the UF decoder that exploits parallel computing re-  sources for further speedup.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' Using an FPGA-based implemen-  tation, we empirically show that this distributed UF decoder  has a sublinear average time complexity with regard to d,  given O(d3) parallel computing resources.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' The decoding time  per measurement round decreases as d increases, a ﬁrst time  for a quantum error decoder.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' The implementation employs  a scalable architecture called Helios that organizes parallel  computing resources into a hybrid tree-grid structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' Using  Xilinx’s cycle-accurate simulator, we present cycle-accurate  decoding time for d up to 15, with the phenomenological  noise model with p = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='1%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' We are able to implement d  up to 7 with a Xilinx ZC106 FPGA, for which an average  decoding time is 120 ns per measurement round.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' Since the  decoding time per measurement round of Helios decreases  with d, Helios can decode a surface code of arbitrarily large  d without a growing backlog.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  1  Introduction  The high error rates of quantum devices pose a signiﬁcant ob-  stacle to the realization of a practical quantum computer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' As a  result, the development of effective quantum error correction  (QEC) mechanisms is crucial for the successful implementa-  tion of a fault-tolerant quantum computer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  One promising approach for implementing QEC is the use  of surface codes [1–3] in which information of a single qubit  (called a logical qubit) is redundantly encoded across many  physical data qubits, with a set of ancillary qubits interacting  with the data qubits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' By periodically measuring the ancillary  qubits, one can detect and potentially correct errors in physical  qubits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  Once the presence of errors has been detected through  the measurement of ancillary qubits, a classical algorithm, or  decoder, guesses the underlying error pattern based on the  measurement results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' The faster errors can be corrected, the  more time a quantum computer can spend on useful work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  Due to the error rate of the state of the art qubits, very large  surface codes (d > 25) are necessary to achieve fault-tolerant  quantum computing [2, 4, 5].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' See §2 for more background.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  As surveyed in §3, previously reported decoders capable  of decoding errors as fast as measured, or backlog-free, either  exploit limited parallelism [6, 7], or sacriﬁce accuracy [8, 9].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  The largest d reported for any backlog-free implementations  is 5 [6], based on a design that is physically infeasible beyond  d = 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  In this paper we report a distributed Union-Find (UF) de-  coder (§4) and its FPGA implementation called Helios (§5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  Given O(d3) parallel resources, our decoder achieves sublin-  ear average time complexity according to empirical results  for d up to 15, the ﬁrst to the best of our knowledge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' No-  tably, adding more parallel resources will not reduce the time  complexity of the decoder, due to the inherent nature of error  patterns.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' Our decoder is a distributed design of and logically  equivalent to the UF decoder ﬁrst proposed in [10].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' We im-  plement the distributed UF decoder with Helios, a scalable  architecture for organizing the parallel computation units.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  Helios is the ﬁrst architecture of its kind that can scale to  arbitrarily large surface codes by exploiting parallelism at  the vertex level of the model graph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' In §6, we report experi-  mental validations of the distributed UF decoder and Helios  with a ZCU106 FPGA board [11] which is capable of run-  ning surface codes up to d = 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' For d = 7 the decoder has  an average decoding time of 120 ns per measurement round,  faster than any existing decoder.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' We validate our design for  surface codes of d > 7 by using Xilinx Vivado cycle accurate  simulator [12].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' These validations successfully demonstrate,  for the ﬁrst time, a decoder design with decreasing average  time per measurement round when d increases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' This shows  evidence that the decoder can scale to arbitrarily large surface  codes without a growing backlog.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='08419v1  [quant-ph]  20 Jan 2023  2  Background  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='1  Qubit and Errors  Qubit is the basic unit of quantum computing which is rep-  resented as |ψ⟩ = α|0⟩ + β|1⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' Here α and β are complex  numbers such that |α|2 + |β|2 = 1 and |0⟩ and |1⟩ are the  basis states of a qubit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  Unlike classical bits, qubits are highly susceptible to er-  rors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' A qubit can unintentionally interact with its surrounding  resulting in a change of its quantum state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' Even the latest  quantum computers still have an error rate of 10−3 [4] which  is signiﬁcantly worse than classical computers which have  error rates lower than 10−18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' In contrast a useful quantum  application requires an error rate of 10−15 or below necessi-  tating error correction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' Errors in qubits can be modeled as  bit ﬂip errors and phase ﬂip errors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' A bit ﬂip is marked by  the X operator, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=', X|ψ⟩ = β|0⟩+α|1⟩, while a phase ﬂip is  marked by Z operator, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=', Z|ψ⟩ = α|0⟩−β|1⟩ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='2  Error Correction and Surface Code  Quantum Error Correction (QEC) is more challenging than  classical error correction due to the nature of Quantum bits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  First, qubits cannot be copied to achieve redundancy due to  the no-cloning theorem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' Second, the value of the qubits cannot  be directly measured as measurements perturb the state of  qubits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' Therefore QEC is achieved by encoding the logical  state of a qubit, as a highly entangled state of many physical  qubits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' Such an encoded qubit is called a logical qubit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  The surface code is the widely used error correction code  for quantum computing due to its high error correction capa-  bility and the ease of implementation due to only requiring  connectivity between adjacent qubits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' A distance d surface  code is a topological code made out of a (2d −1)×(2d −1)  array of qubits as shown in Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' A key feature of surface  codes is that a larger d can exponentially reduce the rate of  logical errors making them advantageous.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' For example, even  if the physical error rate is 10 times below the threshold, d  should be greater than 17 to achieve a logical error rate below  10−10 [2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  A surface code contains two types of qubits, namely data  qubits and ancilla qubits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' The data qubits collectively encode  the logical state of the qubit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' The ancilla qubits (called X-type  and Z-type) entangle with the data qubits and by periodically  measuring the ancilla qubits, physical errors in all qubits can  be discovered and corrected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' An X error occurring in a data  qubit will ﬂip the measurement outcome of Z ancilla qubits  connected with the data qubit and Z error will ﬂip the X ancilla  qubits likewise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' Such a measurement outcome is called non-  trivial measurement value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' Because ancilla qubits themselves  could also suffer from physical qubit errors, multiple rounds  of measurements are necessary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' Figure 2 shows some example  physical qubit errors occurring in a surface code and how  Z  Z  Z  Z  Z  Z  X  X  X  X  X  X  X  X  X  X  Z  Z  Z  Z  Z  Z  Z  Z  X  X  X  X  X  X  X  X  X  X  Z  Z  Z  Z  Z  Z  d = 3  d = 3  (a)  Z  Z  Z  Z  S  A  B  C  D  A  B  C  D  S  |0  Z  (b)  X  X  X  X  S  A  B  C  D  A  B  C  D  S  |+  X  (c)  Figure 1: (a) : CSS surface code (d = 3), a commonly used type of surface  code.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' The white circles are data qubits and the black the Z-type and X-type  ancillas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' (b) and (c) : Measurement circuit of Z-type and X-type ancillas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  Excluding the ancillas in the border, each Z-type and X-type ancilla interacts  with 4 adjacent data qubits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  X  (a)  Z  (b)  X  X  X  (c)  X  X  X  (d)  Round 1  Round 2  Round 3  X  X  M  M  time  (e)  (f)  Figure 2: (a) to (d) : Various error patterns on d = 3 surface code.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' X and Z  mark the corresponding physical qubit errors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' Ancillas reporting non trivial  measurements are shown in red.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' The red lines are to visualize error chains.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  (a) isolated X error (b) isolated Z error (c) error chain of three X errors (d)  error chain introducing a logical error which has no non-trivial measurements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  Note that even though (a) and (c) are different error patterns, they produce  the same syndrome.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' (e) Error patterns spread across multiple measurement  rounds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' Here single X and Z errors can also spread across two rounds and  error chains can include measurement errors (indicated by ‘M’) as well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' (f)  Decoding graph with vertices with nontrivial measurement marked red for  the error pattern in (e).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  they are detected by ancilla qubits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' We show X and Z errors  separately because they can be independently dealt with in  the same way.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' The outcomes from these multiple rounds of  measurements of ancilla qubits constitute a syndrome.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  A syndrome can be conveniently represented by a graph  called decoding graph in which a vertex represents a measure-  ment outcome of an ancilla and an edge a data qubit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' Vertices  of nontrivial measurement outcome are specially marked.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' The  weight of edge is determined by the probability of error in  the corresponding data qubit or measurement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' For distance  d surface code, there are d ×(d −1) vertices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' This decoding  graph can be extended to three dimensional in which multi-  ple identical planar layers are stacked on each other.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' Each  layer represents a round of measurement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' The total number of  rounds is usually the same as the distance of the surface code.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  Corresponding vertices in adjacent layers are connected by  edges which represent the probability of measurement error  of the corresponding ancilla.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' That is, there are d ×d ×(d −1)  vertices in this three-dimensional graph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' Figure 2f shows the  decoding graph for a syndrome from d = 3 surface code.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  2  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='3  Error Decoders  Given a syndrome, an error decoder identiﬁes the underlying  error pattern, which will be used to generate a correction  pattern.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' As multiple error patterns can generate the same  syndrome, the decoder has to make a probabilistic guess of  the underlying physical error.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' The objective is that when the  correction pattern is applied, the chance of the surface code  entering a different logical state (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='e a logical error) will be  minimized.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  Metrics  The two important aspects of decoders are accu-  racy and speed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' A decoder must correct errors faster than  syndromes are produced to avoid a backlog.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' A faster decoder  also allows more time for the quantum hardware to do actual  useful work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' The average decoding time per measurement  round is a widely used criteria for speed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  A decoder must make careful tradeoff between speed and  accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' A faster decoder with lower accuracy requires a  larger d to achieve any given logical error rate, which may  require more computation overall.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  Union-Find (UF) Decoder  The UF decoder is a fast sur-  face code decoder design ﬁrst described by Delfosse and  Nickerson [10].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' According to [13], it can be viewed as an  approximation to the blossom algorithm that solves minimum-  weight perfect matching (MWPM) problems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' It has a worst  case time complexity of O(d3α(d)), where α is the inverse  of Ackermann’s function, a slow growing function that is less  than three for any practical code distances.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' Based on our anal-  ysis, it has an average case time complexity slightly higher  than O(d3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  algorithm 1 describes the UF decoder.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' It takes a decoding  graph G(V,E) as input.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' Each edge e ∈ E has a weight and a  growth, denoted by e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='w and e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='g, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='g is initialized  with 0 and the decoder may grow e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='g until it reaches e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  When that happens, we say the edge is fully grown.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  The decoder maintains a set of odd clusters, denoted by  L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' L is initialized to include all {v} that v ∈ V is non-trivial  (L81).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' Each cluster C keeps track of whether its cardinality is  odd or even as well as its root element.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  The UF decoder iterates over growing and merging the  odd cluster list until there are no more odd clusters (inside  the while loop of algorithm 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' Each iteration has two stages:  Growing and Merging.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' In the Growing stage, each odd cluster  “grows” by increasing the growth of the edges incidental to its  boundary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' This process creates a set of fully grown edges F  (L86 to L95).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' The Growing stage is the more time-consuming  step as it requires traversing all the edges in the boundary of  all the odd clusters and updating the global edge table.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' Since  the number of edges is O(d3), the UF decoder is not scalable  for surface codes with large d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  In the Merging stage, the decoder goes through each fully-  grown edge to merge the two clusters connected by the edge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  Algorithm 1: Union Find Decoder  input :A decoding graph G(V,E) with X (or Z) syndrome  output :A correction pattern  77 % Initialization  78 for each v ∈ V do  79  if v is non-trivial then  80  Create a cluster {v}  81  end  82 end  83 while there is an odd cluster do  84  % Growing  85  F ← /0  86  for each odd cluster C do  87  for each e =< u,v >, u ∈ C,v ̸∈ C do  88  if e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='growth < e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='w then  89  e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='growth ← e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='growth+1  90  if e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='growth = e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='w then  91  F ← F ∪{e}  92  end  93  end  94  end  95  end  96  % Merging  97  for each e =< u,v >∈ F do  98  UNION(u, v)  99  end  100 end  101 Build correction within each cluster  When two clusters merge, the new cluster may become even.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  When there is no more odd cluster, the decoder ﬁnds a  correction within each cluster and combines them to produce  the correction pattern (L101).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  3  Related Work  There is a large body of literature on fast QEC decoding, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=',  [14–16].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' The most related are solutions that leverage parallel  compute resources.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  Fowler [17] describes a method for decoding at the rate of  measurement (O(d)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' The proposed design divides the decod-  ing graph among specialized hardware units arranged in a grid.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  Each unit contains a subset of vertices and can independently  decode error chains contained within it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' The design is based  on the observation that large error patterns spanning multiple  units are exponentially rare, so inter-unit communication is  not frequently required.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' It, however, paradoxically assumes  that the number of vertices per unit is “sufﬁcient large” and  a unit can ﬁnd an MWPM for its vertices within half the  measurement time on average.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' Not surprisingly, to date, no  implementation or empirical data have been reported for this  work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' Our approach distributes computation to a vertex-level  and leverages the same observation that communication be-  tween distant vertices is infrequent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  NISQ+[8] and QECOOL[9] parallelize computation at the  ancilla level, where all vertices in the decoding graph repre-  senting measurements of one ancilla are handled by a single  3  compute unit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' This results in an increase in decoding time  per measurement round as d increases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' In contrast we allo-  cate a processing element per each vertex, which results in  decreasing decoding time per measurement round with d at  the expense of number of parallel units growing O(d3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' Fur-  thermore, they both implement the same greedy decoding  algorithm that has much lower accuracy than the UF decoder  used in this work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' QECOOL has an accuracy that is approx-  imately four orders of magnitude lower than that of a UF  decoder [7] and NISQ+ ignores measurement errors further  lowering its accuracy than QECOOL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  Skoric et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' [18] propose a method of using measurement  round-level parallelism, in which a decoder waits for a large  number of measurement rounds to be completed and then  decodes multiple blocks of measurement rounds in parallel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  By using sufﬁcient parallel resources this method can achieve  a rate of decoding faster than the rate of measurement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' How-  ever, the latency of this approach grows with the number of  measurement rounds the decoder needs to batch to achieve  a throughput equal to the rate of measurement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' In contrast,  our approach exploits vertex-level parallelism and completes  decoding of every d rounds of measurements with an average  latency that grows sublinearly with d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  Pipelining can be considered a special form of using com-  pute resources in parallel, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=', in different pipeline stages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  AFS [7] is a UF decoder architected in three pipeline stages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  The authors estimate the decoder will have a 42 ns latency  for d = 11 surface code, which is three times lower than what  we report based on implementation and measurement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' The  authors assume a specialized hardware that is capable of run-  ning at 4 GHz and as a result, the decoding latency will be  dominated by memory access.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' However, no implementation  or cycle-accurate simulation is known for this decoder.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' Im-  portantly, pipelining is limited in how much parallelism it can  leverage: the number of pipeline stages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' In contrast, paral-  lelism of our decoder grows along d3, which enables us to  achieve a sublinear average case latency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  LILLIPUT [6] is a three stage look-up-table based decoder  similar to AFS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' Look-up-table based decoders can achieve  fast decoding but are not scalable beyond d = 5 as the size  of the look-up table grows O(2d3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' For d = 7 surface code  with 7 measurement rounds, it would require a memory of  2168 Bytes, which is infeasible in any foreseeable future.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  4  Distributed UF Decoder Design  Our goal to build a QEC decoder is scalability to the number  of qubits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' As surface codes can exponentially reduce logical  error rate with respect to d, larger surface codes with hundreds  or even thousands of qubits are necessary for fault-tolerant  quantum computing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' Therefore, the average decoding time  per measurement round should not grow with d, to avoid  exponential backlog for any larger d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  We choose the UF decoder for two reasons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' First, it has  much lower time complexity than the MWPM algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' Al-  though in general the UF decoder achieve lower decoding  accuracy than MWPM decoders, it is as accurate in many  interesting surface codes and noise models [13].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' Second, the  UF decoder maintains much less intermediate states, which  makes it easier to implement in a distributed manner.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' We  observe that growing stage from L86 to L95 in algorithm 1  operates on each vertex independently without dependencies  from other vertices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' A vertex requires only the parity of the  cluster it is a part of for the growing stage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' Second, during  the merging stage, a vertex only needs to interact with its  immediate neighbors (L98).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  Like the original UF decoder, our distributed UF decoder  is also based on the decoding graph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' Logically, the distributed  decoder associates a processing element (PE) with each ver-  tex in the decoding graph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' Therefore, When describing the  distributed decoder, we often use PE and vertex in an inter-  exchangeable manner.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' PEs operate with the same algorithm,  speciﬁed by algorithm 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' The PE algorithm iterates over three  stages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='1  PE States  A PE has direct read access to its local states and some states  of incident PEs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' A PE can only modify its local states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  Thanks to the decoding graph, a PE has immediate access  to the following objects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  v, the vertex it is associated with.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='E, the set of edges incident to v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='U, the set of vertices that are incident to any e ∈ v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' We  say these vertices are adjacent to v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  The algorithm augments the data structures of vertex and  edge of the decoding graph, according to the UF decoder  design [10].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' For each vertex v ∈ V, the following information  is added  id : a unique identity number which ranges from 1 to n  where n = |V|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' id is statically assigned and never changes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  m is a binary indicating whether the measurement outcome  is trivial (false) or not (true).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' m is initialized according  to the syndrome.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  cid: a unique integer identiﬁer for the cluster to which v  belongs to, and is equal to the lowest id of all the vertices  inside the cluster.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' The vertex with this lowest id is called  the cluster root.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='cid is initialized to be v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='id.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' That is, each  vertex starts with its own single-vertex cluster.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' When cid =  id, the vertex is a root of a cluster.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  odd is a binary indicating whether the cluster is odd.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' odd  is initialized to be m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  codd is a copy of odd.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  stage indicates the stage the PE currently operates in  4  busyis a binary indicating whether the PE has any pending  operations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  For each edge e ∈ E, the decoder maintains e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='growth, which  indicates the growth of the edge, in addition to e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='w, the weight.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='growth is initialized as 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' The decoder grows e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='growth  until it reaches e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='w and e becomes fully grown.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  For clarity of exposition, we introduce a mathematical  shorthand v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='nb, the set of vertices connected with v by full-  grown edges, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=', v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='nb={u|e = ⟨v,u⟩ ∈ v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='E & e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='growth=  e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='w}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' We call these vertices the neighbors of v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' Note neigh-  bors are always adjacent but not all adjacent vertices are neigh-  bors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='2  Shared memory based communication  We use coherent shared memory for shared state that has a  single writer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' For all shared memories, given the coherence,  a read always returns the most recently written value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' Like  ordinary memory, we also assume both read and write are  atomic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  memory read/write for PE (v) and read-only for adjacent  PEs, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=', ∀u ∈ v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='cid and v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='odd reside in this memory  (S1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  memory read/write for PE (v) and read-only for the con-  troller.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' The PE local states, v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='codd, v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='stage and v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='busy  reside in this memory (S2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  memory for e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='growth, which can be written by incident  PEs (S3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  memory read/write for the controller and read-only for all  PEs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' The controller state global_stage is stored in this  memory (S4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='3  Message based communication  Only instance in our decoder where a PE needs to commu-  nicate with a distant PE is when a PE needs to notify the  root when joining a new cluster (L32).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' Implementing this  using shared memory is costly because the PE is not neces-  sarily adjacent to the root.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' As there is one type of message in  our decoder, each message M contains only the destination of  the message.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' The destination take value from 1 to n, which  represents the vertex identiﬁer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  For the correctness of the decoder we only assume guaran-  teed delivery of messages and do not assume a time bound  for message delivery.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='4  PE Algorithm  All PEs iterate over three stages of operation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' Within each  stage, they operate independently but transit from one stage to  the next when the controller updates global_stage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' When a  PE enters a stage, it sets v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='stage accordingly and keep v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='busy  Algorithm 2: Algorithm for vertex v in the distributed  UF decoder.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  1 v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='cid ← v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='id;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='odd ← v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='m  2 while true do  3  if global_stage =terminate then  4  return  5  end  6  growing(v)  7  merging(v)  8  syncing(v)  9 end  as true until it ﬁnishes all work in the stage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' The controller  uses these two pieces of information from all PEs to determine  if a stage has started and completed, respectively (See §4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  We next describe the three stages of the PE algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  In the Growing stage, vertices at the boundary of an odd  cluster increase e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='growth for boundary edges (L16).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' As PEs  perform Growing simultaneously, two adjacent PEs may com-  pare e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='w and e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='growth and update e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='growth for the same e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  Such compare-and-update operations must be atomic to avoid  data race.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  In the Merging stage, two clusters connected through a  fully-grown edge merge by adopting the lower cluster id (cid)  of theirs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' To achieve this each PE compares its cid with PEs  connected through fully-grown edges (L31).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' If the other in-  cident vertex of a fully grown edge has a lower cid the PE  adopts the lower cid as its own (L31).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' Merging process con-  tinues until every PE in the cluster have the same cid which  is the lowest v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='id of the cluster.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' This procedure is related to  leader election in a distributed systems: vertices in a newly  formed cluster must adopt the lowest id.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' The Merging stage  also calculates the parity of the cluster.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' Each PE representing  a non-trivial measurement (m is true) messages the root of  the cluster it joins (L32).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' Likewise, the root updates its parity  when it receives a message from a PE (L38).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  In the Syncing stage, a root broadcasts its v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='odd to all PEs  in its cluster, which is necessary for the next Growing stage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  We achieve this using a modiﬁed version of the ﬂooding  algorithm, which uses shared memory instead of message  passing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' Every non-root node initially set its v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='odd as false  and continues comparing v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='odd with PEs with fully connected  edges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' If any of the PEs connected with a fully grown edge has  v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='odd as true the PE set its v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='odd as true (L53).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' If a cluster  has v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='odd as truein the root, this results in propagating true  to all vertices in the cluster similar to a ﬂooding algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='5  Controller Algorithm  The controller moves all PEs and itself along the three stages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  In each stage, it checks for v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='busy signals and in addition  in merging stage it checks for outstanding messages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' The  controller determines completion of a stage when all PEs  have v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='busy as false and there are no outstanding messages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  5  Algorithm 3: Vertex growing algorithm  10 function growing(vertex v)  11  Wait until global_stage=growing  12  v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='busy← true;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='stage← growing  13  if v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='odd then  14  for each e = ⟨u,v⟩ ∈ v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='E atomic do  15  if e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='growth< e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='w and u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='cid ̸= v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='cid then  16  e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='growth← e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='growth+1  17  end  18  end  19  end  20  v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='busy← false;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  21 end  Algorithm 4: Vertex merging algorithm  22 function merging(vertex v)  23  Wait until global_stage=merging  24  v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='busy← true;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='stage← merging  25  26  while true do  27  if global_stage ̸=merging then return  28  29  if ∃u ∈ v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='nb s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='cid < v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='cid then  30  v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='busy← true  31  v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='cid ← MIN(u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='cid|u ∈ v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='nb)  32  if v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='m then send M(v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='cid)  33  else if ∀u ∈ v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='nb,u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='cid = v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='cid then  34  v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='busy← false  35  end  36  37  for each received message M do  38  v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='odd ← ¬v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='odd  39  end  40  end  41 end  Algorithm 5: Vertex syncing algorithm  42 function syncing(vertex v)  43  v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='busy← true;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='stage← syncing  44  if v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='cid ̸= v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='id then v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='odd ← false  45  v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='codd ← v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='odd  46  47  while true do  48  if global_stage ̸=syncing then return  49  50  if ∀u ∈ v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='nb,u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='odd = v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='odd then  51  v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='busy← false  52  else  53  v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='odd ← true  54  v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='busy← true  55  end  56  end  57 end  Upon completion, the controller updates the global_stage  variable to move to the next stage and the PEs acknowledge  this update by updating their own v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='stage variable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  The controller also calculates the presence of odd clusters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  At the end of the syncing stage, it reads the v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='odd value of  Algorithm 6: The controller coordinates all PEs along  stages and detects the presence of odd clusters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  58 while true do  59  global_stage← growing  60  wait until ∀v ∈ V,v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='stage= growing  61  wait until ∀v ∈ V,v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='busy= false  62  63  global_stage← merging  64  wait until ∀v ∈ V,v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='stage= merging  65  wait until ∀v ∈ V,v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='busy= false  66  wait until no outstanding messages in the system  67  68  global_stage← syncing  69  wait until ∀v ∈ V,v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='syncing= growing  70  wait until ∀v ∈ V,v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='busy= false  71  72  if ∀v ∈ V,v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='codd = false then  73  global_stage← terminate  74  return  75  end  76 end  each vertex.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' If any vertex has v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='odd = true, the controller  updates the global stage variable to Growing to continue the  algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' Otherwise, it updates it to Terminate to end the  algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='6  Time Complexity Analysis  The worst case time complexity of our distributed UF decoder  is O(d3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' The worst case occurs when parallelism is maxi-  mally lost in the system;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' all vertices are non-trivial and merge  into a single cluster and the root must process all incoming  messages from all other vertices (L38).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' However, the occur-  rence of the worst case scenario is extremely rare as larger  clusters are exponentially unlikely to occur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' Empirical results  reported in §6 show that average time grows sublinearly with  d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  The time complexity of the controller depends on the im-  plementation of the shared memory for v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='busy and checking  for outstanding messages in the system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' As both checks are  logical OR operators of individual PE information, the most  efﬁcient implementation is a logical tree of OR operations  which results in a time complexity of O(log(d)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' Thus, the  overhead of coordination is signiﬁcantly smaller than the  worst case time complexity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  PE Communication Complexity  The communication  complexity of the shared memory based communication is  O(d3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' The leader election in the Merging stage and the broad-  casting of v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='odd in the Syncing stage are implemented using a  shared memory based ﬂooding algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' The time complex-  ity of a ﬂooding operation is O(D), where D is the diameter of  the cluster.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' Therefore, in the worst case the time complexity  of ﬂooding messages is O(d3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  6  The communication complexity of the message based com-  munication is O(d6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' Messages from each trivial measure-  ment to the root of the cluster is proportional to the number  of trivial vertices in the cluster and number of changes of cid  of each vertex.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' Thus in the worst case there would be O(d6)  messages and the time complexity will be O(d3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  5  Helios Architecture and Implementation  We next describe Helios, the architecture for the distributed  UF decoder.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='1  Overview  Helios organizes PEs and controller in a custom topology that  combines a 3-D grid and a B+ tree as illustrated by Figure 3  and explained below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  PEs are organized according to the position of vertices  they represent in the model graph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' We assign v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='id sequen-  tially, starting with 1 from bottom left corner and continuing  in row-major order for each measurement round.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' Shared  memory S1 (v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='cid and v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='odd) and S2 (v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='codd, v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='stage, and  v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='busy) are added alongside each PE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  Shared memory S3 (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='growth) is added to the incident PE  with the lower id.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  A link between every two adjacent PEs to read from each  other’s S1 and for the one with the higher id to read the  other’s S4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' This results in a network of links in a 3-D grid  topology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' As a PE represents a vertex in the model graph,  a link represents an edge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' Broad pink lines in Figure 3  represent these links.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  A directional link between two adjacent PEs and between  PEs with consecutive v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='id values for message passing (L32).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  These links are directed from the PE with higher v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='id to the  other and are buffered.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' They are represented by blue arrows  in Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  The controller, realized as a tree of control nodes (§5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  The leaf control nodes of the tree contain shared memory  S4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  A link between each PE and the controller for the controller  to read from S2 and for the PEs to read from S4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' Dashed  orange lines in Figure 3 represent these links.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='2  Message-passing between PEs  To implement the vertex merging algorithm (algorithm 4), a  PE may send and receive messages from another PE, which  is not necessarily adjacent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' Helios implements this with the  directional links and allows a PE to forward messages over  directional links.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' The forward logic is trivially simple because  PE 5  PE 1  PE 2  PE 6  PE 13  PE 17  Control  node  Control  node  Root  control  node  Control  node  Controller  PE 3  PE 4  PE 9  PE 11  PE 15  PE 14  PE 18  PE 16  PE 8  PE 12  PE 10  PE 7  Figure 3: Helios architecture for d=3 surface code for 3 measurement rounds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  As d=3 surface code has 6 (3 by 2) ancilla qubits, Helios contains of a 3x2x3  PE array.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' PE n indicates PE with v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='id = n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  S3  growth  grow  logic_busy  S3  mem  logic  PE 1  FIFO  growth  grow  logic_busy  S3  growth  grow  logic_busy  S2  stage  codd  busy  mem  logic  FIFO  mem  logic  FIFO  nonempty  growth, odd, cid  odd, cid  growth  odd  cid  odd  cid  PE 2  odd, cid  growth, odd, cid  nonempty  nonempty  To/from controller  PE 3  PE 7  codd  busy  stage  Figure 4: The bottom left corner of the PE array shown in Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' Only part  of the logic and memory inside PE 1 is shown : growth (S3) is per edge and  is stored in the PE with lower id.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' grow logic (in pink) calculates the updated  growth value (Figure 5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' logic_busy(in green) (Figure 6) is per adjacent PE  and is used to calculate the busy signal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  (1) a PE only messages another PE with a lower id per al-  gorithm 4 and (2) the links are directional from a PE with a  higher id to that with a lower one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  We note that the directional links consist of the 3-D grid  structure, from the edges of the model graph, and additional  links between PEs with consecutive v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='id values, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=', the “di-  agonal” ones in Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' The 3-D grid topology is optimal  for exchanging messages between nearby PEs, which is fre-  quent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' The additional “diagonal” links prevent deadlocks by  breaking potential circular dependency amongst several PEs,  e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=', PE 1 to PE 4 in Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  7  The directional links between PEs are buffered because a  PE can receive multiple messages at a time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' Because these  buffers have a ﬁnite size, the sending PE can stall if a buffer  is full.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' In §6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='2, we show empirical evidence that stall rarely  happens.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='3  Controller  Helios implements the controller as a tree of nodes to avoid  the scalability bottleneck.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' The controller requires four pieces  of information from each PE: v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='codd, v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='stage, v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='busy and  the presence of outstanding messages of the system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' Each  leaf node of the tree is directly connected with a subset of  PEs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' We can consider these PEs as the children of the leaf  node.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' Each node in the tree gathers vertex information from  its children and reports it to the parent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' With information  from all vertices, the root node runs algorithm 6 and decides  whether to advance the stage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  We leave height, branching factor and the subset of PEs  connected to each leaf node as implementation choices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' The  necessary requirement is that the controller should not slow  down the overall design.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='4  FPGA Implementation  We next describe an implementation of Helios targeting a  single FPGA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' We choose FPGA for two reasons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' It supports  massively parallel logic, which is essential as the number of  PEs grows proportional to d3 in our distributed UF design.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  Moreover, it allows deterministic latency for each operation,  which facilitates synchronizing all the PEs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  Figure 4 shows a minimal diagram of a PE and a controller  in the FPGA implementation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  Controller: Since we only use a single FPGA and evaluate  with d below 20, a single node controller sufﬁces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  Directional links: We implement the directional links as  ﬁrst-in-ﬁst-out (FIFO) buffers, which are mapped by Xilinx  Vivado to LUT based RAMs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' We choose the buffer size of four  because our evaluations in §6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='2 show that increasing the buffer  size beyond four does not improve decoding time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' Reducing  the buffer size below four slightly increases decoding time  (by 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='01%) while using the same number of LUTs as memory  as a buffer of size four (up to 32).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  Shared memory:  We implement all shared memories as  FPGA registers, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=', reg in Verilog.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' FPGA registers by de-  sign guarantee that a read returns the last written value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' In  order to ensure that the S4 memory has a single writer, we  modify the PE logic as shown in Figure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' Compare and up-  date operation (L15) is implemented in the PE that the S3  memory resides in, and the PE increases e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='growth by two if  both endpoints of the edge have v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='odd as true.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  Detecting outstanding messages:  Each PE updates its  busy state based on pending messages in addition to condi-  tions in L33 and L50 as shown in the code snippet in Figure 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  Adder  odd[0]  odd[1]  Min  w  2x1  Mux  ==  stage  growing  grow  D  Q  Q  growth  clk  reg growth;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  always@(posedge clk)  if(stage == growing)  growth <= ‘MIN(growth  + odd[0] + odd[1], w);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  Figure 5: Circuit diagram of grow sub-module and Verilog implementation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  This implements the atomic compare and update operation in L15 as part  of the PE module.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' odd[0] and odd[1] represents the odd state of the two  incident PEs of the edge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  ==  w  ==  cid[0]  u∈nb  cid[i]  ==  stage  merging  ==  odd[0]  odd[i]  ==  stage  syncing  growth[i]  assign logic_busy[i] =  (growth[i] == w &&  stage == merging  && cid[i] !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='= cid[0]) ||  (growth[i] == w &&  stage == syncing  && odd[i] !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='= odd[0]);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  Figure 6: Circuit diagram of logic_busy sub-module and Verilog imple-  mentation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' The sub-module is implemented per each adjacent PE which are  indexed from 1 to the number of edges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' The variables odd[0] and cid[0]  represent the odd and cid of the PE, while odd[i], cid[i] and growth[i]  represent the corresponding values for the ith adjacent PE and the edge  connecting them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  The sub-circuit logic_busychecks for the conditions in L33  and L50 for each incident edge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' In our FPGA implementation  of FIFO buffers, when a value is written to a FIFO (using  the we signal), nonempty state of the FIFO will be true in  the next cycle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' This results in at least one PE having busy  as true when there are outstanding messages in the system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  The controller reads busy every clock cycle to identify the  completion of a stage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  In total, our implementation contains approximately 6000  lines of Verilog code.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' The code is available at [19].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  On the ZCU106 FPGA development board [11], we are  able to support the distributed UF decoder with d up to 7,  due to resource limits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' Table 1 shows the resource usage for  various d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' While the numbers of vertices and edges grow  by O(d3), the resource usage grows faster for the following  reasons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' First, resource usage by a PE grows due to the in-  crease of bitwidth required for v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='id, and v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='cid.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' A PE for d = 7  with six adjacent PEs requires 182 LUTs and a similar PE for  d = 3 requires only 127 LUTs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' Second, PEs on the surface  of the three-dimensional array as shown in Figure 3 use less  resources than those inside because the latter have more in-  cident edges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' When d increases a higher portion of PEs are  inside the array.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  We ﬁnd that LUTs are the most critical resource in the  FPGA for our design.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' It may be possible to run a design with  d = 15 on a Xilinx VU19 FPGA [20], which currently has  the highest number of LUTs among commercially available  FPGAs at the time of this writing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  Existing commercial FPGAs like ZCU106 often dedicate  a lot of silicon to digital signal processing (DSP) units and  block RAMs (BRAMs).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' However, our design does not use  8  Table 1: Resource usage of Helios on ZCU106 FPGA board for various code  distances  d  # of LUTs  # of  registers  as logic  as memory (FIFOs)  3  2419  608  1187  5  18655  3236  7189  7  61793  12636  27664  any DSPs because it only requires comparison operators and  ﬁxed point additions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' Our design does not use any BRAMs  because the FIFOs have a depth of four and can be efﬁciently  implemented using LUTs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' Each BRAM tile in Xilinx has a  default size of 18 Kbits and using BRAM for FIFOs would re-  sult in signiﬁcant unused space in each BRAM tile.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' Therefore,  an ideal FPGA designed to run our distributed UF decoder  would be simpler than current large FPGAs, as it would only  need a large number of LUTs, no DSP units and a limited  amount of BRAM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  6  Evaluation  The main objective of our evaluation is to assess the scalability  of our distributed UF implementation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' To that end, we ﬁrst  describe our methodology and then show that the latency of  our implementation grows sub-linearly with respect to the  surface code size d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='1  Methodology  For speed, we measure the number of cycles required to de-  code a syndrome.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' To evaluate correctness, we compare the  result of clustering generated by our distributed UF decoder  with the clustering generated by the original UF decoder.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' We  compare clusters because the original UF decoder and ours  only differ in the clustering process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' This shows that both  decoders generate identical clusters in all cases tested, con-  ﬁrming the correctness of our decoder.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' In the rest of our  evaluation, we will focus only on the speed of the distributed  UF decoder and not on the accuracy of its results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  Experimental Setup  We use two setups to evaluate our  FPGA implementation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' The primary setup is a Xilinx  ZCU106 FPGA development board [11], which is capable  of handling surface codes with d up to 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' As an alternative  setup, we run our implementation on the Xilinx Vivado simu-  lator [12], which emulates the behavior of FPGA in a cycle-  accurate manner, allowing us to evaluate the performance of  our implementation for surface codes of any size.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' We simu-  lated up to d = 15 as this is the upper bound of d possible in  the largest FPGA currently available [20].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  We also compare the results obtained from the Vivado  simulator with those obtained from the FPGA development  board for surface code sizes 7 and smaller, to gain conﬁdence  in the correctness of the simulator itself.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  Noise Model  We use the phenomenological noise model [1]  that accounts for errors in both data and ancilla qubits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' As  decoding for X-errors and Z-errors are independent and iden-  tical, we only focus on decoding X-errors in the evaluation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  To emulate noise, we independently ﬂip each qubit with  a probability of p (the physical error rate) between every  two measurement rounds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' This is a widely used approach  by prior QEC decoders [7, 8, 18].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' We then generate the  syndrome from the physical errors and provides it as input to  our decoder.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  For most of our experiments, we use as default p = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='001,  like other works [7].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' This value is reasonable for surface  codes, as p should be sufﬁciently below the threshold (at least  ten times lower) to exponentially reduce errors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' We note that  the UF decoder has a threshold of p = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='026, calculated by  Delfosse and Nickerson [10].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='2  Decoding Time  We experimentally show how average time for decoding  grows with the size of the surface code.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' Additionally, we  show the effect of noise and buffer size on the average time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  Average time  To demonstrate the scalability of our algo-  rithm with respect to the size of the surface code, we plot  the average time for decoding against the size of the surface  code.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' In Figure 7 (left) the y-axis shows the average FPGA  clock cycle count and the x-axis shows the distance (d) of the  surface code.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' We obtained these values from running the dis-  tributed UF decoder on the Vivado simulator where each data  point represents the average of 1000 trials.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' We see that for all  3 physical error rates we tested, average decoding time grows  sub-linearly with respect to the surface code size, which sat-  isﬁes the scalability criteria to avoid an exponential backlog.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  This implies that the average time to decode a measurement  round reduces with increasing d as shown in Figure 7 (right).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  Distribution of decoding time  To understand the growth  of decoding time with respect to the code distance, in Fig-  ure 8a we plot the distribution of decoding time for different  code distances.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' The y-axis shows the FPGA clock cycle count  and the x-axis shows the distance (d) of the surface code.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' We  ran both our test setups for this experiment and the distribu-  tion of FPGA clock cycle count for each surface code size is  shown in green, while the distribution of clock cycle count  on the Vivado simulator is shown in gray.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' The average cycle  count is indicated with ×.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  Due to resource limitations on the ZCU106 FPGA, we  are unable to run surface codes with d > 7 on the FPGA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  9  40  60  80  100  120  140  160  180  200  220  240  1  3  5  7  9  11  13  15  17  decoding time  code distance (d)  p = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='0005  p = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='001  p = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='005  6  8  10  12  14  16  18  20  22  1  3  5  7  9  11  13  15  17  time per measurement round  code distance (d)  p = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='0005  p = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='001  p = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='005  Figure 7: Average decoding time scales sub-linearly with d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' We measure the average decoding time for 3 different noise levels using the Vivado simulator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  (Left) The average decoding time in FPGA clock cycles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' (Right) The average decoding time per measurement round in FPGA clock cycles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' Average time per  measurement round reducing continuously justiﬁes that our decoder is scalable for large surface codes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' We show the distributions separately in Figure 8a  For d = 3,5 and 7, the results from the FPGA and those  from the Vivado simulator agree.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' The statistical parameters  such as mean, median, and percentile values(P25, P75, P90)  differ between running on the FPGA and using the simulator  by less than 1%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' Only noticeable difference is the higher  maximum observed value on the FPGA, which is caused  by exponentially unlikely long error chains appearing when  running for 108 trials in the FPGA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' This justiﬁes the use of  the Vivado simulator to obtain results for large surface codes  that cannot be mapped to the ZCU 106 FPGA board due to  resource limitations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  The key factor determining the decoding time is the number  of iterations of growing, merging and syncing the distributed  UF decoder requires.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' The peaks in the probability distribution  for each distance in Figure 8a correspond to the number of  iterations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' The variation around each peak is caused by the  delay due to routing messages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' The number of iterations is  related to the size of the largest cluster, which in turn corre-  lates with the size of the longest error chain in the syndrome.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  As the size of the surface code increases, the probability of a  longer error chain also increases, resulting in the probability  distribution shifting to the right.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  Furthermore, as seen in Figure 8a, the distribution for each  surface code size is right-skewed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' For example, for d = 7,  90% of trials required two iterations or fewer, which were  completed within 140 cycles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' In the same test, 99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='99% of  trials were completed within 237 cycles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' Only a very small  number of error patterns require long decoding times, corre-  sponding to syndromes with long error chains.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' Since such  syndromes occur rarely and have poor decoding accuracy  even if the decoding time is bounded, the impact on accuracy  will be minimal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  Effect of physical error rate  To understand the effect of  the physical error rate on decoding time, in Figure 8b we plot  the distribution of latency for three different noise levels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' We  obtained this distribution by running on the ZCU106 FPGA  with 108 trials.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' The y-axis shows the FPGA clock cycle count  and the x-axis shows the physical error rate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  As the noise level increases, the probability distribution  of latency shifts to the right.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' This is caused by the increased  probability of a longer error chain when the physical error rate  increases, which in turn requires more iterations to decode.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' As  a result, the average decoding time increases with the physical  error rate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  Effect of buffer size  To measure the impact of the buffer  size on decoding time, we varied the buffer size and analyzed  the latency distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' In Figure 8c, the x-axis shows the cy-  cle count and the y-axis shows the cumulative distribution of  the latency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' We varied the buffer size from 1 to 32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' Our results  showed that there was no noticeable difference in latency with  respect to the buffer size.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' The obtained results were identical  for all buffer sizes above 4 and showed a slowdown of less  than 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='01% for buffer sizes of 1 and 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' This indicates that  the communication overhead in our design is minimal for the  average case  We can explain this result using statistics on the number of  messages generated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' For example, when the physical error rate  is 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='001 and d = 7, 97.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='7% of trials are statistically unaffected  by the buffer size.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' This includes 46% of trials resulting in  fully non-trivial syndromes, 47.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='6% of trials resulting in a  single qubit error in each cluster, and 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='1% of trials resulting  in a chain of two qubit errors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' In all of these cases, at most a  single message is generated in each cluster, making the buffer  size irrelevant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' In the remaining 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='3% of trials, the buffer size  will only affect the results if error chains occur close to each  other and share a common link in their message paths.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' In our  experiments, such congestion occurred in less than 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='1% of  runs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' Therefore, the buffer size can be reduced without any  signiﬁcant impact on average decoding time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  10  0  50  100  150  200  250  300  350  400  1  3  5  7  9  11  13  15  17  decoding time  distance (d)  (a) Simulator and implementation results agree  0  100  200  300  400  500  600  700  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='0005  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='001  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='005  decoding time  physical error rate (p)  (b) Decoding time grows with physical error rate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  0  50  100  150  200  250  300  350  400  1  2  4  8  16  decoding time  buﬀer size  (c) Buffer size does not matter for decoding time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  Figure 8: Distribution of decoding time with the average marked with ×.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' For  each error rate we ran 108 trials.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' Results from implementation with Xilinx  ZCU 106 FPGA are in green;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' those from Xilinx Vivado simulator gray.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' By  default d = 7, p = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='001.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='3  Comparison with related work  Our empirical results as shown in Figure 8a suggest that He-  lios has a lower asymptotic complexity than any existing  MWPM or UF implementation for which asymptotic com-  plexities are available, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=', [10, 17].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' Indeed, the empirical  results suggest that our decoder has a sub-linear time complex-  ity: the decoding time per round decreases with the number  of measurement rounds, which has never been achieved be-  fore.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' This implies that Helios can support arbitrarily large  d as rate of decoding will always be faster than the rate of  measurement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  Das et al [7] calculate an average latency for their AFS de-  coder based on memory access cycles and assuming a design  running at 4 GHz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' As the number of memory access cycles  grows quadratically with d, the average decoding time per  measurement round of AFS grows O(d2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' Similarly, Ueno et  al [9] estimate the decoding time of QECOOL from d = 5  to d = 13 based on SPICE-level simulations with a clock  frequency of 5 GHz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' For the given range of d the decoding  time per measurement round increases quadratically with d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  In comparison, the decoding time of Helios decreases per  measurement round.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  We should like to point out that AFS and QECOOL assume  very high clock frequencies, which is key to their estimated  low latency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' For example, for d = 11, AFS and QECOOL  respectively report latencies of 42 ns and 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='32 ns per measure-  ment round.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' Helios, in contrast, requires 107 ns per measure-  ment round with a 100 MHz clock.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' In terms of clock cycles,  Helios requires on average 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='7 cycles for d = 11 surface  code, lower than both AFS (168 cycles) and QECOOL (41  cycles).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  To the best of our knowledge, LILLIPUT [6] is the only  hardware decoder in literature that provides implementation-  based results, for d = 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' The decoder has an average time of  21 ns per measurement round, which is shorter than that of  Helios for d = 5, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=', 126 ns.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' However, as analyzed in §3,  LILLIPUT is not scalable for d > 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' Our work, in contrast,  has successfully demonstrated the implementation of a d = 7  surface code on a ZCU106 FPGA with 120 ns per measure-  ment round.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' The architecture of Helios can potentially support  larger d using a larger FPGA, for example d = 15 for Xilinx  VU19P [20], and even larger d using a network of FPGAs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  7  Conclusion  We describe a distributed design of the Union Find decoder for  quantum error-correcting surface codes and present Helios, a  system architecture for realizing it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' We report an FPGA-based  implementation Helios.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' Using Xilinx Vivaldo cycle-accurate  simulator, we demonstrate empirically that the average decod-  ing time of Helios grows sub-linearly with d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' Using a ZCU106  FPGA, we implement the fastest decoding of distance 7 sur-  face codes, which achieves 120ns average decoding time per  measurement round.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' Helios is faster and more scalable than  any reported implementation of surface code decoder.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' Our  results suggest that by leveraging parallel hardware resources,  Helios can avoid a growing backlog of syndrome measure-  ments for arbitrarily large surface codes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  Acknowledgments  This work was supported in part by Yale University and NSF  MRI Award #2216030.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  11  References  [1] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' Dennis, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' Kitaev, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' Landahl, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' Preskill, “Topological quantum  memory,” Journal of Mathematical Physics, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' 43, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' 9, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' 4452–  4505, 2002.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  [2] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' Fowler, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' Mariantoni, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' Martinis, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' Cleland, “Sur-  face codes: Towards practical large-scale quantum computation,” Phys-  ical Review A, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' 86, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' 3, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' 032324, 2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  [3] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' Bonilla-Ataides, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' Tuckett, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
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+page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' Niu, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
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+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' Yao, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
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+page_content=' Boixo, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' Smelyanskiy, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' Chen, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' Megrant,  and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' Kelly, “Exponential suppression of bit or phase errors with cyclic  error correction,” Nature, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' 595, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' 7867, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' 383–387, Jul 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  [Online].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' Available: https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='1038/s41586-021-03588-y  [5] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' Gidney and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' Ekerå, “How to factor 2048 bit rsa integers in 8 hours  using 20 million noisy qubits,” Quantum, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' 5, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' 433, Apr 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  [Online].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' Available: http://dx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='22331/q-2021-04-15-433  [6] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' Das, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' Locharla, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' Jones, “LILLIPUT: A lightweight  low-latency lookup-table based decoder for near-term quantum error  correction,” 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' [Online].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' Available: https://arxiv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='org/abs/2108.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='065  69  [7] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' Das, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' Pattison, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' Manne, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' Carmean, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' Svore, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' Qureshi, and  N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' Delfosse, “A scalable decoder micro-architecture for fault-tolerant  quantum computing,” arXiv preprint arXiv:2001.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='06598, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  [8] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' Holmes, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' Jokar, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' Pasandi, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' Ding, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' Pedram, and  F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' Chong, “NISQ+: Boosting quantum computing power by  approximating quantum error correction,” 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' [Online].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' Available:  https://arxiv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='org/abs/2004.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='04794  [9] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' Ueno, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' Kondo, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' Tanaka, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' Suzuki, and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' Tabuchi, “QECOOL:  On-line quantum error correction with a superconducting decoder for  surface code,” in Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' ACM/IEEE Design Automation Conference  (DAC), 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  [10] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' Delfosse and N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' Nickerson, “Almost-linear time decoding algo-  rithm for topological codes,” arXiv preprint arXiv:1709.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='06218, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  [11] Xilinx, “Zynq UltraScale+ RFSoC ZCU106 evaluation kit,” https://ww  w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='xilinx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='com/products/boards-and-kits/zcu106.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='html.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  [12] Vivado  Design  Suite  User  Guide:  Logic  Sim-  ulation,  Xilinx  Inc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=',  04  2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  [Online].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  Avail-  able: https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='xilinx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='com/content/dam/xilinx/support/document  s/sw_manuals/xilinx2022_1/ug900-vivado-logic-simulation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='pdf  [13] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' Wu, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' Liyanage, and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' Zhong, “An interpretation of union-  ﬁnd decoder on weighted graphs,” 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' [Online].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' Available:  https://arxiv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='org/abs/2211.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='03288  [14] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' Terhal, “Quantum error correction for quantum memories,”  Reviews of Modern Physics, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' 87, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' 2, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' 307–346, apr 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  [Online].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' Available: https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='1103%2Frevmodphys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='87.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='307  [15] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' Gottesman, “An introduction to quantum error correction and  fault-tolerant quantum computation,” 2009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' [Online].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' Available:  https://arxiv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='org/abs/0904.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='2557  [16] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' Bombín, Topological codes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  Cambridge University Press, 2013, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  455–481.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  [17] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' Fowler, “Minimum weight perfect matching of fault-tolerant  topological quantum error correction in average O(1) parallel time,”  2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  [18] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' Skoric, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' Browne, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' Barnes, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' Gillespie, and  E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' Campbell, “Parallel window decoding enables scalable  fault tolerant quantum computation,” 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' [Online].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content=' Available:  https://arxiv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='org/abs/2209.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='08552  [19] “Distributed UF on FPGA,” https://github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='com/NamiLiy/qec_fpga,  2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  [20] Xilinx, “Virtex UltraScale+ VU19P FPGA,” https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='xilinx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='com  /content/dam/xilinx/publications/product-briefs/virtex-ultrascale-plu  s-vu19p-product-brief.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='pdf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
+page_content='  12' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3NFAT4oBgHgl3EQfEBxO/content/2301.08419v1.pdf'}
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+arXiv:2301.02154v1  [math.AP]  5 Jan 2023
+Generalised Young Measures
+and
+characterisation of gradient Young Measures
+Tommaso Seneci
+Abstract
+Given a function f ∈ C(Rd) of linear growth, we give a new way of representing
+accumulation points of
+ˆ
+Ω
+f(vi(z))dµ(z),
+where µ ∈ M+(Ω), and (vi)i∈N ⊂ L1(Ω, µ) is norm bounded. We call such representa-
+tions "generalised Young Measures". With the help of the new representations, we then
+characterise these limits when they are generated by gradients, i.e. when vi = Dui for
+ui ∈ W 1,1(Ω, Rm), via a set of integral inequalities.
+
+Contents
+1
+Intro
+3
+1.1
+Terminology and symbols
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+3
+1.2
+Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+5
+2
+Generalised Young Measures on separable compactiﬁcations
+8
+2.1
+Generalised Young Measures as generalised objects . . . . . . . . . . . . . . . .
+8
+2.1.1
+Parametrized measures . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+9
+2.1.2
+Generalized Young measures . . . . . . . . . . . . . . . . . . . . . . . . .
+9
+2.1.3
+Functional analytic setup
+. . . . . . . . . . . . . . . . . . . . . . . . . .
+10
+2.2
+Hausdorﬀ compactiﬁcation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+11
+2.2.1
+Preliminaries on Hausdorﬀ compactiﬁcations
+. . . . . . . . . . . . . . .
+11
+2.2.2
+Representation of compactiﬁcations . . . . . . . . . . . . . . . . . . . . .
+12
+2.3
+Restriction on non-linearity . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+13
+2.4
+Representation of Young measures
+. . . . . . . . . . . . . . . . . . . . . . . . .
+14
+2.5
+Properties of generalised Young Measures and connection to Young Measures
+on the sphere . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+17
+2.6
+Terminology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+25
+2.7
+Stronger notions of convergence . . . . . . . . . . . . . . . . . . . . . . . . . . .
+28
+3
+Characterisation of gradient Young Measure
+on general compactiﬁcations
+32
+3.1
+Non-separability of the space of quasi-convex functions . . . . . . . . . . . . . .
+32
+3.2
+Characterisation of Gradient Young Measures . . . . . . . . . . . . . . . . . . .
+36
+3.2.1
+Inhomogenization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+40
+A Appendix
+48
+2
+
+1
+Intro
+1.1
+Terminology and symbols
+• For a vector v ∈ Rm, we write |v| =
+��m
+i=1 v2
+i otherwise speciﬁed.
+• Given a function f : X → Z and W an arbitrary set, we call
+graph(f) ≡graphX(f) = {(x, f(x)) ∈ X × Z such that x ∈ X},
+graphX×W (f) = {(x, w, f(x)) ∈ X × W × Z such that x ∈ X, w ∈ W}.
+• We say that a function f : Rd → R has p growth if there is C > 0 such that
+|f(z)| ≤ C(1 + |z|p).
+• The identity matrix is indicated by
+1, or
+1d ∈ Rd×d if we need to specify the dimension.
+• The Lebesgue measure is indicated by dx, or Ln depending on the context. The set of
+ﬁnite Borel d-vector measures is indicated by M(Ω, Rd). For E ⊂ M(Ω), E+ is the set
+of positive Borel measures that belong to E.
+• For a measure µ ∈ M(Ω)+, we write Lp(Ω, µ, Rd) to mean the space of µ-measurable
+functions f : Ω → Rm such that
+ˆ
+Ω
+|f(x)|pdµ(x) < +∞.
+• For µ ∈ M(Ω, Rd), we write its restriction to a µ-measurable set E ⊂ Ω
+µ
+E : A Borel set �→ µ(E ∩ A).
+• If µ ∈ M(Ω) and f ∈ L(Ω, µ, Rd), we call fdµ the measure in M(Ω, Rd) deﬁned by
+U �→
+ˆ
+U
+fdµ,
+where U runs through all µ-measurable sets.
+• If X is any space, the Dirac delta is indicated, for x ∈ X, by
+ˆ
+X
+f(y)dδx(y) = f(x),
+where f : X → Rd is an arbitrary function.
+• Let X be a metric space, µ ∈ M+(Ω) and (fj)j∈N ⊂ Lp(Ω, µ, Rd). We say that the se-
+quence (fj)j is p-equi-integrable (or simply equi-integrable if p is clear from the context)
+if it is norm bounded and
+lim
+k↑∞ sup
+j∈N
+ˆ
+|fj|p>k
+|fj|pdµ = 0.
+3
+
+• The set of test functions is
+D(Ω, Rd) = C∞
+c (Ω, Rd) = {f : Ω → Rd : f is inﬁnitely diﬀerentiable and has compact support}.
+We do not insist on the topology this space is endowed with, as it is standard and
+nowhere used in the work.
+• For the derivative of a function u ∈ L1(Ω, Rm) we mean the matrix-valued distribution
+Du = [∂jui]i,j ∈ (D(Ω, Rm)∗)n such that
+ˆ
+Ω
+ui∂jφdx = −⟨∂jui, φ⟩.
+• The Sobolev space of functions with integrable derivatives is
+W 1,1(Ω, Rm) = {u ∈ L1(Ω, Rm) : Du ∈ L1(Ω, Rm×n)}.
+• The set of functions of bounded variation is
+BV (Ω, Rm) = {u ∈ L1(Ω, Rm) : Du ∈ M(Ω, Rm×n)}.
+• For a function u ∈ BV (Ω, Rm) we can write
+Du = ∇udLn
+Ω + Dsu,
+Dsu = Dju
+Ju + Dcu
+where ∇udLn is the absolutely continuous part, Dju is the jump part concentrated on a
+n − 1 rectiﬁable set Ju, and Ds is the Cantor part, which is absolutely continuous with
+respect to Hn−1.
+• For a function U ∈ BV (Ω, Rm), we call
+BVU(Ω, Rm) =
+�
+u ∈ BV (Ω, Rm) : there is a sequence uj ∈ D(Ω, Rm)
+such that uj
+weak* in BV
+−−−−−−−−→ u − U
+�
+.
+• The set of special functions of bounded variation is
+SBV (Ω, Rm) = {u ∈ BV (Ω, Rm) : Dsu = Dju, or equivalently Dcu = 0}.
+4
+
+1.2
+Introduction
+Young Measures were ﬁrst introduced by Young in [You37] to study the minima of integral
+energies of the form
+inf
+�ˆ 1
+0
+f(u(t), u′(t))dt : u ∈ C1([0, 1]), u(0) = a, u(1) = b, ∥u′∥∞ ≤ K
+�
+.
+The author wanted to understand what conditions on f would guarantee the existence of a
+minimizing curve u(t). Young had the intuition that, for an extremely general class of functions
+f, minimising sequences always converge to a "generalised" curve t �→ (u(t), νt) where ν is a
+probability measure on the image of f. This translates to the following equality
+inf
+u(0)=1,u(1)=b
+ˆ 1
+0
+f(u(t), u′(t))dt = lim
+j
+ˆ 1
+0
+f(uj(t), u′
+j(t))dt =
+ˆ 1
+0
+ˆ
+R
+f(u(t), y)dνt(y)dt.
+So the question of the existence of a minimiser can be reformulated as to whether such objects
+are gradients of a curve or not. νt might fail to be a gradient when the minimizing sequence
+oscillates.
+Young’s original work focused on the case n = 1 and was carried out via functional analytic
+methods. This approach was later extended in [Bal89, BL73] to higher dimensions. We call
+these generalised functions "oscillation Young Measures". The method developed by Young
+is not powerful enough to tackle problems arising in modern mathematics, as it can only
+handle sequences (vj)j∈N that are bounded in L∞ rather than in some Lebesgue space Lp.
+The ﬁrst attempt to well represent generalised limits of integrable functions is due to DiPerna
+and Majda, [DM87]. Functions vj : Ω → Rd are seen as Dirac deltas on the product space
+Ω × Rd, which is subsequently compactiﬁed. An accumulation point, in the sense of these new
+generalised functions, is then found. Such an accumulation point is a measure deﬁned on an
+abstract compactiﬁcation of Ω × Rd, and as such, it is not clear how to represent it in the
+original, non-compact, space. In [AB97], an explicit formula for such accumulation points was
+obtained for a class of integrands that grow "nicely" inﬁnity.
+In what follows, we give a general formula for describing Young Measures for a large class
+of integrands. The construction of Young Measures follows mainly the work by DiPerna and
+Majda [DM87] and lecture notes taken from a class given by Kristensen [Kri15], see also
+[Rin18], chapter 12. This generalisation is based on the canonical way of constructing Haus-
+dorﬀ compactiﬁcations starting from continuous functions, see [CC76].
+A small reduction
+lemma gives a clearer, and somehow geometrical interpretation of such limits. This formula
+captures oscillations at inﬁnity, which are now let occur. We also prove a few structure theo-
+rems that relate diﬀerent compactiﬁcations and Young Measures representations to each other.
+This generalisation of Young Measures is then applied to study extensions and variations -
+within the class of functions of bounded variations BV (Ω, Rm) - of energies that depend on
+gradients
+u �→
+ˆ
+Ω
+f(Du(x))dx,
+(1.16)
+where u ∈ D(Ω, Rd), Ω ⊂ Rn is a bounded domain, and f ∈ C(Rm×n) has linear growth.
+Given any such f, there is no way to extend (1.16) to the class BV so that such extension is
+5
+
+continuous with respect to sequential weak* convergence in C0(Ω, Rm×n)∗. We can however
+ﬁnd an extension which is lower semi-continuous for certain fs. In [Mor52], Morrey established
+the equivalence of lower semi-continuity of (1.16) to a condition named "quasi-convexity",
+which can be written as a Jensen-type inequality
+ˆ
+Ω
+f(z + Dφ(x))dx ≥ |Ω|f(z)
+∀φ ∈ D(Ω).
+(1.17)
+The original result by Morrey works in the setting of weak* convergence in W 1,∞(Ω, Rm),
+and it was subsequently extended to the case W 1,p(Ω, Rm), 1 ≤ p < ∞ and weak convergence
+in [AF84], for positive integrands. As for signed integrands, the same result was proven in
+[BZ90] and it is one of the ﬁrst examples where Young Measures are employed for proving
+lower semi-continuity in the space of gradients. To be more speciﬁc, (1.17) can be rephrased
+as a Jensen-type inequality for measures of the form
+{νx : νx = Dφ(x)#dLn
+Ω, φ ∈ C∞
+c (Ω, Rm)},
+(1.18)
+where νx acts on f in the following way:
+ˆ
+Ω
+f(z + Dφ(x))dx =
+ˆ
+Ω
+ˆ
+Rm×n f(z + w)dνx(w)dx ≡
+ˆ
+Ω
+⟨νx, f⟩dx.
+The lower semi-continuity of (1.16) becomes a functional analytic inequality of the form
+ˆ
+Ω
+⟨νx, f⟩dx ≥
+ˆ
+Ω
+f(Du(x))dx
+and
+Du(x) =
+ˆ
+Rm×n zdνx,
+and in this case we call x �→ νx a "Gradient Young Measure". This class can be seen as the
+closure of the set (1.18) in the weak* topology of measures over the graph of f. The opposite
+is also true and was proven for the ﬁrst time in [KP91, KP94], i.e. every measure-valued
+function x �→ νx, for which a Jensen’s type inequality holds against quasi-convex functions of
+suitable growth, is the limit of a sequence of gradients.
+The aforementioned results hold in the setting of weak convergence in W 1,p, 1 ≤ p < ∞ and
+weak* convergence in W 1,∞. This is a natural condition to assume when p > 1, but not when
+p = 1, as the Lebesgue space L1(Ω, Ln) is not reﬂexive. In particular, a bounded sequence
+in L1(Ω, Ln) can concentrate and converge to measures that are singular with respect to the
+Lebesgue measure. In terms of gradients, the closure of W 1,1(Ω, Rm) so that its unit ball
+is weak* compact is the set of functions of bounded variations BV (Ω, Rm), precisely the set
+of functions whose derivatives are measures. This concentration phenomenon is exclusive of
+the case p = 1, and so regards integrands that have linear growth at inﬁnity. It turns out,
+as proven in [ADM92], that when f has linear growth and it’s quasi-convex, the integral
+functional u �→
+´
+Ω f(∇u)dx, f ≥ 0 is still lower semi-continuous in BV (Ω, Rm) with respect
+to the weak* topology, but there is a deﬁcit of mass when gradients concentrate. Letting f be
+so that
+f ∞(z) =
+lim
+t→∞,zn→z
+f(tzn)
+t
+(1.21)
+6
+
+exists for all zn → z, t → ∞, the lower semi-continuous envelope of (1.16) in the space
+BV (Ω, Rm), with respect to sequential weak* convergence, is, for f non-negative,
+u �→
+ˆ
+Ω
+f(∇u(x))dx + f ∞
+� Dsu
+|Dsu|(x)
+�
+d|Dsu|(x).
+In this case, a Young Measure formulation of the Jensen’s-type inequality (1.17) has to take
+into account the singular part of Du. In the spirit of the previous results, one is tempted to
+prove a duality-type characterisation of Young Measures with concentrations and quasi-convex
+functions. Diﬀerently from the case without concentration, here we assumed f ∞ to exist as
+in eq. (1.21), p. 6. However, as shown in [Mül92], quasi-convex functions can oscillate at
+inﬁnity, meaning that f ∞(z) may not exist for some z ∈ Rm. This suggests that to obtain
+a Jensen-type inequality and characterisation result for gradient Young Measure in the case
+p = 1, it is necessary to specify a compactiﬁcation at inﬁnity.
+The characterisation for gradient Young Measures when p = 1 has been already obtained
+on the so-called "sphere compactiﬁcation" - functions for which f ∞(z) exists for all z - see
+[KR10a, KR10b]. After showing that the class of quasi-convex functions of linear growth is
+too big to be included within any separable compactiﬁcation, we reprove the characterisation
+result for gradient Young Measures on separable compactiﬁcations of quasi-convex functions.
+This restricts the number of quasi-convex functions to be considered at once. However, it is
+also inevitable because a compactiﬁcation containing all quasi-convex functions would be so
+big that its topology would fail to be metrisable and separable.
+7
+
+2
+Generalised Young Measures on separable compactiﬁcations
+In this section, we construct generalised Young Measures and provide a new geometric rep-
+resentation. Concentration is let "oscillate with diﬀerent amplitudes at inﬁnity". To do so,
+we embed a space of functions into a bigger compact set and subsequently use the theory of
+Hausdorﬀ compactiﬁcations.
+2.1
+Generalised Young Measures as generalised objects
+Generalised Young Measures are objects that were known to exist since Majda and Di Perna
+[DM87], and have been used in a few instances, see for example [FK10, KR96]. However, their
+existence per se does not give enough clarity on their properties, and so makes it hard to work
+with such objects.
+We give a new interpretation and geometric representation that better captures oscillation and
+concentration eﬀects that occur in limits of the form
+lim
+j
+ˆ
+Ω
+f(vj(x))dµ(x),
+where vj ∈ Lp(Ω, µ, Rd) is a norm-bounded sequence and f ∈ C(Rd) has p-growth. Under
+these assumptions, it is easy to see that, up to a subsequence, f ◦ vj converges to a measure
+ν; mathematically this means that
+ˆ
+Ω
+f(vj(x))φ(x)dµ(x) →
+ˆ
+Ω
+φ(x)dν(x)
+for all φ ∈ C0(Ω). It’s clear that ν = ν(f) is a linear function of f. What is not clear is
+how such dependence can be represented in terms of µ and f. Without a clear representation,
+it is not possible to set up a system of calculus. This section is dedicated to working out
+a geometric interpretation of the relation between ν and f, which we will then call Young
+Measure. We will mainly concentrate on the more interesting and harder case of p = 1 and
+vj = Duj gradients, where concentration eﬀects create rather complicated structures, and
+cannot in general be separated from oscillation.
+Deﬁnition 2.1 A function f : Rd → R is said to have p-growth if there is a constant C ≥ 0
+such that
+|f(z)| ≤ C(1 + |z|p)
+∀z ∈ Rm.
+When p = 1, we say that such functions have linear growth.
+Before proceeding with formal deﬁnitions, we give a heuristic interpretation of Young Measures.
+When vj → v strongly in L1(µ) then the limit Young Measure is trivial, meaning that
+ˆ
+Ω
+f(vj(x))φ(x)dµ(x) →
+ˆ
+Ω
+f(v(x))φ(x)dµ(x)
+for all f ∈ C(Rd) of linear growth and φ ∈ C0(Ω). This is a simple consequence of the Vitali
+convergence Theorem A.1, p. 48 (or the generalised dominated convergence theorem).
+When strong L1 convergence fails, only two things can go wrong:
+8
+
+• oscillation - vj oscillates around µ-almost every point x ∈ E ⊂ Ω with µ(E) > 0, and
+generates a probability distribution on the target space
+f(vj(x)) ⇝ ⟨νx, f⟩ =
+ˆ
+Rd f(z)dνx;
+• concentration - |vj| concentrates to a measure 0 ̸= λ ∈ M+(Ω) - equivalently (x, vj(x))
+concentrates to the boundary of some compactiﬁcation of Ω×Rd. Around λ-almost every
+point, vj(x) goes to inﬁnity and its "support" collapse to 0. That is to say,
+f(vj(x)) ⇝
+�f(z)
+|z|
+with |z| ≫ 0
+�
+∼
+ˆ
+∂K
+f ∞(w)dν∞
+x (w),
+where K is some compactiﬁcation containing Rd that extends f to f ∞ on the remainder
+of Rd within K.
+2.1.1
+Parametrized measures
+In order to construct Young Measures, we regard functions as maps from a domain Ω into the
+set of probability measures over a target space Rd. Ordinary functions f : Ω → Rd, x �→ f(x)
+are embedded into maps Ω → M+
+1 (Rd), x �→ δf(x).
+Preliminary to the construction, we
+introduce two basic concepts that are at the core of this theory.
+Deﬁnition 2.2 Let X and Z be locally compact, separable metric spaces and λ ∈ M+(X).
+A map ν : X → M+(Z) is said to be λ-measurable if for each φ ∈ C0(Z) the function x �→
+⟨ν(x), φ⟩ is λ-measurable.
+We shall often write the measure-valued map ν as a parametrized measure (νx)x∈X, where
+νx : = ν(x). Given a measure ν on a product space X × Z, it can always be decomposed as a
+product of its projection onto X and its cross section on Z.
+Theorem 2.3 (Disintegration of measures) Let X and Z be compact metric spaces and
+denote by π: X × Y → Z the projection mapping onto the ﬁrst coordinate π(x, y) = x. For
+u ∈ M+(X ×Z) and λ = π#ν ∈ M+(X) (the pushforward of ν via π) there exists a unique λ-
+measurable parametrized measure (ηx)x∈X, ηx ∈ M+
+1 (Z) such that for all φ ∈ C(X), ψ ∈ C(Z)
+we have
+⟨ν, φ ⊗ ψ⟩ =
+ˆ
+X
+⟨ηx, ψ⟩φ(x)dλ(x) =
+ˆ
+X
+ˆ
+Z
+ψ(z)dηx(z)φ(x)dλ(x).
+For a proof of this result see [AFP00], p. 57. In this case we write
+ν = ηxdλ.
+2.1.2
+Generalized Young measures
+In what follows, we show how to obtain a good representation of Young Measures on general
+compactiﬁcations. The procedure is adapted from some lecture notes taken from a homonym
+course given by Jan Kristensen at the University of Oxford, [Kri15]. Some of the results can
+also be found in [Rin18], chapter 12, where they are only proven on the sphere compactiﬁcation.
+9
+
+Throughout this section, Ω ⊂ Rn is open and bounded, µ ∈ M+(Ω) and (vj)j ⊂ Lp(Ω, µ, Rd)
+is a bounded sequence, 1 ≤ p < ∞. Assume
+vj ⇀ v in Lp when 1 < p < ∞
+or
+vj ⇀∗ v in C0(Ω, Rd)∗ when p = 1.
+Given a continuous integrand Φ: Ω × Rd → R satisfying the p-growth condition
+|Φ(x, z)| ≤ C(1 + |z|)p
+∀(x, z) ∈ Ω × Rd,
+we seek to represent limits of
+�´
+Ω Φ(x, vj(x))dx
+�
+j as j → ∞, possibly passing through suitable
+subsequences.
+Remark 2.4 For each j, the map Φ acts on the graph of vj, i.e. Φ(x, vj(x)) = Φ ◦ (x, vj(x)).
+Therefore, we look for the limiting distribution of (x, vj(x)) as j → ∞, and more precisely the
+Φ-moment of this limiting distribution.
+Morally speaking, since (Φ(·, vj))j is bounded in L1(Ω, µ), (Φ(·, vj)dµ)j is bounded in M(Ω) ≂
+C(Ω)∗, so by the abstract compactness principle Theorem A.4, p. 48, there exists a limit
+measure which depends on the integrand Φ.
+2.1.3
+Functional analytic setup
+Let z ∈ Rd �→ ˆz =
+z
+1+|z| ∈ Bd be a homeomorphism Rd �→ Bd. Deﬁne the class of functions of
+p-growth in the z variable to be
+Gp = Gp(Ω, Rd) :=
+�
+Φ ∈ C(Ω × Rd) : sup
+(x,z)
+|Φ(x, z)|
+(1 + |z|)p < ∞
+�
+,
+and for Φ ∈ Gp put
+(TΦ)(x, ˆz) := (1 − |ˆz|)pΦ
+�
+x,
+ˆz
+1 − |ˆz|
+�
+.
+Then T : Gp → BC(Ω × Bd) is an isometric isomorphism provided Gp is normed by ∥TΦ∥∞
+and BC(Ω × Bd) by ∥ · ∥∞. The inverse operator is
+(T −1Ψ)(x, z) = (1 + |z|)pΨ
+�
+x,
+z
+1 + |z|
+�
+,
+where Ψ ∈ BC(Ω × Bd).
+The dual operator T ∗ : BC(Ω×Bd)∗ → G∗
+p is again an isometric isomorphism. We are interested
+in the limits of
+´
+Ω Φ(x, vj(x))dx for Φ ∈ Gp and may deﬁne ξvj ∈ G∗
+p by
+ξvj(Φ) :=
+ˆ
+Ω
+Φ(x, vj(x))dx, Φ ∈ Gp.
+Note
+∥ξvj∥ = sup
+∥Φ∥Gp
+ξvj(Φ) =
+ˆ
+Ω
+(1 + |vj|)pdx
+so (ξvj) is a bounded sequence in G∗
+p. But G∗
+p ≂ BC(Ω × Bd)∗, and because BC (hence Gp)
+is not separable we do not necessarily have sequential compactness.
+We must restrict the
+integrands Φ to a separable subspace of Gp.
+10
+
+2.2
+Hausdorﬀ compactiﬁcation
+In this subsection, we present how to construct a compactiﬁcation of the space X = Ω × Rd
+from a family of bounded and continuous functions F ⊂ BC(X). Roughly speaking, such
+compactiﬁcation is a compact set eF X that contains X as a dense subset and on which all
+f ∈ F admit a continuous extension. The idea behind such construction is to look at the
+graph of each f ∈ F. Because of the boundedness assumption, each function has its image
+contained in a closed bounded interval of R. Therefore, the graph is embedded into a closed
+subset of an (inﬁnite-dimensional) hypercube, which is compact in the product topology by
+Tychonoﬀ theorem, Theorem A.3, p. 48.
+2.2.1
+Preliminaries on Hausdorﬀ compactiﬁcations
+Most of the results will be stated without proof, which can be found in chapters 1 and 2 of
+[CC76] and in chapter 4 of [Fol99].
+We ﬁrst deﬁne three classes of functions that are rich enough to determine the topological
+structure of their domains:
+Deﬁnition 2.5 Consider a family of functions F ⊂ BC(X), we say that F separates points
+from closed sets if for each C ⊂ X closed and x ∈ X \ C there exists f ∈ C(X) such that
+f(x) ̸∈ f(C).
+Next, we deﬁne what a compactiﬁcation of a topological space is.
+Deﬁnition 2.6 A compactiﬁcation of X is a compact Hausdorﬀ space αX and an embedding
+α: X → αX (continuous and so that α−1 : αX → X exists and is continuous) such that α(X)
+is dense in αX.
+It is useful to remark that because α is continuous, any function f ∈ C(αX) can be restricted
+to a continuous function on X. Indeed, f ◦ α is the composition of a bounded continuous
+function with continuous function, and thus it belongs to BC(X). On the other hand, because
+α(X) is dense in αX, each f ∈ C(αX) is uniquely recovered from f ◦ α ∈ C(X).
+Given a family F ⊂ BC(X) that separates points from closed sets, there is a canonical way of
+generating a compactiﬁcation αX on which every f ∈ F has a continuous extension.
+Theorem 2.7 To each family F ⊂ BC(X) that separates points from closed sets, we associate
+a canonical embedding
+eF : X → Πf∈F
+�
+inf f, sup f
+�
+, x �→ {f(x)}f∈F .
+eF X := eF(X) is a compactiﬁcation of X
+The above theorem is a direct implication of Tychonoﬀ’s theorem. When F ⊂ BC(X) is a
+family that separates points from closed sets, then eF : X �→ Πf∈F
+�
+inf f, sup f
+�
+is open and
+continuous, and so it is an embedding.
+However, the map eF makes sense even if F does not separate points from closed sets, and
+eF X is always a compact subset of Πf∈F
+�
+inf f, sup f
+�
+.
+11
+
+Lemma 2.8 Let F ⊂ BC(X) be a family that separates points from closed sets and eF X its
+induced compactiﬁcation. Each f ∈ F embeds into C(eF (X)) in an obvious way and admits a
+unique extension f ∈ C(eF X).
+Every y ∈ eFX is an accumulation point of eF (X), so we can ﬁnd a net yλ = Πf∈F f(xλ) such
+that yλ → y. A way of extending f ∈ F is by setting
+f : eF X → R, y
+�
+= lim
+λ Πf∈F f(xλ)
+�
+�→ f(y) = lim
+λ f(xλ),
+which does not depend on the choice of xγ as far as limγ f(xγ) = limλ f(xλ) for each f ∈ F.
+Suppose that we have given a family F and its associated compactiﬁcation eF X, and we
+consider the compactiﬁcation of F ∪ {f}, where f ∈ BC(X). We expect the latter compacti-
+ﬁcation to be bigger than the former, i.e. to be a space where all the previous extensions can
+be further extended to continuous functions.
+Deﬁnition 2.9 Given two compactiﬁcations αX and γX of X, we say that αX ≥ γX if there
+exists a continuous function f : αX → γX such that f ◦ α = γ. Moreover, we write αX ≂ γX
+if αX ≥ γX and γX ≥ αX, or equivalently if f : αX → γX is a homeomorphism.
+In the following paper, we will sometimes refer to a generic compactiﬁcation K without specify-
+ing the underlying family generating it. The reason why is stated by the following astonishing
+result.
+Theorem 2.10 Given a compactiﬁcation αX of X, there exists a family F ⊂ BC(X) that
+separates points from closed sets such that eF X ≂ αX.
+2.2.2
+Representation of compactiﬁcations
+Consider a family F ⊂ BC(X) that separates points from closed sets.
+According to the
+Hausdorﬀ compactiﬁcation theory (see above subsections), its induced compactiﬁcation can
+be written as a subset of the hypercube Πf∈F
+�
+inf f, sup f
+�
+, where the sides of this cube are
+as many as the functions f ∈ F. Because F can be uncountable, its compactiﬁcation could be
+hard to deal with from an analytical point of view. We seek a better representation of such
+space.
+The idea behind the following result is that if we know the limits of functions f, g ∈ BC(Ω, R),
+we also know the limits of f n + gm, n, m ∈ N.
+Deﬁnition 2.11 Let F be a family of functions f : X → R.
+We call A(F) the algebra
+generated by F, i.e.
+A(F) = {f n + gm : f, g ∈ F, n, m ∈ N}.
+Follows.
+Theorem 2.12 (Representation theorem) Let F ⊂ BC(X) be a closed sub-algebra that
+separates points from closed sets and let F ′ ⊂ F be such that A(F ′) = F. Then eF ′X is a
+compactiﬁcation of X and eF ′X ≂ eF X.
+12
+
+Proof. Let eF ′X be the (formal) compactiﬁcation of F ′. Clearly eF X ≥ eF ′X. To prove the
+opposite inclusion, we must ﬁnd a continuous function T : eF ′X → eF X such that T ◦eF ′ = eF .
+Fix y = limλ Πf∈F ′f(xλ) ∈ eF X. If g ∈ A(F ′), limλ g(xλ) exists and coincides on all nets
+xγ such that y = limγ Πf∈F ′f(xγ). Next, let g ∈ A(F ′) and ﬁnd a sequence {fn}n∈N ⊂ A(F ′)
+such that fn → g uniformly. Because ∥fn∥∞ is bounded, so is {limλ fn(xλ)}n∈N, and so we can
+extract a subsequence {fnk}k∈N such that limk limλ fnk(xλ) = L ∈ R. Fix ε > 0 and N ∈ N
+such that ∥fnN − g∥∞ < ε
+3 and ﬁnd ˜λ ∈ Λ such that |fnN(xλ) − limλ fnN(xλ)| < ε
+3 for all
+λ ≥ ˜λ. Finally
+|g(xλ) − L| ≤ |g(xλ) − fnN(xλ)| + |fnN (xλ) − lim
+λ fnN(xλ)| + | lim
+λ fnN(xλ) − L| < ε
+for all λ ≥ ˜λ, i.e. the net g(xλ) converges to L ∈ R. In particular, by the uniqueness of
+limλ g(xλ), we conclude that the original sequence {limλ fn(xλ)}n∈N converges to L, which also
+proves that the limit does not depend on the particular net xγ as far as limλ f(xλ) = limγ f(xγ)
+for all f ∈ F ′. This shows that the map
+T : eF ′X → eF X, y = lim
+λ Πf∈F ′f(xλ) �→ Ty = lim
+λ Πf∈F f(xλ).
+is a well-deﬁned isomorphism. Because its inverse is the projection map πF ′|T(eF ′X), which is
+continuous and open, then
+T ◦ eF ′ : x �→ Πf∈F ′f(x) �→ Πf∈F f(x) = eF (x)
+is a homeomorphism. To prove that eF ′X is a compactiﬁcation of X, we notice that F separates
+points, as so does F ′. If U ⊂ X is open, so is
+eF ′(U) = T −1(eF (U)),
+and eF ′ is an injective continuous open map, thus it is an embedding onto its image.
+□
+2.3
+Restriction on non-linearity
+For the sake of this work, it is important that the set of functions we work with is separable
+(has a countable dense set). Let F ⊂ BC(Ω×Bd) be a closed separable algebra that separates
+points from closed sets and let eF Ω × Bd be its compactiﬁcation.
+Because eF Ω × Bd is a
+compact Hausdorﬀ space we have the following isometric isomorphism of its dual
+C(eF Ω × Bd)∗ ≂ M(eF Ω × Bd).
+Lemma 2.13 If F ⊂ BC(X) is separable, so is C(eFX).
+Proof. Let {fn}n∈N be dense in F. By the Stone-Weierstrass theorem, the algebra generated
+by {1} ∪ {fn}n∈N ⊂ C(eF X) is dense in C(eF X), and so C(eF X) is separable.
+□
+Because C(eF Ω × Bd) is separable we also have the abstract sequential compactness prin-
+ciple Theorem A.4, p.
+48 on its dual M(eF Ω × Bd).
+Let T −1F ⊂ Gp the corresponding
+13
+
+algebra (w.r.t. ×p) on the set of continuous functions with p-growth. There is an isometric
+isomorphism
+T −1F
+˜T≂ C(eF Ω × Bd).
+By the Riesz representation theorem, we can write its adjoint as
+˜T ∗ : M(eF Ω × Bd) → (T −1F)∗, ν �→
+�
+Φ �→ ( ˜T ∗ν, Φ) = (ν, ˜TΦ) =
+ˆ
+eF Ω×Bd
+˜TΦdν.
+�
+Lemma 2.14 Let X, Z be completely regular Hausdorﬀ spaces and let F ⊂ BC(X) and G ⊂
+BC(Z) be closed sub-algebras that separate points from closed sets and contain the constant
+function. The following spaces are all isometrically isomorphic to each other
+C(eF ∪GX × Z) ≂ C(eF X × eGZ) ≂ A(C(eF X) × C(eGZ)) ≂ A(F ∪ G),
+where each f ∈ F and g ∈ G is extended to a function on the product space by keeping constant
+the other variable. Moreover, F ∪ G ⊂ BC(X × Z) separates points from closed sets.
+The proof of the above lemma is a straightforward application of the Stone-Weierstrass the-
+orem.
+We underline that it’s important to take families F, G deﬁned exclusively on each
+respective space, and the theorem is false if we instead add f = f(x, y) that is not of the form
+above.
+Morally speaking, what the previous lemma says is that on product spaces it is enough to
+work with the compactiﬁcations in each coordinate separately. Moreover, their dual elements
+(measures) can be tested against tensor products of functions that depend on each variable
+independently.
+2.4
+Representation of Young measures
+Let Ω ⊂ Rn be open and bounded and G′ ⊂ BC(Bd) and F ′ ⊂ BC(Ω) be closed separable sub-
+algebras that separate points from closed sets. Let T −1F = A ⊂ Gp the corresponding algebra,
+with respect to the ×p product, in the set of functions having p-growth. F is isometrically
+isomorphic to C(eFΩ × Bd).
+With abuse of notation, we are going to call T the isomorphism between A and C(eF Ω × Bd).
+To each function u ∈ Lp(Ω, Rd) we associate an elementary Young measure ξu ∈ A∗ by setting
+ξu : A → R, Φ �→
+ˆ
+Ω
+Φ(x, u(x))dµ(x).
+Next, consider a bounded sequence {un}n∈N ⊂ Lp(Ω, Rd), supn ∥un∥p ≤ C. As Φ ∈ Gp, the
+sequence of elementary Young measures is also bounded
+∥ξun∥ = sup
+∥Φ∥≤1
+����
+ˆ
+Ω
+Φ(x, un(x))dµ(x)
+���� =
+ˆ
+Ω
+(1 + |un|)pdµ ≤ µ(Ω) + Cp.
+Because of the isomorphism A∗ ≂ C(eF Ω × Bd)∗ ≂ M(eF Ω × Bd), there exists a subsequence,
+relabelled in the same way, and ν ∈ A∗ such that ξun ⇀∗ ν in A∗. Set
+L := (T ∗)−1ν ∈ M(eF Ω × Bd).
+14
+
+We now study the measure L to ﬁnd a better representation for ν ∈ A∗. Let ψ ∈ C(eF Ω×Bd),
+we immediately notice that L ∈ M+(eF Ω × Bd) as a consequence of the following equality
+≪ ν, T −1ψ ≫= lim
+n
+ˆ
+Ω
+(T −1ψ)(x, un(x))dµ(x).
+Because the constant functions belong to G′, we can plug T −1ψ = φ(x)(1+ |z|)p, φ ∈ C(eF ′Ω)
+into the previous equation and obtain the identity
+ˆ
+eF Ω×Bd φ(x)dL(x, z) = lim
+n
+ˆ
+Ω
+φ(x)(1 + |un(x)|)pdµ(x) =
+ˆ
+eF ′
+φ(x)dλ(x).
+By Lemma 2.14, p. 14, the projection
+π: eF Ω × Bd → eF ′Ω
+is well-deﬁned, and we can write ˜λ = π#L. Note that hereby ˜λ ∈ M+(eF ′(Ω)). Find the
+unique ˜λ-measurable parametrized family {˜νx}x∈eF ′Ω such that νx ∈ M+
+1 (eG′Bd) ˜λ-almost
+every x and
+⟨L, Φ⟩ =
+ˆ
+eF ′Ω
+⟨˜νx, Φ(x, ·)⟩d˜λ(x)
+∀ Φ ∈ C(eF Ω × Bd).
+For any φ ∈ C0(Ω) take Φ = φ(1 − | · |)p. We compute
+ˆ
+eF ′Ω
+φ(x)⟨˜νx, (1 − | · |)p⟩d˜λ(x) =
+ˆ
+eF Ω×Bd φ(x)(1 − |z|)pdL(x, z)
+= lim
+n
+ˆ
+Ω
+(φ1Rd)(x, un(x))dµ(x) =
+ˆ
+Ω
+φ(x)dµ(x).
+Because µ ∈ C0(Ω)∗ we immediately conclude that
+µ = ⟨˜νx, (1 − | · |)p⟩˜λ
+Ω,
+where µ is extended on eF ′Ω by µ(E) ≡ µ(e−1
+F ′ (E)), E ⊂ eF ′Ω Borel.
+Apply the Radon-
+Nikodym theorem and write
+˜λ =
+˜λ
+µdµ + ˜λs.
+From the previous identiﬁcation, we get
+�
+⟨˜νx, (1 − | · |)p⟩ ˜λ
+µ = 1
+µ − a.e.
+⟨˜νx, (1 − | · |)p⟩ = 0
+˜λs − a.e.,
+where the second condition implies that ˜νx(eG′(Bd)) = 0 ˜λs-a.e., i.e. the measures are concen-
+trated on the boundary ∂eG′(Bd). On eG′(Bd) we have 0 < (1 − |z|)p ≤ 1, whereas |z| = 1 on
+∂eG′(Bd). In particular
+� ˜λ
+µ =
+1
+⟨˜νx,(1−|·|)p⟩ ≥ 1
+µ − a.e.
+˜νx(∂eG′(Bd)) = 1
+˜λs − a.e.
+15
+
+Now let φ ∈ BC(Rd) and deﬁne
+⟨νx, φ⟩ =
+˜λ
+µ(x)
+ˆ
+eG′(Bd)
+(1 − |z|)pφ
+�
+z
+1 − |z|
+�
+d˜νx(z)
+=
+˜λ
+µ(x)
+ˆ
+Bd(1 − |z|)pφ
+�
+z
+1 − |z|
+�
+d(eG′)#˜νx(z)
+In particular νx ∈ M+
+1 (Rd) and {νx}x∈Ω is µ-measurable. Let λ = ˜νx(∂eG′(Bd))˜λ. Then
+λ ∈ M+(eF ′Ω) and it decomposes into
+λ =˜νx(∂eG′(Bd))
+˜λ
+µµ + ˜νx(∂eG′(Bd))˜λs
+=˜νx(∂eG′(Bd))
+˜λ
+µµ + ˜λs.
+For λ-almost every x ∈ eF ′Ω and for ψ ∈ C(∂eG′Bd) set
+⟨ν∞
+x , ψ⟩ =
+1
+˜νx(∂eG′(Bd))
+ˆ
+∂eG′(Bd)
+ψ(z)d˜νx(z),
+hereby
+ν∞
+x ∈ M+
+1 (∂eG′(Bd)).
+For each Φ ∈ A, its recession function is deﬁned to be the restriction
+φ∞ = φ|eF ′Ω×∂eG′(Bd).
+Finally, we obtain the formula
+⟨L, TΦ⟩ =
+ˆ
+eF ′(Ω)
+⟨˜νx, TΦ(x, ·)⟩d˜λ
+=
+ˆ
+eF ′Ω
+ˆ
+eG′(Bd)
+TΦd˜νx
+
+
+
+˜λ
+µdµ +
+=0
+����
+d˜λs
+
+
+ +
+ˆ
+eF ′Ω
+ 
+∂eG′(Bd)
+TΦd˜νx (˜νx(∂eG′(Bd))d˜λ)
+=
+ˆ
+Ω
+⟨νx, Φ(x, ·)⟩dµ +
+ˆ
+eF ′Ω
+⟨ν∞
+x , Φ∞(x, ·)⟩dλ
+and the representation of the Young Measure as the triple
+ν =
+�
+{νx}x∈Ω, λ, {ν∞
+x }x∈eF ′Ω
+�
+.
+where
+νx ∈ M+
+1 (Rd) for µ-almost every x ∈ Ω,
+λ ∈ M+(eF ′Ω), and
+ν∞
+x ∈ M+
+1 (∂eG′(Bd)) for λ-almost every x ∈ Ω.
+16
+
+We say that un converges in the sense of Young measures to ν, and write
+un
+Y p(µ,eA)
+−−−−−−→ ν
+or just
+un
+Y p(µ,A)
+−−−−−→ ν,
+where µ is the measure that "regulates and weights" oscillation and concentration of un, and
+eA is the compactiﬁcation at inﬁnity, generated by the family A.
+From this point onwards the family F ′ in Ω will always be the set of functions C(Ω).
+2.5
+Properties of generalised Young Measures and connection to Young
+Measures on the sphere
+Here we show how the above construction generalises the more classical setting of Young
+Measures on the sphere, see [Res68] for the original idea behind their representation, and
+[AB97] for their modern implementation in the calculus of variations. We then study how the
+new representation for generalised Young Measures behaves geometrically, and its properties.
+As a reminder, we state here the deﬁnition of integrands with a regular recession at inﬁnity.
+Deﬁnition 2.15 The set of integrands admitting a regular recession at inﬁnity is
+Ep(Ω, Rd) =
+�
+Φ ∈ C(Ω × Rd) : lim
+t→∞
+Φ(x, tz)
+tp
+∈ R locally uniformly in (x, z) ∈ Ω × Rd
+�
+.
+Because we intend to generalise the theory of Young Measures on functions with a regular
+recession, we need to extend the above class and at the same time preserve good topological
+properties of such a larger class. To do so, consider countably many functions gi ∈ BC(Bd)
+and their representations as integrands of p-growth gi(
+z
+1+|z|)(1 + |z|)p. We are interested in
+understanding how to represent, in a simple way, Young Measures relative to the compactiﬁ-
+cation generated by Ep ∪ {gi(
+z
+1+|z|)(1 + |z|)p}. In the language of Hausdorﬀ compactiﬁcations,
+set G′ = C(Bd) ∪ {gi, i ∈ N} and F ′ = C(Ω). Because C(Bd) ⊂ G′, the closure of the algebra
+generated by either family is separable, separates points from closed sets and contains the
+constants. Call F = G′ ∪ F ′, and without loss of generality, we can assume that ∥gi∥ ≤ 1 for
+all i.
+Lemma 2.16 C(eF Ω×Bd) is isometrically isomorphic to C(Ω×graph(gi)), where (gi): Bd →
+[−1, 1]N, z �→ (gi(z))i∈N and the topology on the target space is the product topology.
+It is
+metrised by
+d(z, w) = |z − w| +
+�
+i
+2−i|gi(z) − gi(w)|.
+Proof. By Lemma 2.14, p.
+14 it is enough to prove that C(egi,i∈NBd) ≂ C(graph(gi)).
+Theorem 2.12, p. 12 provides the isomorphism
+A(C(Bd) ∪ {gi, i ∈ N}) = A(1, z1, . . . , zd, gi, i ∈ N),
+and we conclude by noticing that (1, z1, . . . , zd, gi, i ∈ N)(Bd) is homeomorphic to graph(gi).
+The topological equivalence between such metrics and the product topology is standard.
+□
+17
+
+When gi ∈ C(Bd), then C(eF Ω × Bd) ≂ C(Ω × Bd), and therefore we recover the usual
+sphere representation for the compactiﬁcation induced by Ep. This means the obvious, that
+we can add functions that have a regular recession and we still obtain the same space (up to
+homeomorphisms).
+By deﬁnition, the compactiﬁcation of Bd can be represented by the space Γ of sequences
+{zn}n∈N ⊂ Bd such that zn → z ∈ Bd and gi(zn) converges for all i ∈ N, and two such
+sequences {zn}n∈N and {wn}n∈N are identiﬁed provided
+lim
+n |zn − wn| +
+�
+i
+2−i|gi(zn) − gi(wn)| = 0.
+Deﬁnition 2.17 We call egi,i∈N the compactiﬁcation, and ∂egi,i∈N = egi,i∈N\graph(gi, i ∈ N),
+we can write the triple Young measure as
+ν =
+�
+{νx}x∈Ω, λ, {ν∞
+x }x∈Ω
+�
+,
+where νx ∈ M+
+1 (Rd) for µ-almost every x ∈ Ω, λ ∈ M+(Ω), and ν∞
+x
+∈ M+
+1 (∂egi,i∈N) for
+λ-almost every x ∈ Ω.
+Notice that ∂egi,i∈N is an abuse of notation and refers to the boundary of the embedded space
+within the compactiﬁcation.
+So far we have constructed compactiﬁcations by "glueing" gis on top of the functions z1, . . . , zd;
+that is to say on top of the unit ball. It is sometimes useful to iterate this argument, to stack
+another countable family {fi, i ∈ N} on top of the compactiﬁcation egi,i∈N. This process gives
+the same compactiﬁcation as if we were considering the two families at once, as the following
+lemma shows.
+Lemma 2.18 Let egi,i∈N be a compactiﬁcation of Bd and fi ∈ BC(Bd). Then
+egi,fi,i∈N ≂ graphgraph(gi)fi.
+Proof. This is a trivial consequence of the fact that
+{(z1, . . . , zd, gi(z), fi(z)), z ∈ Bd} ={(z1, . . . , zd, w, z) : w = gi(z), y = fi(z), z ∈ Bd}
+(extending fi to constant in the variable w) ={(z1, . . . , zd, w, z) : y = fi(z, w), w = gi(z), z ∈ Bd}
+=graphgraph(gi)(fi), z ∈ Bd.
+□
+A standard application of the disintegration lemma yields the following.
+Corollary 2.19 Consider a compactiﬁcation egi,fi,i∈N and ν∞ ∈ M(∂egi,fi,i∈N), then
+ν∞ = P(zn)n∈Nd˜ν∞
+where ˜ν∞ ∈ M(∂egi), (zn)n ∈ ∂egi, and P(zn)n is a probability measure deﬁned on the space
+of subsequences (zni)i of (zn)n so that fi(zni) converges for all i ∈ N (with sequences being
+equivalents if all the limits are).
+18
+
+For the case of oscillating functions fi, we also write the compactiﬁcation as efiX ≡ efi and
+the convergence as
+vj
+Y p(µ,fi)
+−−−−−→ ν.
+When working with the sphere compactiﬁcation, we will simply write
+vj
+Y p(µ,Bd)
+−−−−−−→ ν, or just vj
+Y p(µ)
+−−−−→ ν.
+Also, because here we mainly consider the case p = 1, we omit the superscript p in Y p and
+write
+vj
+Y (µ,efi)
+−−−−−→ ν.
+We now study the relation of Young Measures with respect to diﬀerent compactiﬁcations and
+diﬀerent underlying measures µ ∈ M+(Ω). Using Chacon Lemma A.5, p. 48, we can prove
+the following structure theorems.
+Lemma 2.20 Let vj
+Y (µ,efi,i∈N)
+−−−−−−−→ (νx, λ, ν∞
+x ). Then for all ψ ∈ C0(Rd), we have
+ψ(vj) ⇀ ⟨νx, ψ⟩ weakly in L1(µ).
+Proof. Because ψ(vj) ∈ L∞ then is the sequence is equi-integrable and there is a subsequence
+that converges weakly in L1 to v. Because ψ∞ = 0, testing against φ ∈ D(Ω) we get
+ˆ
+Ω
+φψ(uj)dµ →
+ˆ
+Ω
+φvdµ =
+ˆ
+Ω
+φ⟨νx, ψ⟩dµ.
+□
+We can improve the above weak convergence result to show the following.
+Lemma 2.21 Let uj
+Y (µ)
+−−−→
+�
+νx, 0, N/A
+�
+. For every a ∈ L1(Ω, µ) such that a > 0 µ-a.e. and
+for all ψ ∈ C0(Rd) we have
+ψ
+�uj
+a
+�
+a ⇀ ⟨νx, ψ
+�
+·
+a(x)
+�
+⟩a(x) in L1(Ω, µ).
+As expected, this implies that oscillations do not depend on the particular compactiﬁcation
+chosen.
+Before proving the above results we show the following uniform approximation result:
+Lemma 2.22 Let µ ∈ M+(Ω) and a ∈ L1(Ω, µ), a > 0 µ-almost everywhere. There exists
+an ∈ L1(Ω), 0 < an < a, so that an(x) ∈ Q for all x ∈ Ω and
+∥an − a∥∞ +
+����
+a
+an
+− 1
+����
+∞
+n→∞
+−−−→ 0.
+19
+
+Proof. Let
+an =
+�
+k∈N,k≥1
+χa−1�
+[ k
+n, k+1
+n )
+� k
+n,
+where N is the set of strictly positive integers. Because an ≤ a then an ∈ L1 and it also
+assumes countably many values at a time. Also |an(x) − a(x)| ≤ 1
+n so it converges uniformly
+to a. Furthermore
+1 =
+k
+n
+k
+n
+≤ a(x)
+an(x) ≤
+k+1
+n
+k
+n
+= k + 1
+k
+and so
+a
+an converges uniformly to 1.
+□
+Now we can prove Lemma 2.21, p. 19
+Proof. Using the previous approximation, we write, for 1-Lipschitz ψ : Rd → R,
+ˆ
+Ω
+ψ
+�uj
+a
+�
+a =
+ˆ
+Ω
+=I
+�
+��
+�
+ψ
+�uj
+a
+�
+a − ψ
+�uj
+an
+�
+a +
+=II
+�
+��
+�
+ψ
+�uj
+an
+�
+a − ψ
+�uj
+an
+�
+an +ψ
+� uj
+an
+�
+an.
+The ﬁrst two terms are bounded by
+|I| ≤
+ˆ
+Ω
+a
+����
+uj
+a − uj
+an
+���� =
+ˆ
+Ω
+|uj|
+����1 − a
+an
+���� ≤ sup
+j
+∥uj∥
+����1 − a
+an
+����
+∞
+|II| ≤
+ˆ
+Ω
+�
+1 + |uj|
+an
+�
+|a − an| ≤ (1 + sup
+j
+|uj|)
+����1 − a
+an
+����
+∞
+,
+which goes to 0 as n → ∞ uniformly in j. As for the third term, calling Ek = a−1�
+[ k
+n, k+1
+n )
+�
+,
+we can use dominated convergence theorem to pass to the limit
+lim
+j
+ˆ
+Ω
+ψ
+�uj
+an
+�
+an = lim
+j
+�
+k
+ˆ
+Ek
+ψ
+�
+uj
+k
+n
+�
+k
+n =
+�
+k
+ˆ
+Ek
+⟨νx, ψ
+�
+·
+k
+n
+�
+⟩k
+n =
+ˆ
+Ω
+⟨νx, ψ
+� ·
+an
+�
+⟩an.
+Another application of the dominated convergence theorem will let us conclude the result.
+□
+We can ﬁnally conclude with a structure theorem regarding concentration.
+Proposition 2.23 Consider two separable algebras (that separate points from closed sets) A
+and B of G1 and let a ∈ L1(Ω, µ), a > 0 µ-a.e. Let vj ∈ L1(Ω, µ) be a sequence so that
+vj
+Y (µ,A)
+−−−−→
+�
+νx, λν, ν∞
+x
+�
+and
+vj
+a
+Y (a dµ,B)
+−−−−−−→
+�
+ηx, λη, η∞
+x
+�
+.
+Then νx =
+�
+·
+a(x)
+�
+# ηx, λν = λη = λ. Moreover, decomposing
+ν∞
+x = P ν
+(zn)nd˜ν∞
+x
+and
+η∞
+x = P η
+(zn)nd˜η∞
+x ,
+where ˜ν∞
+x
+and ˜η∞
+x
+are the projections on the sphere according to Corollary 2.19, p. 18, then
+˜ν∞
+x = ˜η∞
+x λ-a.e. with
+vj
+Y (µ,Bd)
+−−−−−→
+�
+νx, λ, ˜ν∞
+x
+�
+.
+20
+
+Proof. For all ψ ∈ C0(Rd) we have that ψ(vj) is equi-integrable so that
+ψ(vj) ⇀ ⟨ηx, ψ⟩ in L1(µ)
+and
+ψ
+�vj
+a
+�
+⇀ ⟨νx, ψ⟩ in L1(adµ).
+Next, identify vj with its subsequence and ﬁnd Ek so that vj ⇀ v in L1(Ek, µ) for all k. By
+inner approximation, we can assume that all such E′
+ks are compact. Consider now the sequence
+vjχEk. Then
+vjχEk
+Y (µ,A)
+−−−−→
+�
+ηxχEk + δ0χEc
+k, 0, N/A
+�
+.
+By Lemma 2.21, p. 19 we then have, for φ ∈ C0(Ω) and ψ ∈ C0(Rd), because Ω \ Ek is open,
+ˆ
+Ω
+φ⟨νx, ψ⟩a(x)dµ = lim
+j
+ˆ
+Ω
+φψ
+�vj
+a
+�
+adµ = lim
+j
+ˆ
+Ω\Ek
+φψ
+�vj
+a
+�
+adµ +
+ˆ
+Ek
+φψ
+�vj
+a
+�
+adµ
+=
+ˆ
+Ω\Ek
+φ⟨νx, ψ⟩adµ +
+ˆ
+Ek
+φ⟨ηx, ψ
+� ·
+a
+�
+⟩adµ.
+Next, let φ ∈ C(Ω), then
+lim
+j
+ˆ
+Ω
+φ|vj|dµ =
+ˆ
+Ω
+⟨νx, | · |⟩φdµ +
+ˆ
+Ω
+φdλν
+= lim
+j
+ˆ
+Ω
+φ
+���vj
+a
+��� adµ =
+ˆ
+Ω
+⟨ηx, | · |
+a(x)⟩φa(x)dµ +
+ˆ
+Ω
+φdλη.
+Using the previous part we conclude that λν = λη = λ.
+Finally, let f ∈ C(∂Bd) and extending by 1-homogeneity we obtain that
+lim
+j
+ˆ
+Ω
+φf(vj)dµ =
+ˆ
+Ω
+φ⟨νx, f⟩dµ +
+ˆ
+Ω
+φ⟨ν∞
+x , f ∞⟩dλ =
+ˆ
+Ω
+φ⟨νx, f⟩dµ +
+ˆ
+Ω
+φ
+ˆ ˆ
+f ∞dP ν
+(zn)d˜ν∞
+x dλν
+=
+ˆ
+Ω
+φ⟨νx, f⟩dµ +
+ˆ
+Ω
+φ
+ˆ
+f ∞d˜ν∞
+x dλν
+=
+ˆ
+Ω
+φ⟨νx, f
+�
+·
+a(x)
+�
+⟩a(x)dµ +
+ˆ
+Ω
+φ⟨η∞
+x , f ∞⟩dλ
+=
+ˆ
+Ω
+φ⟨νx, f⟩dµ +
+ˆ
+Ω
+φ
+ˆ
+f ∞dP η
+(zn)d˜η∞
+x dλη
+=
+ˆ
+Ω
+φ⟨νx, f⟩dµ +
+ˆ
+Ω
+φ
+ˆ
+f ∞d˜η∞
+x dλη.
+□
+Notice that the previous identiﬁcation with the concentration angle measure fails if we only
+consider Γ = A ∩ B which does not necessarily generate the sphere compactiﬁcation. This is
+so because sequences (uj)j can concentrate around values of a that are measure-discontinuous.
+However, equality holds true if a = 1.
+21
+
+Lemma 2.24 Following the assumptions of Proposition 2.23, p. 20, if a = 1, Γ = A ∩ B and
+writing
+ν∞
+x = P ν
+(zn)nd(γν)∞
+x
+and
+η∞
+x = P η
+(zn)nd(γη)∞
+x ,
+where γη and γν are the projections onto the compactiﬁcation generated by Γ, then
+(γν)∞
+x = (γη)∞
+x
+λ-a.e.
+Proof. This is proven similarly at the end of Proposition 2.23, p.
+20 and testing against
+functions belonging in A(Γ) and using the decomposition of angle Young Measures.
+□
+Next, we show that the lack of concentration is equivalent to the equi-integrability of the
+generating sequence.
+Theorem 2.25 Let (vj)j ∈ L1(Ω, µ, Rd) be so that
+vj
+Y (µ,efi,i∈N)
+−−−−−−−→
+�
+νx, λ, ν∞
+x
+�
+.
+Then the sequence (vj)j∈N is equi-integrable if and only if λ = 0.
+Moreover vj → v strongly in L1(Ω, µ, Rd) if and only if λ = 0 and νx = δv(x) for µ-a.e. x ∈ Ω.
+Proof. Because λ does not depend on the compactiﬁcation (see Proposition 2.23, p. 20), we
+can apply the same theorem from the sphere compactiﬁcation, [Rin18], p. 347, lemma 12.14
+and [Rin18], p. 348, corollary 12.15, to conclude.
+□
+Before stating the next two structure results, we prove that T −1 is a bounded operator from
+Lip(efi,i∈N) to Lip(Rd), provided the compactiﬁcation is generated by Lipschitz functions. In
+this case, by Lip(Rd) we mean the weighted norm
+∥f∥Lip(Rd) := ∥Tf∥∞ + sup
+x̸=y
+|f(x) − f(y)|
+|x − y|
+=
+����
+f
+1 + | · |
+����
+∞
++ sup
+x̸=y
+|f(x) − f(y)|
+|x − y|
+.
+As for the compactiﬁcation, the metric is always intended as in Lemma 2.16, p. 17.
+Lemma 2.26 Let efi,i∈N be a separable compactiﬁcation metrised by the usual metric, where
+fi ∈ Lip(Rd) are normalised so that ∥f∥Lip(Rd) ≤ 1. Then
+sup
+x̸=y
+|g(x) − g(y)|
+|x − y|
+≤ 5Lip(Tg, efi,i∈N)
+for all maps g: Rd → R.
+Proof. Without loss of generality assume that ∥Tg∥Lip ≤ 1, i.e. for all |x|, |y| < 1,
+����g
+�
+x
+1 − |x|
+�
+(1 − |x|) − g
+�
+y
+1 − |y|
+�
+(1 − |y|)
+���� ≤ |x − y| +
+�
+i
+2−i|Tfi(x) − Tfi(y)|.
+22
+
+Then
+|g(x) − g(y)| =
+����
+g(x)
+1 + |x|(1 + |x|) −
+g(x)
+1 + |x|(1 + |y|) +
+g(x)
+1 + |x|(1 + |y|) −
+g(y)
+1 + |y|(1 + |y|)
+����
+= |g(x)|
+1 + |x|
+���1 + |x| − 1 − |y|
+��� + (1 + |y|)
+����
+g(x)
+1 + |x| −
+g(y)
+1 + |y|
+����
+≤|x − y| + (1 + |y|)
+�����
+x
+1 + |x| −
+y
+1 + |y|
+���� +
+�
+i
+2−i
+����Tfi(
+x
+1 + |x|) − Tfi(
+y
+1 + |y|)
+����
+�
+.
+For all i we have that
+����Tfi
+�
+x
+1 + |x|
+�
+− Tfi
+�
+y
+1 + |y|
+����� =
+����
+fi(x)
+1 + |x| − fi(y)
+1 + |y|
+���� ,
+and therefore after multiplying by 1 + |y| we obtain
+����
+fi(x)
+1 + |x|
+�
+1 + |x| + (|y| − |x|)
+�
+− fi(y)
+���� =
+����fi(x) − fi(y) + fi(x)
+1 + |x|(|y| − |x|)
+����
+≤|fi(x) − fi(y)| + |fi(x)|
+1 + |x||x − y| ≤ 2|x − y|.
+□
+We now show that the above lemma allows us to test Young Measures on Lipschitz compact-
+iﬁcations against Lipschitz functions of Rd.
+Deﬁnition 2.27 (Kantorovich semi-norm) Let X be a metric space and µ ∈ M(X), then
+the (formal) Kantorovich norm of µ is
+∥µ∥K =
+sup
+∥φ∥Lip≤1
+ˆ
+X
+φdµ.
+The above formula induces a pseudo-distance between measures by setting d(µ, η)K = ∥µ −
+η∥K. It turns out that this is indeed a metric on the positive cone of non-negative Measures,
+Lemma A.6, p. 48.In particular, by taking Ψ ∈ Lip(efi,i∈N) and the pull-back T −1 we deduce
+the following.
+Lemma 2.28 Let efi,i∈N be a separable compactiﬁcation.
+Then every ν ∈ Y (efi,i∈N, µ) is
+deﬁned by testing it against Lipschitz functions of the form
+φ ⊗ ψ, where ∥φ∥Lip(Ω) ≤ 1, ∥ψ∥Lip(Rd) ≤ 1.
+For this reason, we remind once again of the norm we will be using on the space efi,i∈N
+throughout this thesis.
+Deﬁnition 2.29 We say that efi,i∈N is a Lipschitz compactiﬁcation if each fi is Lipschitz
+continuous, and renormalised so that Lip(Tf) ≤ 1. The norm on Lip(efi,i∈N) will always be
+∥g∥Lip(efi,i∈N) :=
+sup
+x∈efi,i∈N
+|g(x)| + sup
+x̸=y
+|g(x) − g(y)|
+defi,i∈N(x, y)
+23
+
+where
+defi,i∈N(x, y) = |x − y| +
+�
+i
+2−i|Tfi(x) − Tfi(y)|.
+To conclude this subsection, we state decomposition results for Young Measures regarding
+oscillation and concentration. Originally proven in the context of the sphere compactiﬁcation,
+[KR19], p. 29, we here extend them to general compactiﬁcations.
+Lemma 2.30 Let vj ∈ L1(Ω, µ) so that
+vj
+Y (efi,i∈N,µ)
+−−−−−−−→
+�
+νx, λ, ν∞
+x
+�
+.
+We can write vj = oj + cj, where oj ∈ L1(Ω, µ) is equi-integrable,
+oj
+Y (efi,i∈N,µ)
+−−−−−−−→
+�
+νx, 0, N/A
+�
+and cj ∈ L1(Ω, µ) so that
+cj
+Y (efi,i∈N,µ)
+−−−−−−−→
+�
+δ0, λ, ν∞
+x
+�
+.
+The converse is also true, for each such sequence oj, cj as above, their sum converges to the
+former Young Measure.
+Proof. A standard diagonal argument gives us kj ↑ ∞ so that oj = vjχ|vj| ≤ kj is equi-
+integrable and generates oj
+Y (efi,i∈N,µ)
+−−−−−−−→
+�
+νx, 0, N/A
+�
+. Then, letting cj = vj − oj, for η ∈ C(Ω),
+Tψ ∈ C(efi,i∈N) we have
+ˆ
+Ω
+η(ψ(cj) − ψ(vj)) =
+ˆ
+|vj|≤kj
+η(ψ(0) − ψ(oj)) +
+ˆ
+|vj|>kj
+η(ψ(vj) − ψ(vj))
+=
+ˆ
+Ω
+η(ψ(0) − ψ(oj)) →
+ˆ
+Ω
+η(ψ(0) − ⟨νx, ψ⟩).
+Writing ψ(cj) =
+�
+ψ(cj) − ψ(vj)
+�
++ ψ(vj) and letting j → ∞ we conclude.
+□
+We remark here that, when considering certain subsets of Y (for example Young Measures
+generated by gradients, see next section), oj and cj might generate diﬀerent types of Young
+Measures.
+The next lemma is an extension of the previous result.
+Lemma 2.31 Let vj ∈ L1(µ) and wj ∈ L1(µ) generate
+vj
+Y (µ,efi,i∈N)
+−−−−−−−→
+�
+δv(x), λη, η∞
+x
+�
+and
+wj
+Y (µ,efi,i∈N)
+−−−−−−−→
+�
+νx, λν, ν∞
+x
+�
+with λη ⊥ λν, for some v ∈ L1(µ). Then the sum of the sequence generates
+vj + wj
+Y (µ,efi,i∈N)
+−−−−−−−→
+�
+δv(x) ∗ νx, λν + λη, k∞
+x
+�
+,
+where
+k∞
+x =
+�
+ν∞
+x
+λν-a.e.
+η∞
+x
+λη-a.e.
+24
+
+Proof. Write wj = oj + cj as in the previous lemma and put bj = vj − v. We claim that
+bj + cj
+Y (µ,efi,i∈N)
+−−−−−−−→
+�
+δ0, λν + λη, k∞
+x
+�
+.
+No oscillation is a consequence of the fact that bj + cj → 0 in µ-measure.
+Next, let φ ∈
+C(Ω), ∥φ∥Lip ≤ 1 and Ψ ∈ efi,i∈N, ∥TΦ∥Lip ≤ 1 with Ψ(0) = 0. Let Eν and Eη be sets where
+λν and λη are concentrated, respectively. For ε > 0 ﬁnd Cν ⊂ Eν, Cη ⊂ Eη compact sets and
+Oν ⊃ Cν, Oη ⊃ Cη open sets such that
+λη(Ω \ Cη) + λν(Oη) + λν(Ω \ Cν) + λη(Oν) < ε.
+Consider a function ρ ∈ C(Rn) with χCη ≤ ρ ≤ χOη. We write
+ˆ
+Ω
+φ
+�
+Ψ(bj + cj) − Ψ(bj) − Ψ(cj)
+�
+(
+=I
+����
+ρ
++
+II
+� �� �
+1 − ρ)dµ.
+We estimate the ﬁrst guy by
+lim sup
+j
+|I| ≤ lim sup
+j
+2
+ˆ
+Ω
+ρ|bj| = 2
+ˆ
+Ω
+ρdλν ≤ 2λν(Ω ∩ Oη) ≤ 2ε.
+Similarly for the second term
+lim sup
+j
+|II| ≤ lim sup
+j
+2
+ˆ
+Ω
+(1 − ρ)|cj| ≤ 2λη(Ω \ Cη) ≤ 2ε.
+But the ﬁrst term converges to 0 and therefore we conclude for the representation of Young
+Measures.
+□
+2.6
+Terminology
+We dedicate this part to clarifying the terminology of Young Measures adopted throughout
+this paper.
+Deﬁnition 2.32 Given a separable algebra A of Gp that separates points from closed sets, a
+p-Young measure is a triple
+ν =
+�
+(νx)x∈Ω, λ, (ν∞
+x )x∈Ω
+�
+where
+1. (νx)x∈Ω is µ-measurable and νx ∈ M+
+1 (Rd) µ-a.e. x ∈ Ω.
+We call it the oscillation Young measure;
+2. λ ∈ M+(Ω).
+We call it the concentration measure;
+3. (ν∞
+x )x∈Ω is λ-measurable and ν∞
+x ∈ M+
+1 (∂eA) λ-a.e. x ∈ Ω. We call it the concentration
+angle Young measure;
+25
+
+4. the moment condition
+ˆ
+Ω
+ˆ
+Rd |z|pdνx(z) < ∞
+must hold.
+The collection of all such triples is denoted by Y p = Y p(Ω, µ, eA).
+Where obvious from the context, we will not specify the domain Ω, the measure µ, the family
+A or the target space Rd. Also, when λ = 0, i.e. when there is no concentration, there is no
+point in specifying the compactiﬁcation we are working with.
+From every triple ν =
+�
+νx, λ, ν∞
+x
+�
+one can construct the measure L ∈ C(eF Ω × Rd) and
+vice-versa.
+Lemma 2.33 The following equality holds:
+Y p = T ∗
+�
+L ∈ M+(eF Ω × Bd)+ :
+ˆ
+eF Ω×Bd φ(x)(1 − |ˆz|)pdL =
+ˆ
+Ω
+φ(x)dµ(x) ∀φ ∈ C(eGΩ)
+�
+.
+In particular Y p is a weak* closed and convex subset of A∗.
+Proof. Let L ∈ M+(eF Ω × Rd)+ as above. It was already shown that T ∗L ∈ Y p. On the
+other side, if ν =
+�
+νx, λ, ν∞
+x
+�
+, we let
+L = νxdµ + ν∞
+x dλ.
+Testing against a test function φ = φ(x) that only depends on x,
+ˆ
+eF Ω×Bd TφdL =
+ˆ
+eF Ω×Bd φ(x)(1 − |ˆz|)pdL =
+ˆ
+Ω
+φdµ.
+Conclude by noticing that the above characterisation amounts to
+Y p = T ∗
+
+
+�
+φ∈C(eF Ω)
+�
+L ∈ M+(eF Ω × Bd)+ :
+ˆ
+eF Ω×Bd φ(x)(1 − ˆz)pdL =
+ˆ
+Ω
+φdµ
+�
+ .
+□
+Remark 2.34 With a straightforward adaptation of a classical argument for the sphere com-
+pactiﬁcation, one can prove that given any Young Measure of the above form ν ∈ Y (Ω, µ, efi,i∈N)
+with supp(µ
+Ω) = Ω and µ non-atomic, then there is a sequence of smooth functions
+uj ∈ D(Ω, Rd) such that
+uj
+Y (Ω,µ,efi,i∈N)
+−−−−−−−−−→ ν.
+We do not transcribe the proof here because it won’t be used at any point in this work.
+26
+
+We now give a formal deﬁnition of what elementary Young Measures are, as a way to embed
+functions and measures.
+Deﬁnition 2.35 Let µ ∈ M+(Ω) and v ∈ Lp(Ω, µ, Rd), 1 ≤ p ≤ ∞.
+The corresponding
+elementary p-Young measure is
+ξv :=
+�
+(δv(x))x∈Ω, 0, N/A
+�
+∈ Y (µ).
+When p = 1, we extend the deﬁnition to l ∈ M(Ω, Rd) by setting, for l = l
+µdµ + ls,µ,
+ξl :=
+��
+δ l(x)
+µ(x)
+�
+x∈Ω
+, |ls,µ|,
+�
+δ ls,µ
+|ls,µ|
+�
+x∈Ω
+�
+∈ Y (µ, ∂Bd)
+Note that for Φ ∈ Ep we have
+≪ ξv, Φ ≫=
+ˆ
+Ω
+Φ(x, v(x))dν(x)
+and
+≪ ξl, Φ ≫=
+ˆ
+Ω
+Φ
+�
+x, l
+µ(x)
+�
+dµ(x) +
+ˆ
+Ω
+Φ∞
+�
+x, ls,µ
+|ls,µ|(x)
+�
+d|ls,µ|(x).
+In general, there is no clear way of deﬁning elementary Young Measures on compactiﬁcations
+that are larger than the sphere. We will see later, however, that this can be done in very speciﬁc
+cases when we have more structure on A and more information on the measure l ∈ M(Ω, Rd)
+we are trying to embed.
+Deﬁnition 2.36 (Barycentre of a p-Young measure) Let ν =
+�
+(νx)x∈Ω, λ, (ν∞
+x )x∈Ω
+�
+∈
+Y p(µ, A), where A is so that eA ≥ Bd (in the sense of compactiﬁcations, see Deﬁnition 2.9, p.
+12). We call its barycentre
+ν =
+�
+νx
+1 < p < ∞
+νxµ + ν∞
+x λ
+p = 1,
+which is the following quantity
+νx =
+ˆ
+Rd zdνx(z)
+ν∞
+x =
+ˆ
+∂eA
+zdν∞
+x .
+In the above deﬁnition, "≥" is the ordering over the set of Hausdorﬀ compactiﬁcations of a
+topological space (see the subsection on Hausdorﬀ compactiﬁcations). Moreover, the barycen-
+tre does not depend on the compactiﬁcation, as far as eA ≥ Bd.
+Indeed z = [zj]j=1,...,d
+extended to eA coordinate-wise, and so
+ˆ
+∂eA
+zdν∞
+x =
+ˆ
+∂Bd
+ˆ
+{(wn)n}
+zdPz((wn)n)dπ∂Bdν∞
+x =
+ˆ
+∂Bd zdπ∂Bdν∞
+x ,
+as the coordinate map z �→ zj is constant on sequences (wn)n that converge to the same value
+w ∈ ∂Bd.
+Notice that x �→ νx is µ-measurable and x �→ ν∞
+x is λ-measurable. In particular,
+ν ∈ Lp(Ω, µ, Rd) for 1 < p < ∞
+and
+ν ∈ M(Ω, Rd) for p = 1.
+It is easy to see that when 1 < p < ∞, vj ⇀ v ∈ Lp(Ω, µ, Rd) we have v = νv, and when
+p = 1, ρj ⇀∗ ρ ∈ C0(Ω, Rd)∗, then ρ = ξρ.
+27
+
+2.7
+Stronger notions of convergence
+To conclude the discussion about generalised Young Measures, we mention some stronger
+notions of convergence such as strict convergence and µ-strict convergence. These modes of
+convergence explain why we chose such canonical embedding for measures in the previous
+paragraph. Moreover, we give a simple example of why such canonical embedding has no
+meaning when the compactiﬁcation is larger than the sphere one.
+Deﬁnition 2.37 Let ηj, η ∈ M(Ω, Rd), we say that ηj
+s−→ η (ηj converges strictly to η) if
+ηj → η weakly* in C0(Ω, Rd)∗ and |ηj|(Ω) → |η|(Ω).
+It is easy to see that if ηj → η strictly, then |ηj| ⇀∗ |η| in C0(Ω, Rd)∗. The above convergence
+prevents small-scale cancellations and concentration on the boundary. However, it does not
+prevent oscillation. To prevent oscillation, we must choose a "weight" µ ∈ M+(Ω) and ask
+for convergence of ηj on the graph (µ, ηj). We thus obtain a notion of µ-strict convergence.
+Deﬁnition 2.38 We say that ηj
+µ−s
+−−→ η (ηj converges µ-strictly to η) if ηj → η weakly* in
+C0(Ω, Rd)∗ and (µ, ηj) s−→ (µ, η) in C0(Ω, R × Rd)∗.
+Similarly to what was observed in the case of strict convergence, such a notion implies that
+|(µ, ηj)| ⇀∗ |(µ, ηj)| in C0(Ω)∗. Moreover, µ-strict convergence of ηj to η simply amounts
+to weak* convergence and additional convergence of the following quantity: writing ηj =
+ηj
+µ dµ + ηs,µ
+j
+, ηs,µ
+j
+⊥ µ,
+|(ηj, µ)|(Ω) =
+����
+�ηj
+µ dµ, µ
+�
++ (ηs,µ
+j
+, 0)
+����
+=
+ˆ
+Ω
+�
+1 +
+����
+ηj
+µ
+����
+2
+dµ + |ηs,µ
+j
+|(Ω) →
+ˆ
+Ω
+�
+1 +
+����
+η
+µ
+����
+2
+dµ + |ηs,µ|(Ω) = |(η, µ)|(Ω).
+When µ = Ln, we refer to such convergence as area-strict convergence, in analogy with the
+area formula for smooth functions.
+Reshetnyak continuity theorem (see [Res68] for the original) shows that strict convergence is
+equivalent to the convergence of 1-homogeneous functionals.
+Theorem 2.39 Let f(x, z) ∈ C(Ω × Rd) be 1-homogeneous in z. If ηj → η strictly in the
+sense of measures, then
+ˆ
+Ω
+f
+�
+x, ηj
+|ηj|
+�
+d|ηj|(x) →
+ˆ
+Ω
+f
+�
+x, η
+|η|
+�
+d|η|(x)
+In case f is not 1-homogeneous but has an extension on the sphere compactiﬁcation, we can
+obtain the following auto-convergence result by requiring µ-strict convergence instead.
+Corollary 2.40 Let f ∈ E(Ω × Rd). If ηj
+µ−s
+−−→ η in C0(Ω, Rd)∗ then
+ˆ
+Ω
+f
+�
+x, ηj
+µ
+�
+dµ + f ∞
+�
+x,
+ηs,µ
+j
+|ηs,µ
+j
+|
+�
+d|ηs,µ
+j
+| →
+ˆ
+Ω
+f
+�
+x, η
+µ
+�
+dµ + f ∞
+�
+x, ηs,µ
+|ηs,µ|
+�
+d|ηs,µ|.
+28
+
+These are well-known results, but we write down a proof of the latter one because it gives an
+insight into how to move from one type of convergence to the other.
+Proof. Consider the so-called perspective functional
+˜f(x, z, t) =
+�
+f(x, z
+t )|t|
+t ̸= 0
+f ∞(x, z)
+t = 0
+which is positively 1-homogeneous in the last variable. By the Reshetnyak continuity theorem,
+we know that, for η ∈ M(Ω, Rd),
+ˆ
+Ω
+˜f(x, (η, µ)) =
+ˆ
+Ω
+f
+�
+x, η
+dµ
+�
+dµ + f ∞
+�
+x, ηs,µ
+|ηs,µ|
+�
+d|ηs,µ|
+is sequentially continuous in the µ-strict topology.
+□
+Upon taking f(x, z) = |z| we get that µ-strict convergence implies strict convergence, for every
+µ ∈ M+(Ω).
+In light of these results, for a ﬁxed measure µ ∈ M+(Ω), the canonical embedding of measures
+η ∈ M(Ω, Rd) into the set of Young Measures on the sphere
+η ∈ M(Ω, Rd) �→ ξη =
+�
+δ η
+µ , |ηs,µ|, δ ηs,µ
+|ηs,µ|
+�
+is sequentially µ-strictly continuous. This is a solid justiﬁcation for this choice of embedding.
+For the same reason, we can show why on larger compactiﬁcations we don’t have, in general,
+a canonical choice.
+Theorem 2.41 Let µ ∈ M+(Ω) with the property that there is x ∈ supp(µ
+Ω) with δx ⊥ µ,
+and let f ∈ C(Rd) of linear growth, f ̸∈ E1(Rd) (oscillate at inﬁnity). There is (uj)j∈N ⊂
+D(Ω, Rd), uj
+µ−strictly
+−−−−−−→ zδx in M(Ω, Rd) for some z ∈ ∂Bd, but
+ˆ
+Ω
+f(uj(x))dµ(x) does not converge.
+The above theorem implies that for all efi,i∈N ≥ ef (in the sense of compactiﬁcations), ξuj
+does not converge in Y (µ, efi,i∈N).
+Proof. Because of the assumptions on µ, we can ﬁnd x ∈ supp(µ
+Ω) so that δx ⊥ µ. Notice
+that the result is unchanged if we instead consider f(x) + C1|z| + C2, so taking C1, C2 > 0 big
+enough we can assume that f ≥ 0 everywhere. Find z ∈ ∂Bd and zj, wj → z so that
+lim
+n Tf(zj) = M and lim
+j Tf(wj) = m exist, and M > m.
+Next, because x ∈ supp(µ) then µ(Br(x)) > 0 for all r. There are two possible scenarios.
+First, x ∈ Ω, in which case we consider only those balls Br(x) so that B2r(x) ⊂ Ω. If x ∈ ∂Ω
+then we can δr ↓ 0 so that µ(Br(x))∩Ω−δ(r)) > 0. Either way, we call Br(x) or Br(x)∩Ω−δ(r)
+simply Br. Furthermore, we can ﬁnd ε = ε(r) > 0 so that
+Bε
+r = (Br)ε = {x ∈ Rn : d(x, Br) < ε} ⊂ Ω
+29
+
+and
+lim
+r↓0
+µ(Bε
+r)
+µ(Br) = 1.
+For each such r ﬁnd φr ∈ D(Bε
+r), 0 ≤ φr ≤ 1 so that φr(Br) = 1. Put ur =
+φr
+´ φrdµ. Clearly
+ur ⇀∗ δx in C(Ω)∗. Next, reﬁne the sequences (zj)j and (wj)j so that there is rj ↓ 0 so that
+ˆ
+Br2j
+φ2jdµ = 1 − |zj|
+and
+ˆ
+Bεr2j+1
+φ2j+1dµ = 1 − |wj|,
+and put
+uj =
+
+
+
+urjz j
+2
+if j is even,
+urjw j−1
+2
+if j is odd.
+First we show that uj
+µ−strictly
+−−−−−−→ zδx in M(Ω, Rd). Because zj, wj → z, it is enough to show
+that ur
+µ−strictly
+−−−−−−→ δx in M(Ω) as r ↓ 0. Because ur ⇀∗ δx in C(Ω)∗ then
+lim inf
+r→0 |(urdµ, µ)|(Ω) ≥ |(δx, µ)|(Ω).
+To achieve the opposite inequality, we calculate
+|(urdµ, µ)|(Ω) =|(0, µ)|(Ω \ Bε
+r) + |(ur, 1)dµ|(Ω ∩ Bε
+r) = µ(Ω \ Bε
+r) +
+ˆ
+Bεr
+�
+1 + usrdµ
+=µ(Ω \ Bε
+r) +
+´
+Bεr
+��´
+φrdµ
+�2 + φsrdµ
+´
+φrdµ
+≤µ(Ω \ Bε
+r) +
+´
+Bεr
+�
+µ(Bεr)2 + 1dµ
+µ(Br)
+=µ(Ω \ Bε
+r) + µ(Bε
+r)
+�
+µ(Bεr)2 + 1
+µ(Br)
+→ µ(Ω) + 1 = |(δx, µ)|(Ω).
+Next, we study how the integral behaves on alternating integers of the sequence (uj)j∈N. If
+j = 2i then
+lim inf
+i
+ˆ
+Ω
+f(u2i(x))dµ(x) ≥ lim inf
+i
+ˆ
+Br2i
+f
+�
+zi
+1 − |zi|
+�
+dµ = lim
+i Tf(zi) = M.
+On the other side, if j = 2i + 1 we get the upper bound
+lim sup
+i
+ˆ
+Ω
+f(u2i+1(x))dµ(x) ≤ lim sup
+i
+ˆ
+Bεr2i+1
+f
+�
+wi
+1 − |wi|
+�
+dµ = lim
+i Tf(wi) = m.
+□
+30
+
+Remark 2.42 The assumption on µ is sharp. If for all x ∈ supp(µ
+Ω) we have δx ̸⊥ µ, then
+all such x’s belong to Ω. Consider the atomic decomposition of µ:
+µ = µa + µn−a =
+�
+n
+µ(xn)δxn + µn−a,
+see Theorem A.8, p. 49. If µ(Ω \ {xn, n ∈ N}) > 0 then we could ﬁnd x ∈ Ω \ {xn, n ∈ N}
+and δx ⊥ µ, so that µn−a = 0. Then µ = �
+n µ(xn)δxn, and the set {xn, n ∈ N} contains its
+accumulation points. In particular {xn, n ∈ N} = supp(µ) is a compact subset of Ω. It is easy
+to see that, in this setting, if (φj)j∈N ⊂ L1(µ) is bounded in norm and
+φj
+Y (µ,efi,i∈N)
+−−−−−−−→
+�
+νx, λ, ν∞
+x
+�
+,
+then λ ≪ µ, i.e. λ = �
+n λ(xn)δxn (because the space is countable and compact). Also
+φj ⇀∗ φ =
+�
+νx + ν∞
+x
+λ
+µ
+�
+dµ
+in C0(X)∗, X = {xn, n ∈ N}. Assume also that φj → φ µ-strictly. This amounts to the
+following
+ˆ
+X
+f(φj)dµ →
+ˆ
+X
+⟨νx, f⟩ + ⟨ν∞
+x , f ∞⟩λ
+µdµ =
+ˆ
+X
+f(φ)dµ,
+(2.157)
+where f(z) =
+�
+1 + |z|2. f is a strictly convex function, therefore the inequality f(x + y) ≤
+f(x) + f ∞(y) is strict unless y = 0. We have
+⟨νx, f⟩ + ⟨ν∞
+x , f ∞⟩λ
+µ ≥f(νx) + f ∞
+�
+ν∞
+x
+λ
+µ
+�
+> f
+�
+νx + ν∞
+x
+λ
+µ
+�
+= f(φ)
+unless ν∞
+x
+= 0 λ-a.e. So φ = νx µ-a.e., and using convexity once again in (2.157), and the
+fact that f ∞ = 1, we get
+f(φ) =⟨νx, f⟩ + ⟨ν∞
+x , f ∞⟩λ
+µ ≥ f(νx) + λ
+µ = f(φ) + λ
+µ.
+So λ = 0, which implies that the sequence φj does not concentrate. Moreover, φ(x) = νx,
+which means that φj → φ in measure. Then φj → φ strongly in L1(µ), and Theorem 2.41, p.
+29 is false.
+31
+
+3
+Characterisation of gradient Young Measure
+on general compactiﬁcations
+In this section, we show that generalised gradient Young Measures are characterised by a
+set of integral inequalities. A characterisation result was previously obtained in the context
+of the sphere compactiﬁcation, see [KR10a] and [KR19] for the result on general diﬀerential
+operators, and it’s here extended to general compactiﬁcations.
+3.1
+Non-separability of the space of quasi-convex functions
+We start by showing that the set of quasi-convex functions having linear growth is non-
+separable. Lack of separability prevents sequential compactness and other essential properties
+that were used to develop the theory of generalised Young Measures (see the section above).
+Therefore, we are forced to consider only smaller countable collections of quasi-convex functions
+at the time, and cannot work with the entire class. To show that the class is non-separable,
+we modify the example by Muller [Mül92] and generate quasi-convex functions that oscillate
+at diﬀerent amplitudes in the same direction.
+Theorem 3.1 The space of quasi-convex functions f : R2×2 → R having linear growth is not
+separable with respect to ∥T · ∥∞,B2×2.
+The idea behind the proof is to construct an uncountable family {fΛ}Λ so that ∥TfΛ−TfΓ∥∞ ≥
+c for some universal constant c > 0 and all Λ ̸= Γ. We will split the proof of the above result
+into two diﬀerent parts. First, we show that we have quasi-convex functions that oscillate
+along every possible sequence of natural numbers.
+Proposition 3.2 There is c > 0 such that for every Λ ⊂ N inﬁnite so that Λc is also inﬁnite
+there exists fΛ : R2×2 → R quasi-convex and having linear growth such that
+1. fΛ(3j
+1) = 0 for all j ∈ Λ and
+2.
+fΛ(3j
+1)
+3j
+≥ c for all j ∈ Λc suﬃciently large.
+To prove this theorem we ﬁrst need a preliminary lemma, whose proof can be found in [Mül92],
+p. 299, lemma 4.
+Lemma 3.3 For k ∈ R+ we let
+gk : R2×2 → R, F �→ |F1,1 − F2,2| + |F1,2 + F2,1| + (2k − |F1,1 + F2,2|)+.
+Then there exists c1 > 0 such that
+Qgk(0) ≥ c1k
+for all suﬃciently large ks.
+We can then prove Proposition 3.2, p. 32.
+32
+
+Proof. Let Λ ⊂ N as in the proposition above and set fΛ = QgΛ where
+gΛ(F) = |F1,1 − F2,2| + |F1,2 + F2,1| + inf{|F1,1 + F2,2 − 2 · 3i|, i ∈ Λ}.
+We have that gΛ(3j
+1) = 0 for all j ∈ Λ and so fΛ(3j
+1) = 0 as well given that gΛ ≥ 0.
+We ﬁrst derive the following lower bound: compute
+gΛ(3j
+1 + G) = |G1,1 − G2,2| + |G1,2 + G2,1| + inf{|G1,1 + G2,2 + 2(3j − 3i)| : i ∈ Λ};
+because 3j is increasing we estimate, for arbitrary β ∈ R,
+inf
+i∈Λ |2(3j − 3i) + β| ≥
+�
+inf
+i̸=j |2(3j − 3i)| − |β|
+�+
+=
+�
+2(3j − 3j−1) − |β|
+�+,
+and so gΛ(3j
+1 + G) ≥ gk(G) for all matrices G and k = 3j − 3j−1, and gk given by
+gk(F) = |F1,1 − F2,2| + |F1,2 + F2,1| + (2k − |F1,1 + F2,2|)+
+does not depend on Λ. Apply Lemma 3.3, p. 32 to ﬁnd c > 0 (independent of Λ) such that
+fΛ(3j
+1) = QgΛ(3j
+1) ≥ Qgk(0) ≥ c1(3j − 3j−1) for j big enough.
+Dividing everything by 3j we get
+fΛ(3j
+1)
+3j
+≥ 2
+3c1 ≡ c.
+□
+It’s not a priori clear if these functions are "far away from each other at inﬁnity", as subsets
+of natural numbers could intersect inﬁnitely many times. To show that there is a wide variety
+of sequences that diﬀer at inﬁnity, we deﬁne the following relation.
+Deﬁnition 3.4 Given Γ, Λ any two sequences (not necessarily subsets of N), we say that
+Γ ≤ Λ provided Γ is eventually a subset of Λ, i.e.
+Λ = (ai),i∈N, Γ = (bi)i∈N,
+Λ ≤ Γ
+⇐⇒
+there exists k > 0 : (ai)i≥k is a subsequence of (bi)i≥0.
+Let [Λ] be the equivalence class of Λ with respect to ≤, i.e. Γ ∈ [Λ] if Γ ≤ Λ ≤ Γ.
+If Λ′ ∈ [Λ] and Γ′ ∈ [Γ] then Λ ≤ Γ if and only if Λ′ ≤ Γ′.
+We use
+�
+F, ≤
+�
+to indicate the set of equivalence classes with the inherited order.
+The above ordering is needed because, to show that we have uncountably many sequences
+that are independent of each other at inﬁnity, we will use Zorn’s lemma and ﬁnd a maximal
+set. One could also reason that the Stone-Cech compactiﬁcation of natural numbers is not
+metrisable and reason by contradiction using a suitably adapted version of Theorem 2.12, p.
+12, but we decided to not pursue this path.
+Lemma 3.5 There exists an uncountable family G ⊂ F such that for every diﬀerent pair
+Λ, Γ ∈ G, Λ is not comparable to either Γ nor Γc with respect to ≤.
+33
+
+The above means that we can ﬁnd a set G such that given any two sequences of natural
+numbers in Λ, Γ ∈ G, one is frequently in the other sequence and its complement, i.e. Λ ∩ Γ
+and Λ ∩ Γc are both inﬁnite.
+Proof. Consider the set of subsets
+G = {G ⊂ F : no pair within G is comparable according to ≤},
+ordered by inclusion ⊂. The above set is non-empty, which can be seen by taking Λ = 2N and
+Γ = 4N ∪ (4N + 1). Every chain in G has an upper limit given by its union. By Zorn’s lemma,
+there exists a maximal element.
+I claim that the maximal element has uncountably many
+elements. To prove the claim we ﬁrst assume that the maximal element G ⊂ G is countable or
+ﬁnite and show that it is always possible to extract an extra incomparable element.
+To do so, I will show that given any countable or ﬁnite collection of inﬁnite natural numbers
+{cj
+i, i ∈ N}j∈N there is {ci, i ∈ N} such that {ci, i ∈ N} ∩ {cj
+i, i ∈ N} is inﬁnite for all j and
+{ci, i ∈ N} ∩ {cj
+i , i ∈ N} < {cj
+i, i ∈ N} according to the order previously established. Consider
+the isomorphism
+N : F → {0, 1}N, {ci, i ∈ N} �→
+�
+Nci =
+�
+1
+if i ∈ {ck, k ∈ N}
+0
+otherwise
+�
+i∈N
+Practically speaking, we are replacing subsets of natural numbers to sequences that take values
+1 when the i-th number is in the set, 0 otherwise.
+Set initially Nci = 0 for all i. At i1 so that Nc1
+i1 = 1 for the ﬁrst time put Nci1 = 1. We then
+iterate "diagonally" in the following way. At the n-th iteration ﬁnd in+1 so that Ncj
+kj = 1
+for all 1 ≤ j ≤ n and some in < kj−1 < kj and Ncj
+tj = 1 for all 1 ≤ j ≤ n + 1 and
+kn < tj−1 < tj < tn+1 = in+1. Set Nctj = 1 for all 1 ≤ j ≤ n + 1. This procedure stops if the
+maximal set is ﬁnite, otherwise can be iterated countably many times.
+This way we guarantee that Nckj = 0 for in < kj and Ncj
+kj = 1, which means that Nci skips
+inﬁnitely many 1s from each sequence (Ncj
+i)i∈N, for all j ∈ N. On the other side Nctj = 1 =
+Ncj
+tj, tj ≤ in+1, so Nci is also frequently in every sequence (Ncj
+i)i∈N.
+Going back to our countable maximum element G =
+�
+{aj
+i, i ∈ N}, j ∈ N
+�
+, we can apply the
+previous construction to ﬁnd {ci, i ∈ N} ∈ F generated by the countable family
+{cj
+i , i ∈ N}j∈N =
+�
+{aj
+i, i ∈ N} , N \ {aj
+i, i ∈ N}
+�
+j∈N
+Because {ci, i ∈ N} is frequently and properly in {aj
+i, i ∈ N} and its complement N\{aj
+i, i ∈ N}
+for all j, then {ci, i ∈ N} is not comparable to any member of the family and this contradicts
+the maximality of our set.
+□
+We are now ready to prove Proposition 3.2, p. 32.
+Proof. By the lemma we can ﬁnd an uncountable set of uncomparable subsequences of N, call
+it G. I claim that if Λ, Γ ∈ G, Λ ̸= Γ then fΛ and fΓ have diﬀerent recessions at inﬁnity.
+Find {xn} ∈ efΛ with {xn} ≥ {3j
+1, j ∈ Λ}, where the inequality could be strict given that
+there might be more zero points at inﬁnity. Given our construction, we immediately have that
+34
+
+{xn} ̸≥ {3j
+1, j ∈ N \ Λ} as fΛ(3j
+1) ≥ c3j for all j ∈ N \ Λ. Also, Γ intersects N \ Λ and Λ
+inﬁnitely many times, and vice versa, so that
+lim sup
+n
+fΓ(xn)
+|xn|
+≥ lim sup
+j∈Λ∩Γ
+fΓ(3j
+1)
+3j
+≥ c,
+and
+lim inf
+n
+fΓ(xn)
+|xn|
+≤ lim inf
+j∈Λ∩Γ
+fΓ(3j
+1)
+3j
+= 0,
+which shows that {xn} ̸∈ efΓ. In terms of the non-separability, by the deﬁnition of xn, we have
+lim
+n
+fΛ(xn)
+|xn|
+= 0,
+thus
+∥TfΛ − TfΓ∥∞ ≥ lim sup
+n
+����
+fΓ(xn)
+|xn|
+− fΛ(xn)
+|xn|
+���� = lim sup
+n
+����
+fΓ(xn)
+|xn|
+���� ≥ c,
+where c is independent of Λ or Γ.
+□
+Given that the space is metric, having such a property prevents separability. We can end this
+section with the following corollary that incorporates higher dimensions:
+Corollary 3.6 The set of quasi-convex functions having linear growth f : Rm×n → R is sep-
+arable in the topology induced by ∥T(·)∥∞ if and only if min(m, n) = 1.
+Proof. If m or n is 1, quasi-convex functions are convex and therefore the space is separable.
+This is because convex functions admit a limit at inﬁnity in every direction; in this case, we
+actually recover the sphere compactiﬁcation.
+On the other side, for a function g: R2×2 → R we let
+gP ≡ g ◦ P : Rn×m → R,
+P : Rm×n → R2×2, M �→
+�M1,1, M1,2
+M2,1, M2,2
+�
+.
+If g is quasi-convex and locally bounded we let φ ∈ D(Q, Rm) and compute
+ˆ
+Q
+gP(Dφ + z) =
+ˆ
+Q⊂Rn−2 dLn−2
+ˆ
+[0,1]2 dx1x2g(PDφ + Pz) ≥
+ˆ
+Q⊂Rn−2 dLn−2gP(z) = gP(z),
+i.e. gP is quasi-convex. Then the set fΛP is uncountable and
+∥T(fΛP − fΓP)∥∞,Bm×n = ∥T(fΛ − fΓ)∥∞,B2×2 ≥ c
+if Γ ̸= Λ, so the space cannot be separable.
+□
+Notice that separability is important to achieve both the Young Measure representation and
+for sequential compactness in the inherited weak star topology of Young Measures.
+35
+
+3.2
+Characterisation of Gradient Young Measures
+In this section, we characterise Gradient Young Measures (on separable compactiﬁcation) via
+certain Jensen-like integral inequalities.
+It is worth mentioning that the result for the sphere compactiﬁcation, achieved in [KR10a], can
+be easily improved in consideration of the fact that lim supt→∞ f(tz)t−1 is 1-homogeneous rank
+one convex, and so convex at points rank(z) = 1 (see [KK16], p. 528)). In what follows, we
+cannot use this type of auto-convexity. In our context, f ∞ lives on a general compactiﬁcation
+and convexity at points of rank one, as a Jensen’s type inequality, is not necessarily true.
+To prove our result, we will adopt the same strategy as in [KR19].
+Preliminarily to stating the theorem, we deﬁne the upper recession of a function relative to a
+general compactiﬁcation.
+Deﬁnition 3.7 Let efi,i∈N be a separable compactiﬁcation. For any f having linear growth,
+we deﬁne
+f ♯,efi,i∈N((zn)) =
+sup
+(wn)n∈[(zn)n]
+lim sup
+n
+Tf(wn),
+where (wn)n are sequences belonging to the equivalence class of (zn)n within efi,i∈N.
+The reason why we introduce this notion is that the strategy for proving the characterisation
+theorem makes use of the trivial fact that f ≥ f qc, f qc being the quasi-convex envelope of f
+(see, for example, [Dac07])
+f qc(z) =
+inf
+φ∈D(Q)
+ˆ
+Q
+f(z + Dφ(x))dx.
+However, f qc does not need to live in the same class of separable quasi-convex functions, so
+the implication
+lim
+n
+f(zn)
+|zn|
+exists ⇒ lim
+n
+f qc(zn)
+|zn|
+exists
+could be false for some functions f.
+Fix any compactiﬁcation efi,i∈N and a function Tg ∈ efi,i∈N. If g ≥ f then
+g∞((zn)) = lim
+n Tg(zn) ≥
+sup
+(zn)∈[(zn)]
+lim sup
+n
+Tf(zn) = f ♯,efi,i∈N((zn)).
+f ♯,efi,i∈N does not need to be continuous on efi,i∈N with respect to its product topology. How-
+ever, we can show that it is still upper semi-continuous.
+Lemma 3.8 Let efi,i∈N be a separable compactiﬁcation and f a function having linear growth,
+then f ♯,efi,i∈N is upper semi-continuous on ∂efi,i∈N.
+Proof. Notice that ∂efi,i∈N is metrisable, so it is enough to show sequential upper semi-
+continuity. Let (zj
+n)n ∈ ∂efi,i∈N so that (zj
+n)n
+j−→ (zn)n. By the very deﬁnition of g♯,efi,i∈N((zj
+n)n),
+for ﬁxed ε > 0 we can ﬁnd nj ≥ kj, where kj is a natural number to be selected, so that
+g♯,efi,i∈N((zj
+n)n) ≤ ε + Tg((zj
+nj)), where (zj
+nj) is a constant sequence and belongs to efi,i∈N \
+36
+
+∂efi,i∈N. We want to show that we can select kj so that (zj
+nj)j belongs in the equivalence class
+of (zn)n. By applying the dominated convergence theorem we get
+lim
+j
+�
+i
+lim
+n 2−i|fi(zj
+n) − fi(zn)| = 0 = lim
+j lim
+n
+�
+i
+2−i|fi(zj
+n) − fi(zn)|,
+and so can ﬁnd kj so that
+�
+i
+2−i|fi(zj
+n) − fi(zn)| ≤ εj
+∀n ≥ kj,
+where 0 ≤ εj ↓ 0. This shows that the above sequence (zj
+nj)j ∈ [(zn)n] (the equivalence class),
+thus
+lim sup
+j
+g♯,efi,i∈N((zj
+n)n) ≤ ε + lim sup
+j
+Tg((zj
+nj)) ≤ ε + g♯,efi,i∈N((zn)n).
+By the arbitrariness of ε > 0 we conclude upper semi-continuity of g♯,efi,i∈N
+□
+In particular, g♯,efi,i∈N is Borel measurable on efi,i∈N. The above statement can be generalised
+to extensions of functions over more general compact metric spaces, but this version suﬃces
+for our scopes.
+We are interested in studying those Young Measures that are generated by gradients. So we
+deﬁne the following.
+Deﬁnition 3.9 We say that ν ∈ Y (efi,i∈N) is a (generalised) gradient Young Measure if there
+exists a sequence uj ∈ BV (Ω, Rm) such that
+Duj
+Y (efi,i∈N)
+−−−−−−→
+�
+νx, λ, ν∞
+x
+�
+.
+We use GY (efi,i∈N) to refer to these subsets of Young Measures.
+The convergence of measure derivatives has not been fully comprehended yet and it is still the
+subject of active research. This means that it is not so clear how rich the above class is, and
+with which frequency gradients oscillate - or at least within the setting of weak* convergence
+of measures.
+Remark 3.10 We can use the characterisation lemma for Young Measure on the sphere to
+show that the class is still quite vast. Indeed, by [KR10a], p. 541 Theorem 1, ﬁx any z = a ⊗ b
+and ν∞ ∈ P(∂B) with ν∞ = z. Then gradient Young Measure on the sphere
+�
+δ0, Hn−1
+(B ∩ b⊥), ν∞�
+satisﬁes the characterisation theorem from [KR10a], with u = aχx·b≥0 and so it is generated
+by a sequence of gradients Duj ∈ BV (B1(0)), B1(0) ⊂ Rn. Because Duj is bounded in BV ,
+we can ﬁnd a subsequence (ujk)k∈N such that
+Dujk
+Y (efi,i∈N), as k→∞
+−−−−−−−−−−−−→
+�
+δ0, Hn−1
+(B ∩ b⊥), η∞�
+,
+with clearly π∂Bη∞ = ν∞. Using Corollary 2.19, p. 18 to write η∞ = Pzdν∞, z ∈ ∂Bd, it
+remains an open question to understand how many probabilities Pz over subsequences zn → z
+can be generated by gradients.
+37
+
+We now state the main theorem of this section.
+Theorem 3.11 Let Ω ⊂ Rn be a bounded Lipschitz domain and efi,i∈N be a separable compact-
+iﬁcation of quasi-convex functions and consider a generalised Young Measure ν ∈ Y (efi,i∈N)
+that satisﬁes λ(∂Ω) = 0.
+Then ν ∈ GY (efi,i∈N) is a Young Measure generated by a sequence
+(φj ⋆ (Du
+Ω) + Duj)
+Y (efi,i∈N)
+−−−−−−→
+�
+νx, λ, ν∞
+x
+�
+,
+where u ∈ BV (Ω, Rm), uj ∈ D(Ω, Rm) and ∥uj∥1 → 0, and φj is any sequence of molliﬁers
+with φj ⇀∗ δ0, if and only if there is u ∈ BV (Ω, Rm) such that
+1. ≪ 1 ⊗ | · |, ν ≫< +∞, and for all f quasi-convex and having linear growth,
+2. f(∇u(x))dx ≤ ⟨νx, f⟩dx + ⟨ν∞
+x , f ♯,efi,i∈N⟩ λ
+Ln dx and
+3. f ∞(Dsu) ≤ ⟨ν∞
+x , f ♯,efi,i∈N⟩dλs.
+We can adjust the above theorem to ﬁx the boundary of the converging sequence so that it’s
+always equal to u in the sense of trace.
+Lemma 3.12 If ν ∈ Y (efi,i∈N) is generated by a sequence
+φj ⋆ (Du
+Ω) + Duj
+as above, then there exists another sequence vj ∈ C∞(Ω) ∩ W 1,1
+u (Ω) such that
+D(vj + uj)
+Y (efi,i∈N)
+−−−−−−→ ν.
+In particular, ν ∈ GY (efi,i∈N).
+Proof. We can ﬁnd uj → u strictly in BV (Ω) with uj ∈ C∞(Ω) ∩ W 1,1
+u (Ω), see for example
+[KR10a] Lemma 1 for a proof of this fact. In the construction of the ujs just mentioned, it is
+possible to select φj ⋆ (Du
+Ω) on Ω−ε for j big enough, φj as in Theorem 3.11, p. 38. Also,
+without loss of generality, we can assume that |Du|(∂Ω−ε) = |Duj|(∂Ω−ε) = 0. Because the
+fis are all Lipschitz, it is enough to test against f ∈ Lip(Rm×n) with Lip(f) ≤ 1. We then
+compute
+ˆ
+Ω
+|f(φj ⋆ (Du
+Ω) + Dvj) − f(Duj + Dvj)|dx ≤
+ˆ
+Ω
+|φj ⋆ (Du
+Ω) − Duj|
+≤
+ˆ
+Ω\Ω−ε
+|φj ⋆ (Du
+Ω)| + |Duj| = Ij + IIj
+By strict convergence of both integrands, we have that
+lim sup
+j
+Ij + IIj ≤ 2|Du|(Ω \ Ω−ε),
+and so use a diagonal argument to conclude the existence and equality of the limit Young
+Measure.
+□
+38
+
+It’s implicit in Theorem 3.11, p. 38 that
+Du = ν = ⟨νx, ·⟩dx + ⟨ν∞
+x , ·⟩dλ.
+Also, the above inequalities can be written in the sense of distribution, in the form
+ˆ
+Ω
+φ(x)⟨νx, f⟩dx +
+ˆ
+Ω
+φ(x)
+ˆ
+∂efi,i∈N
+f ♯,efi,i∈Ndν∞
+x dλ
+≥
+ˆ
+Ω
+φ(x)f(∇u(x))dx + φ(x)f ∞
+� Dsu
+|Dsu|
+�
+d|Dsu|
+for all φ ∈ D(Ω), φ ≥ 0.
+To prove the characterisation result we will follow the same strategy as in [KR19]. We initially
+prove the result for homogeneous gradient Young Measures and then extend the theorem to
+the inhomogeneous case. Notice that Young Measures that act on functions f = f(z) that
+only depend on z can be represented by
+ˆ
+Ω
+⟨νx, f⟩dx +
+ˆ
+Ω
+⟨ν∞
+x , f ∞⟩dλ =
+ˆ
+Ω
+fdν0 +
+ˆ
+∂efi,i∈N
+f ∞dν∞,
+where for efi,i∈N the separable compactiﬁcation that extends f,
+ν0 = νxdLn ∈ M+(Ω)
+and
+ν∞ = ν∞
+x dλ ∈ M+(∂efi,i∈N).
+The (push-forward) Kantorovich metric is then
+∥(ν0, ν∞)∥K =
+sup
+Φ∈H,∥TΦ∥Lip(efi,i∈N)≤1
+�����
+ˆ
+Rd Φdν0 +
+ˆ
+efi,i∈N
+Φ∞dν∞
+����� .
+For z ∈ Rd we let Y be the set of pairs
+�
+ν0, ν∞�
+∈ M+
+1 (Rd) × M+(efi,i∈N) such that there is
+a sequence uj ∈ D(Q, Rm), where Q is the unit cube, so that z + Duj
+Y (efi,i∈N)
+−−−−−−→
+�
+ν0, ν∞�
+and
+∥uj∥1 → 0. The following proposition follows from obvious variations of the proofs contained
+in [KR19], p. 8, lemmas 3.7,3.8,3.9. The proofs are essentially the same as they only use the
+separability of the compactiﬁcation.
+Lemma 3.13 The family {εz+Du : u ∈ D(Q, Rm)} is weakly* dense in Y, and Y is a weak*
+closed and convex subset of homogeneous Young Measures.
+We can now prove the main theorem in case
+�
+ν0, ν∞�
+is a homogeneous gradient Young
+Measure.
+Proposition 3.14 Let ν =
+�
+ν0, ν∞�
+∈ M+
+1 (Ω) × M+(∂efi,i∈N) and z ∈ Rm×n. Then ν ∈ Y
+if and only if there is z ∈ Rm×n such that
+ˆ
+Rm×n fdν0 +
+ˆ
+∂efi,i∈N
+f ♯,efi,i∈Ndν∞ ≥ f(z)
+for all f : Rm×n → R quasi-convex and having linear growth.
+39
+
+Proof. Suppose that ν ∈ Y and let z + Duj, uj ∈ D(Q, Rm) be the generating sequence, i.e.
+for all Φ ∈ T −1efi,i∈N,
+ˆ
+Q
+Φ(z + Duj)dx → ⟨ν, Φ⟩ =
+ˆ
+Rm×n Φdν0 +
+ˆ
+∂efi,i∈N
+Φdν∞.
+Fix an arbitrary f having linear growth and quasi-convex and let ef,fi,i∈N the bigger compact-
+iﬁcation. Upon extracting a subsequence we have that
+z + Duj
+Y (ef,fi,i∈N)
+−−−−−−−→
+�
+ν0, ˜ν∞�
+,
+where we identify the gradient Young Measure with its tensor products as f = f(z). By quasi-
+convexity, we have
+ˆ
+Rm×n fdν0 +
+ˆ
+∂ef,fi,i∈N
+f ∞d˜ν∞ = lim sup
+j
+ˆ
+Q
+f(z + Duj)dx ≥ f(z).
+On the other side, using the decomposition of angle concentration Young Measure Corollary 2.19,
+p. 18 we also obtain that
+ˆ
+∂ef,fi,i∈N
+f ∞d˜ν∞ =
+ˆ
+∂efi,i∈N
+ˆ
+f ∞dP(zn)ndν∞ ≤
+ˆ
+∂efi,i∈N
+f ♯,efi,i∈Ndν∞.
+For the other implication, because Y is weakly* closed and convex, we can write Y = ∩H where
+H are half-spaces containing Y, which can be written as
+H = {l ∈ H∗ : l(Φ) ≥ t}.
+In particular, we can test the above inequality against εz+Du and get
+t ≤ εz+Du(Φ) ≤
+ˆ
+Q
+Φ(z + Du)dx
+for all u ∈ D(Q, Rm). Passing to the inﬁmum over all such us we deduce t ≤ Φqc(z) and so
+⟨ν, Φ⟩ =
+ˆ
+Rm×n Φdν0 +
+ˆ
+∂efi,i∈N
+Φ∞dν∞
+≥
+ˆ
+Rm×n Φqcdν0 +
+ˆ
+∂efi,i∈N
+(Φqc)♯,efi,i∈Ndν∞ ≥ Φqc(z) ≥ t
+which shows that ν ∈ H.
+□
+3.2.1
+Inhomogenization
+In what follows, we will prove a semi-approximation result for the absolutely continuous and
+singular parts separately and then put them together via Lemma 2.31, p. 24. In each case,
+we will use a covering argument to boil it down to the homogeneous case, which was solved in
+the above section.
+Consider a standard molliﬁer φt(x) = tn−1φ(x
+t ), where φ ∈ D(Q) and let M = ∥Dφ∥∞. Also,
+unless otherwise speciﬁed, the norm on Rn is the maximum norm ∥x∥ = maxi |xi|.
+40
+
+Lemma 3.15 Given ε > 0 there is tε > 0 and a family ϕt ∈ D(Ω, Rm) with ∥ϕt∥1 ≤ ε so that
+����
+ˆ
+Ω
+ηΦ(0) + η⟨Φ∞, ν∞
+x ⟩dλs −
+ˆ
+Ω
+ηΦ(φt ⋆ (ν∞dλs) + Dϕt)dx
+���� < ε
+for all t ∈ (0, tε) uniformly in ∥η∥Lip ≤ 1 and ∥TΦ∥Lip,graph(f) ≤ 1.
+The idea behind this approximation result is the following. The singular part of the centre
+of mass (which is just Du ∈ M(Ω, Rd)) is approximated by molliﬁcation. Such a procedure
+generates area-strictly convergent smooth approximations.
+At the same time, we generate
+angle concentration and oscillation via compactly supported functions. Because the ﬁrst type
+of convergence is very strong, and the latter doesn’t concentrate, the two modes of convergence
+don’t interfere with each other. Notice that this strategy would not be possible using the bare
+notion of weak* convergence because of the lack of quantiﬁability, whereas the (equivalent in
+this case) Kantorovich metric gives us an "exact" quantity to approximate.
+Before proving the above statement we remind that, according to Lemma 2.26, p. 22, T pulls
+back bounded sets of Lipschitz functions on efi,i∈N to bounded sets of Lipschitz functions on
+Rm×n (provided fi are Lipschitz). Therefore, all the functions in the following theorem can
+be taken to be, after renormalisation, 1-Lipschitz in both spaces.
+From now on, after ﬁxing a compactiﬁcation, we will always identify
+∥TΦ∥Lip = ∥TΦ∥Lip(efi,i∈N) = ∥TΦ∥∞ + sup
+x̸=y
+|TΦ(x) − TΦ(y)|
+|x − y| + �
+i 2−i|Tfi(x) − Tfi(y)|.
+Proof. Fix ε > 0 and apply Luzin’s theorem to the λs map
+x ∈ Ω → (δ0, ν∞
+x ) ∈ M+
+1 (Rd) × M+(∂efi,i∈N) ֒→
+�
+(T −1efi,i∈N)∗�+
+to ﬁnd a compact set C = Cε ⊂ Ω with λs(Ω \ C) < λs(Ω)ε restricted to which the above
+map is uniformly continuous, with modulus of continuity ω = ωε. Without loss of generality,
+assume that Ln(Cs) = 0 and because λs(∂Ω) = 0 then
+∆ = ∆ε = d(Cs, ∂Ω) > 0.
+For the moment, ﬁx two integers a, b ∈ N and put t = 2−a, so that φt > 0 if and only if
+∥x∥ < t. Let a be so large that
+2t ≤ ∆
+and
+a ≥ log2
+� 2
+∆
+�
+.
+Denote by F the collection of a+b-th generation dyadic cubes Q in Rn so that d(Q, ∂Ω) > 2−a,
+and for each such Q ∈ F we deﬁne
+rQ =
+ 
+Q
+φ ⋆ (λs
+Cs)dx.
+Notice that rQ > 0 means that dist(Q, Cs) < t, and so for each such Q we can ﬁnd xQ ∈ Cs
+so that d(xQ, Q) < t. Denote by Fs the set of those Q ∈ F for which rQ > 0. In particular, if
+Q ∈ Fs we can ﬁnd xQ ∈ Cs so that supQ ∥x − xQ∥ < 2t.
+41
+
+For every quasi-convex function having linear growth we have
+f(z + w) ≤ f(z) + f ∞(w)
+for all z ∈ Rm×n and rank(w) = 1, see [KK16], p. 536, lemma 2.5 (we don’t need regular
+recession for this result to hold). Then by assumption, we have
+f(rQν∞
+xQ) ≤ f(0) + rQf ∞(ν∞
+xQ) ≤ f(0) + rQ
+ˆ
+∂efi,i∈N
+f ♯,efi,i∈Ndν∞
+xQ
+for all f quasi-convex and having linear growth.
+Going back to the homogeneous case Proposition 3.14, p. 39, we can select ϕQ ∈ D(Q, Rm)
+with ∥ϕQ∥1 < ελs(Q) such that
+∥(δ0, ν∞
+xQrQ) − εrQν∞
+xQ+DϕQ∥K < ε.
+Deﬁne ϕ = �
+Q∈Fd ϕQ ∈ D(Ω, Rm) and ∥ϕ∥1 ≤ ελs(Ω). The sought-after map is then
+ξs = φ ⋆ (ν∞
+x dλs + Dϕ) ∈ D(Rn, Rd).
+To prove that this function is the desired one, we ﬁx ∥η∥Lip ≤ 1, ∥Ψ∥Lip(efi,i∈N) ≤ 1 as in the
+assumptions. We have
+ˆ
+Ω
+η⟨Φ∞, φ ⋆ (ν∞dλs)⟩dx =
+ˆ
+Ω
+η⟨Φ∞, φ ⋆ (ν∞dλs
+Cs)⟩dx +
+=E1
+�
+��
+�
+ˆ
+Ω
+η⟨Φ∞, φ ⋆ (ν∞dλs
+Ω \ Cs)⟩dx,
+and |E1| ≤ ελs(Ω). Notice that here
+ˆ
+Ω
+η⟨Φ∞, φ ⋆ (ν∞dλs
+U)⟩dx =
+ˆ
+Ω
+η(x)
+ˆ
+U
+φ(x − y)
+ˆ
+∂efi,i∈N
+Φ∞dν∞
+y dλs(y)dx
+where U = Ω or Cs. Since for each Q ∈ F with rQ = 0
+ˆ
+Q
+η⟨Φ∞, φ ⋆ (ν∞dλs
+Cs)⟩dx = 0
+and dist(∪F, ∂Ω) > 2t, we get
+ˆ
+Ω
+⟨Φ∞, φ ⋆ (ν∞dλs
+Cs)⟩dx =
+�
+Q∈Fs
+ˆ
+Q
+η⟨Φ∞, φ ⋆ (ν∞dλs
+Cs)⟩dx + E2
+=
+�
+Q∈Fs
+�ˆ
+Q
+ηdx⟨Φ∞, ν∞
+xQ⟩rQ + EQ
+3
+�
++ E2,
+42
+
+where |E2| ≤ λs(Cs ∩ (∂Ω)2t). The third error is estimated in the following way:
+|EQ
+3 | ≤
+����
+ˆ
+Q
+�
+η −
+ˆ
+Q
+η
+�
+⟨Φ∞, φ ⋆ (ν∞dλs
+Cs)⟩dx
+����
++
+����
+ˆ
+Q
+η
+�ˆ
+Q
+⟨Φ∞, φ ⋆ (ν∞dλs
+Cs)⟩dx − ⟨Φ∞, ν∞
+xQ⟩rQ
+�����
+≤∥η∥Lip Ln(Q)
+1
+n ∥Φ∞∥
+ˆ
+Q
+φ ⋆ λsdx
++ ∥η∥Lip
+ˆ
+Q
+ˆ
+Cs φ(x − y)⟨Φ∞, ν∞
+y − ν∞
+xQ⟩dλs(y)dx.
+In particular, we obtain
+|EQ
+3 | ≤t
+ˆ
+Q
+φ ⋆ λsdx +
+ˆ
+Q
+ˆ
+Cs φ(x − y)ω(∥y − xQ∥)dλs(y)dx
+≤(t + ω(3t))
+ˆ
+Q
+φ ⋆ λsdx.
+From each Q ∈ Fs we get
+Φ(0) + ⟨Φ∞, ν∞
+xQ⟩rQ =
+ˆ
+Q
+Φ(rQν∞
+xQ + DφQ)dx +
+|·|≤ε
+����
+EQ
+4 .
+Further computations show that
+ˆ
+Q
+|Φ(rQν∞
+xQ + DφQ) − Φ(0)|dx ≤∥εrQν∞
+xQ+DφQ∥K
+≤∥(δ0, ν∞
+xQrQ)∥K + ε ≤ 1 + rQ + ε
+and consequently
+ˆ
+Q
+η
+ˆ
+Q
+Φ(rQν∞
+xQ + DφQ)dx =
+ˆ
+Q
+ηΦ(rQν∞
+xQ + DφQ)dx + EQ
+5 ,
+where the error term is upper bounded by
+|EQ
+5 | ≤ sup
+Q
+����η −
+ˆ
+Q
+η
+���� Ln(Q)(1 + rQ + ε) ≤ Ln(Q)
+1
+n
+ˆ
+Q
+(2 + φ ⋆ λs)dx.
+Finally, we estimate the last term with
+ˆ
+Q
+ηΦ(rQν∞
+xQ + DφQ)dx =
+ˆ
+Q
+ηΦ(φ ⋆ ν∞dλs) + DφQ)dx + EQ
+6 .
+To bound the 6th error term we introduce an extra quantity
+����
+ˆ
+Q
+η
+�
+Φ(φ ⋆ ν∞dλs) + DφQ)dx − Φ(φ ⋆ ν∞dλs
+Cs) + DφQ)
+�
+dx
+���� ≤
+ˆ
+Q
+φ ⋆ (λs
+Ω \ Cs)dx,
+43
+
+and
+����
+ˆ
+Q
+η
+�
+Φ(rQν∞
+xQ + DφQ)dx − Φ(φ ⋆ ν∞dλs
+Cs) + DφQ)
+�
+dx
+����
+≤
+ˆ
+Q
+|rQν∞
+xQ − φ ⋆ (ν∞dλs
+Cs)|dx
+≤
+����
+ˆ
+Q
+φ ⋆
+�
+(ν∞
+xQ − ν∞�
+dλs
+Cs)dx
+���� +
+ˆ
+Q
+����
+ 
+Q
+φ ⋆ (ν∞dλs
+Cs)dx′ − φ ⋆ (ν∞dλs
+Cs)
+���� dx
+≤
+ˆ
+Q
+ˆ
+Cs φ(x − y)|ν∞
+xQ − ν∞
+y |dλsdx +
+ˆ
+Q
+����
+ 
+Q
+φ ⋆ (ν∞dλs
+Cs)dx′ − φ ⋆ (ν∞dλs
+Cs)
+���� dx
+≤ω(3t)
+ˆ
+Q
+φ ⋆ λsdx + EQ
+7 .
+The 7th error term is estimated by
+EQ
+7 ≤
+ˆ
+Q
+ 
+Q
+ˆ
+Cs
+��φ(x′ − y) − φ(x − y)
+��|ν∞
+y |dλs(y)dx′dx
+≤√n
+ˆ
+Q
+ 
+Q
+ˆ
+Q+tQ
+∥x − x′∥
+ˆ 1
+0
+��Dφ(x + (x′ − x)τ)(x′ − x)
+��dτdλs(y)dx′dx.
+Given the scaling of φ = φt with respect to t, we have |Dφ| ≤ t−1M(χQ)t, so the above can be
+bounded by
+EQ
+7 ≤ √nM Ln(Q)
+1
+n
+t
+ˆ
+Q
+(χ2Q)t ⋆ λsdx.
+For our choice of a and b, we have that Ln(Q) = 2−n(a+b). With ξs deﬁned above we obtain
+that
+ˆ
+Ω
+η⟨Φ∞, φ ⋆ (ν∞dλs)⟩dx =
+ˆ
+⋒Fs ηΦ(ξs) + E,
+where
+|E| ≤ελs(Ω) + (t + ω(3t))
+ˆ
+∪Fs
+�
+φ ⋆ λs + 2−a−b(2 + φ ⋆ λs)
++ φ ⋆ (λs
+Ω \ Cs) + ω(3t) φ ⋆ λsdx + √nM2−b(χ2Q)t ⋆ λs�
+dx
+≤
+�
+2ε + 2−a + 2ω(32−a) + 2−a−b + cnM2−b�
+λs(Ω) + 21−a−bLn(Ω).
+To conclude we add
+ˆ
+Ω\∪Fs ηΦ(ξs)dx =
+ˆ
+Ω\∪Fs ηdxΦ(0)
+to both sides, and obtain
+ˆ
+Ω
+η
+�
+Φ(0) + ⟨Φ∞, φ ⋆ (ν∞dλs
+Ω)⟩
+�
+dx =
+ˆ
+Ω
+Φ(ξs)dx + E +
+ˆ
+∪Fs ηdxΦ(0).
+44
+
+Because ∪Fs ⊂ (Cs)2t and since Ln(Cs) = 0 we can ﬁnd aε ≥ a, bε ≥ b such that
+|E| +
+����
+ˆ
+∪Fs ηdxΦ(0)
+���� ≤ 3ε(Ln + λs)(Ω).
+The left-hand side tends to
+ˆ
+Ω
+ηdxΦ(0) +
+ˆ
+Ω
+η⟨Φ∞, ν∞
+x ⟩dλs(x)
+as a → ∞, uniformly in η and Φ, and this concludes the proof.
+□
+We now move on to the absolutely continuous part, which is proven similar and is a bit easier
+to construct.
+Lemma 3.16 Let ε > 0, there is tε > 0 and ψt ∈ D(Ω, Rm) with ∥ψt∥1 ≤ ε so that
+����
+ˆ
+Ω
+η(⟨Φ, νx⟩ + λa(x)⟨Φ∞, ν∞
+x ⟩)dx −
+ˆ
+Ω
+ηΦ
+�
+φt ⋆ (ν + ν∞λa(x))dx
+Ω + Dψt
+�
+dx
+���� < ε
+holds for t ∈ (0, tε), uniformly in ∥η∥Lip ≤ 1 and ∥TΦ∥Lip(efi,i∈N) ≤ 1.
+Proof. Fix ε ∈ (0, 1) and apply Luzin’s theorem to the Ln-measurable map
+Ω ∋ x �→ (νx, λa(x)ν∞
+x ) ∈ M+
+1 (Rd) × M+(∂efi,i∈N) ֒→
+�
+(T −1efi,i∈N)∗�+
+to ﬁnd a compact set Ca ⊂ Ω such that
+ˆ
+Ω\Ca M(x)dx < ε, M(x) = ⟨νx, | · |⟩ + λa(x),
+and ω be the modulus of continuity over Ca, i.e.
+∥(νx, λa(x)ν∞
+x ) − (νy, λa(y)ν∞
+y )∥K ≤ ω(∥x − y∥)
+for all x, y ∈ Ca.
+Fix d ∈ N and s ∈ (0, 1) and let Fa be the family of dyadic cubes in Rn of side length t = 2−d,
+i.e.
+Fa = {Q ∈ Dd : d(Q, ∂Ω) > t, Ln(Q ∩ Ca) > sLn(Q)},
+where the distance is induced by ∥ · ∥∞ over vectors in Rn, and d and s will be selected later in
+the proof. For every Q ∈ Fa select xQ. By Proposition 3.14, p. 39 we have ψQ ∈ D(Q, Rn×m)
+with ∥ψQ∥1 < εLn(Q)
+Ln(Ω) and
+∥(νxQ, λa(xQ)ν∞
+xQ) − ενxQ+λa(xQ)ν∞
+xQ+Dψ∞∥K < ε.
+Let ψ = �
+Q ψQ ∈ D(Ω, Rm×n) and ∥ψ∥1 ≤ ε. Then
+ˆ
+Ω
+η(⟨Ψ, νx⟩ + λa(x)⟨Ψ∞, ν∞
+x ⟩)dx =
+�
+Q∈Fa
+ˆ
+Q
+η(⟨Ψ, νx⟩ + λa(x)⟨Ψ∞, ν∞
+x ⟩)dx + E1
+with |E1| ≤
+ˆ
+Ω\∪Fa M(x)dx ≤ ε
+45
+
+for large enough d. Next
+�
+Q∈Fa
+ˆ
+Q
+η(⟨Ψ, νx⟩ + λa(x)⟨Ψ∞, ν∞
+x ⟩)dx =
+�
+Q∈Fa
+ 
+Q
+η
+ˆ
+Q
+(⟨Ψ, νx⟩ + λa(x)⟨Ψ∞, ν∞
+x ⟩)dx + E2,
+where
+|E2| ≤ t
+�
+Q∈Fa
+ˆ
+Q
+|⟨Φ, νx⟩ + λa(x)⟨Φ∞, ν∞
+x ⟩|dx ≤ t
+ˆ
+Ω
+M(x)dx.
+We further estimate, on every set Q ∈ Fa,
+����
+ˆ
+Q
+⟨Φ, νx⟩ + λa(x)⟨Φ∞, ν∞
+x ⟩ − Ln(Q)
+�
+⟨Φ, νxQ⟩ + λa(xQ)⟨Φ∞, ν∞
+xQ⟩
+�����
+≤ω(t)
+s Ln(Q) + 1 − s
+s
+ˆ
+Q
+|⟨Φ, νx⟩ + λa(x)⟨Φ∞, ν∞
+x ⟩|dx +
+ˆ
+Q\Ca |⟨Φ, νx⟩ + λa(x)⟨Φ∞, ν∞
+x ⟩|dx.
+By the linear growth of f, we get that
+�
+Q∈Fa
+ 
+Q
+η
+ˆ
+Q
+⟨Φ, νx⟩ + λa(x)⟨Φ∞, ν∞
+x ⟩dx =
+�
+Q∈Fa
+�
+⟨Φ, νxQ⟩ + λa(xQ)⟨Φ∞, ν∞
+xQ⟩
+� ˆ
+Q
+η + E3
+where
+|E3| ≤ ω(t)
+s Ln(Q) + 1 − s
+s
+ˆ
+Q
+M(x)dx + ε.
+For every Q ∈ Fa we have that
+f(xQ) =
+ 
+Q
+Φ(νxQ + λa(xQ)ν∞
+xQ + DφQ) +
+|·|≤ε
+����
+EQ
+4 .
+Set va(x) = νx + λa(x)ν∞
+x . Letting Φ = z · ei, (ei) canonical basis of Rm×n, we obtain, from
+continuity over Ca, |va − va(xQ)| ≤ ω(t) on Q ∩ Ca for each Q ∈ Fa. Consequently,
+ˆ
+Q
+|va − va(xQ)|dx ≤ ω(t)
+s Ln(Q) +
+ˆ
+Q\Ca |va|dx + 1 − s
+s
+ˆ
+Q
+|va|dx
+for all Q ∈ Fa. Because |va| ≤ M(x) and Lip(Φ) ≤ 5, then
+�
+Q∈Fa
+ 
+Q
+ηdx
+ˆ
+Q
+Φ(va(xQ) + DψQ)dx =
+�
+Q∈Fa
+ 
+Q
+ηdx
+ˆ
+Q
+Φ(va + DψQ)dx + E5
+with
+|E5| ≤ 5ω(t)
+s Ln(Q) + 5ε + 51 − s
+s
+ˆ
+Ω
+M(x)dx.
+46
+
+Combining some of the previous estimates, we get
+�
+Q∈Fa
+ 
+Q
+ηdx
+ˆ
+Q
+Φ(va + DψQ)dx =
+�
+Q∈Fa
+ˆ
+Q
+ηΦ(va + DψQ)dx + E6,
+and
+|E6| ≤t
+�
+Q∈Fa
+ˆ
+Q
+|Φ(va + DψQ)|dx ≤ t|E5| + t
+�
+Q∈Fa
+ˆ
+Q
+|Φ(va(xQ) + DψQ)|dx
+≤t|E5| + tεLn(Ω) + t
+�
+Q∈Fa
+Ln(Q)(⟨|Φ|, νxQ⟩ + λa(xQ)⟨|Φ|∞, ν∞
+xQ⟩)
+≤t|E5| + tεLn(Ω) + tω(t)
+s Ln(|) +
+�ˆ
+Q\Ca +1 − s
+s
+ˆ
+Ω
+�
+M(x)dx.
+Finally, if φt is a standard molliﬁer, then φt ⋆ va
+Ω
+L1(Ω)
+−−−−→ va as t → 0, and so
+ˆ
+Ω
+ηΦ(va + Dψ)dx =
+ˆ
+Ω
+ηΦ(φt ⋆ va
+Ω + Dψ)dx + E7,
+where using again that Φ is Lipschitz over Rm×n,
+|E7| ≤ Lip(Φ)
+ˆ
+Ω
+|φt ⋆ va
+Ω − va|dx ≤ 5
+ˆ
+Ω
+|φt ⋆ va
+Ω − va|dx.
+This concludes the proof.
+□
+47
+
+A
+Appendix
+Theorem A.1 (Vitali convergence theorem) Let µ ∈ M+(Ω) and fn, f ∈ L1(Ω, µ). Then
+fn → f in L1(Ω, µ) if and only if fn → f in measure and fn is uniformly integrable.
+Proof. See [BR07], p. 268, theorem 4.5.4.
+□
+Theorem A.2 (Stone-Weierstrass) Let X be a compact Hausdorﬀ space. If A is a closed
+subalgebra of C(X) that separates points, then either A = C(X) or there is x0 ∈ X so that
+A = {f ∈ C(X) : f(x0) = 0}. In particular, A = C(X) if and only if A contains the constant
+functions.
+Proof. See [Fol99], p. 139, theorem 4.45.
+□
+Theorem A.3 (Tychonoﬀ) If {Xα}α∈A is a family of compact spaces, Πα∈AXα is compact
+in the product topology.
+Theorem A.4 (Banach-Alaoglu sequential version) Let X be a separable Banach space
+and B ⊂ X∗ the closed unit ball of the dual. Then B is weakly* sequentially compact.
+Proof. See [Lax14], p. 107, theorem 12.
+□
+Lemma A.5 (Chacon biting lemma) Let µ ∈ M+(Ω) and vj ∈ L1(Ω, µ) be a sequence
+such that supj ∥vj∥ < ∞. There are sets Ek ⊂ Ek+1, µ(Ω \ Ek) → 0 and a subsequence (vji)i
+of (vj)j and v ∈ L1(µ) so that vji ⇀ v in L1(Ek, µ) for all k.
+Proof. See [BM89].
+□
+Lemma A.6 (Kantorovich metric) Let (X, d) be a metric space. The Kantorich metric
+on M+(X) generates the same topology as the weak* topology of measures.
+Proof. See [KR19].
+□
+Lemma A.7 Let η ∈ M(Ω, Rd), Ω ⊂ Rn open bounded set, and (φε)0<ε≤1 be a family of
+standard molliﬁers, supp(φ1) ⊂ B. Then
+η ⋆ φε
+area-strictly
+−−−−−−−→ η.
+Proof. Because (Ln
+Ω, ηε) ⇀∗ (Ln
+Ω, η), we immediately obtain the lower bound
+lim inf
+ε→0 |(Ln, ρε)|(Ω) ≥ |(Ln, ρ)|(Ω).
+To prove the upper semi-continuity of the above quantity, notice the following equality:
+(Ln
+Ω, ρε) = (Ln
+Ω, ρ) ⋆ φε − (Ln
+Ω−ε ⋆ (δ0 − φε), 0),
+where
+Ω−ε = {x ∈ Ω : d(x, ∂Ω) > ε}.
+48
+
+Using then Jensen’s inequality
+lim sup
+ε→0
+|(Ln, ρε)|(Ω) ≤ lim sup
+ε→0
+|(Ln
+Ω, ρ) ⋆ φε|(Ω) + |(Ln
+Ω−ε ⋆ (δ0 − φε), 0)|(Ω)
+≤|(Ln
+Ω, ρ)|(Ω) + lim sup
+ε→0
+2Ln(Ω \ Ω−ε) = |(Ln, ρ)|(Ω)
+□
+Theorem A.8 (Atomic decomposition) Let µ ∈ M(Ω). Then there exists a purely atomic
+measure µa and a non-atomic measure µn−a such that µ = µa + µn−a.
+Proof. See [FL07], p. 13.
+□
+49
+
+References
+[AB97]
+Jean-Jacques Alibert and Guy Bouchitté. Non-uniform integrability and generalized
+young measure. Journal of Convex Analysis, 4:129–148, 1997.
+[ADM92] Luigi Ambrosio and Gianni Dal Maso. On the relaxation in bv (Ω; rm) of quasi-
+convex integrals. Journal of functional analysis, 109(1):76–97, 1992.
+[AF84]
+Emilio Acerbi and Nicola Fusco. Semicontinuity problems in the calculus of varia-
+tions. Archive for Rational Mechanics and Analysis, 86(2):125–145, 1984.
+[AFP00]
+Luigi Ambrosio, Nicola Fusco, and Diego Pallara. Functions of bounded variation
+and free discontinuity problems. Courier Corporation, 2000.
+[Bal89]
+John M Ball. A version of the fundamental theorem for young measures. In PDEs
+and continuum models of phase transitions, pages 207–215. Springer, 1989.
+[BL73]
+Henri Berliocchi and Jean-Michel Lasry.
+Intégrandes normales et mesures
+paramétrées en calcul des variations. Bulletin de la Société Mathématique de France,
+101:129–184, 1973.
+[BM89]
+John M Ball and F Murat. Remarks on chacon’s biting lemma. Proceedings of the
+American Mathematical Society, 107(3):655–663, 1989.
+[BR07]
+Vladimir Igorevich Bogachev and Maria Aparecida Soares Ruas. Measure theory,
+volume 1. Springer, 2007.
+[BZ90]
+JM Ball and K-W Zhang. Lower semicontinuity of multiple integrals and the biting
+lemma.
+Proceedings of the Royal Society of Edinburgh Section A: Mathematics,
+114(3-4):367–379, 1990.
+[CC76]
+R.E. Chandler and R.E. Chandler. Hausdorﬀ Compactiﬁcations. Lecture notes in
+pure and applied mathematics. M. Dekker, 1976.
+[Dac07]
+Bernard Dacorogna.
+Direct methods in the calculus of variations, volume 78.
+Springer Science & Business Media, 2007.
+[DM87]
+Ronald J DiPerna and Andrew J Majda. Oscillations and concentrations in weak
+solutions of the incompressible ﬂuid equations. Communications in mathematical
+physics, 108(4):667–689, 1987.
+[FK10]
+Irene Fonseca and Martin Kružík. Oscillations and concentrations generated by-free
+mappings and weak lower semicontinuity of integral functionals. ESAIM: Control,
+Optimisation and Calculus of Variations, 16(2):472–502, 2010.
+[FL07]
+Irene Fonseca and Giovanni Leoni. Modern Methods in the Calculus of Variations:
+Lˆ p Spaces. Springer Science & Business Media, 2007.
+[Fol99]
+Gerald B Folland. Real analysis: modern techniques and their applications. Wiley,
+1999.
+50
+
+[KK16]
+Bernd Kirchheim and Jan Kristensen. On rank one convex functions that are homo-
+geneous of degree one. Archive for rational mechanics and analysis, 221(1):527–558,
+2016.
+[KP91]
+David Kinderlehrer and Pablo Pedregal. Characterizations of young measures gen-
+erated by gradients. Archive for rational mechanics and analysis, 115(4):329–365,
+1991.
+[KP94]
+David Kinderlehrer and Pablo Pedregal. Gradient young measures generated by
+sequences in sobolev spaces. The Journal of Geometric Analysis, 4(1):59, 1994.
+[KR96]
+Martin Kružík and Tomáš Roubíček. Explicit characterization oﬂp-young measures.
+Journal of mathematical analysis and applications, 198(3):830–843, 1996.
+[KR10a]
+Jan Kristensen and Filip Rindler. Characterization of generalized gradient young
+measures generated by sequences in w1, 1 and bv. Archive for rational mechanics
+and analysis, 197(2):539–598, 2010.
+[KR10b]
+Jan Kristensen and Filip Rindler. Relaxation of signed integral functionals in bv.
+Calculus of Variations and Partial Diﬀerential Equations, 37(1-2):29–62, 2010.
+[KR19]
+Jan Kristensen and Bogdan Raiţă. Oscillation and concentration in sequences of
+pde constrained measures. arXiv preprint arXiv:1912.09190, 2019.
+[Kri15]
+Jan Kristensen. Lecture notes on young measures, 2015.
+[Lax14]
+Peter D Lax. Functional analysis. John Wiley & Sons, 2014.
+[Mor52]
+Charles B. Morrey. Quasi-convexity and the lower semicontinuity of multiple inte-
+grals. Paciﬁc J. Math., 2(1):25–53, 1952.
+[Mül92]
+Stefan Müller. On quasiconvex functions which are homogeneous of degree 1. Indi-
+ana University mathematics journal, pages 295–301, 1992.
+[Res68]
+Yu G Reshetnyak. Weak convergence of completely additive vector functions on a
+set. Siberian Mathematical Journal, 9(6):1039–1045, 1968.
+[Rin18]
+Filip Rindler. Calculus of variations, volume 5. Springer, 2018.
+[You37]
+Laurence Chisholm Young.
+Generalized curves and the existence of an attained
+absolute minimum in the calculus of variations. Comptes Rendus de la Societe des
+Sci. et des Lettres de Varsovie, 30:212–234, 1937.
+51
+
diff --git a/59A0T4oBgHgl3EQfN_9T/content/tmp_files/load_file.txt b/59A0T4oBgHgl3EQfN_9T/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..9a6ce54a62b3426f33eb6b34e45c41305446bc25
--- /dev/null
+++ b/59A0T4oBgHgl3EQfN_9T/content/tmp_files/load_file.txt
@@ -0,0 +1,1546 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf,len=1545
+page_content='arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='02154v1  [math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='AP]  5 Jan 2023  Generalised Young Measures  and  characterisation of gradient Young Measures  Tommaso Seneci  Abstract  Given a function f ∈ C(Rd) of linear growth, we give a new way of representing  accumulation points of  ˆ  Ω  f(vi(z))dµ(z),  where µ ∈ M+(Ω), and (vi)i∈N ⊂ L1(Ω, µ) is norm bounded.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' We call such representa-  tions "generalised Young Measures".' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' With the help of the new representations, we then  characterise these limits when they are generated by gradients, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' when vi = Dui for  ui ∈ W 1,1(Ω, Rm), via a set of integral inequalities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Contents  1  Intro  3  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='1  Terminology and symbols  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
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+page_content='6  Terminology .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
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+page_content='  28  3  Characterisation of gradient Young Measure  on general compactiﬁcations  32  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='1  Non-separability of the space of quasi-convex functions .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
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+page_content='  32  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='2  Characterisation of Gradient Young Measures .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
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+page_content='  36  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='1  Inhomogenization .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
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+page_content='  40  A Appendix  48  2  1  Intro  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='1  Terminology and symbols  For a vector v ∈ Rm, we write |v| =  ��m  i=1 v2  i otherwise speciﬁed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Given a function f : X → Z and W an arbitrary set, we call  graph(f) ≡graphX(f) = {(x, f(x)) ∈ X × Z such that x ∈ X},  graphX×W (f) = {(x, w, f(x)) ∈ X × W × Z such that x ∈ X, w ∈ W}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  We say that a function f : Rd → R has p growth if there is C > 0 such that  |f(z)| ≤ C(1 + |z|p).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  The identity matrix is indicated by  1, or  1d ∈ Rd×d if we need to specify the dimension.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  The Lebesgue measure is indicated by dx, or Ln depending on the context.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' The set of  ﬁnite Borel d-vector measures is indicated by M(Ω, Rd).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' For E ⊂ M(Ω), E+ is the set  of positive Borel measures that belong to E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  For a measure µ ∈ M(Ω)+, we write Lp(Ω, µ, Rd) to mean the space of µ-measurable  functions f : Ω → Rm such that  ˆ  Ω  |f(x)|pdµ(x) < +∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  For µ ∈ M(Ω, Rd), we write its restriction to a µ-measurable set E ⊂ Ω  µ  E : A Borel set �→ µ(E ∩ A).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  If µ ∈ M(Ω) and f ∈ L(Ω, µ, Rd), we call fdµ the measure in M(Ω, Rd) deﬁned by  U �→  ˆ  U  fdµ,  where U runs through all µ-measurable sets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  If X is any space, the Dirac delta is indicated, for x ∈ X, by  ˆ  X  f(y)dδx(y) = f(x),  where f : X → Rd is an arbitrary function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Let X be a metric space, µ ∈ M+(Ω) and (fj)j∈N ⊂ Lp(Ω, µ, Rd).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' We say that the se-  quence (fj)j is p-equi-integrable (or simply equi-integrable if p is clear from the context)  if it is norm bounded and  lim  k↑∞ sup  j∈N  ˆ  |fj|p>k  |fj|pdµ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  3  The set of test functions is  D(Ω, Rd) = C∞  c (Ω, Rd) = {f : Ω → Rd : f is inﬁnitely diﬀerentiable and has compact support}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  We do not insist on the topology this space is endowed with, as it is standard and  nowhere used in the work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  For the derivative of a function u ∈ L1(Ω, Rm) we mean the matrix-valued distribution  Du = [∂jui]i,j ∈ (D(Ω, Rm)∗)n such that  ˆ  Ω  ui∂jφdx = −⟨∂jui, φ⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  The Sobolev space of functions with integrable derivatives is  W 1,1(Ω, Rm) = {u ∈ L1(Ω, Rm) : Du ∈ L1(Ω, Rm×n)}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  The set of functions of bounded variation is  BV (Ω, Rm) = {u ∈ L1(Ω, Rm) : Du ∈ M(Ω, Rm×n)}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  For a function u ∈ BV (Ω, Rm) we can write  Du = ∇udLn  Ω + Dsu,  Dsu = Dju  Ju + Dcu  where ∇udLn is the absolutely continuous part, Dju is the jump part concentrated on a  n − 1 rectiﬁable set Ju, and Ds is the Cantor part, which is absolutely continuous with  respect to Hn−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  For a function U ∈ BV (Ω, Rm), we call  BVU(Ω, Rm) =  �  u ∈ BV (Ω, Rm) : there is a sequence uj ∈ D(Ω, Rm)  such that uj  weak* in BV  −−−−−−−−→ u − U  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  The set of special functions of bounded variation is  SBV (Ω, Rm) = {u ∈ BV (Ω, Rm) : Dsu = Dju, or equivalently Dcu = 0}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  4  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='2  Introduction  Young Measures were ﬁrst introduced by Young in [You37] to study the minima of integral  energies of the form  inf  �ˆ 1  0  f(u(t), u′(t))dt : u ∈ C1([0, 1]), u(0) = a, u(1) = b, ∥u′∥∞ ≤ K  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  The author wanted to understand what conditions on f would guarantee the existence of a  minimizing curve u(t).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Young had the intuition that, for an extremely general class of functions  f, minimising sequences always converge to a "generalised" curve t �→ (u(t), νt) where ν is a  probability measure on the image of f.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' This translates to the following equality  inf  u(0)=1,u(1)=b  ˆ 1  0  f(u(t), u′(t))dt = lim  j  ˆ 1  0  f(uj(t), u′  j(t))dt =  ˆ 1  0  ˆ  R  f(u(t), y)dνt(y)dt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  So the question of the existence of a minimiser can be reformulated as to whether such objects  are gradients of a curve or not.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' νt might fail to be a gradient when the minimizing sequence  oscillates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Young’s original work focused on the case n = 1 and was carried out via functional analytic  methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' This approach was later extended in [Bal89, BL73] to higher dimensions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' We call  these generalised functions "oscillation Young Measures".' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' The method developed by Young  is not powerful enough to tackle problems arising in modern mathematics, as it can only  handle sequences (vj)j∈N that are bounded in L∞ rather than in some Lebesgue space Lp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  The ﬁrst attempt to well represent generalised limits of integrable functions is due to DiPerna  and Majda, [DM87].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Functions vj : Ω → Rd are seen as Dirac deltas on the product space  Ω × Rd, which is subsequently compactiﬁed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' An accumulation point, in the sense of these new  generalised functions, is then found.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Such an accumulation point is a measure deﬁned on an  abstract compactiﬁcation of Ω × Rd, and as such, it is not clear how to represent it in the  original, non-compact, space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' In [AB97], an explicit formula for such accumulation points was  obtained for a class of integrands that grow "nicely" inﬁnity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  In what follows, we give a general formula for describing Young Measures for a large class  of integrands.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' The construction of Young Measures follows mainly the work by DiPerna and  Majda [DM87] and lecture notes taken from a class given by Kristensen [Kri15], see also  [Rin18], chapter 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' This generalisation is based on the canonical way of constructing Haus-  dorﬀ compactiﬁcations starting from continuous functions, see [CC76].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  A small reduction  lemma gives a clearer, and somehow geometrical interpretation of such limits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' This formula  captures oscillations at inﬁnity, which are now let occur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' We also prove a few structure theo-  rems that relate diﬀerent compactiﬁcations and Young Measures representations to each other.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  This generalisation of Young Measures is then applied to study extensions and variations -  within the class of functions of bounded variations BV (Ω, Rm) - of energies that depend on  gradients  u �→  ˆ  Ω  f(Du(x))dx,  (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='16)  where u ∈ D(Ω, Rd), Ω ⊂ Rn is a bounded domain, and f ∈ C(Rm×n) has linear growth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Given any such f, there is no way to extend (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='16) to the class BV so that such extension is  5  continuous with respect to sequential weak* convergence in C0(Ω, Rm×n)∗.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' We can however  ﬁnd an extension which is lower semi-continuous for certain fs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' In [Mor52], Morrey established  the equivalence of lower semi-continuity of (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='16) to a condition named "quasi-convexity",  which can be written as a Jensen-type inequality  ˆ  Ω  f(z + Dφ(x))dx ≥ |Ω|f(z)  ∀φ ∈ D(Ω).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='17)  The original result by Morrey works in the setting of weak* convergence in W 1,∞(Ω, Rm),  and it was subsequently extended to the case W 1,p(Ω, Rm), 1 ≤ p < ∞ and weak convergence  in [AF84], for positive integrands.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' As for signed integrands, the same result was proven in  [BZ90] and it is one of the ﬁrst examples where Young Measures are employed for proving  lower semi-continuity in the space of gradients.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' To be more speciﬁc, (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='17) can be rephrased  as a Jensen-type inequality for measures of the form  {νx : νx = Dφ(x)#dLn  Ω, φ ∈ C∞  c (Ω, Rm)},  (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='18)  where νx acts on f in the following way:  ˆ  Ω  f(z + Dφ(x))dx =  ˆ  Ω  ˆ  Rm×n f(z + w)dνx(w)dx ≡  ˆ  Ω  ⟨νx, f⟩dx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  The lower semi-continuity of (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='16) becomes a functional analytic inequality of the form  ˆ  Ω  ⟨νx, f⟩dx ≥  ˆ  Ω  f(Du(x))dx  and  Du(x) =  ˆ  Rm×n zdνx,  and in this case we call x �→ νx a "Gradient Young Measure".' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' This class can be seen as the  closure of the set (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='18) in the weak* topology of measures over the graph of f.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' The opposite  is also true and was proven for the ﬁrst time in [KP91, KP94], i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' every measure-valued  function x �→ νx, for which a Jensen’s type inequality holds against quasi-convex functions of  suitable growth, is the limit of a sequence of gradients.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  The aforementioned results hold in the setting of weak convergence in W 1,p, 1 ≤ p < ∞ and  weak* convergence in W 1,∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' This is a natural condition to assume when p > 1, but not when  p = 1, as the Lebesgue space L1(Ω, Ln) is not reﬂexive.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' In particular, a bounded sequence  in L1(Ω, Ln) can concentrate and converge to measures that are singular with respect to the  Lebesgue measure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' In terms of gradients, the closure of W 1,1(Ω, Rm) so that its unit ball  is weak* compact is the set of functions of bounded variations BV (Ω, Rm), precisely the set  of functions whose derivatives are measures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' This concentration phenomenon is exclusive of  the case p = 1, and so regards integrands that have linear growth at inﬁnity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' It turns out,  as proven in [ADM92], that when f has linear growth and it’s quasi-convex, the integral  functional u �→  ´  Ω f(∇u)dx, f ≥ 0 is still lower semi-continuous in BV (Ω, Rm) with respect  to the weak* topology, but there is a deﬁcit of mass when gradients concentrate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Letting f be  so that  f ∞(z) =  lim  t→∞,zn→z  f(tzn)  t  (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='21)  6  exists for all zn → z, t → ∞, the lower semi-continuous envelope of (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='16) in the space  BV (Ω, Rm), with respect to sequential weak* convergence, is, for f non-negative,  u �→  ˆ  Ω  f(∇u(x))dx + f ∞  � Dsu  |Dsu|(x)  �  d|Dsu|(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  In this case, a Young Measure formulation of the Jensen’s-type inequality (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='17) has to take  into account the singular part of Du.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' In the spirit of the previous results, one is tempted to  prove a duality-type characterisation of Young Measures with concentrations and quasi-convex  functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Diﬀerently from the case without concentration, here we assumed f ∞ to exist as  in eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='21), p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' However, as shown in [Mül92], quasi-convex functions can oscillate at  inﬁnity, meaning that f ∞(z) may not exist for some z ∈ Rm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' This suggests that to obtain  a Jensen-type inequality and characterisation result for gradient Young Measure in the case  p = 1, it is necessary to specify a compactiﬁcation at inﬁnity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  The characterisation for gradient Young Measures when p = 1 has been already obtained  on the so-called "sphere compactiﬁcation" - functions for which f ∞(z) exists for all z - see  [KR10a, KR10b].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' After showing that the class of quasi-convex functions of linear growth is  too big to be included within any separable compactiﬁcation, we reprove the characterisation  result for gradient Young Measures on separable compactiﬁcations of quasi-convex functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  This restricts the number of quasi-convex functions to be considered at once.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' However, it is  also inevitable because a compactiﬁcation containing all quasi-convex functions would be so  big that its topology would fail to be metrisable and separable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  7  2  Generalised Young Measures on separable compactiﬁcations  In this section, we construct generalised Young Measures and provide a new geometric rep-  resentation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Concentration is let "oscillate with diﬀerent amplitudes at inﬁnity".' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' To do so,  we embed a space of functions into a bigger compact set and subsequently use the theory of  Hausdorﬀ compactiﬁcations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='1  Generalised Young Measures as generalised objects  Generalised Young Measures are objects that were known to exist since Majda and Di Perna  [DM87], and have been used in a few instances, see for example [FK10, KR96].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' However, their  existence per se does not give enough clarity on their properties, and so makes it hard to work  with such objects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  We give a new interpretation and geometric representation that better captures oscillation and  concentration eﬀects that occur in limits of the form  lim  j  ˆ  Ω  f(vj(x))dµ(x),  where vj ∈ Lp(Ω, µ, Rd) is a norm-bounded sequence and f ∈ C(Rd) has p-growth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Under  these assumptions, it is easy to see that, up to a subsequence, f ◦ vj converges to a measure  ν;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' mathematically this means that  ˆ  Ω  f(vj(x))φ(x)dµ(x) →  ˆ  Ω  φ(x)dν(x)  for all φ ∈ C0(Ω).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' It’s clear that ν = ν(f) is a linear function of f.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' What is not clear is  how such dependence can be represented in terms of µ and f.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Without a clear representation,  it is not possible to set up a system of calculus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' This section is dedicated to working out  a geometric interpretation of the relation between ν and f, which we will then call Young  Measure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' We will mainly concentrate on the more interesting and harder case of p = 1 and  vj = Duj gradients, where concentration eﬀects create rather complicated structures, and  cannot in general be separated from oscillation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Deﬁnition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='1 A function f : Rd → R is said to have p-growth if there is a constant C ≥ 0  such that  |f(z)| ≤ C(1 + |z|p)  ∀z ∈ Rm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  When p = 1, we say that such functions have linear growth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Before proceeding with formal deﬁnitions, we give a heuristic interpretation of Young Measures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  When vj → v strongly in L1(µ) then the limit Young Measure is trivial, meaning that  ˆ  Ω  f(vj(x))φ(x)dµ(x) →  ˆ  Ω  f(v(x))φ(x)dµ(x)  for all f ∈ C(Rd) of linear growth and φ ∈ C0(Ω).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' This is a simple consequence of the Vitali  convergence Theorem A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='1, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' 48 (or the generalised dominated convergence theorem).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  When strong L1 convergence fails, only two things can go wrong:  8  oscillation - vj oscillates around µ-almost every point x ∈ E ⊂ Ω with µ(E) > 0, and  generates a probability distribution on the target space  f(vj(x)) ⇝ ⟨νx, f⟩ =  ˆ  Rd f(z)dνx;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  concentration - |vj| concentrates to a measure 0 ̸= λ ∈ M+(Ω) - equivalently (x, vj(x))  concentrates to the boundary of some compactiﬁcation of Ω×Rd.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Around λ-almost every  point, vj(x) goes to inﬁnity and its "support" collapse to 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' That is to say,  f(vj(x)) ⇝  �f(z)  |z|  with |z| ≫ 0  �  ∼  ˆ  ∂K  f ∞(w)dν∞  x (w),  where K is some compactiﬁcation containing Rd that extends f to f ∞ on the remainder  of Rd within K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='1  Parametrized measures  In order to construct Young Measures, we regard functions as maps from a domain Ω into the  set of probability measures over a target space Rd.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Ordinary functions f : Ω → Rd, x �→ f(x)  are embedded into maps Ω → M+  1 (Rd), x �→ δf(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Preliminary to the construction, we  introduce two basic concepts that are at the core of this theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Deﬁnition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='2 Let X and Z be locally compact, separable metric spaces and λ ∈ M+(X).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  A map ν : X → M+(Z) is said to be λ-measurable if for each φ ∈ C0(Z) the function x �→  ⟨ν(x), φ⟩ is λ-measurable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  We shall often write the measure-valued map ν as a parametrized measure (νx)x∈X, where  νx : = ν(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Given a measure ν on a product space X × Z, it can always be decomposed as a  product of its projection onto X and its cross section on Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='3 (Disintegration of measures) Let X and Z be compact metric spaces and  denote by π: X × Y → Z the projection mapping onto the ﬁrst coordinate π(x, y) = x.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' For  u ∈ M+(X ×Z) and λ = π#ν ∈ M+(X) (the pushforward of ν via π) there exists a unique λ-  measurable parametrized measure (ηx)x∈X, ηx ∈ M+  1 (Z) such that for all φ ∈ C(X), ψ ∈ C(Z)  we have  ⟨ν, φ ⊗ ψ⟩ =  ˆ  X  ⟨ηx, ψ⟩φ(x)dλ(x) =  ˆ  X  ˆ  Z  ψ(z)dηx(z)φ(x)dλ(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  For a proof of this result see [AFP00], p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' 57.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' In this case we write  ν = ηxdλ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='2  Generalized Young measures  In what follows, we show how to obtain a good representation of Young Measures on general  compactiﬁcations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' The procedure is adapted from some lecture notes taken from a homonym  course given by Jan Kristensen at the University of Oxford, [Kri15].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Some of the results can  also be found in [Rin18], chapter 12, where they are only proven on the sphere compactiﬁcation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  9  Throughout this section, Ω ⊂ Rn is open and bounded, µ ∈ M+(Ω) and (vj)j ⊂ Lp(Ω, µ, Rd)  is a bounded sequence, 1 ≤ p < ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Assume  vj ⇀ v in Lp when 1 < p < ∞  or  vj ⇀∗ v in C0(Ω, Rd)∗ when p = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Given a continuous integrand Φ: Ω × Rd → R satisfying the p-growth condition  |Φ(x, z)| ≤ C(1 + |z|)p  ∀(x, z) ∈ Ω × Rd,  we seek to represent limits of  �´  Ω Φ(x, vj(x))dx  �  j as j → ∞, possibly passing through suitable  subsequences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Remark 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='4 For each j, the map Φ acts on the graph of vj, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Φ(x, vj(x)) = Φ ◦ (x, vj(x)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Therefore, we look for the limiting distribution of (x, vj(x)) as j → ∞, and more precisely the  Φ-moment of this limiting distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Morally speaking, since (Φ(·, vj))j is bounded in L1(Ω, µ), (Φ(·, vj)dµ)j is bounded in M(Ω) ≂  C(Ω)∗, so by the abstract compactness principle Theorem A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='4, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' 48, there exists a limit  measure which depends on the integrand Φ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='3  Functional analytic setup  Let z ∈ Rd �→ ˆz =  z  1+|z| ∈ Bd be a homeomorphism Rd �→ Bd.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Deﬁne the class of functions of  p-growth in the z variable to be  Gp = Gp(Ω, Rd) :=  �  Φ ∈ C(Ω × Rd) : sup  (x,z)  |Φ(x, z)|  (1 + |z|)p < ∞  �  ,  and for Φ ∈ Gp put  (TΦ)(x, ˆz) := (1 − |ˆz|)pΦ  �  x,  ˆz  1 − |ˆz|  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Then T : Gp → BC(Ω × Bd) is an isometric isomorphism provided Gp is normed by ∥TΦ∥∞  and BC(Ω × Bd) by ∥ · ∥∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' The inverse operator is  (T −1Ψ)(x, z) = (1 + |z|)pΨ  �  x,  z  1 + |z|  �  ,  where Ψ ∈ BC(Ω × Bd).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  The dual operator T ∗ : BC(Ω×Bd)∗ → G∗  p is again an isometric isomorphism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' We are interested  in the limits of  ´  Ω Φ(x, vj(x))dx for Φ ∈ Gp and may deﬁne ξvj ∈ G∗  p by  ξvj(Φ) :=  ˆ  Ω  Φ(x, vj(x))dx, Φ ∈ Gp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Note  ∥ξvj∥ = sup  ∥Φ∥Gp  ξvj(Φ) =  ˆ  Ω  (1 + |vj|)pdx  so (ξvj) is a bounded sequence in G∗  p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' But G∗  p ≂ BC(Ω × Bd)∗, and because BC (hence Gp)  is not separable we do not necessarily have sequential compactness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  We must restrict the  integrands Φ to a separable subspace of Gp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  10  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='2  Hausdorﬀ compactiﬁcation  In this subsection, we present how to construct a compactiﬁcation of the space X = Ω × Rd  from a family of bounded and continuous functions F ⊂ BC(X).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Roughly speaking, such  compactiﬁcation is a compact set eF X that contains X as a dense subset and on which all  f ∈ F admit a continuous extension.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' The idea behind such construction is to look at the  graph of each f ∈ F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Because of the boundedness assumption, each function has its image  contained in a closed bounded interval of R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Therefore, the graph is embedded into a closed  subset of an (inﬁnite-dimensional) hypercube, which is compact in the product topology by  Tychonoﬀ theorem, Theorem A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='3, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' 48.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='1  Preliminaries on Hausdorﬀ compactiﬁcations  Most of the results will be stated without proof, which can be found in chapters 1 and 2 of  [CC76] and in chapter 4 of [Fol99].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  We ﬁrst deﬁne three classes of functions that are rich enough to determine the topological  structure of their domains:  Deﬁnition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='5 Consider a family of functions F ⊂ BC(X), we say that F separates points  from closed sets if for each C ⊂ X closed and x ∈ X \\ C there exists f ∈ C(X) such that  f(x) ̸∈ f(C).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Next, we deﬁne what a compactiﬁcation of a topological space is.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Deﬁnition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='6 A compactiﬁcation of X is a compact Hausdorﬀ space αX and an embedding  α: X → αX (continuous and so that α−1 : αX → X exists and is continuous) such that α(X)  is dense in αX.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  It is useful to remark that because α is continuous, any function f ∈ C(αX) can be restricted  to a continuous function on X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Indeed, f ◦ α is the composition of a bounded continuous  function with continuous function, and thus it belongs to BC(X).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' On the other hand, because  α(X) is dense in αX, each f ∈ C(αX) is uniquely recovered from f ◦ α ∈ C(X).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Given a family F ⊂ BC(X) that separates points from closed sets, there is a canonical way of  generating a compactiﬁcation αX on which every f ∈ F has a continuous extension.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='7 To each family F ⊂ BC(X) that separates points from closed sets, we associate  a canonical embedding  eF : X → Πf∈F  �  inf f, sup f  �  , x �→ {f(x)}f∈F .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  eF X := eF(X) is a compactiﬁcation of X  The above theorem is a direct implication of Tychonoﬀ’s theorem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' When F ⊂ BC(X) is a  family that separates points from closed sets, then eF : X �→ Πf∈F  �  inf f, sup f  �  is open and  continuous, and so it is an embedding.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  However, the map eF makes sense even if F does not separate points from closed sets, and  eF X is always a compact subset of Πf∈F  �  inf f, sup f  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  11  Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='8 Let F ⊂ BC(X) be a family that separates points from closed sets and eF X its  induced compactiﬁcation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Each f ∈ F embeds into C(eF (X)) in an obvious way and admits a  unique extension f ∈ C(eF X).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Every y ∈ eFX is an accumulation point of eF (X), so we can ﬁnd a net yλ = Πf∈F f(xλ) such  that yλ → y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' A way of extending f ∈ F is by setting  f : eF X → R, y  �  = lim  λ Πf∈F f(xλ)  �  �→ f(y) = lim  λ f(xλ),  which does not depend on the choice of xγ as far as limγ f(xγ) = limλ f(xλ) for each f ∈ F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Suppose that we have given a family F and its associated compactiﬁcation eF X, and we  consider the compactiﬁcation of F ∪ {f}, where f ∈ BC(X).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' We expect the latter compacti-  ﬁcation to be bigger than the former, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' to be a space where all the previous extensions can  be further extended to continuous functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Deﬁnition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='9 Given two compactiﬁcations αX and γX of X, we say that αX ≥ γX if there  exists a continuous function f : αX → γX such that f ◦ α = γ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Moreover, we write αX ≂ γX  if αX ≥ γX and γX ≥ αX, or equivalently if f : αX → γX is a homeomorphism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  In the following paper, we will sometimes refer to a generic compactiﬁcation K without specify-  ing the underlying family generating it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' The reason why is stated by the following astonishing  result.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='10 Given a compactiﬁcation αX of X, there exists a family F ⊂ BC(X) that  separates points from closed sets such that eF X ≂ αX.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='2  Representation of compactiﬁcations  Consider a family F ⊂ BC(X) that separates points from closed sets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  According to the  Hausdorﬀ compactiﬁcation theory (see above subsections), its induced compactiﬁcation can  be written as a subset of the hypercube Πf∈F  �  inf f, sup f  �  , where the sides of this cube are  as many as the functions f ∈ F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Because F can be uncountable, its compactiﬁcation could be  hard to deal with from an analytical point of view.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' We seek a better representation of such  space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  The idea behind the following result is that if we know the limits of functions f, g ∈ BC(Ω, R),  we also know the limits of f n + gm, n, m ∈ N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Deﬁnition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='11 Let F be a family of functions f : X → R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  We call A(F) the algebra  generated by F, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  A(F) = {f n + gm : f, g ∈ F, n, m ∈ N}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='12 (Representation theorem) Let F ⊂ BC(X) be a closed sub-algebra that  separates points from closed sets and let F ′ ⊂ F be such that A(F ′) = F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Then eF ′X is a  compactiﬁcation of X and eF ′X ≂ eF X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  12  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Let eF ′X be the (formal) compactiﬁcation of F ′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Clearly eF X ≥ eF ′X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' To prove the  opposite inclusion, we must ﬁnd a continuous function T : eF ′X → eF X such that T ◦eF ′ = eF .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Fix y = limλ Πf∈F ′f(xλ) ∈ eF X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' If g ∈ A(F ′), limλ g(xλ) exists and coincides on all nets  xγ such that y = limγ Πf∈F ′f(xγ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Next, let g ∈ A(F ′) and ﬁnd a sequence {fn}n∈N ⊂ A(F ′)  such that fn → g uniformly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Because ∥fn∥∞ is bounded, so is {limλ fn(xλ)}n∈N, and so we can  extract a subsequence {fnk}k∈N such that limk limλ fnk(xλ) = L ∈ R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Fix ε > 0 and N ∈ N  such that ∥fnN − g∥∞ < ε  3 and ﬁnd ˜λ ∈ Λ such that |fnN(xλ) − limλ fnN(xλ)| < ε  3 for all  λ ≥ ˜λ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Finally  |g(xλ) − L| ≤ |g(xλ) − fnN(xλ)| + |fnN (xλ) − lim  λ fnN(xλ)| + | lim  λ fnN(xλ) − L| < ε  for all λ ≥ ˜λ, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' the net g(xλ) converges to L ∈ R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' In particular, by the uniqueness of  limλ g(xλ), we conclude that the original sequence {limλ fn(xλ)}n∈N converges to L, which also  proves that the limit does not depend on the particular net xγ as far as limλ f(xλ) = limγ f(xγ)  for all f ∈ F ′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' This shows that the map  T : eF ′X → eF X, y = lim  λ Πf∈F ′f(xλ) �→ Ty = lim  λ Πf∈F f(xλ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  is a well-deﬁned isomorphism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Because its inverse is the projection map πF ′|T(eF ′X), which is  continuous and open, then  T ◦ eF ′ : x �→ Πf∈F ′f(x) �→ Πf∈F f(x) = eF (x)  is a homeomorphism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' To prove that eF ′X is a compactiﬁcation of X, we notice that F separates  points, as so does F ′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' If U ⊂ X is open, so is  eF ′(U) = T −1(eF (U)),  and eF ′ is an injective continuous open map, thus it is an embedding onto its image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  □  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='3  Restriction on non-linearity  For the sake of this work, it is important that the set of functions we work with is separable  (has a countable dense set).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Let F ⊂ BC(Ω×Bd) be a closed separable algebra that separates  points from closed sets and let eF Ω × Bd be its compactiﬁcation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Because eF Ω × Bd is a  compact Hausdorﬀ space we have the following isometric isomorphism of its dual  C(eF Ω × Bd)∗ ≂ M(eF Ω × Bd).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='13 If F ⊂ BC(X) is separable, so is C(eFX).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Let {fn}n∈N be dense in F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' By the Stone-Weierstrass theorem, the algebra generated  by {1} ∪ {fn}n∈N ⊂ C(eF X) is dense in C(eF X), and so C(eF X) is separable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  □  Because C(eF Ω × Bd) is separable we also have the abstract sequential compactness prin-  ciple Theorem A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='4, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  48 on its dual M(eF Ω × Bd).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Let T −1F ⊂ Gp the corresponding  13  algebra (w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' ×p) on the set of continuous functions with p-growth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' There is an isometric  isomorphism  T −1F  ˜T≂ C(eF Ω × Bd).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  By the Riesz representation theorem, we can write its adjoint as  ˜T ∗ : M(eF Ω × Bd) → (T −1F)∗, ν �→  �  Φ �→ ( ˜T ∗ν, Φ) = (ν, ˜TΦ) =  ˆ  eF Ω×Bd  ˜TΦdν.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  �  Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='14 Let X, Z be completely regular Hausdorﬀ spaces and let F ⊂ BC(X) and G ⊂  BC(Z) be closed sub-algebras that separate points from closed sets and contain the constant  function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' The following spaces are all isometrically isomorphic to each other  C(eF ∪GX × Z) ≂ C(eF X × eGZ) ≂ A(C(eF X) × C(eGZ)) ≂ A(F ∪ G),  where each f ∈ F and g ∈ G is extended to a function on the product space by keeping constant  the other variable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Moreover, F ∪ G ⊂ BC(X × Z) separates points from closed sets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  The proof of the above lemma is a straightforward application of the Stone-Weierstrass the-  orem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  We underline that it’s important to take families F, G deﬁned exclusively on each  respective space, and the theorem is false if we instead add f = f(x, y) that is not of the form  above.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Morally speaking, what the previous lemma says is that on product spaces it is enough to  work with the compactiﬁcations in each coordinate separately.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Moreover, their dual elements  (measures) can be tested against tensor products of functions that depend on each variable  independently.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='4  Representation of Young measures  Let Ω ⊂ Rn be open and bounded and G′ ⊂ BC(Bd) and F ′ ⊂ BC(Ω) be closed separable sub-  algebras that separate points from closed sets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Let T −1F = A ⊂ Gp the corresponding algebra,  with respect to the ×p product, in the set of functions having p-growth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' F is isometrically  isomorphic to C(eFΩ × Bd).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  With abuse of notation, we are going to call T the isomorphism between A and C(eF Ω × Bd).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  To each function u ∈ Lp(Ω, Rd) we associate an elementary Young measure ξu ∈ A∗ by setting  ξu : A → R, Φ �→  ˆ  Ω  Φ(x, u(x))dµ(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Next, consider a bounded sequence {un}n∈N ⊂ Lp(Ω, Rd), supn ∥un∥p ≤ C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' As Φ ∈ Gp, the  sequence of elementary Young measures is also bounded  ∥ξun∥ = sup  ∥Φ∥≤1  ����  ˆ  Ω  Φ(x, un(x))dµ(x)  ���� =  ˆ  Ω  (1 + |un|)pdµ ≤ µ(Ω) + Cp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Because of the isomorphism A∗ ≂ C(eF Ω × Bd)∗ ≂ M(eF Ω × Bd), there exists a subsequence,  relabelled in the same way, and ν ∈ A∗ such that ξun ⇀∗ ν in A∗.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Set  L := (T ∗)−1ν ∈ M(eF Ω × Bd).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  14  We now study the measure L to ﬁnd a better representation for ν ∈ A∗.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Let ψ ∈ C(eF Ω×Bd),  we immediately notice that L ∈ M+(eF Ω × Bd) as a consequence of the following equality  ≪ ν, T −1ψ ≫= lim  n  ˆ  Ω  (T −1ψ)(x, un(x))dµ(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Because the constant functions belong to G′, we can plug T −1ψ = φ(x)(1+ |z|)p, φ ∈ C(eF ′Ω)  into the previous equation and obtain the identity  ˆ  eF Ω×Bd φ(x)dL(x, z) = lim  n  ˆ  Ω  φ(x)(1 + |un(x)|)pdµ(x) =  ˆ  eF ′  φ(x)dλ(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  By Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='14, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' 14, the projection  π: eF Ω × Bd → eF ′Ω  is well-deﬁned, and we can write ˜λ = π#L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Note that hereby ˜λ ∈ M+(eF ′(Ω)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Find the  unique ˜λ-measurable parametrized family {˜νx}x∈eF ′Ω such that νx ∈ M+  1 (eG′Bd) ˜λ-almost  every x and  ⟨L, Φ⟩ =  ˆ  eF ′Ω  ⟨˜νx, Φ(x, ·)⟩d˜λ(x)  ∀ Φ ∈ C(eF Ω × Bd).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  For any φ ∈ C0(Ω) take Φ = φ(1 − | · |)p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' We compute  ˆ  eF ′Ω  φ(x)⟨˜νx, (1 − | · |)p⟩d˜λ(x) =  ˆ  eF Ω×Bd φ(x)(1 − |z|)pdL(x, z)  = lim  n  ˆ  Ω  (φ1Rd)(x, un(x))dµ(x) =  ˆ  Ω  φ(x)dµ(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Because µ ∈ C0(Ω)∗ we immediately conclude that  µ = ⟨˜νx, (1 − | · |)p⟩˜λ  Ω,  where µ is extended on eF ′Ω by µ(E) ≡ µ(e−1  F ′ (E)), E ⊂ eF ′Ω Borel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Apply the Radon-  Nikodym theorem and write  ˜λ =  ˜λ  µdµ + ˜λs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  From the previous identiﬁcation, we get  �  ⟨˜νx, (1 − | · |)p⟩ ˜λ  µ = 1  µ − a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  ⟨˜νx, (1 − | · |)p⟩ = 0  ˜λs − a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=',  where the second condition implies that ˜νx(eG′(Bd)) = 0 ˜λs-a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=', i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' the measures are concen-  trated on the boundary ∂eG′(Bd).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' On eG′(Bd) we have 0 < (1 − |z|)p ≤ 1, whereas |z| = 1 on  ∂eG′(Bd).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' In particular  � ˜λ  µ =  1  ⟨˜νx,(1−|·|)p⟩ ≥ 1  µ − a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  ˜νx(∂eG′(Bd)) = 1  ˜λs − a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  15  Now let φ ∈ BC(Rd) and deﬁne  ⟨νx, φ⟩ =  ˜λ  µ(x)  ˆ  eG′(Bd)  (1 − |z|)pφ  �  z  1 − |z|  �  d˜νx(z)  =  ˜λ  µ(x)  ˆ  Bd(1 − |z|)pφ  �  z  1 − |z|  �  d(eG′)#˜νx(z)  In particular νx ∈ M+  1 (Rd) and {νx}x∈Ω is µ-measurable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Let λ = ˜νx(∂eG′(Bd))˜λ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Then  λ ∈ M+(eF ′Ω) and it decomposes into  λ =˜νx(∂eG′(Bd))  ˜λ  µµ + ˜νx(∂eG′(Bd))˜λs  =˜νx(∂eG′(Bd))  ˜λ  µµ + ˜λs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  For λ-almost every x ∈ eF ′Ω and for ψ ∈ C(∂eG′Bd) set  ⟨ν∞  x , ψ⟩ =  1  ˜νx(∂eG′(Bd))  ˆ  ∂eG′(Bd)  ψ(z)d˜νx(z),  hereby  ν∞  x ∈ M+  1 (∂eG′(Bd)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  For each Φ ∈ A, its recession function is deﬁned to be the restriction  φ∞ = φ|eF ′Ω×∂eG′(Bd).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Finally, we obtain the formula  ⟨L, TΦ⟩ =  ˆ  eF ′(Ω)  ⟨˜νx, TΦ(x, ·)⟩d˜λ  =  ˆ  eF ′Ω  ˆ  eG′(Bd)  TΦd˜νx  \uf8eb  \uf8ec  \uf8ed  ˜λ  µdµ +  =0  ����  d˜λs  \uf8f6  \uf8f7  \uf8f8 +  ˆ  eF ′Ω  ∂eG′(Bd)  TΦd˜νx (˜νx(∂eG′(Bd))d˜λ)  =  ˆ  Ω  ⟨νx, Φ(x, ·)⟩dµ +  ˆ  eF ′Ω  ⟨ν∞  x , Φ∞(x, ·)⟩dλ  and the representation of the Young Measure as the triple  ν =  �  {νx}x∈Ω, λ, {ν∞  x }x∈eF ′Ω  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  where  νx ∈ M+  1 (Rd) for µ-almost every x ∈ Ω,  λ ∈ M+(eF ′Ω), and  ν∞  x ∈ M+  1 (∂eG′(Bd)) for λ-almost every x ∈ Ω.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  16  We say that un converges in the sense of Young measures to ν, and write  un  Y p(µ,eA)  −−−−−−→ ν  or just  un  Y p(µ,A)  −−−−−→ ν,  where µ is the measure that "regulates and weights" oscillation and concentration of un, and  eA is the compactiﬁcation at inﬁnity, generated by the family A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  From this point onwards the family F ′ in Ω will always be the set of functions C(Ω).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='5  Properties of generalised Young Measures and connection to Young  Measures on the sphere  Here we show how the above construction generalises the more classical setting of Young  Measures on the sphere, see [Res68] for the original idea behind their representation, and  [AB97] for their modern implementation in the calculus of variations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' We then study how the  new representation for generalised Young Measures behaves geometrically, and its properties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  As a reminder, we state here the deﬁnition of integrands with a regular recession at inﬁnity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Deﬁnition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='15 The set of integrands admitting a regular recession at inﬁnity is  Ep(Ω, Rd) =  �  Φ ∈ C(Ω × Rd) : lim  t→∞  Φ(x, tz)  tp  ∈ R locally uniformly in (x, z) ∈ Ω × Rd  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Because we intend to generalise the theory of Young Measures on functions with a regular  recession, we need to extend the above class and at the same time preserve good topological  properties of such a larger class.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' To do so, consider countably many functions gi ∈ BC(Bd)  and their representations as integrands of p-growth gi(  z  1+|z|)(1 + |z|)p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' We are interested in  understanding how to represent, in a simple way, Young Measures relative to the compactiﬁ-  cation generated by Ep ∪ {gi(  z  1+|z|)(1 + |z|)p}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' In the language of Hausdorﬀ compactiﬁcations,  set G′ = C(Bd) ∪ {gi, i ∈ N} and F ′ = C(Ω).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Because C(Bd) ⊂ G′, the closure of the algebra  generated by either family is separable, separates points from closed sets and contains the  constants.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Call F = G′ ∪ F ′, and without loss of generality, we can assume that ∥gi∥ ≤ 1 for  all i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='16 C(eF Ω×Bd) is isometrically isomorphic to C(Ω×graph(gi)), where (gi): Bd →  [−1, 1]N, z �→ (gi(z))i∈N and the topology on the target space is the product topology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  It is  metrised by  d(z, w) = |z − w| +  �  i  2−i|gi(z) − gi(w)|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' By Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='14, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  14 it is enough to prove that C(egi,i∈NBd) ≂ C(graph(gi)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='12, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' 12 provides the isomorphism  A(C(Bd) ∪ {gi, i ∈ N}) = A(1, z1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' , zd, gi, i ∈ N),  and we conclude by noticing that (1, z1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' , zd, gi, i ∈ N)(Bd) is homeomorphic to graph(gi).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  The topological equivalence between such metrics and the product topology is standard.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  □  17  When gi ∈ C(Bd), then C(eF Ω × Bd) ≂ C(Ω × Bd), and therefore we recover the usual  sphere representation for the compactiﬁcation induced by Ep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' This means the obvious, that  we can add functions that have a regular recession and we still obtain the same space (up to  homeomorphisms).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  By deﬁnition, the compactiﬁcation of Bd can be represented by the space Γ of sequences  {zn}n∈N ⊂ Bd such that zn → z ∈ Bd and gi(zn) converges for all i ∈ N, and two such  sequences {zn}n∈N and {wn}n∈N are identiﬁed provided  lim  n |zn − wn| +  �  i  2−i|gi(zn) − gi(wn)| = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Deﬁnition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='17 We call egi,i∈N the compactiﬁcation, and ∂egi,i∈N = egi,i∈N\\graph(gi, i ∈ N),  we can write the triple Young measure as  ν =  �  {νx}x∈Ω, λ, {ν∞  x }x∈Ω  �  ,  where νx ∈ M+  1 (Rd) for µ-almost every x ∈ Ω, λ ∈ M+(Ω), and ν∞  x  ∈ M+  1 (∂egi,i∈N) for  λ-almost every x ∈ Ω.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Notice that ∂egi,i∈N is an abuse of notation and refers to the boundary of the embedded space  within the compactiﬁcation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  So far we have constructed compactiﬁcations by "glueing" gis on top of the functions z1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' , zd;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  that is to say on top of the unit ball.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' It is sometimes useful to iterate this argument, to stack  another countable family {fi, i ∈ N} on top of the compactiﬁcation egi,i∈N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' This process gives  the same compactiﬁcation as if we were considering the two families at once, as the following  lemma shows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='18 Let egi,i∈N be a compactiﬁcation of Bd and fi ∈ BC(Bd).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Then  egi,fi,i∈N ≂ graphgraph(gi)fi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' This is a trivial consequence of the fact that  {(z1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' , zd, gi(z), fi(z)), z ∈ Bd} ={(z1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' , zd, w, z) : w = gi(z), y = fi(z), z ∈ Bd}  (extending fi to constant in the variable w) ={(z1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' , zd, w, z) : y = fi(z, w), w = gi(z), z ∈ Bd}  =graphgraph(gi)(fi), z ∈ Bd.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  □  A standard application of the disintegration lemma yields the following.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Corollary 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='19 Consider a compactiﬁcation egi,fi,i∈N and ν∞ ∈ M(∂egi,fi,i∈N), then  ν∞ = P(zn)n∈Nd˜ν∞  where ˜ν∞ ∈ M(∂egi), (zn)n ∈ ∂egi, and P(zn)n is a probability measure deﬁned on the space  of subsequences (zni)i of (zn)n so that fi(zni) converges for all i ∈ N (with sequences being  equivalents if all the limits are).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  18  For the case of oscillating functions fi, we also write the compactiﬁcation as efiX ≡ efi and  the convergence as  vj  Y p(µ,fi)  −−−−−→ ν.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  When working with the sphere compactiﬁcation, we will simply write  vj  Y p(µ,Bd)  −−−−−−→ ν, or just vj  Y p(µ)  −−−−→ ν.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Also, because here we mainly consider the case p = 1, we omit the superscript p in Y p and  write  vj  Y (µ,efi)  −−−−−→ ν.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  We now study the relation of Young Measures with respect to diﬀerent compactiﬁcations and  diﬀerent underlying measures µ ∈ M+(Ω).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Using Chacon Lemma A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='5, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' 48, we can prove  the following structure theorems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='20 Let vj  Y (µ,efi,i∈N)  −−−−−−−→ (νx, λ, ν∞  x ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Then for all ψ ∈ C0(Rd), we have  ψ(vj) ⇀ ⟨νx, ψ⟩ weakly in L1(µ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Because ψ(vj) ∈ L∞ then is the sequence is equi-integrable and there is a subsequence  that converges weakly in L1 to v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Because ψ∞ = 0, testing against φ ∈ D(Ω) we get  ˆ  Ω  φψ(uj)dµ →  ˆ  Ω  φvdµ =  ˆ  Ω  φ⟨νx, ψ⟩dµ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  □  We can improve the above weak convergence result to show the following.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='21 Let uj  Y (µ)  −−−→  �  νx, 0, N/A  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' For every a ∈ L1(Ω, µ) such that a > 0 µ-a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' and  for all ψ ∈ C0(Rd) we have  ψ  �uj  a  �  a ⇀ ⟨νx, ψ  � a(x)  �  ⟩a(x) in L1(Ω, µ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  As expected, this implies that oscillations do not depend on the particular compactiﬁcation  chosen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Before proving the above results we show the following uniform approximation result:  Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='22 Let µ ∈ M+(Ω) and a ∈ L1(Ω, µ), a > 0 µ-almost everywhere.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' There exists  an ∈ L1(Ω), 0 < an < a, so that an(x) ∈ Q for all x ∈ Ω and  ∥an − a∥∞ +  ����  a  an  − 1  ����  ∞  n→∞  −−−→ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  19  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Let  an =  �  k∈N,k≥1  χa−1�  [ k  n, k+1  n )  � k  n,  where N is the set of strictly positive integers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Because an ≤ a then an ∈ L1 and it also  assumes countably many values at a time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Also |an(x) − a(x)| ≤ 1  n so it converges uniformly  to a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Furthermore  1 =  k  n  k  n  ≤ a(x)  an(x) ≤  k+1  n  k  n  = k + 1  k  and so  a  an converges uniformly to 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  □  Now we can prove Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='21, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' 19  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Using the previous approximation, we write, for 1-Lipschitz ψ : Rd → R,  ˆ  Ω  ψ  �uj  a  �  a =  ˆ  Ω  =I  �  ��  �  ψ  �uj  a  �  a − ψ  �uj  an  �  a +  =II  �  ��  �  ψ  �uj  an  �  a − ψ  �uj  an  �  an +ψ  � uj  an  �  an.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  The ﬁrst two terms are bounded by  |I| ≤  ˆ  Ω  a  ����  uj  a − uj  an  ���� =  ˆ  Ω  |uj|  ����1 − a  an  ���� ≤ sup  j  ∥uj∥  ����1 − a  an  ����  ∞  |II| ≤  ˆ  Ω  �  1 + |uj|  an  �  |a − an| ≤ (1 + sup  j  |uj|)  ����1 − a  an  ����  ∞  ,  which goes to 0 as n → ∞ uniformly in j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' As for the third term, calling Ek = a−1�  [ k  n, k+1  n )  �  ,  we can use dominated convergence theorem to pass to the limit  lim  j  ˆ  Ω  ψ  �uj  an  �  an = lim  j  �  k  ˆ  Ek  ψ  �  uj  k  n  �  k  n =  �  k  ˆ  Ek  ⟨νx, ψ  � k  n  �  ⟩k  n =  ˆ  Ω  ⟨νx, ψ  � ·  an  �  ⟩an.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Another application of the dominated convergence theorem will let us conclude the result.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  □  We can ﬁnally conclude with a structure theorem regarding concentration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='23 Consider two separable algebras (that separate points from closed sets) A  and B of G1 and let a ∈ L1(Ω, µ), a > 0 µ-a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Let vj ∈ L1(Ω, µ) be a sequence so that  vj  Y (µ,A)  −−−−→  �  νx, λν, ν∞  x  �  and  vj  a  Y (a dµ,B)  −−−−−−→  �  ηx, λη, η∞  x  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Then νx =  � a(x)  �  # ηx, λν = λη = λ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Moreover, decomposing  ν∞  x = P ν  (zn)nd˜ν∞  x  and  η∞  x = P η  (zn)nd˜η∞  x ,  where ˜ν∞  x  and ˜η∞  x  are the projections on the sphere according to Corollary 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='19, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' 18, then  ˜ν∞  x = ˜η∞  x λ-a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' with  vj  Y (µ,Bd)  −−−−−→  �  νx, λ, ˜ν∞  x  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  20  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' For all ψ ∈ C0(Rd) we have that ψ(vj) is equi-integrable so that  ψ(vj) ⇀ ⟨ηx, ψ⟩ in L1(µ)  and  ψ  �vj  a  �  ⇀ ⟨νx, ψ⟩ in L1(adµ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Next, identify vj with its subsequence and ﬁnd Ek so that vj ⇀ v in L1(Ek, µ) for all k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' By  inner approximation, we can assume that all such E′  ks are compact.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Consider now the sequence  vjχEk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Then  vjχEk  Y (µ,A)  −−−−→  �  ηxχEk + δ0χEc  k, 0, N/A  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  By Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='21, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' 19 we then have, for φ ∈ C0(Ω) and ψ ∈ C0(Rd), because Ω \\ Ek is open,  ˆ  Ω  φ⟨νx, ψ⟩a(x)dµ = lim  j  ˆ  Ω  φψ  �vj  a  �  adµ = lim  j  ˆ  Ω\\Ek  φψ  �vj  a  �  adµ +  ˆ  Ek  φψ  �vj  a  �  adµ  =  ˆ  Ω\\Ek  φ⟨νx, ψ⟩adµ +  ˆ  Ek  φ⟨ηx, ψ  � ·  a  �  ⟩adµ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Next, let φ ∈ C(Ω), then  lim  j  ˆ  Ω  φ|vj|dµ =  ˆ  Ω  ⟨νx, | · |⟩φdµ +  ˆ  Ω  φdλν  = lim  j  ˆ  Ω  φ  ���vj  a  ��� adµ =  ˆ  Ω  ⟨ηx, | · |  a(x)⟩φa(x)dµ +  ˆ  Ω  φdλη.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Using the previous part we conclude that λν = λη = λ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Finally, let f ∈ C(∂Bd) and extending by 1-homogeneity we obtain that  lim  j  ˆ  Ω  φf(vj)dµ =  ˆ  Ω  φ⟨νx, f⟩dµ +  ˆ  Ω  φ⟨ν∞  x , f ∞⟩dλ =  ˆ  Ω  φ⟨νx, f⟩dµ +  ˆ  Ω  φ  ˆ ˆ  f ∞dP ν  (zn)d˜ν∞  x dλν  =  ˆ  Ω  φ⟨νx, f⟩dµ +  ˆ  Ω  φ  ˆ  f ∞d˜ν∞  x dλν  =  ˆ  Ω  φ⟨νx, f  � a(x)  �  ⟩a(x)dµ +  ˆ  Ω  φ⟨η∞  x , f ∞⟩dλ  =  ˆ  Ω  φ⟨νx, f⟩dµ +  ˆ  Ω  φ  ˆ  f ∞dP η  (zn)d˜η∞  x dλη  =  ˆ  Ω  φ⟨νx, f⟩dµ +  ˆ  Ω  φ  ˆ  f ∞d˜η∞  x dλη.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  □  Notice that the previous identiﬁcation with the concentration angle measure fails if we only  consider Γ = A ∩ B which does not necessarily generate the sphere compactiﬁcation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' This is  so because sequences (uj)j can concentrate around values of a that are measure-discontinuous.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  However, equality holds true if a = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  21  Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='24 Following the assumptions of Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='23, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' 20, if a = 1, Γ = A ∩ B and  writing  ν∞  x = P ν  (zn)nd(γν)∞  x  and  η∞  x = P η  (zn)nd(γη)∞  x ,  where γη and γν are the projections onto the compactiﬁcation generated by Γ, then  (γν)∞  x = (γη)∞  x  λ-a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' This is proven similarly at the end of Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='23, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  20 and testing against  functions belonging in A(Γ) and using the decomposition of angle Young Measures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  □  Next, we show that the lack of concentration is equivalent to the equi-integrability of the  generating sequence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='25 Let (vj)j ∈ L1(Ω, µ, Rd) be so that  vj  Y (µ,efi,i∈N)  −−−−−−−→  �  νx, λ, ν∞  x  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Then the sequence (vj)j∈N is equi-integrable if and only if λ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Moreover vj → v strongly in L1(Ω, µ, Rd) if and only if λ = 0 and νx = δv(x) for µ-a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' x ∈ Ω.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Because λ does not depend on the compactiﬁcation (see Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='23, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' 20), we  can apply the same theorem from the sphere compactiﬁcation, [Rin18], p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' 347, lemma 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='14  and [Rin18], p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' 348, corollary 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='15, to conclude.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  □  Before stating the next two structure results, we prove that T −1 is a bounded operator from  Lip(efi,i∈N) to Lip(Rd), provided the compactiﬁcation is generated by Lipschitz functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' In  this case, by Lip(Rd) we mean the weighted norm  ∥f∥Lip(Rd) := ∥Tf∥∞ + sup  x̸=y  |f(x) − f(y)|  |x − y|  =  ����  f  1 + | · |  ����  ∞  + sup  x̸=y  |f(x) − f(y)|  |x − y|  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  As for the compactiﬁcation, the metric is always intended as in Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='16, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' 17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='26 Let efi,i∈N be a separable compactiﬁcation metrised by the usual metric, where  fi ∈ Lip(Rd) are normalised so that ∥f∥Lip(Rd) ≤ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Then  sup  x̸=y  |g(x) − g(y)|  |x − y|  ≤ 5Lip(Tg, efi,i∈N)  for all maps g: Rd → R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Without loss of generality assume that ∥Tg∥Lip ≤ 1, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' for all |x|, |y| < 1,  ����g  �  x  1 − |x|  �  (1 − |x|) − g  �  y  1 − |y|  �  (1 − |y|)  ���� ≤ |x − y| +  �  i  2−i|Tfi(x) − Tfi(y)|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  22  Then  |g(x) − g(y)| =  ����  g(x)  1 + |x|(1 + |x|) −  g(x)  1 + |x|(1 + |y|) +  g(x)  1 + |x|(1 + |y|) −  g(y)  1 + |y|(1 + |y|)  ����  = |g(x)|  1 + |x|  ���1 + |x| − 1 − |y|  ��� + (1 + |y|)  ����  g(x)  1 + |x| −  g(y)  1 + |y|  ����  ≤|x − y| + (1 + |y|)  �����  x  1 + |x| −  y  1 + |y|  ���� +  �  i  2−i  ����Tfi(  x  1 + |x|) − Tfi(  y  1 + |y|)  ����  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  For all i we have that  ����Tfi  �  x  1 + |x|  �  − Tfi  �  y  1 + |y|  ����� =  ����  fi(x)  1 + |x| − fi(y)  1 + |y|  ���� ,  and therefore after multiplying by 1 + |y| we obtain  ����  fi(x)  1 + |x|  �  1 + |x| + (|y| − |x|)  �  − fi(y)  ���� =  ����fi(x) − fi(y) + fi(x)  1 + |x|(|y| − |x|)  ����  ≤|fi(x) − fi(y)| + |fi(x)|  1 + |x||x − y| ≤ 2|x − y|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  □  We now show that the above lemma allows us to test Young Measures on Lipschitz compact-  iﬁcations against Lipschitz functions of Rd.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Deﬁnition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='27 (Kantorovich semi-norm) Let X be a metric space and µ ∈ M(X), then  the (formal) Kantorovich norm of µ is  ∥µ∥K =  sup  ∥φ∥Lip≤1  ˆ  X  φdµ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  The above formula induces a pseudo-distance between measures by setting d(µ, η)K = ∥µ −  η∥K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' It turns out that this is indeed a metric on the positive cone of non-negative Measures,  Lemma A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='6, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' 48.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='In particular, by taking Ψ ∈ Lip(efi,i∈N) and the pull-back T −1 we deduce  the following.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='28 Let efi,i∈N be a separable compactiﬁcation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Then every ν ∈ Y (efi,i∈N, µ) is  deﬁned by testing it against Lipschitz functions of the form  φ ⊗ ψ, where ∥φ∥Lip(Ω) ≤ 1, ∥ψ∥Lip(Rd) ≤ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  For this reason, we remind once again of the norm we will be using on the space efi,i∈N  throughout this thesis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Deﬁnition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='29 We say that efi,i∈N is a Lipschitz compactiﬁcation if each fi is Lipschitz  continuous, and renormalised so that Lip(Tf) ≤ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' The norm on Lip(efi,i∈N) will always be  ∥g∥Lip(efi,i∈N) :=  sup  x∈efi,i∈N  |g(x)| + sup  x̸=y  |g(x) − g(y)|  defi,i∈N(x, y)  23  where  defi,i∈N(x, y) = |x − y| +  �  i  2−i|Tfi(x) − Tfi(y)|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  To conclude this subsection, we state decomposition results for Young Measures regarding  oscillation and concentration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Originally proven in the context of the sphere compactiﬁcation,  [KR19], p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' 29, we here extend them to general compactiﬁcations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='30 Let vj ∈ L1(Ω, µ) so that  vj  Y (efi,i∈N,µ)  −−−−−−−→  �  νx, λ, ν∞  x  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  We can write vj = oj + cj, where oj ∈ L1(Ω, µ) is equi-integrable,  oj  Y (efi,i∈N,µ)  −−−−−−−→  �  νx, 0, N/A  �  and cj ∈ L1(Ω, µ) so that  cj  Y (efi,i∈N,µ)  −−−−−−−→  �  δ0, λ, ν∞  x  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  The converse is also true, for each such sequence oj, cj as above, their sum converges to the  former Young Measure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' A standard diagonal argument gives us kj ↑ ∞ so that oj = vjχ|vj| ≤ kj is equi-  integrable and generates oj  Y (efi,i∈N,µ)  −−−−−−−→  �  νx, 0, N/A  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Then, letting cj = vj − oj, for η ∈ C(Ω),  Tψ ∈ C(efi,i∈N) we have  ˆ  Ω  η(ψ(cj) − ψ(vj)) =  ˆ  |vj|≤kj  η(ψ(0) − ψ(oj)) +  ˆ  |vj|>kj  η(ψ(vj) − ψ(vj))  =  ˆ  Ω  η(ψ(0) − ψ(oj)) →  ˆ  Ω  η(ψ(0) − ⟨νx, ψ⟩).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Writing ψ(cj) =  �  ψ(cj) − ψ(vj)  �  + ψ(vj) and letting j → ∞ we conclude.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  □  We remark here that, when considering certain subsets of Y (for example Young Measures  generated by gradients, see next section), oj and cj might generate diﬀerent types of Young  Measures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  The next lemma is an extension of the previous result.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='31 Let vj ∈ L1(µ) and wj ∈ L1(µ) generate  vj  Y (µ,efi,i∈N)  −−−−−−−→  �  δv(x), λη, η∞  x  �  and  wj  Y (µ,efi,i∈N)  −−−−−−−→  �  νx, λν, ν∞  x  �  with λη ⊥ λν, for some v ∈ L1(µ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Then the sum of the sequence generates  vj + wj  Y (µ,efi,i∈N)  −−−−−−−→  �  δv(x) ∗ νx, λν + λη, k∞  x  �  ,  where  k∞  x =  �  ν∞  x  λν-a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  η∞  x  λη-a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  24  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Write wj = oj + cj as in the previous lemma and put bj = vj − v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' We claim that  bj + cj  Y (µ,efi,i∈N)  −−−−−−−→  �  δ0, λν + λη, k∞  x  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  No oscillation is a consequence of the fact that bj + cj → 0 in µ-measure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Next, let φ ∈  C(Ω), ∥φ∥Lip ≤ 1 and Ψ ∈ efi,i∈N, ∥TΦ∥Lip ≤ 1 with Ψ(0) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Let Eν and Eη be sets where  λν and λη are concentrated, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' For ε > 0 ﬁnd Cν ⊂ Eν, Cη ⊂ Eη compact sets and  Oν ⊃ Cν, Oη ⊃ Cη open sets such that  λη(Ω \\ Cη) + λν(Oη) + λν(Ω \\ Cν) + λη(Oν) < ε.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Consider a function ρ ∈ C(Rn) with χCη ≤ ρ ≤ χOη.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' We write  ˆ  Ω  φ  �  Ψ(bj + cj) − Ψ(bj) − Ψ(cj)  �  (  =I  ����  ρ  +  II  � �� �  1 − ρ)dµ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  We estimate the ﬁrst guy by  lim sup  j  |I| ≤ lim sup  j  2  ˆ  Ω  ρ|bj| = 2  ˆ  Ω  ρdλν ≤ 2λν(Ω ∩ Oη) ≤ 2ε.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Similarly for the second term  lim sup  j  |II| ≤ lim sup  j  2  ˆ  Ω  (1 − ρ)|cj| ≤ 2λη(Ω \\ Cη) ≤ 2ε.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  But the ﬁrst term converges to 0 and therefore we conclude for the representation of Young  Measures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  □  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='6  Terminology  We dedicate this part to clarifying the terminology of Young Measures adopted throughout  this paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Deﬁnition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='32 Given a separable algebra A of Gp that separates points from closed sets, a  p-Young measure is a triple  ν =  �  (νx)x∈Ω, λ, (ν∞  x )x∈Ω  �  where  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' (νx)x∈Ω is µ-measurable and νx ∈ M+  1 (Rd) µ-a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' x ∈ Ω.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  We call it the oscillation Young measure;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' λ ∈ M+(Ω).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  We call it the concentration measure;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' (ν∞  x )x∈Ω is λ-measurable and ν∞  x ∈ M+  1 (∂eA) λ-a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' x ∈ Ω.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' We call it the concentration  angle Young measure;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  25  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' the moment condition  ˆ  Ω  ˆ  Rd |z|pdνx(z) < ∞  must hold.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  The collection of all such triples is denoted by Y p = Y p(Ω, µ, eA).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Where obvious from the context, we will not specify the domain Ω, the measure µ, the family  A or the target space Rd.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Also, when λ = 0, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' when there is no concentration, there is no  point in specifying the compactiﬁcation we are working with.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  From every triple ν =  �  νx, λ, ν∞  x  �  one can construct the measure L ∈ C(eF Ω × Rd) and  vice-versa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='33 The following equality holds:  Y p = T ∗  �  L ∈ M+(eF Ω × Bd)+ :  ˆ  eF Ω×Bd φ(x)(1 − |ˆz|)pdL =  ˆ  Ω  φ(x)dµ(x) ∀φ ∈ C(eGΩ)  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  In particular Y p is a weak* closed and convex subset of A∗.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Let L ∈ M+(eF Ω × Rd)+ as above.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' It was already shown that T ∗L ∈ Y p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' On the  other side, if ν =  �  νx, λ, ν∞  x  �  , we let  L = νxdµ + ν∞  x dλ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Testing against a test function φ = φ(x) that only depends on x,  ˆ  eF Ω×Bd TφdL =  ˆ  eF Ω×Bd φ(x)(1 − |ˆz|)pdL =  ˆ  Ω  φdµ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Conclude by noticing that the above characterisation amounts to  Y p = T ∗  \uf8eb  \uf8ed  �  φ∈C(eF Ω)  �  L ∈ M+(eF Ω × Bd)+ :  ˆ  eF Ω×Bd φ(x)(1 − ˆz)pdL =  ˆ  Ω  φdµ  �\uf8f6  \uf8f8 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  □  Remark 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='34 With a straightforward adaptation of a classical argument for the sphere com-  pactiﬁcation, one can prove that given any Young Measure of the above form ν ∈ Y (Ω, µ, efi,i∈N)  with supp(µ  Ω) = Ω and µ non-atomic, then there is a sequence of smooth functions  uj ∈ D(Ω, Rd) such that  uj  Y (Ω,µ,efi,i∈N)  −−−−−−−−−→ ν.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  We do not transcribe the proof here because it won’t be used at any point in this work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  26  We now give a formal deﬁnition of what elementary Young Measures are, as a way to embed  functions and measures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Deﬁnition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='35 Let µ ∈ M+(Ω) and v ∈ Lp(Ω, µ, Rd), 1 ≤ p ≤ ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  The corresponding  elementary p-Young measure is  ξv :=  �  (δv(x))x∈Ω, 0, N/A  �  ∈ Y (µ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  When p = 1, we extend the deﬁnition to l ∈ M(Ω, Rd) by setting, for l = l  µdµ + ls,µ,  ξl :=  ��  δ l(x)  µ(x)  �  x∈Ω  , |ls,µ|,  �  δ ls,µ  |ls,µ|  �  x∈Ω  �  ∈ Y (µ, ∂Bd)  Note that for Φ ∈ Ep we have  ≪ ξv, Φ ≫=  ˆ  Ω  Φ(x, v(x))dν(x)  and  ≪ ξl, Φ ≫=  ˆ  Ω  Φ  �  x, l  µ(x)  �  dµ(x) +  ˆ  Ω  Φ∞  �  x, ls,µ  |ls,µ|(x)  �  d|ls,µ|(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  In general, there is no clear way of deﬁning elementary Young Measures on compactiﬁcations  that are larger than the sphere.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' We will see later, however, that this can be done in very speciﬁc  cases when we have more structure on A and more information on the measure l ∈ M(Ω, Rd)  we are trying to embed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Deﬁnition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='36 (Barycentre of a p-Young measure) Let ν =  �  (νx)x∈Ω, λ, (ν∞  x )x∈Ω  �  ∈  Y p(µ, A), where A is so that eA ≥ Bd (in the sense of compactiﬁcations, see Deﬁnition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='9, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  12).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' We call its barycentre  ν =  �  νx  1 < p < ∞  νxµ + ν∞  x λ  p = 1,  which is the following quantity  νx =  ˆ  Rd zdνx(z)  ν∞  x =  ˆ  ∂eA  zdν∞  x .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  In the above deﬁnition, "≥" is the ordering over the set of Hausdorﬀ compactiﬁcations of a  topological space (see the subsection on Hausdorﬀ compactiﬁcations).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Moreover, the barycen-  tre does not depend on the compactiﬁcation, as far as eA ≥ Bd.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Indeed z = [zj]j=1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=',d  extended to eA coordinate-wise, and so  ˆ  ∂eA  zdν∞  x =  ˆ  ∂Bd  ˆ  {(wn)n}  zdPz((wn)n)dπ∂Bdν∞  x =  ˆ  ∂Bd zdπ∂Bdν∞  x ,  as the coordinate map z �→ zj is constant on sequences (wn)n that converge to the same value  w ∈ ∂Bd.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Notice that x �→ νx is µ-measurable and x �→ ν∞  x is λ-measurable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' In particular,  ν ∈ Lp(Ω, µ, Rd) for 1 < p < ∞  and  ν ∈ M(Ω, Rd) for p = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  It is easy to see that when 1 < p < ∞, vj ⇀ v ∈ Lp(Ω, µ, Rd) we have v = νv, and when  p = 1, ρj ⇀∗ ρ ∈ C0(Ω, Rd)∗, then ρ = ξρ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  27  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='7  Stronger notions of convergence  To conclude the discussion about generalised Young Measures, we mention some stronger  notions of convergence such as strict convergence and µ-strict convergence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' These modes of  convergence explain why we chose such canonical embedding for measures in the previous  paragraph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Moreover, we give a simple example of why such canonical embedding has no  meaning when the compactiﬁcation is larger than the sphere one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Deﬁnition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='37 Let ηj, η ∈ M(Ω, Rd), we say that ηj  s−→ η (ηj converges strictly to η) if  ηj → η weakly* in C0(Ω, Rd)∗ and |ηj|(Ω) → |η|(Ω).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  It is easy to see that if ηj → η strictly, then |ηj| ⇀∗ |η| in C0(Ω, Rd)∗.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' The above convergence  prevents small-scale cancellations and concentration on the boundary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' However, it does not  prevent oscillation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' To prevent oscillation, we must choose a "weight" µ ∈ M+(Ω) and ask  for convergence of ηj on the graph (µ, ηj).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' We thus obtain a notion of µ-strict convergence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Deﬁnition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='38 We say that ηj  µ−s  −−→ η (ηj converges µ-strictly to η) if ηj → η weakly* in  C0(Ω, Rd)∗ and (µ, ηj) s−→ (µ, η) in C0(Ω, R × Rd)∗.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Similarly to what was observed in the case of strict convergence, such a notion implies that  |(µ, ηj)| ⇀∗ |(µ, ηj)| in C0(Ω)∗.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Moreover, µ-strict convergence of ηj to η simply amounts  to weak* convergence and additional convergence of the following quantity: writing ηj =  ηj  µ dµ + ηs,µ  j  , ηs,µ  j  ⊥ µ,  |(ηj, µ)|(Ω) =  ����  �ηj  µ dµ, µ  �  + (ηs,µ  j  , 0)  ����  =  ˆ  Ω  �  1 +  ����  ηj  µ  ����  2  dµ + |ηs,µ  j  |(Ω) →  ˆ  Ω  �  1 +  ����  η  µ  ����  2  dµ + |ηs,µ|(Ω) = |(η, µ)|(Ω).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  When µ = Ln, we refer to such convergence as area-strict convergence, in analogy with the  area formula for smooth functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Reshetnyak continuity theorem (see [Res68] for the original) shows that strict convergence is  equivalent to the convergence of 1-homogeneous functionals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='39 Let f(x, z) ∈ C(Ω × Rd) be 1-homogeneous in z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' If ηj → η strictly in the  sense of measures, then  ˆ  Ω  f  �  x, ηj  |ηj|  �  d|ηj|(x) →  ˆ  Ω  f  �  x, η  |η|  �  d|η|(x)  In case f is not 1-homogeneous but has an extension on the sphere compactiﬁcation, we can  obtain the following auto-convergence result by requiring µ-strict convergence instead.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Corollary 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='40 Let f ∈ E(Ω × Rd).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' If ηj  µ−s  −−→ η in C0(Ω, Rd)∗ then  ˆ  Ω  f  �  x, ηj  µ  �  dµ + f ∞  �  x,  ηs,µ  j  |ηs,µ  j  |  �  d|ηs,µ  j  | →  ˆ  Ω  f  �  x, η  µ  �  dµ + f ∞  �  x, ηs,µ  |ηs,µ|  �  d|ηs,µ|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  28  These are well-known results, but we write down a proof of the latter one because it gives an  insight into how to move from one type of convergence to the other.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Consider the so-called perspective functional  ˜f(x, z, t) =  �  f(x, z  t )|t|  t ̸= 0  f ∞(x, z)  t = 0  which is positively 1-homogeneous in the last variable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' By the Reshetnyak continuity theorem,  we know that, for η ∈ M(Ω, Rd),  ˆ  Ω  ˜f(x, (η, µ)) =  ˆ  Ω  f  �  x, η  dµ  �  dµ + f ∞  �  x, ηs,µ  |ηs,µ|  �  d|ηs,µ|  is sequentially continuous in the µ-strict topology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  □  Upon taking f(x, z) = |z| we get that µ-strict convergence implies strict convergence, for every  µ ∈ M+(Ω).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  In light of these results, for a ﬁxed measure µ ∈ M+(Ω), the canonical embedding of measures  η ∈ M(Ω, Rd) into the set of Young Measures on the sphere  η ∈ M(Ω, Rd) �→ ξη =  �  δ η  µ , |ηs,µ|, δ ηs,µ  |ηs,µ|  �  is sequentially µ-strictly continuous.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' This is a solid justiﬁcation for this choice of embedding.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  For the same reason, we can show why on larger compactiﬁcations we don’t have, in general,  a canonical choice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='41 Let µ ∈ M+(Ω) with the property that there is x ∈ supp(µ  Ω) with δx ⊥ µ,  and let f ∈ C(Rd) of linear growth, f ̸∈ E1(Rd) (oscillate at inﬁnity).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' There is (uj)j∈N ⊂  D(Ω, Rd), uj  µ−strictly  −−−−−−→ zδx in M(Ω, Rd) for some z ∈ ∂Bd, but  ˆ  Ω  f(uj(x))dµ(x) does not converge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  The above theorem implies that for all efi,i∈N ≥ ef (in the sense of compactiﬁcations), ξuj  does not converge in Y (µ, efi,i∈N).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Because of the assumptions on µ, we can ﬁnd x ∈ supp(µ  Ω) so that δx ⊥ µ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Notice  that the result is unchanged if we instead consider f(x) + C1|z| + C2, so taking C1, C2 > 0 big  enough we can assume that f ≥ 0 everywhere.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Find z ∈ ∂Bd and zj, wj → z so that  lim  n Tf(zj) = M and lim  j Tf(wj) = m exist, and M > m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Next, because x ∈ supp(µ) then µ(Br(x)) > 0 for all r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' There are two possible scenarios.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  First, x ∈ Ω, in which case we consider only those balls Br(x) so that B2r(x) ⊂ Ω.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' If x ∈ ∂Ω  then we can δr ↓ 0 so that µ(Br(x))∩Ω−δ(r)) > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Either way, we call Br(x) or Br(x)∩Ω−δ(r)  simply Br.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Furthermore, we can ﬁnd ε = ε(r) > 0 so that  Bε  r = (Br)ε = {x ∈ Rn : d(x, Br) < ε} ⊂ Ω  29  and  lim  r↓0  µ(Bε  r)  µ(Br) = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  For each such r ﬁnd φr ∈ D(Bε  r), 0 ≤ φr ≤ 1 so that φr(Br) = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Put ur =  φr  ´ φrdµ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Clearly  ur ⇀∗ δx in C(Ω)∗.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Next, reﬁne the sequences (zj)j and (wj)j so that there is rj ↓ 0 so that  ˆ  Br2j  φ2jdµ = 1 − |zj|  and  ˆ  Bεr2j+1  φ2j+1dµ = 1 − |wj|,  and put  uj =  \uf8f1  \uf8f2  \uf8f3  urjz j  2  if j is even,  urjw j−1  2  if j is odd.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  First we show that uj  µ−strictly  −−−−−−→ zδx in M(Ω, Rd).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Because zj, wj → z, it is enough to show  that ur  µ−strictly  −−−−−−→ δx in M(Ω) as r ↓ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Because ur ⇀∗ δx in C(Ω)∗ then  lim inf  r→0 |(urdµ, µ)|(Ω) ≥ |(δx, µ)|(Ω).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  To achieve the opposite inequality, we calculate  |(urdµ, µ)|(Ω) =|(0, µ)|(Ω \\ Bε  r) + |(ur, 1)dµ|(Ω ∩ Bε  r) = µ(Ω \\ Bε  r) +  ˆ  Bεr  �  1 + usrdµ  =µ(Ω \\ Bε  r) +  ´  Bεr  ��´  φrdµ  �2 + φsrdµ  ´  φrdµ  ≤µ(Ω \\ Bε  r) +  ´  Bεr  �  µ(Bεr)2 + 1dµ  µ(Br)  =µ(Ω \\ Bε  r) + µ(Bε  r)  �  µ(Bεr)2 + 1  µ(Br)  → µ(Ω) + 1 = |(δx, µ)|(Ω).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Next, we study how the integral behaves on alternating integers of the sequence (uj)j∈N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' If  j = 2i then  lim inf  i  ˆ  Ω  f(u2i(x))dµ(x) ≥ lim inf  i  ˆ  Br2i  f  �  zi  1 − |zi|  �  dµ = lim  i Tf(zi) = M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  On the other side, if j = 2i + 1 we get the upper bound  lim sup  i  ˆ  Ω  f(u2i+1(x))dµ(x) ≤ lim sup  i  ˆ  Bεr2i+1  f  �  wi  1 − |wi|  �  dµ = lim  i Tf(wi) = m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  □  30  Remark 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='42 The assumption on µ is sharp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' If for all x ∈ supp(µ  Ω) we have δx ̸⊥ µ, then  all such x’s belong to Ω.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Consider the atomic decomposition of µ:  µ = µa + µn−a =  �  n  µ(xn)δxn + µn−a,  see Theorem A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='8, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' 49.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' If µ(Ω \\ {xn, n ∈ N}) > 0 then we could ﬁnd x ∈ Ω \\ {xn, n ∈ N}  and δx ⊥ µ, so that µn−a = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Then µ = �  n µ(xn)δxn, and the set {xn, n ∈ N} contains its  accumulation points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' In particular {xn, n ∈ N} = supp(µ) is a compact subset of Ω.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' It is easy  to see that, in this setting, if (φj)j∈N ⊂ L1(µ) is bounded in norm and  φj  Y (µ,efi,i∈N)  −−−−−−−→  �  νx, λ, ν∞  x  �  ,  then λ ≪ µ, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' λ = �  n λ(xn)δxn (because the space is countable and compact).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Also  φj ⇀∗ φ =  �  νx + ν∞  x  λ  µ  �  dµ  in C0(X)∗, X = {xn, n ∈ N}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Assume also that φj → φ µ-strictly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' This amounts to the  following  ˆ  X  f(φj)dµ →  ˆ  X  ⟨νx, f⟩ + ⟨ν∞  x , f ∞⟩λ  µdµ =  ˆ  X  f(φ)dµ,  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='157)  where f(z) =  �  1 + |z|2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' f is a strictly convex function, therefore the inequality f(x + y) ≤  f(x) + f ∞(y) is strict unless y = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' We have  ⟨νx, f⟩ + ⟨ν∞  x , f ∞⟩λ  µ ≥f(νx) + f ∞  �  ν∞  x  λ  µ  �  > f  �  νx + ν∞  x  λ  µ  �  = f(φ)  unless ν∞  x  = 0 λ-a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' So φ = νx µ-a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=', and using convexity once again in (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='157), and the  fact that f ∞ = 1, we get  f(φ) =⟨νx, f⟩ + ⟨ν∞  x , f ∞⟩λ  µ ≥ f(νx) + λ  µ = f(φ) + λ  µ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  So λ = 0, which implies that the sequence φj does not concentrate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Moreover, φ(x) = νx,  which means that φj → φ in measure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Then φj → φ strongly in L1(µ), and Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='41, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  29 is false.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  31  3  Characterisation of gradient Young Measure  on general compactiﬁcations  In this section, we show that generalised gradient Young Measures are characterised by a  set of integral inequalities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' A characterisation result was previously obtained in the context  of the sphere compactiﬁcation, see [KR10a] and [KR19] for the result on general diﬀerential  operators, and it’s here extended to general compactiﬁcations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='1  Non-separability of the space of quasi-convex functions  We start by showing that the set of quasi-convex functions having linear growth is non-  separable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Lack of separability prevents sequential compactness and other essential properties  that were used to develop the theory of generalised Young Measures (see the section above).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Therefore, we are forced to consider only smaller countable collections of quasi-convex functions  at the time, and cannot work with the entire class.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' To show that the class is non-separable,  we modify the example by Muller [Mül92] and generate quasi-convex functions that oscillate  at diﬀerent amplitudes in the same direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='1 The space of quasi-convex functions f : R2×2 → R having linear growth is not  separable with respect to ∥T · ∥∞,B2×2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  The idea behind the proof is to construct an uncountable family {fΛ}Λ so that ∥TfΛ−TfΓ∥∞ ≥  c for some universal constant c > 0 and all Λ ̸= Γ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' We will split the proof of the above result  into two diﬀerent parts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' First, we show that we have quasi-convex functions that oscillate  along every possible sequence of natural numbers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='2 There is c > 0 such that for every Λ ⊂ N inﬁnite so that Λc is also inﬁnite  there exists fΛ : R2×2 → R quasi-convex and having linear growth such that  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' fΛ(3j  1) = 0 for all j ∈ Λ and  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  fΛ(3j  1)  3j  ≥ c for all j ∈ Λc suﬃciently large.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  To prove this theorem we ﬁrst need a preliminary lemma, whose proof can be found in [Mül92],  p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' 299, lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='3 For k ∈ R+ we let  gk : R2×2 → R, F �→ |F1,1 − F2,2| + |F1,2 + F2,1| + (2k − |F1,1 + F2,2|)+.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Then there exists c1 > 0 such that  Qgk(0) ≥ c1k  for all suﬃciently large ks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  We can then prove Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='2, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' 32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  32  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Let Λ ⊂ N as in the proposition above and set fΛ = QgΛ where  gΛ(F) = |F1,1 − F2,2| + |F1,2 + F2,1| + inf{|F1,1 + F2,2 − 2 · 3i|, i ∈ Λ}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  We have that gΛ(3j  1) = 0 for all j ∈ Λ and so fΛ(3j  1) = 0 as well given that gΛ ≥ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  We ﬁrst derive the following lower bound: compute  gΛ(3j  1 + G) = |G1,1 − G2,2| + |G1,2 + G2,1| + inf{|G1,1 + G2,2 + 2(3j − 3i)| : i ∈ Λ};' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  because 3j is increasing we estimate, for arbitrary β ∈ R,  inf  i∈Λ |2(3j − 3i) + β| ≥  �  inf  i̸=j |2(3j − 3i)| − |β|  �+  =  �  2(3j − 3j−1) − |β|  �+,  and so gΛ(3j  1 + G) ≥ gk(G) for all matrices G and k = 3j − 3j−1, and gk given by  gk(F) = |F1,1 − F2,2| + |F1,2 + F2,1| + (2k − |F1,1 + F2,2|)+  does not depend on Λ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Apply Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='3, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' 32 to ﬁnd c > 0 (independent of Λ) such that  fΛ(3j  1) = QgΛ(3j  1) ≥ Qgk(0) ≥ c1(3j − 3j−1) for j big enough.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Dividing everything by 3j we get  fΛ(3j  1)  3j  ≥ 2  3c1 ≡ c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  □  It’s not a priori clear if these functions are "far away from each other at inﬁnity", as subsets  of natural numbers could intersect inﬁnitely many times.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' To show that there is a wide variety  of sequences that diﬀer at inﬁnity, we deﬁne the following relation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Deﬁnition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='4 Given Γ, Λ any two sequences (not necessarily subsets of N), we say that  Γ ≤ Λ provided Γ is eventually a subset of Λ, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Λ = (ai),i∈N, Γ = (bi)i∈N,  Λ ≤ Γ  ⇐⇒  there exists k > 0 : (ai)i≥k is a subsequence of (bi)i≥0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Let [Λ] be the equivalence class of Λ with respect to ≤, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Γ ∈ [Λ] if Γ ≤ Λ ≤ Γ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  If Λ′ ∈ [Λ] and Γ′ ∈ [Γ] then Λ ≤ Γ if and only if Λ′ ≤ Γ′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  We use  �  F, ≤  �  to indicate the set of equivalence classes with the inherited order.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  The above ordering is needed because, to show that we have uncountably many sequences  that are independent of each other at inﬁnity, we will use Zorn’s lemma and ﬁnd a maximal  set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' One could also reason that the Stone-Cech compactiﬁcation of natural numbers is not  metrisable and reason by contradiction using a suitably adapted version of Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='12, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  12, but we decided to not pursue this path.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='5 There exists an uncountable family G ⊂ F such that for every diﬀerent pair  Λ, Γ ∈ G, Λ is not comparable to either Γ nor Γc with respect to ≤.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  33  The above means that we can ﬁnd a set G such that given any two sequences of natural  numbers in Λ, Γ ∈ G, one is frequently in the other sequence and its complement, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Λ ∩ Γ  and Λ ∩ Γc are both inﬁnite.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Consider the set of subsets  G = {G ⊂ F : no pair within G is comparable according to ≤},  ordered by inclusion ⊂.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' The above set is non-empty, which can be seen by taking Λ = 2N and  Γ = 4N ∪ (4N + 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Every chain in G has an upper limit given by its union.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' By Zorn’s lemma,  there exists a maximal element.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  I claim that the maximal element has uncountably many  elements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' To prove the claim we ﬁrst assume that the maximal element G ⊂ G is countable or  ﬁnite and show that it is always possible to extract an extra incomparable element.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  To do so, I will show that given any countable or ﬁnite collection of inﬁnite natural numbers  {cj  i, i ∈ N}j∈N there is {ci, i ∈ N} such that {ci, i ∈ N} ∩ {cj  i, i ∈ N} is inﬁnite for all j and  {ci, i ∈ N} ∩ {cj  i , i ∈ N} < {cj  i, i ∈ N} according to the order previously established.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Consider  the isomorphism  N : F → {0, 1}N, {ci, i ∈ N} �→  �  Nci =  �  1  if i ∈ {ck, k ∈ N}  0  otherwise  �  i∈N  Practically speaking, we are replacing subsets of natural numbers to sequences that take values  1 when the i-th number is in the set, 0 otherwise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Set initially Nci = 0 for all i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' At i1 so that Nc1  i1 = 1 for the ﬁrst time put Nci1 = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' We then  iterate "diagonally" in the following way.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' At the n-th iteration ﬁnd in+1 so that Ncj  kj = 1  for all 1 ≤ j ≤ n and some in < kj−1 < kj and Ncj  tj = 1 for all 1 ≤ j ≤ n + 1 and  kn < tj−1 < tj < tn+1 = in+1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Set Nctj = 1 for all 1 ≤ j ≤ n + 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' This procedure stops if the  maximal set is ﬁnite, otherwise can be iterated countably many times.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  This way we guarantee that Nckj = 0 for in < kj and Ncj  kj = 1, which means that Nci skips  inﬁnitely many 1s from each sequence (Ncj  i)i∈N, for all j ∈ N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' On the other side Nctj = 1 =  Ncj  tj, tj ≤ in+1, so Nci is also frequently in every sequence (Ncj  i)i∈N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Going back to our countable maximum element G =  �  {aj  i, i ∈ N}, j ∈ N  �  , we can apply the  previous construction to ﬁnd {ci, i ∈ N} ∈ F generated by the countable family  {cj  i , i ∈ N}j∈N =  �  {aj  i, i ∈ N} , N \\ {aj  i, i ∈ N}  �  j∈N  Because {ci, i ∈ N} is frequently and properly in {aj  i, i ∈ N} and its complement N\\{aj  i, i ∈ N}  for all j, then {ci, i ∈ N} is not comparable to any member of the family and this contradicts  the maximality of our set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  □  We are now ready to prove Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='2, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' 32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' By the lemma we can ﬁnd an uncountable set of uncomparable subsequences of N, call  it G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' I claim that if Λ, Γ ∈ G, Λ ̸= Γ then fΛ and fΓ have diﬀerent recessions at inﬁnity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Find {xn} ∈ efΛ with {xn} ≥ {3j  1, j ∈ Λ}, where the inequality could be strict given that  there might be more zero points at inﬁnity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Given our construction, we immediately have that  34  {xn} ̸≥ {3j  1, j ∈ N \\ Λ} as fΛ(3j  1) ≥ c3j for all j ∈ N \\ Λ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Also, Γ intersects N \\ Λ and Λ  inﬁnitely many times, and vice versa, so that  lim sup  n  fΓ(xn)  |xn|  ≥ lim sup  j∈Λ∩Γ  fΓ(3j  1)  3j  ≥ c,  and  lim inf  n  fΓ(xn)  |xn|  ≤ lim inf  j∈Λ∩Γ  fΓ(3j  1)  3j  = 0,  which shows that {xn} ̸∈ efΓ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' In terms of the non-separability, by the deﬁnition of xn, we have  lim  n  fΛ(xn)  |xn|  = 0,  thus  ∥TfΛ − TfΓ∥∞ ≥ lim sup  n  ����  fΓ(xn)  |xn|  − fΛ(xn)  |xn|  ���� = lim sup  n  ����  fΓ(xn)  |xn|  ���� ≥ c,  where c is independent of Λ or Γ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  □  Given that the space is metric, having such a property prevents separability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' We can end this  section with the following corollary that incorporates higher dimensions:  Corollary 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='6 The set of quasi-convex functions having linear growth f : Rm×n → R is sep-  arable in the topology induced by ∥T(·)∥∞ if and only if min(m, n) = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' If m or n is 1, quasi-convex functions are convex and therefore the space is separable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  This is because convex functions admit a limit at inﬁnity in every direction;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' in this case, we  actually recover the sphere compactiﬁcation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  On the other side, for a function g: R2×2 → R we let  gP ≡ g ◦ P : Rn×m → R,  P : Rm×n → R2×2, M �→  �M1,1, M1,2  M2,1, M2,2  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  If g is quasi-convex and locally bounded we let φ ∈ D(Q, Rm) and compute  ˆ  Q  gP(Dφ + z) =  ˆ  Q⊂Rn−2 dLn−2  ˆ  [0,1]2 dx1x2g(PDφ + Pz) ≥  ˆ  Q⊂Rn−2 dLn−2gP(z) = gP(z),  i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' gP is quasi-convex.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Then the set fΛP is uncountable and  ∥T(fΛP − fΓP)∥∞,Bm×n = ∥T(fΛ − fΓ)∥∞,B2×2 ≥ c  if Γ ̸= Λ, so the space cannot be separable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  □  Notice that separability is important to achieve both the Young Measure representation and  for sequential compactness in the inherited weak star topology of Young Measures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  35  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='2  Characterisation of Gradient Young Measures  In this section, we characterise Gradient Young Measures (on separable compactiﬁcation) via  certain Jensen-like integral inequalities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  It is worth mentioning that the result for the sphere compactiﬁcation, achieved in [KR10a], can  be easily improved in consideration of the fact that lim supt→∞ f(tz)t−1 is 1-homogeneous rank  one convex, and so convex at points rank(z) = 1 (see [KK16], p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' 528)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' In what follows, we  cannot use this type of auto-convexity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' In our context, f ∞ lives on a general compactiﬁcation  and convexity at points of rank one, as a Jensen’s type inequality, is not necessarily true.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  To prove our result, we will adopt the same strategy as in [KR19].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Preliminarily to stating the theorem, we deﬁne the upper recession of a function relative to a  general compactiﬁcation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Deﬁnition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='7 Let efi,i∈N be a separable compactiﬁcation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' For any f having linear growth,  we deﬁne  f ♯,efi,i∈N((zn)) =  sup  (wn)n∈[(zn)n]  lim sup  n  Tf(wn),  where (wn)n are sequences belonging to the equivalence class of (zn)n within efi,i∈N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  The reason why we introduce this notion is that the strategy for proving the characterisation  theorem makes use of the trivial fact that f ≥ f qc, f qc being the quasi-convex envelope of f  (see, for example, [Dac07])  f qc(z) =  inf  φ∈D(Q)  ˆ  Q  f(z + Dφ(x))dx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  However, f qc does not need to live in the same class of separable quasi-convex functions, so  the implication  lim  n  f(zn)  |zn|  exists ⇒ lim  n  f qc(zn)  |zn|  exists  could be false for some functions f.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Fix any compactiﬁcation efi,i∈N and a function Tg ∈ efi,i∈N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' If g ≥ f then  g∞((zn)) = lim  n Tg(zn) ≥  sup  (zn)∈[(zn)]  lim sup  n  Tf(zn) = f ♯,efi,i∈N((zn)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  f ♯,efi,i∈N does not need to be continuous on efi,i∈N with respect to its product topology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' How-  ever, we can show that it is still upper semi-continuous.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='8 Let efi,i∈N be a separable compactiﬁcation and f a function having linear growth,  then f ♯,efi,i∈N is upper semi-continuous on ∂efi,i∈N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Notice that ∂efi,i∈N is metrisable, so it is enough to show sequential upper semi-  continuity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Let (zj  n)n ∈ ∂efi,i∈N so that (zj  n)n  j−→ (zn)n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' By the very deﬁnition of g♯,efi,i∈N((zj  n)n),  for ﬁxed ε > 0 we can ﬁnd nj ≥ kj, where kj is a natural number to be selected, so that  g♯,efi,i∈N((zj  n)n) ≤ ε + Tg((zj  nj)), where (zj  nj) is a constant sequence and belongs to efi,i∈N \\  36  ∂efi,i∈N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' We want to show that we can select kj so that (zj  nj)j belongs in the equivalence class  of (zn)n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' By applying the dominated convergence theorem we get  lim  j  �  i  lim  n 2−i|fi(zj  n) − fi(zn)| = 0 = lim  j lim  n  �  i  2−i|fi(zj  n) − fi(zn)|,  and so can ﬁnd kj so that  �  i  2−i|fi(zj  n) − fi(zn)| ≤ εj  ∀n ≥ kj,  where 0 ≤ εj ↓ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' This shows that the above sequence (zj  nj)j ∈ [(zn)n] (the equivalence class),  thus  lim sup  j  g♯,efi,i∈N((zj  n)n) ≤ ε + lim sup  j  Tg((zj  nj)) ≤ ε + g♯,efi,i∈N((zn)n).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  By the arbitrariness of ε > 0 we conclude upper semi-continuity of g♯,efi,i∈N  □  In particular, g♯,efi,i∈N is Borel measurable on efi,i∈N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' The above statement can be generalised  to extensions of functions over more general compact metric spaces, but this version suﬃces  for our scopes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  We are interested in studying those Young Measures that are generated by gradients.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' So we  deﬁne the following.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Deﬁnition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='9 We say that ν ∈ Y (efi,i∈N) is a (generalised) gradient Young Measure if there  exists a sequence uj ∈ BV (Ω, Rm) such that  Duj  Y (efi,i∈N)  −−−−−−→  �  νx, λ, ν∞  x  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  We use GY (efi,i∈N) to refer to these subsets of Young Measures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  The convergence of measure derivatives has not been fully comprehended yet and it is still the  subject of active research.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' This means that it is not so clear how rich the above class is, and  with which frequency gradients oscillate - or at least within the setting of weak* convergence  of measures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Remark 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='10 We can use the characterisation lemma for Young Measure on the sphere to  show that the class is still quite vast.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Indeed, by [KR10a], p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' 541 Theorem 1, ﬁx any z = a ⊗ b  and ν∞ ∈ P(∂B) with ν∞ = z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Then gradient Young Measure on the sphere  �  δ0, Hn−1  (B ∩ b⊥), ν∞�  satisﬁes the characterisation theorem from [KR10a], with u = aχx·b≥0 and so it is generated  by a sequence of gradients Duj ∈ BV (B1(0)), B1(0) ⊂ Rn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Because Duj is bounded in BV ,  we can ﬁnd a subsequence (ujk)k∈N such that  Dujk  Y (efi,i∈N), as k→∞  −−−−−−−−−−−−→  �  δ0, Hn−1  (B ∩ b⊥), η∞�  ,  with clearly π∂Bη∞ = ν∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Using Corollary 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='19, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' 18 to write η∞ = Pzdν∞, z ∈ ∂Bd, it  remains an open question to understand how many probabilities Pz over subsequences zn → z  can be generated by gradients.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  37  We now state the main theorem of this section.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='11 Let Ω ⊂ Rn be a bounded Lipschitz domain and efi,i∈N be a separable compact-  iﬁcation of quasi-convex functions and consider a generalised Young Measure ν ∈ Y (efi,i∈N)  that satisﬁes λ(∂Ω) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Then ν ∈ GY (efi,i∈N) is a Young Measure generated by a sequence  (φj ⋆ (Du  Ω) + Duj)  Y (efi,i∈N)  −−−−−−→  �  νx, λ, ν∞  x  �  ,  where u ∈ BV (Ω, Rm), uj ∈ D(Ω, Rm) and ∥uj∥1 → 0, and φj is any sequence of molliﬁers  with φj ⇀∗ δ0, if and only if there is u ∈ BV (Ω, Rm) such that  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' ≪ 1 ⊗ | · |, ν ≫< +∞, and for all f quasi-convex and having linear growth,  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' f(∇u(x))dx ≤ ⟨νx, f⟩dx + ⟨ν∞  x , f ♯,efi,i∈N⟩ λ  Ln dx and  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' f ∞(Dsu) ≤ ⟨ν∞  x , f ♯,efi,i∈N⟩dλs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  We can adjust the above theorem to ﬁx the boundary of the converging sequence so that it’s  always equal to u in the sense of trace.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='12 If ν ∈ Y (efi,i∈N) is generated by a sequence  φj ⋆ (Du  Ω) + Duj  as above, then there exists another sequence vj ∈ C∞(Ω) ∩ W 1,1  u (Ω) such that  D(vj + uj)  Y (efi,i∈N)  −−−−−−→ ν.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  In particular, ν ∈ GY (efi,i∈N).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' We can ﬁnd uj → u strictly in BV (Ω) with uj ∈ C∞(Ω) ∩ W 1,1  u (Ω), see for example  [KR10a] Lemma 1 for a proof of this fact.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' In the construction of the ujs just mentioned, it is  possible to select φj ⋆ (Du  Ω) on Ω−ε for j big enough, φj as in Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='11, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' 38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Also,  without loss of generality, we can assume that |Du|(∂Ω−ε) = |Duj|(∂Ω−ε) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Because the  fis are all Lipschitz, it is enough to test against f ∈ Lip(Rm×n) with Lip(f) ≤ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' We then  compute  ˆ  Ω  |f(φj ⋆ (Du  Ω) + Dvj) − f(Duj + Dvj)|dx ≤  ˆ  Ω  |φj ⋆ (Du  Ω) − Duj|  ≤  ˆ  Ω\\Ω−ε  |φj ⋆ (Du  Ω)| + |Duj| = Ij + IIj  By strict convergence of both integrands, we have that  lim sup  j  Ij + IIj ≤ 2|Du|(Ω \\ Ω−ε),  and so use a diagonal argument to conclude the existence and equality of the limit Young  Measure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  □  38  It’s implicit in Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='11, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' 38 that  Du = ν = ⟨νx, ·⟩dx + ⟨ν∞  x , ·⟩dλ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Also, the above inequalities can be written in the sense of distribution, in the form  ˆ  Ω  φ(x)⟨νx, f⟩dx +  ˆ  Ω  φ(x)  ˆ  ∂efi,i∈N  f ♯,efi,i∈Ndν∞  x dλ  ≥  ˆ  Ω  φ(x)f(∇u(x))dx + φ(x)f ∞  � Dsu  |Dsu|  �  d|Dsu|  for all φ ∈ D(Ω), φ ≥ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  To prove the characterisation result we will follow the same strategy as in [KR19].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' We initially  prove the result for homogeneous gradient Young Measures and then extend the theorem to  the inhomogeneous case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Notice that Young Measures that act on functions f = f(z) that  only depend on z can be represented by  ˆ  Ω  ⟨νx, f⟩dx +  ˆ  Ω  ⟨ν∞  x , f ∞⟩dλ =  ˆ  Ω  fdν0 +  ˆ  ∂efi,i∈N  f ∞dν∞,  where for efi,i∈N the separable compactiﬁcation that extends f,  ν0 = νxdLn ∈ M+(Ω)  and  ν∞ = ν∞  x dλ ∈ M+(∂efi,i∈N).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  The (push-forward) Kantorovich metric is then  ∥(ν0, ν∞)∥K =  sup  Φ∈H,∥TΦ∥Lip(efi,i∈N)≤1  �����  ˆ  Rd Φdν0 +  ˆ  efi,i∈N  Φ∞dν∞  ����� .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  For z ∈ Rd we let Y be the set of pairs  �  ν0, ν∞�  ∈ M+  1 (Rd) × M+(efi,i∈N) such that there is  a sequence uj ∈ D(Q, Rm), where Q is the unit cube, so that z + Duj  Y (efi,i∈N)  −−−−−−→  �  ν0, ν∞�  and  ∥uj∥1 → 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' The following proposition follows from obvious variations of the proofs contained  in [KR19], p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' 8, lemmas 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='7,3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='8,3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' The proofs are essentially the same as they only use the  separability of the compactiﬁcation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='13 The family {εz+Du : u ∈ D(Q, Rm)} is weakly* dense in Y, and Y is a weak*  closed and convex subset of homogeneous Young Measures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  We can now prove the main theorem in case  �  ν0, ν∞�  is a homogeneous gradient Young  Measure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='14 Let ν =  �  ν0, ν∞�  ∈ M+  1 (Ω) × M+(∂efi,i∈N) and z ∈ Rm×n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Then ν ∈ Y  if and only if there is z ∈ Rm×n such that  ˆ  Rm×n fdν0 +  ˆ  ∂efi,i∈N  f ♯,efi,i∈Ndν∞ ≥ f(z)  for all f : Rm×n → R quasi-convex and having linear growth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  39  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Suppose that ν ∈ Y and let z + Duj, uj ∈ D(Q, Rm) be the generating sequence, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  for all Φ ∈ T −1efi,i∈N,  ˆ  Q  Φ(z + Duj)dx → ⟨ν, Φ⟩ =  ˆ  Rm×n Φdν0 +  ˆ  ∂efi,i∈N  Φdν∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Fix an arbitrary f having linear growth and quasi-convex and let ef,fi,i∈N the bigger compact-  iﬁcation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Upon extracting a subsequence we have that  z + Duj  Y (ef,fi,i∈N)  −−−−−−−→  �  ν0, ˜ν∞�  ,  where we identify the gradient Young Measure with its tensor products as f = f(z).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' By quasi-  convexity, we have  ˆ  Rm×n fdν0 +  ˆ  ∂ef,fi,i∈N  f ∞d˜ν∞ = lim sup  j  ˆ  Q  f(z + Duj)dx ≥ f(z).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  On the other side, using the decomposition of angle concentration Young Measure Corollary 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='19,  p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' 18 we also obtain that  ˆ  ∂ef,fi,i∈N  f ∞d˜ν∞ =  ˆ  ∂efi,i∈N  ˆ  f ∞dP(zn)ndν∞ ≤  ˆ  ∂efi,i∈N  f ♯,efi,i∈Ndν∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  For the other implication, because Y is weakly* closed and convex, we can write Y = ∩H where  H are half-spaces containing Y, which can be written as  H = {l ∈ H∗ : l(Φ) ≥ t}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  In particular, we can test the above inequality against εz+Du and get  t ≤ εz+Du(Φ) ≤  ˆ  Q  Φ(z + Du)dx  for all u ∈ D(Q, Rm).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Passing to the inﬁmum over all such us we deduce t ≤ Φqc(z) and so  ⟨ν, Φ⟩ =  ˆ  Rm×n Φdν0 +  ˆ  ∂efi,i∈N  Φ∞dν∞  ≥  ˆ  Rm×n Φqcdν0 +  ˆ  ∂efi,i∈N  (Φqc)♯,efi,i∈Ndν∞ ≥ Φqc(z) ≥ t  which shows that ν ∈ H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  □  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='1  Inhomogenization  In what follows, we will prove a semi-approximation result for the absolutely continuous and  singular parts separately and then put them together via Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='31, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' 24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' In each case,  we will use a covering argument to boil it down to the homogeneous case, which was solved in  the above section.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Consider a standard molliﬁer φt(x) = tn−1φ(x  t ), where φ ∈ D(Q) and let M = ∥Dφ∥∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Also,  unless otherwise speciﬁed, the norm on Rn is the maximum norm ∥x∥ = maxi |xi|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  40  Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='15 Given ε > 0 there is tε > 0 and a family ϕt ∈ D(Ω, Rm) with ∥ϕt∥1 ≤ ε so that  ����  ˆ  Ω  ηΦ(0) + η⟨Φ∞, ν∞  x ⟩dλs −  ˆ  Ω  ηΦ(φt ⋆ (ν∞dλs) + Dϕt)dx  ���� < ε  for all t ∈ (0, tε) uniformly in ∥η∥Lip ≤ 1 and ∥TΦ∥Lip,graph(f) ≤ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  The idea behind this approximation result is the following.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' The singular part of the centre  of mass (which is just Du ∈ M(Ω, Rd)) is approximated by molliﬁcation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Such a procedure  generates area-strictly convergent smooth approximations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  At the same time, we generate  angle concentration and oscillation via compactly supported functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Because the ﬁrst type  of convergence is very strong, and the latter doesn’t concentrate, the two modes of convergence  don’t interfere with each other.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Notice that this strategy would not be possible using the bare  notion of weak* convergence because of the lack of quantiﬁability, whereas the (equivalent in  this case) Kantorovich metric gives us an "exact" quantity to approximate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Before proving the above statement we remind that, according to Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='26, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' 22, T pulls  back bounded sets of Lipschitz functions on efi,i∈N to bounded sets of Lipschitz functions on  Rm×n (provided fi are Lipschitz).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Therefore, all the functions in the following theorem can  be taken to be, after renormalisation, 1-Lipschitz in both spaces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  From now on, after ﬁxing a compactiﬁcation, we will always identify  ∥TΦ∥Lip = ∥TΦ∥Lip(efi,i∈N) = ∥TΦ∥∞ + sup  x̸=y  |TΦ(x) − TΦ(y)|  |x − y| + �  i 2−i|Tfi(x) − Tfi(y)|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Fix ε > 0 and apply Luzin’s theorem to the λs map  x ∈ Ω → (δ0, ν∞  x ) ∈ M+  1 (Rd) × M+(∂efi,i∈N) ֒→  �  (T −1efi,i∈N)∗�+  to ﬁnd a compact set C = Cε ⊂ Ω with λs(Ω \\ C) < λs(Ω)ε restricted to which the above  map is uniformly continuous, with modulus of continuity ω = ωε.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Without loss of generality,  assume that Ln(Cs) = 0 and because λs(∂Ω) = 0 then  ∆ = ∆ε = d(Cs, ∂Ω) > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  For the moment, ﬁx two integers a, b ∈ N and put t = 2−a, so that φt > 0 if and only if  ∥x∥ < t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Let a be so large that  2t ≤ ∆  and  a ≥ log2  � 2  ∆  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Denote by F the collection of a+b-th generation dyadic cubes Q in Rn so that d(Q, ∂Ω) > 2−a,  and for each such Q ∈ F we deﬁne  rQ =  Q  φ ⋆ (λs  Cs)dx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Notice that rQ > 0 means that dist(Q, Cs) < t, and so for each such Q we can ﬁnd xQ ∈ Cs  so that d(xQ, Q) < t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Denote by Fs the set of those Q ∈ F for which rQ > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' In particular, if  Q ∈ Fs we can ﬁnd xQ ∈ Cs so that supQ ∥x − xQ∥ < 2t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  41  For every quasi-convex function having linear growth we have  f(z + w) ≤ f(z) + f ∞(w)  for all z ∈ Rm×n and rank(w) = 1, see [KK16], p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' 536, lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='5 (we don’t need regular  recession for this result to hold).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Then by assumption, we have  f(rQν∞  xQ) ≤ f(0) + rQf ∞(ν∞  xQ) ≤ f(0) + rQ  ˆ  ∂efi,i∈N  f ♯,efi,i∈Ndν∞  xQ  for all f quasi-convex and having linear growth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Going back to the homogeneous case Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='14, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' 39, we can select ϕQ ∈ D(Q, Rm)  with ∥ϕQ∥1 < ελs(Q) such that  ∥(δ0, ν∞  xQrQ) − εrQν∞  xQ+DϕQ∥K < ε.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Deﬁne ϕ = �  Q∈Fd ϕQ ∈ D(Ω, Rm) and ∥ϕ∥1 ≤ ελs(Ω).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' The sought-after map is then  ξs = φ ⋆ (ν∞  x dλs + Dϕ) ∈ D(Rn, Rd).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  To prove that this function is the desired one, we ﬁx ∥η∥Lip ≤ 1, ∥Ψ∥Lip(efi,i∈N) ≤ 1 as in the  assumptions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' We have  ˆ  Ω  η⟨Φ∞, φ ⋆ (ν∞dλs)⟩dx =  ˆ  Ω  η⟨Φ∞, φ ⋆ (ν∞dλs  Cs)⟩dx +  =E1  �  ��  �  ˆ  Ω  η⟨Φ∞, φ ⋆ (ν∞dλs  Ω \\ Cs)⟩dx,  and |E1| ≤ ελs(Ω).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Notice that here  ˆ  Ω  η⟨Φ∞, φ ⋆ (ν∞dλs  U)⟩dx =  ˆ  Ω  η(x)  ˆ  U  φ(x − y)  ˆ  ∂efi,i∈N  Φ∞dν∞  y dλs(y)dx  where U = Ω or Cs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Since for each Q ∈ F with rQ = 0  ˆ  Q  η⟨Φ∞, φ ⋆ (ν∞dλs  Cs)⟩dx = 0  and dist(∪F, ∂Ω) > 2t, we get  ˆ  Ω  ⟨Φ∞, φ ⋆ (ν∞dλs  Cs)⟩dx =  �  Q∈Fs  ˆ  Q  η⟨Φ∞, φ ⋆ (ν∞dλs  Cs)⟩dx + E2  =  �  Q∈Fs  �ˆ  Q  ηdx⟨Φ∞, ν∞  xQ⟩rQ + EQ  3  �  + E2,  42  where |E2| ≤ λs(Cs ∩ (∂Ω)2t).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' The third error is estimated in the following way:  |EQ  3 | ≤  ����  ˆ  Q  �  η −  ˆ  Q  η  �  ⟨Φ∞, φ ⋆ (ν∞dλs  Cs)⟩dx  ����  +  ����  ˆ  Q  η  �ˆ  Q  ⟨Φ∞, φ ⋆ (ν∞dλs  Cs)⟩dx − ⟨Φ∞, ν∞  xQ⟩rQ  �����  ≤∥η∥Lip Ln(Q)  1  n ∥Φ∞∥  ˆ  Q  φ ⋆ λsdx  + ∥η∥Lip  ˆ  Q  ˆ  Cs φ(x − y)⟨Φ∞, ν∞  y − ν∞  xQ⟩dλs(y)dx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  In particular, we obtain  |EQ  3 | ≤t  ˆ  Q  φ ⋆ λsdx +  ˆ  Q  ˆ  Cs φ(x − y)ω(∥y − xQ∥)dλs(y)dx  ≤(t + ω(3t))  ˆ  Q  φ ⋆ λsdx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  From each Q ∈ Fs we get  Φ(0) + ⟨Φ∞, ν∞  xQ⟩rQ =  ˆ  Q  Φ(rQν∞  xQ + DφQ)dx +  |·|≤ε  ����  EQ  4 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Further computations show that  ˆ  Q  |Φ(rQν∞  xQ + DφQ) − Φ(0)|dx ≤∥εrQν∞  xQ+DφQ∥K  ≤∥(δ0, ν∞  xQrQ)∥K + ε ≤ 1 + rQ + ε  and consequently  ˆ  Q  η  ˆ  Q  Φ(rQν∞  xQ + DφQ)dx =  ˆ  Q  ηΦ(rQν∞  xQ + DφQ)dx + EQ  5 ,  where the error term is upper bounded by  |EQ  5 | ≤ sup  Q  ����η −  ˆ  Q  η  ���� Ln(Q)(1 + rQ + ε) ≤ Ln(Q)  1  n  ˆ  Q  (2 + φ ⋆ λs)dx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Finally, we estimate the last term with  ˆ  Q  ηΦ(rQν∞  xQ + DφQ)dx =  ˆ  Q  ηΦ(φ ⋆ ν∞dλs) + DφQ)dx + EQ  6 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  To bound the 6th error term we introduce an extra quantity  ����  ˆ  Q  η  �  Φ(φ ⋆ ν∞dλs) + DφQ)dx − Φ(φ ⋆ ν∞dλs  Cs) + DφQ)  �  dx  ���� ≤  ˆ  Q  φ ⋆ (λs  Ω \\ Cs)dx,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  43  and  ����  ˆ  Q  η  �  Φ(rQν∞  xQ + DφQ)dx − Φ(φ ⋆ ν∞dλs  Cs) + DφQ)  �  dx  ����  ≤  ˆ  Q  |rQν∞  xQ − φ ⋆ (ν∞dλs  Cs)|dx  ≤  ����  ˆ  Q  φ ⋆  �  (ν∞  xQ − ν∞�  dλs  Cs)dx  ���� +  ˆ  Q  ����  Q  φ ⋆ (ν∞dλs  Cs)dx′ − φ ⋆ (ν∞dλs  Cs)  ���� dx  ≤  ˆ  Q  ˆ  Cs φ(x − y)|ν∞  xQ − ν∞  y |dλsdx +  ˆ  Q  ����  Q  φ ⋆ (ν∞dλs  Cs)dx′ − φ ⋆ (ν∞dλs  Cs)  ���� dx  ≤ω(3t)  ˆ  Q  φ ⋆ λsdx + EQ  7 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  The 7th error term is estimated by  EQ  7 ≤  ˆ  Q  Q  ˆ  Cs  ��φ(x′ − y) − φ(x − y)  ��|ν∞  y |dλs(y)dx′dx  ≤√n  ˆ  Q  Q  ˆ  Q+tQ  ∥x − x′∥  ˆ 1  0  ��Dφ(x + (x′ − x)τ)(x′ − x)  ��dτdλs(y)dx′dx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Given the scaling of φ = φt with respect to t, we have |Dφ| ≤ t−1M(χQ)t, so the above can be  bounded by  EQ  7 ≤ √nM Ln(Q)  1  n  t  ˆ  Q  (χ2Q)t ⋆ λsdx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  For our choice of a and b, we have that Ln(Q) = 2−n(a+b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' With ξs deﬁned above we obtain  that  ˆ  Ω  η⟨Φ∞, φ ⋆ (ν∞dλs)⟩dx =  ˆ  ⋒Fs ηΦ(ξs) + E,  where  |E| ≤ελs(Ω) + (t + ω(3t))  ˆ  ∪Fs  �  φ ⋆ λs + 2−a−b(2 + φ ⋆ λs)  + φ ⋆ (λs  Ω \\ Cs) + ω(3t) φ ⋆ λsdx + √nM2−b(χ2Q)t ⋆ λs�  dx  ≤  �  2ε + 2−a + 2ω(32−a) + 2−a−b + cnM2−b�  λs(Ω) + 21−a−bLn(Ω).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  To conclude we add  ˆ  Ω\\∪Fs ηΦ(ξs)dx =  ˆ  Ω\\∪Fs ηdxΦ(0)  to both sides, and obtain  ˆ  Ω  η  �  Φ(0) + ⟨Φ∞, φ ⋆ (ν∞dλs  Ω)⟩  �  dx =  ˆ  Ω  Φ(ξs)dx + E +  ˆ  ∪Fs ηdxΦ(0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  44  Because ∪Fs ⊂ (Cs)2t and since Ln(Cs) = 0 we can ﬁnd aε ≥ a, bε ≥ b such that  |E| +  ����  ˆ  ∪Fs ηdxΦ(0)  ���� ≤ 3ε(Ln + λs)(Ω).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  The left-hand side tends to  ˆ  Ω  ηdxΦ(0) +  ˆ  Ω  η⟨Φ∞, ν∞  x ⟩dλs(x)  as a → ∞, uniformly in η and Φ, and this concludes the proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  □  We now move on to the absolutely continuous part, which is proven similar and is a bit easier  to construct.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='16 Let ε > 0, there is tε > 0 and ψt ∈ D(Ω, Rm) with ∥ψt∥1 ≤ ε so that  ����  ˆ  Ω  η(⟨Φ, νx⟩ + λa(x)⟨Φ∞, ν∞  x ⟩)dx −  ˆ  Ω  ηΦ  �  φt ⋆ (ν + ν∞λa(x))dx  Ω + Dψt  �  dx  ���� < ε  holds for t ∈ (0, tε), uniformly in ∥η∥Lip ≤ 1 and ∥TΦ∥Lip(efi,i∈N) ≤ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Fix ε ∈ (0, 1) and apply Luzin’s theorem to the Ln-measurable map  Ω ∋ x �→ (νx, λa(x)ν∞  x ) ∈ M+  1 (Rd) × M+(∂efi,i∈N) ֒→  �  (T −1efi,i∈N)∗�+  to ﬁnd a compact set Ca ⊂ Ω such that  ˆ  Ω\\Ca M(x)dx < ε, M(x) = ⟨νx, | · |⟩ + λa(x),  and ω be the modulus of continuity over Ca, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  ∥(νx, λa(x)ν∞  x ) − (νy, λa(y)ν∞  y )∥K ≤ ω(∥x − y∥)  for all x, y ∈ Ca.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Fix d ∈ N and s ∈ (0, 1) and let Fa be the family of dyadic cubes in Rn of side length t = 2−d,  i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Fa = {Q ∈ Dd : d(Q, ∂Ω) > t, Ln(Q ∩ Ca) > sLn(Q)},  where the distance is induced by ∥ · ∥∞ over vectors in Rn, and d and s will be selected later in  the proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' For every Q ∈ Fa select xQ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' By Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='14, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' 39 we have ψQ ∈ D(Q, Rn×m)  with ∥ψQ∥1 < εLn(Q)  Ln(Ω) and  ∥(νxQ, λa(xQ)ν∞  xQ) − ενxQ+λa(xQ)ν∞  xQ+Dψ∞∥K < ε.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Let ψ = �  Q ψQ ∈ D(Ω, Rm×n) and ∥ψ∥1 ≤ ε.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Then  ˆ  Ω  η(⟨Ψ, νx⟩ + λa(x)⟨Ψ∞, ν∞  x ⟩)dx =  �  Q∈Fa  ˆ  Q  η(⟨Ψ, νx⟩ + λa(x)⟨Ψ∞, ν∞  x ⟩)dx + E1  with |E1| ≤  ˆ  Ω\\∪Fa M(x)dx ≤ ε  45  for large enough d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Next  �  Q∈Fa  ˆ  Q  η(⟨Ψ, νx⟩ + λa(x)⟨Ψ∞, ν∞  x ⟩)dx =  �  Q∈Fa  Q  η  ˆ  Q  (⟨Ψ, νx⟩ + λa(x)⟨Ψ∞, ν∞  x ⟩)dx + E2,  where  |E2| ≤ t  �  Q∈Fa  ˆ  Q  |⟨Φ, νx⟩ + λa(x)⟨Φ∞, ν∞  x ⟩|dx ≤ t  ˆ  Ω  M(x)dx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  We further estimate, on every set Q ∈ Fa,  ����  ˆ  Q  ⟨Φ, νx⟩ + λa(x)⟨Φ∞, ν∞  x ⟩ − Ln(Q)  �  ⟨Φ, νxQ⟩ + λa(xQ)⟨Φ∞, ν∞  xQ⟩  �����  ≤ω(t)  s Ln(Q) + 1 − s  s  ˆ  Q  |⟨Φ, νx⟩ + λa(x)⟨Φ∞, ν∞  x ⟩|dx +  ˆ  Q\\Ca |⟨Φ, νx⟩ + λa(x)⟨Φ∞, ν∞  x ⟩|dx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  By the linear growth of f, we get that  �  Q∈Fa  Q  η  ˆ  Q  ⟨Φ, νx⟩ + λa(x)⟨Φ∞, ν∞  x ⟩dx =  �  Q∈Fa  �  ⟨Φ, νxQ⟩ + λa(xQ)⟨Φ∞, ν∞  xQ⟩  � ˆ  Q  η + E3  where  |E3| ≤ ω(t)  s Ln(Q) + 1 − s  s  ˆ  Q  M(x)dx + ε.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  For every Q ∈ Fa we have that  f(xQ) =  Q  Φ(νxQ + λa(xQ)ν∞  xQ + DφQ) +  |·|≤ε  ����  EQ  4 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Set va(x) = νx + λa(x)ν∞  x .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Letting Φ = z · ei, (ei) canonical basis of Rm×n, we obtain, from  continuity over Ca, |va − va(xQ)| ≤ ω(t) on Q ∩ Ca for each Q ∈ Fa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Consequently,  ˆ  Q  |va − va(xQ)|dx ≤ ω(t)  s Ln(Q) +  ˆ  Q\\Ca |va|dx + 1 − s  s  ˆ  Q  |va|dx  for all Q ∈ Fa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Because |va| ≤ M(x) and Lip(Φ) ≤ 5, then  �  Q∈Fa  Q  ηdx  ˆ  Q  Φ(va(xQ) + DψQ)dx =  �  Q∈Fa  Q  ηdx  ˆ  Q  Φ(va + DψQ)dx + E5  with  |E5| ≤ 5ω(t)  s Ln(Q) + 5ε + 51 − s  s  ˆ  Ω  M(x)dx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  46  Combining some of the previous estimates, we get  �  Q∈Fa  Q  ηdx  ˆ  Q  Φ(va + DψQ)dx =  �  Q∈Fa  ˆ  Q  ηΦ(va + DψQ)dx + E6,  and  |E6| ≤t  �  Q∈Fa  ˆ  Q  |Φ(va + DψQ)|dx ≤ t|E5| + t  �  Q∈Fa  ˆ  Q  |Φ(va(xQ) + DψQ)|dx  ≤t|E5| + tεLn(Ω) + t  �  Q∈Fa  Ln(Q)(⟨|Φ|, νxQ⟩ + λa(xQ)⟨|Φ|∞, ν∞  xQ⟩)  ≤t|E5| + tεLn(Ω) + tω(t)  s Ln(|) +  �ˆ  Q\\Ca +1 − s  s  ˆ  Ω  �  M(x)dx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Finally, if φt is a standard molliﬁer, then φt ⋆ va  Ω  L1(Ω)  −−−−→ va as t → 0, and so  ˆ  Ω  ηΦ(va + Dψ)dx =  ˆ  Ω  ηΦ(φt ⋆ va  Ω + Dψ)dx + E7,  where using again that Φ is Lipschitz over Rm×n,  |E7| ≤ Lip(Φ)  ˆ  Ω  |φt ⋆ va  Ω − va|dx ≤ 5  ˆ  Ω  |φt ⋆ va  Ω − va|dx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  This concludes the proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  □  47  A  Appendix  Theorem A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='1 (Vitali convergence theorem) Let µ ∈ M+(Ω) and fn, f ∈ L1(Ω, µ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Then  fn → f in L1(Ω, µ) if and only if fn → f in measure and fn is uniformly integrable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' See [BR07], p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' 268, theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  □  Theorem A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='2 (Stone-Weierstrass) Let X be a compact Hausdorﬀ space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' If A is a closed  subalgebra of C(X) that separates points, then either A = C(X) or there is x0 ∈ X so that  A = {f ∈ C(X) : f(x0) = 0}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' In particular, A = C(X) if and only if A contains the constant  functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' See [Fol99], p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' 139, theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  □  Theorem A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='3 (Tychonoﬀ) If {Xα}α∈A is a family of compact spaces, Πα∈AXα is compact  in the product topology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Theorem A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='4 (Banach-Alaoglu sequential version) Let X be a separable Banach space  and B ⊂ X∗ the closed unit ball of the dual.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Then B is weakly* sequentially compact.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' See [Lax14], p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' 107, theorem 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  □  Lemma A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='5 (Chacon biting lemma) Let µ ∈ M+(Ω) and vj ∈ L1(Ω, µ) be a sequence  such that supj ∥vj∥ < ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' There are sets Ek ⊂ Ek+1, µ(Ω \\ Ek) → 0 and a subsequence (vji)i  of (vj)j and v ∈ L1(µ) so that vji ⇀ v in L1(Ek, µ) for all k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' See [BM89].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  □  Lemma A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='6 (Kantorovich metric) Let (X, d) be a metric space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' The Kantorich metric  on M+(X) generates the same topology as the weak* topology of measures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' See [KR19].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  □  Lemma A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='7 Let η ∈ M(Ω, Rd), Ω ⊂ Rn open bounded set, and (φε)0<ε≤1 be a family of  standard molliﬁers, supp(φ1) ⊂ B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Then  η ⋆ φε  area-strictly  −−−−−−−→ η.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Because (Ln  Ω, ηε) ⇀∗ (Ln  Ω, η), we immediately obtain the lower bound  lim inf  ε→0 |(Ln, ρε)|(Ω) ≥ |(Ln, ρ)|(Ω).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  To prove the upper semi-continuity of the above quantity, notice the following equality:  (Ln  Ω, ρε) = (Ln  Ω, ρ) ⋆ φε − (Ln  Ω−ε ⋆ (δ0 − φε), 0),  where  Ω−ε = {x ∈ Ω : d(x, ∂Ω) > ε}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  48  Using then Jensen’s inequality  lim sup  ε→0  |(Ln, ρε)|(Ω) ≤ lim sup  ε→0  |(Ln  Ω, ρ) ⋆ φε|(Ω) + |(Ln  Ω−ε ⋆ (δ0 − φε), 0)|(Ω)  ≤|(Ln  Ω, ρ)|(Ω) + lim sup  ε→0  2Ln(Ω \\ Ω−ε) = |(Ln, ρ)|(Ω)  □  Theorem A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='8 (Atomic decomposition) Let µ ∈ M(Ω).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Then there exists a purely atomic  measure µa and a non-atomic measure µn−a such that µ = µa + µn−a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' See [FL07], p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  □  49  References  [AB97]  Jean-Jacques Alibert and Guy Bouchitté.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Non-uniform integrability and generalized  young measure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Journal of Convex Analysis, 4:129–148, 1997.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  [ADM92] Luigi Ambrosio and Gianni Dal Maso.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' On the relaxation in bv (Ω;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' rm) of quasi-  convex integrals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Journal of functional analysis, 109(1):76–97, 1992.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  [AF84]  Emilio Acerbi and Nicola Fusco.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Semicontinuity problems in the calculus of varia-  tions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Archive for Rational Mechanics and Analysis, 86(2):125–145, 1984.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  [AFP00]  Luigi Ambrosio, Nicola Fusco, and Diego Pallara.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Functions of bounded variation  and free discontinuity problems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Courier Corporation, 2000.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  [Bal89]  John M Ball.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' A version of the fundamental theorem for young measures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' In PDEs  and continuum models of phase transitions, pages 207–215.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Springer, 1989.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  [BL73]  Henri Berliocchi and Jean-Michel Lasry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Intégrandes normales et mesures  paramétrées en calcul des variations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Bulletin de la Société Mathématique de France,  101:129–184, 1973.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  [BM89]  John M Ball and F Murat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Remarks on chacon’s biting lemma.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Proceedings of the  American Mathematical Society, 107(3):655–663, 1989.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  [BR07]  Vladimir Igorevich Bogachev and Maria Aparecida Soares Ruas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Measure theory,  volume 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Springer, 2007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  [BZ90]  JM Ball and K-W Zhang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Lower semicontinuity of multiple integrals and the biting  lemma.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Proceedings of the Royal Society of Edinburgh Section A: Mathematics,  114(3-4):367–379, 1990.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  [CC76]  R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Chandler and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Chandler.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Hausdorﬀ Compactiﬁcations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Lecture notes in  pure and applied mathematics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Dekker, 1976.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  [Dac07]  Bernard Dacorogna.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Direct methods in the calculus of variations, volume 78.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Springer Science & Business Media, 2007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  [DM87]  Ronald J DiPerna and Andrew J Majda.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Oscillations and concentrations in weak  solutions of the incompressible ﬂuid equations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Communications in mathematical  physics, 108(4):667–689, 1987.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  [FK10]  Irene Fonseca and Martin Kružík.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Oscillations and concentrations generated by-free  mappings and weak lower semicontinuity of integral functionals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' ESAIM: Control,  Optimisation and Calculus of Variations, 16(2):472–502, 2010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  [FL07]  Irene Fonseca and Giovanni Leoni.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Modern Methods in the Calculus of Variations:  Lˆ p Spaces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Springer Science & Business Media, 2007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  [Fol99]  Gerald B Folland.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Real analysis: modern techniques and their applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Wiley,  1999.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  50  [KK16]  Bernd Kirchheim and Jan Kristensen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' On rank one convex functions that are homo-  geneous of degree one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Archive for rational mechanics and analysis, 221(1):527–558,  2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  [KP91]  David Kinderlehrer and Pablo Pedregal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Characterizations of young measures gen-  erated by gradients.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Archive for rational mechanics and analysis, 115(4):329–365,  1991.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  [KP94]  David Kinderlehrer and Pablo Pedregal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Gradient young measures generated by  sequences in sobolev spaces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' The Journal of Geometric Analysis, 4(1):59, 1994.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  [KR96]  Martin Kružík and Tomáš Roubíček.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Explicit characterization oﬂp-young measures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Journal of mathematical analysis and applications, 198(3):830–843, 1996.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  [KR10a]  Jan Kristensen and Filip Rindler.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Characterization of generalized gradient young  measures generated by sequences in w1, 1 and bv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Archive for rational mechanics  and analysis, 197(2):539–598, 2010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  [KR10b]  Jan Kristensen and Filip Rindler.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Relaxation of signed integral functionals in bv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Calculus of Variations and Partial Diﬀerential Equations, 37(1-2):29–62, 2010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  [KR19]  Jan Kristensen and Bogdan Raiţă.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Oscillation and concentration in sequences of  pde constrained measures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' arXiv preprint arXiv:1912.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='09190, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  [Kri15]  Jan Kristensen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Lecture notes on young measures, 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  [Lax14]  Peter D Lax.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Functional analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' John Wiley & Sons, 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  [Mor52]  Charles B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Morrey.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Quasi-convexity and the lower semicontinuity of multiple inte-  grals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Paciﬁc J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=', 2(1):25–53, 1952.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  [Mül92]  Stefan Müller.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' On quasiconvex functions which are homogeneous of degree 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Indi-  ana University mathematics journal, pages 295–301, 1992.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  [Res68]  Yu G Reshetnyak.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Weak convergence of completely additive vector functions on a  set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Siberian Mathematical Journal, 9(6):1039–1045, 1968.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  [Rin18]  Filip Rindler.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Calculus of variations, volume 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Springer, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  [You37]  Laurence Chisholm Young.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  Generalized curves and the existence of an attained  absolute minimum in the calculus of variations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' Comptes Rendus de la Societe des  Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content=' et des Lettres de Varsovie, 30:212–234, 1937.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
+page_content='  51' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/59A0T4oBgHgl3EQfN_9T/content/2301.02154v1.pdf'}
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+Astronomy & Astrophysics manuscript no. aanda
+©ESO 2023
+January 16, 2023
+New upper limits on low-frequency radio emission
+from isolated neutron stars with LOFAR
+I. Pastor-Marazuela1, 2, S. M. Straal3, J. van Leeuwen2, and V. I. Kondratiev2
+1 Anton Pannekoek Institute for Astronomy, University of Amsterdam, Science Park 904, PO Box 94249, 1090 GE Amsterdam, The
+Netherlands
+e-mail: ines.pastormarazuela@uva.nl
+2 ASTRON, the Netherlands Institute for Radio Astronomy, PO Box 2, 7790 AA Dwingeloo, The Netherlands
+3 NYU Abu Dhabi, PO Box 129188, Abu Dhabi, United Arab Emirates
+January 16, 2023
+ABSTRACT
+Neutron stars that show X-ray and γ-ray pulsed emission must, somewhere in the magnetosphere, generate electron-positron pairs.
+Such pairs are also required for radio emission, but then why do a number of these sources appear radio quiet? Here, we carried out
+a deep radio search towards four such neutron stars that are isolated X-ray/γ-ray pulsars but for which no radio pulsations have been
+detected yet. These sources are 1RXS J141256.0+792204 (Calvera), PSR J1958+2846, PSR J1932+1916 and SGR J1907+0919.
+Searching at lower radio frequencies, where the radio beam is thought to be wider, increases the chances of detecting these sources,
+compared to the earlier higher-frequency searches. We thus carried a search for periodic and single-pulse radio emission with the
+LOFAR radio telescope at 150 MHz. We used the known periods, and searched a wide range of dispersion measures, as the distances
+are not well constrained. We did not detect pulsed emission from any of the four sources. However, we put very constraining upper
+limits on the radio ﬂux density at 150 MHz, of ≲ 1.4 mJy.
+Key words. Stars: neutron – pulsars: general
+1. Introduction
+Through their spin and magnetic ﬁeld, neutron stars act as pow-
+erful cosmic dynamos that can generate a wide variety of electro-
+magnetic emission. There thus exist many subclasses of neutron
+stars, with diﬀerent observed behavior. The evolutionary links
+between some of the classes are established, while for others
+these connections are currently unknown. The largest group in
+this varied population is formed by the regular rotation-powered
+radio pulsars. The fast spinning, high magnetic ﬁeld inﬂux to this
+group are the young pulsars. These show a high spin-down en-
+ergy loss rate ˙E, and a number of energetic phenomena such as
+radio giant pulse (GP) emission. The most extreme of these fast-
+spinning and/or high-ﬁeld sources could potentially also power
+Fast Radio Bursts (FRBs; e.g. Pastor-Marazuela et al. 2022).
+On the long-period outskirts of the P- ˙P diagram, slowly-rotating
+pulsars (e.g. Young et al. 1999; Tan et al. 2018) and magnetars
+(e.g. Caleb et al. 2022; Hurley-Walker et al. 2022) sometimes
+continue to shine.
+Some neutron stars, however, only shine intermittently at ra-
+dio frequencies. The rotating radio transients (RRATs) burst very
+irregularly, and in the P- ˙P diagram most are found near the death
+line (Keane et al. 2011), between the canonical radio pulsars and
+magnetars. The exact evolutionary connection between RRATs
+and the steadily radiating normal pulsars is unclear, but studies
+suggest the presence of an evolutionary link between these dif-
+ferent classes (e.g. Burke-Spolaor 2012).
+Finally, populations of neutron stars exist that appear to not
+emit in radio at all: radio-quiet magnetars such as most anoma-
+lous X-ray pulsars (AXPs) and soft gamma repeaters (SGRs),
+X-ray dim isolated neutron stars (XDINSs; Haberl 2007), and
+γ-ray pulsars (e.g. Abdo et al. 2013). These are able to produce
+high-energy emission but are often radio quiet. (Gençali & Er-
+tan 2018) proposed RRATs can evolve into XDINSs through a
+fallback accretion disk, thus becoming radio quiet. However, the
+magnetar SGR 1935+2154 was recently seen to emit a bright ra-
+dio burst bridging the gap in radio luminosities between regular
+pulsars and FRBs (CHIME/FRB Collaboration 2020; Bochenek
+et al. 2020; Maan et al. 2022b). This suggests magnetars could
+explain the origin of some, if not all, extragalactic FRBs.
+Potentially, some of these could produce radio emission only
+visible at low radio frequencies. Detections of radio pulsations of
+the γ and X-ray pulsar Geminga, PSR J0633+1746, have been
+claimed at and below the 100 MHz observing frequency range
+(Malofeev & Malov 1997; Malov et al. 2015; Maan 2015), al-
+though a very deep search using the low frequency array (LO-
+FAR van Haarlem et al. 2013) came up empty (Ch. 6 in Coenen
+2013). Such low-frequency detections oﬀer an intriguing possi-
+bility to better understand the radio emission mechanism of these
+enigmatic objects. Radio detections of a magnetar with LOFAR,
+complementary to higher-frequency studies such as Camilo et al.
+(2006) and Maan et al. (2022a) for XTE J1810−197, could of-
+fer insight into emission mechanisms and propagation in ultra-
+strong magnetic ﬁelds.
+XDINSs feature periods that are as long as those in magne-
+tars, but they display less extreme magnetic ﬁeld strength. The
+XDINSs form a small group of seven isolated neutron stars that
+show thermal emission in the soft X-ray band. Since their dis-
+covery with ROSAT in the 1990s, several attempts were made
+to detect these sources at radio frequencies, but they were un-
+successful (e.g. Kondratiev et al. 2009). As those campaigns
+operated above 800 MHz, a sensitive lower-frequency search
+Article number, page 1 of 7
+arXiv:2301.05509v1  [astro-ph.HE]  13 Jan 2023
+
+A&A proofs: manuscript no. aanda
+could be opportune. It has been proposed (e.g. Komesaroﬀ 1970;
+Cordes 1978) and observed (e.g. Chen & Wang 2014) that pul-
+sar proﬁles are usually narrower at higher frequencies and be-
+come broader at lower radio frequencies. This suggests the radio
+emission cone is broader at low frequencies, and sweeps across
+a larger fraction of the sky as seen from the pulsar. Additionally,
+radio pulsars often present negative spectral indices, and are thus
+brighter at lower frequencies (Bilous et al. 2016). If all neutron
+star radio beams are broader and brighter at lower frequencies,
+chances of detecting radio emission from γ and X-ray Isolated
+Neutron Stars (INSs) increase at the lower radio frequencies of-
+fered through LOFAR. The earlier observations that resulted in
+non-detections could then have just missed the narrower high-
+frequency beam, where the wider lower-frequency beam may, in
+contrast, actually enclose Earth. In that situation, LOFAR could
+potentially detect the source.
+Recently, a number of radio pulsars were discovered that
+shared properties with XDINSs and RRATs, such as soft
+X-ray thermal emission, a similar position in the P- ˙P dia-
+gram, and a short distance to the solar system. These sources,
+PSR J0726−2612 (Rigoselli et al. 2019) and PSR J2251−3711
+(Morello et al. 2020), support the hypothesis that XDINS are in-
+deed not intrinsically radio quiet, but have a radio beam pointed
+away from us. These shared properties could reﬂect a potential
+link between the radio and X-ray emitting pulsars with XDINSs
+and RRATs. A ﬁrm low-frequency radio detection of INSs would
+thus tie together these observationally distinct populations of
+neutron stars.
+In this work we present LOFAR observations of four INSs
+that brightly pulsate at X-ray or γ-ray energies, but have not been
+detected in radio. These sources are listed in Section 2, and their
+parameters are presented in Table 1.
+2. Targeted sources
+2.1. J1412+7922
+The INS 1RXS J141256.0+792204, dubbed "Calvera" and here-
+after J1412+7922, was ﬁrst detected with ROSAT (Voges et al.
+1999) as an X-ray point source, and subsequently with Swift and
+Chandra (Rutledge et al. 2008; Shevchuk et al. 2009). X-ray ob-
+servations conﬁrmed its neutron star nature through the detection
+of P ≃ 59 ms pulsations by Zane et al. (2011), and allowed for
+the determination of its spin-down luminosity ˙E ∼ 6 × 1035 erg
+s−1, characteristic age τc ≡ P/2 ˙P ∼ 3 × 105 years, and surface
+dipole magnetic ﬁeld strength Bs = 4.4×1011 G by Halpern et al.
+(2013). Although these values are not unusual for a rotationally-
+powered pulsar, the source is not detected in radio (Hessels et al.
+2007; Zane et al. 2011) or γ-rays (Mereghetti et al. 2021). The
+X-ray emission can be modelled with a two-temperature black
+body spectrum (Zane et al. 2011), similar to other XDINS (Pires
+et al. 2014). However, J1412+7922 shows a spin period much
+faster than typically observed in XDINS. Since the source is lo-
+cated at high galactic latitudes and its inferred distance is rel-
+atively low (∼3.3 kpc; Mereghetti et al. 2021) the path through
+the interstellar medium is not long enough to explain the radio
+non-detections by high dispersion measure (DM) or scattering
+values.
+2.2. J1958+2846
+Discovered by Abdo et al. (2009) through a blind frequency
+search of Fermi-LAT γ-ray data, INS PSR J1958+2846, here-
+after J1958+2846, has shown no X-ray or radio continuum emis-
+sion counterpart so far (Ray et al. 2011; Frail et al. 2016).
+Arecibo observations have put very constraining upper limits of
+0.005 mJy at 1510 MHz (Ray et al. 2011). Searches for pulsa-
+tions from the source using the single international LOFAR sta-
+tion FR606 by Grießmeier et al. (2021) also found no periodic
+signal.
+The double-peaked pulse proﬁle of J1958+2846 can be inter-
+preted as a broad γ-ray beam. The earlier higher-frequency radio
+non-detections could be due to a narrower radio beam and to an
+unfavourable rotation geometry with respect to the line of sight.
+If the radio beam is indeed wider at lower frequencies, LOFAR
+would have higher chances of detecting it. In that case, a setup
+more sensitive than the Grießmeier et al. (2021) single-station
+search is required.
+Modeling by Pierbattista et al. (2015) indicates that the γ-
+ray pulse proﬁle of J1958+2846 can be well ﬁtted by One Pole
+Caustic emission (OPC, Romani & Watters 2010, Watters et al.
+2009) or an Outer Gap model (OG, Cheng et al. 2000). In both
+cases, the γ-rays are generated at high altitudes above the NS
+surface. Each model constrains the geometry of the pulsar. For
+the OPC model, the angle between the rotation and magnetic
+axes α = 49◦, while the angle between the observer line-of-sight
+and the rotational axis ζ = 85◦. The OG model reports similarly
+large angles, with the NS equator rotating in the plane that also
+contains Earth, and an oblique dipole: α = 64◦, ζ = 90◦. If this
+model is correct, the low-frequency radio beam would thus need
+to be wider than ∼30◦ to encompass the telescope. That is un-
+commonly wide; only 8 out of the 600 pulsars in the ATNF cat-
+alogue that are not recycled and have a published 400 MHz ﬂux,
+have a duty cycle suggestive of a beam wider than 30% (Manch-
+ester et al. 2005). As such a width is unlikely, a total-intensity
+detection would thus suggest to ﬁrst order a geometry where α
+and ζ are closer than follows from Pierbattista et al. (2015), even
+if that suggestion would only be qualitative. Subsequent follow-
+up measurements of polarisation properties throughout the pulse,
+and ﬁtting these to the rotating vector model (RVM; Radhakrish-
+nan & Cooke 1969), can quantify allowed geometries to within
+a relatively precise combinations of α and ζ. As a matter of fact,
+in a similar study on radio-loud γ-ray pulsars, Rookyard et al.
+(2015) already ﬁnd that RVM ﬁts suggest that the magnetic in-
+clination angles α are much lower than predicted by the γ-ray
+light curve models. This, in turn, aﬃrms that deep radio searches
+can lead to detections even when the γ-ray light curves suggest
+the geometry is unfavorable.
+2.3. J1932+1916
+The INS PSR J1932+1916, hereafter J1932+1916, was dis-
+covered in Fermi-LAT data through blind searches with the
+Einstein@Home volunteer computing system (Clark et al.
+2017). J1932+1916 is the youngest and γ-ray brightest among
+the four γ-ray pulsars presented from that eﬀort in (Pletsch et al.
+2013). The period is 0.21 s, the characteristic age is 35 kyr. Frail
+et al. (2016) ﬁnd no continuum 150 MHz source at this position
+with GMRT at a ﬂux density upper limit of 27 mJy beam−1, with
+1σ errors. If the ﬂux density they ﬁnd at the position of the pulsar
+is in fact the pulsed emission from J1932+1916, then a LOFAR
+periodicity search as described here should detect the source at
+a S/N of 15 if the duty cycle is 10%. Karpova et al. (2017) re-
+port on a potential pulsar wind nebula (PWN) association from
+Swift and Suzaku observations. However, no X-ray periodicity
+searches have been carried out before.
+Article number, page 2 of 7
+
+I. Pastor-Marazuela et al.: Upper limits on radio emission from INSs with LOFAR
+2.4. J1907+0919
+The Soft Gamma Repeater J1907+0919, also known as SGR
+1900+14, was detected through its bursting nature by Mazets
+et al. (1979). Later outbursts were detected in 1992 (Kouveliotou
+et al. 1993), 1998 (Hurley et al. 1999) and 2006 (Mereghetti
+et al. 2006). The August 1998 outburst allowed the detection of
+an X-ray period of ∼ 5.16 s, and thus conﬁrmed the nature of
+the source as a magnetar (Hurley et al. 1999; Kouveliotou et al.
+1999). Frail et al. (1999) detected a transient radio counterpart
+that appeared simultaneous to the 1998 outburst, and they
+identiﬁed the radio source as a synchrotron emitting nebula.
+Shitov et al. (2000) claimed to have found radio pulsations at
+111 MHz from four to nine months after the 1998 burst, but the
+number of trials involved in the search, the small bandwidth
+of the system, and the low S/N of the presented plots, lead us
+to conclude the conﬁdence level for these detections is low.
+No other periodic emission has been found at higher radio
+frequencies (Lorimer & Xilouris 2000; Fox et al. 2001; Lazarus
+et al. 2012).
+This paper is organised as follows: in Section 3 we explain
+how we used LOFAR (van Haarlem et al. 2013) to observe the
+sources mentioned above; in Section 4 we detail the data reduc-
+tion procedure, including the periodicity and the single pulse
+searches that we carried; in Section 5 we present our results,
+including the upper limit that we set on the pulsed emission; in
+Section 6 we discuss the consequences of these non-detections
+for the radio-quiet pulsar population, and in Section 7 we give
+our conclusions on this work.
+3. Observations
+We observed the four sources with the largest possible set of
+High Band Antennas (HBAs) that LOFAR can coherently beam
+form. Each observation thus added 22 HBA Core Stations, cov-
+ering 78.125 MHz bandwidth in the 110 MHz to 190 MHz
+frequency range (centered on 148.92 MHz), with 400 channels
+of 195 kHz wide. The LOFAR beam-forming abilities allow
+us to simultaneously observe diﬀerent regions of the sky (van
+Leeuwen & Stappers 2010; Stappers et al. 2011; Coenen et al.
+2014). For our point-source searches of INSs, we used three
+beams per observation; one beam pointed to the source of in-
+terest, one on a nearby known pulsar, and one as a calibrator
+blank-sky beam to cross-check potential candidates as possibly
+arising from Radio Frequency Interference (RFI). We carried out
+observations between 16 January 2015 and 15 February 2015
+under project ID LC3_0361. We integrated for 3 hours on each
+of our sources. The data was taken in Stokes I mode. Since the
+periods of the γ-ray pulsars are known, the time resolution of
+each observation was chosen such to provide good coverage of
+the pulse period, at a sampling time between 0.16−1.3 ms. The
+observation setup is detailed in Table 1.
+4. Data reduction
+The data was pre-processed by the LOFAR pulsar pipeline after
+each observation (Alexov et al. 2010; Stappers et al. 2011) and
+stored on the LOFAR Long Term Archive2 in PSRFITS format
+1 After we completed the current manuscript as Pastor-Marazuela
+(2022, PhD Thesis, Ch. 2), Arias et al. (2022) posted a pre-print pre-
+senting partly the same data.
+2 LTA: https://lta.lofar.eu/
+(Hotan et al. 2004). The 1.5 TB of data was then transferred
+to one of the nodes of the Apertif real-time FRB search cluster
+ARTS (van Leeuwen 2014; van Leeuwen et al. 2022).
+We performed a periodicity search as well as a single-pulse
+search using Presto3 (Ransom 2001). The data was cleaned of
+RFI using ﬁrst rfifind, and then removing impulsive and peri-
+odic signals at DM=0 pc cm−3. Next we searched the clean data
+for periodic signals and single pulses. We searched for counter-
+parts around the known P and ˙P of each pulsar. Additionally, we
+performed a full blind search in order to look for potential pul-
+sars in the same ﬁeld of view, since many new pulsars are found
+at low frequencies (Sanidas et al. 2019) and chance discover-
+ies happen regularly (e.g., Oostrum et al. 2020). Since the DM
+of our sources is unknown, we searched over a range of DMs
+going from 4 pc cm−3 to 400 pc cm−3. The DM-distance rela-
+tion is not precise enough to warrant a much smaller DM range,
+even for sources for which a distance estimate exists; and a wider
+DM range allows for discovery of other pulsars contained in our
+ﬁeld of view. The highest DM pulsar detected with LOFAR has
+a DM = 217 pc cm−3 (Sanidas et al. 2019). We thus searched
+up to roughly twice this value to make sure that any detectable
+sources were covered. We determined the optimal de-dispersion
+parameters with DDplan from Presto. The sampling time varia-
+tion between some of the four observations had a slight impact
+on the exact transitions of the step size but generally the data was
+de-dispersed in steps of 0.01 pc cm−3 up to DM = 100 pc cm−3;
+then by 0.03 pc cm−3 steps up to 300 pc cm−3 and ﬁnally using
+0.05 pc cm−3 steps.
+We manually inspected all candidates down to σ = 4, result-
+ing in ∼1400 candidates per beam. To verify our observational
+setup, we performed the same blind search technique to our test
+pulsars B1322+83 and B1933+16, which we detected. The test
+pulsar B1953+29 was not detected because the sampling time of
+the observation of J1958+2846 was not adapted to its ∼ 6 ms pe-
+riod. However, we were able to detect B1952+29 (Hewish et al.
+1968) in this same pointing. Even though it is located at >1◦
+from the targeted coordinates, it is bright enough to be visible as
+a side-lobe detection.
+The candidates from Presto’s single pulse search were fur-
+ther classiﬁed using the deep learning classiﬁcation algorithm
+developed by Connor & van Leeuwen (2018), which has been
+veriﬁed and successful in the Apertif surveys (e.g. Connor et al.
+2020; Pastor-Marazuela et al. 2021). This reduced the number
+of candidates signiﬁcantly by sifting out the remaining RFI. The
+remaining candidates were visually inspected.
+5. Results
+In our targeted observations we were unable to detect any
+plausible astronomical radio pulsations or single pulses. We
+determine new 150 MHz ﬂux upper limits by computing
+the sensitivity limits of our observations. To establish these
+sensitivity limits, we apply the radiometer equation adapted to
+pulsars, detailed below. We determine the telescope parameters
+that are input to this equation by following the procedure4
+described in Kondratiev et al. (2016) and Mikhailov & van
+Leeuwen (2016). That approach takes into account the system
+temperature (including the sky temperature), the projection
+eﬀects governing the eﬀective area of the ﬁxed tiles, and the
+amount of time and bandwidth removed due to RFI, to produce
+3 Presto: https://www.cv.nrao.edu/~sransom/presto/
+4 https://github.com/vkond/LOFAR-BF-pulsar-scripts/
+blob/master/fluxcal/lofar_fluxcal.py
+Article number, page 3 of 7
+
+A&A proofs: manuscript no. aanda
+Table 1. Parameters of the observed pulsars and observational setup of the observations in the LC3_036 proposal. The beam of each observation
+was centered in the reported pulsar coordinates. Listed in the bottom rows are the earlier periodicity and single pulse search limits. The upper
+limits from Frail et al. (2016) described in the main text are period-averaged ﬂux densities and are not listed here. The last row lists the limits from
+the current work, for S/N=5, with errors of 50% (Bilous et al. 2016).
+J1412+7922
+J1958+2846
+J1932+1916
+J1907+0919
+Right ascension, α (J2000). . . . . . . . . . . . . .
+14 12 56
+19 58 40
+19 32 20
+19 07 14.33
+Declination, δ (J2000) . . . . . . . . . . . . . . . . .
++79 22 04
++28 45 54
++19 16 39
++09 19 20.1
+Period, P (s) . . . . . . . . . . . . . . . . . . . . . . . . . .
+0.05919907107
+0.29038924475
+0.208214903876
+5.198346
+Period derivative, ˙P (s s−1) . . . . . . . . . . . . . .
+3.29134×10−15
+2.12038×10−13
+9.31735×10−14
+9.2×10−11
+Epoch (MJD) . . . . . . . . . . . . . . . . . . . . . . . . .
+58150a
+54800b
+55214c
+53628d
+LOFAR ObsID . . . . . . . . . . . . . . . . . . . . . . . .
+L257877
+L258545
+L259173
+L216886
+Obs. date (MJD) . . . . . . . . . . . . . . . . . . . . . .
+57038
+57046
+57068
+56755
+Sample time (ms) . . . . . . . . . . . . . . . . . . . . .
+0.16384
+1.31072
+1.31072
+0.65536
+Test pulsar detected . . . . . . . . . . . . . . . . . . . .
+B1322+83
+B1952+29
+B1933+16
+B1907+10
+Periodic ﬂux density (mJy @ GHz) . . . . . .
+<4 @ 0.385e
+<2.0 @ 0.15g
+<2.9 @ 0.15g
+50 @ 0.111h
+<0.05 @ 1.36f
+<0.005 @ 1.51b
+<0.075 @ 1.4c
+<0.4 @ 0.43i
+<0.3 @ 1.38e
+<0.3 @ 1.41i
+<0.012 @ 1.95 j
+LOFAR periodic sensitivity S lim,p (mJy). .
+0.26 ± 0.13
+0.53 ± 0.26
+0.73 ± 0.36
+1.39 ± 0.69
+LOFAR single pulse sensitivity S lim,sp (Jy)
+1.47 ± 0.73
+1.35 ± 0.68
+2.20 ± 1.10
+0.84 ± 0.82
+Notes. aBogdanov et al. (2019), bRay et al. (2011), cPletsch et al. (2013), dMereghetti et al. (2006), eHessels et al. (2007), f Zane et al. (2011),
+gGrießmeier et al. (2021), hShitov et al. (2000), iLorimer & Xilouris (2000), jLazarus et al. (2012)
+the overall observation system-equivalent ﬂux density (SEFD).
+For the sensitivity limit on the periodic emission we use the
+following equation (see., e.g., Dewey et al. 1985):
+S lim,p = β
+Tsys
+G �np ∆ν tobs
+× S/Nmin ×
+�
+W
+P − W ,
+(1)
+where β ≲ 1 is a digitisation factor, Tsys (K) is the system temper-
+ature, G (K Jy−1) is the telescope gain, ∆ν (Hz) is the observing
+bandwidth, and tobs (s) is the observation time. P (s) represents
+the spin period, while W (s) gives the pulsed width assuming
+a pulsar duty cycle of 10%. To facilitate direct comparison of
+the periodic emission limits to values reported in e.g., Ray et al.
+(2011) and Grießmeier et al. (2021), we use a minimum signal-
+to-noise ration S/Nmin = 5. A more conservative option, given
+the high number of candidates per beam, would arguably be to
+use a limit of S/N=8. We did, however, review by eye all can-
+didates with S/N>4; and the reader can easily scale the reported
+sensitivity limits to a diﬀerent S/N value.
+The sensitivity limit on the single pulse emission, S lim,sp, is
+computed as follows:
+S lim,sp = β
+Tsys
+G �np ∆ν tobs
+× S/Nmin ×
+�
+tobs
+W ,
+(2)
+where all variables are the same as in Equation 2. We searched
+for single pulses down to a signal-to-noise ratio S/Nmin = 7.
+We report these periodic and single pulse sensitivity limits,
+computed at the coordinates of the central beam of each obser-
+vation, in Table 1. Even though all observations are equally long,
+the estimated S lim,p values are diﬀerent. That is mostly due to the
+strong dependence of the LOFAR eﬀective area, and hence the
+sensitivity, on the elevation.
+In Fig. 1, we compare our upper limits to those established in
+previous searches, mostly using the same techniques. Our upper
+limit on the ﬂux of J1907+0919 is ∼50× deeper than the claimed
+1998-1999 detections, at the same 3-m wavelength, with BSA
+(Shitov et al. 2000). Other searches were generally undertaken
+at higher frequencies (Hessels et al. 2007; Zane et al. 2011; Ray
+et al. 2011; Pletsch et al. 2013; Grießmeier et al. 2021). If we
+assume that these four pulsars have radio spectra described by
+a single power-law S ν ∝ να with a spectral index of α = −1.4
+(Bates et al. 2013; Bilous et al. 2016), the upper limits we present
+here for J1412+7922 and J1932+1916 are the most stringent so-
+far for any search. The upper limits on J1958+2846 (Arecibo;
+Ray et al. 2011) and J1907+0919 (GBT; Lazarus et al. 2012)
+are a factor of 2–3 more sensitive than ours. However, pulsars
+present a broad range of spectral indices. If we take the mean
+±2σ measured by Jankowski et al. (2018), spectral indices can
+vary from −2.7 to −0.5. The ﬂux upper limits we measure would
+be the deepest assuming a −2.7 spectral index, but the shallowest
+at −0.5.
+6. Discussion
+6.1. Comparison to previous limits
+For J1958+2846 and J1932+1916, we can make a straightfor-
+ward relative comparisons between our results presented here
+and the existing limit at 150 MHz, from the single-station LO-
+FAR campaign by Grießmeier et al. (2021). Our 22 Core Sta-
+tions are each 1/4th of the area of the FR606 station and are co-
+herently combined, leading to a factor
+Acore
+AFR606 = 22
+4 diﬀerence in
+area A for the radiometer equation and S lim. The integration time
+t of 3 h is shorter than the FR606 total of 8.3 h (J1958+2846) and
+4.1 h (J1932+1916), leading to a factor
+�
+tcore
+tFR606 =
+�
+3
+8.3 in the ra-
+diometer equation. Other factors such as the sky background and
+the inﬂuence of zenith angle on the sensitivity should be mostly
+the same for both campaigns. Our S lim is thus 22
+4
+�
+3
+8.3 = 3.3
+times deeper than the Grießmeier et al. (2021) upper limit for
+Article number, page 4 of 7
+
+I. Pastor-Marazuela et al.: Upper limits on radio emission from INSs with LOFAR
+0.1
+0.15
+0.4
+1.0
+1.4
+2.0
+Frequency (GHz)
+10−3
+10−2
+10−1
+100
+101
+102
+Flux density (mJy)
+J1412+7922
+J1958+2846
+J1932+1916
+J1907+0919
+Fig. 1. Flux density upper limits of this work at 150 MHz (ﬁlled sym-
+bols) with S/N = 5 for comparison to earlier searches of the same
+sources (empty symbols). Solid lines going through our upper limit es-
+timates with spectral index α = −1.4 are overlaid to show the scaling of
+our sensitivity limits. Our limits are plotted slightly oﬀset from the 150
+MHz observing frequency (dashed line) for better visibility. The faded
+green marker for SGR J1907+0919 represents the claimed detection
+from Shitov et al. (2000).
+J1958+2846, and 4.7 times for J1932+1916. Those factors are
+in good agreement with the actual limits listed in Table 1.
+In Bilous et al. (2016), they measured the mean ﬂux den-
+sity S mean of 158 pulsars detected with LOFAR, where S lim,p =
+S mean × √W/(P − W) = S mean/3. Compared to those LOFAR
+detections, our upper limit on J1412+7922 is deeper than all 158
+sources (100%), J1958+2846 is deeper than 156 sources (99%),
+J1932+1916 is deeper than 144 sources (93%), and J1907+0919
+is deeper than 109 sources (69%). The ﬂux upper limits we have
+set on each of the sources in our sample are some of the deep-
+est compared to other LOFAR radio pulsar detections. Longer
+observing times are thus unlikely to result in a detection or im-
+prove our ﬂux upper limits. Additional follow up would only be
+constraining with more sensitive radio telescopes.
+6.2. Emission angles and intensity
+Diﬀerent pulsar emission mechanism models exist that predict
+radio and γ-ray emission to be simultaneously formed in the
+pulsar magnetosphere. The emission sites are not necessarily co-
+located, though. The periodic radio emission is generally thought
+to be formed just above the polar cap. The high-energy polar cap
+(PC) model next assumes that the γ-ray emission is also pro-
+duced near the surface of the NS, and near the magnetic polar
+caps. In the outer magnetosphere emission models, such as the
+Outer Gap (OG) or the One Pole Caustic (OPC) models, on the
+other hand, the γ-ray emission is produced high up in the mag-
+netosphere of the NS, within the extent of the light cylinder.
+For the sources in our sample, speciﬁc high-energy geome-
+try models have only been proposed for J1958+2846 (Pierbat-
+tista et al. 2015). A detection could have conﬁrmed one of these
+(Sect. 2.2). But also for our sample in general, conclusions can
+be drawn from the non detections. The two general high-energy
+model classes mentioned above predict diﬀerent, testable beam
+widths. Our radio non-detections, when attributed to radio beams
+that are not wide enough to encompass Earth, favor outer mag-
+netospheric models (see, e.g., Romani & Watters 2010). That is
+because in the OG/OPC models, the γ-ray beam (which is de-
+tected for our sources) is much broader than the radio beam. The
+radio beam, being much narrower, is unlikely cut through our
+line of sight. Such a model class is thus more applicable than
+one where the radio and high-energy beam are of similar angu-
+lar size, such as the PC model (or, to a lesser extent, the slot
+gap model; Muslimov & Harding 2003; Pierbattista et al. 2015).
+In that case, detections in both radio and high-energy would be
+more often expected. Our results thus favor OG and OPC models
+over PC models for high-energy emission.
+Note that while it is instructive to discuss the coverage of the
+radio pulsar beam in binary terms – it either hits or misses Earth
+– this visibility is not that unambiguous in practice. The beam
+edge is not sharp. In a beam mapping experiment enabled by the
+geometric precession in PSR J1906+0745 (van Leeuwen et al.
+2015), the ﬂux at the edge of the beam is over 100× dimmer
+than the peak, but it is still present and detectable (Desvignes
+et al. 2019). Deeper searches thus continue to have value, even
+if non-detections at the same frequency already exist.
+That said, the detection of PSR J1732−3131 only at 327 and
+potentially even 34 MHz (Maan & Aswathappa 2014) shows that
+emission beam widening (or, possibly equivalently, a steep spec-
+tral index) at low frequencies is a real eﬀect, also for γ-ray pul-
+sars.
+6.3. Emission mechanism and evolution
+Most models explain the radio quietness of an NS through a
+chance beam misalignment, as above. It could, of course, also
+be a more intrinsic property. There are at least two regions in the
+P- ˙P diagram where radio emission may be increasingly hard to
+generate.
+The ﬁrst parameter space of interest is for sources close to the
+radio death line (Chen & Ruderman 1993). XDINSs are prefer-
+ably found there, which suggests these sources are approach-
+ing, in their evolution, a state in which radio emission gener-
+ally ceases. From what we see in normal pulsars, the death line
+represents the transition into a state in which electron-positron
+pair formation over the polar cap completely ceases. Once the
+pulsar rotates too slowly to generate a large enough potential
+drop over the polar cap, required for this formation, the radio
+emission turns oﬀ (Ruderman & Sutherland 1975). The high-
+energy emission also requires pair formation, but these could
+occur farther out. We note that polar cap pair formation can con-
+tinue at longer periods, if the NS surface magnetic ﬁeld is not
+a pure dipole. With such a decreased curvature radius, the NS
+may keep on shining. Evidence for such higher-order ﬁelds is
+present in a number of pulsars, e.g., PSR J0815+0939 (Szary
+& van Leeuwen 2017) and PSR B1839−04 (Szary et al. 2020).
+This would also inﬂuence the interpretation of any polarization
+information, as the RVM generally assumes a dipole ﬁeld.
+None of the sources in our sample are close to this death
+line (See Fig. 2), but SGR J1907+0919 is beyond a diﬀerent,
+purported boundary: the photon splitting line (Baring & Hard-
+ing 2001). In pulsars in that second parameter space of inter-
+est, where magnetic ﬁelds are stronger than the quantum critical
+ﬁeld, of 4.4 × 1013 G (Fig. 2), pair formation cannot compete
+with magnetic photon splitting. Such high-ﬁeld sources could
+then be radio quiet but X-ray or γ-ray bright. We mark the criti-
+cal ﬁeld line for a dipole in Fig. 2, but note, as Baring & Harding
+(2001) do, that higher multipoles and general relativistic eﬀects
+can subtly change the quiescence limit on a per-source basis.
+That said, given its spindown dipole magnetic ﬁeld strength of
+7 × 1014 G, our non-detection of SGR J1907+0919 supports the
+existence of this limit.
+Article number, page 5 of 7
+
+A&A proofs: manuscript no. aanda
+Death line
+1010 G
+1011 G
+1012 G
+1013 G
+Photon splitting line
+10−3
+10−2
+10−1
+100
+101
+Period (s)
+10−23
+10−21
+10−19
+10−17
+10−15
+10−13
+10−11
+10−9
+Period Derivative
+Magnetars
+Binary
+Radio-IR Emission
+”Radio-Quiet”
+RRAT
+XDINS
+Fig. 2. P − ˙P diagram showing the location of the sources presented in
+this work. All pulsars from the ATNF Pulsar Catalogue (Manchester
+et al. 2005) are shown as grey dots, with diﬀerent pulsar classiﬁca-
+tions encircled by diﬀerent symbols. The sources discussed in this work
+are shown as black stars, from left to right: J1412+7922, J1932+1916,
+J1932+1916, and J1907+0919. The orange shaded region is delimited
+by the death line, while the green shaded region is delimited by the
+photon splitting line. Plot generated with psrqpy (Pitkin 2018).
+6.4. Propagation effects
+While the emission beam widening and the negative spectral
+index provide potential advantages when searching for pulsars
+at low frequencies, some propagation eﬀects such as disper-
+sion and scattering intensify there, impeding detection of cer-
+tain sources. The largest pulsar DM detected with LOFAR is
+217 pc cm−3, while many galactic pulsars are known to have
+DM>1000 pc cm−3. Although the sources studied in this work
+do not have radio detections and thus no known DM, we can
+estimate this DM if a hydrogen column density NH was mea-
+sured from soft X-ray detections. He et al. (2013) ﬁnd a cor-
+relation between NH and DM as follows: NH (1020 cm−2) =
+0.30+0.13
+−0.09 DM (pc cm−3).
+While J1958+2846 and J1932+1916 have only been de-
+tected in γ-rays, J1412+7922 and J1907+0919 have soft X-
+ray detections where NH has been measured. For J1907+0919,
+Kouveliotou et al. (1999) measured a large NH value of
+3.4 − 5.5 × 1022 cm−2. The correlation suggests a DM of
+1100−1800 pc cm−3. At such a large DM the detection limit of
+LOFAR is severly impacted. Because J1907+0919 is a very slow
+rotator, the intra channel dispersion delay still only becomes or
+order 10% of the period, which means peridiocity searches could
+in principle still detect it; but the ﬂux density per bin is of course
+much decreased when the pulse is smeared out over 100s of time
+bins.
+In contrast, Shevchuk et al. (2009) reported a measured NH =
+3.1 ± 0.9 × 1020 cm−2 for J1412+7922. We thus estimate its DM
+to be in the range 5–15 pc cm−3. This low DM would have easily
+been detected with LOFAR.
+7. Conclusion
+We have conducted deep LOFAR searches of periodic and
+single-pulse radio emission from four isolated neutron stars. Al-
+though we validated the observational setup with the detection of
+the test pulsars, we did not detect any of the four targeted pulsars.
+This can be explained with an intrinsic radio-quietness of these
+sources, as was previously proposed. It could also be caused by
+a chance misalignment between the radio beam and the line of
+sight.
+With the new upper limits, we can rule out the hypothesis
+that INSs had not been previously detected at radio frequencies
+around 1 GHz, because of a steeper spectrum than that of regu-
+lar radio pulsars. Since radio emission from magnetars has been
+detected after high energy outbursts (e.g. Maan et al. 2022b),
+additional radio observations of J1907+0919 if the source reac-
+tivates might be successful at detecting single pulse or periodic
+emission in the future.
+Acknowledgements. This research was supported by the Netherlands Research
+School for Astronomy (‘NOVA5-NW3-10.3.5.14’), the European Research
+Council under the European Union’s Seventh Framework Programme (FP/2007-
+2013)/ERC Grant Agreement No. 617199 (‘ALERT’), and by Vici research pro-
+gramme ‘ARGO’ with project number 639.043.815, ﬁnanced by the Dutch Re-
+search Council (NWO). We further acknowledge funding from National Aero-
+nautics and Space Administration (NASA) grant number NNX17AL74G issued
+through the NNH16ZDA001N Astrophysics Data Analysis Program (ADAP) to
+SMS. This paper is based (in part) on data obtained with the International LO-
+FAR Telescope (ILT) under project code LC3_036 (PI: van Leeuwen). LOFAR
+(van Haarlem et al. 2013) is the low frequency array designed and constructed
+by ASTRON. It has observing, data processing, and data storage facilities in
+several countries, that are owned by various parties (each with their own fund-
+ing sources), and that are collectively operated by the ILT foundation under a
+joint scientiﬁc policy. The ILT resources have beneﬁtted from the following re-
+cent major funding sources: CNRS-INSU, Observatoire de Paris and Université
+d’Orléans, France; BMBF, MIWF-NRW, MPG, Germany; Science Foundation
+Ireland (SFI), Department of Business, Enterprise and Innovation (DBEI), Ire-
+land; NWO, The Netherlands; The Science and Technology Facilities Council,
+UK; Ministry of Science and Higher Education, Poland.
+References
+Abdo, A. A., Ackermann, M., Ajello, M., et al. 2009, Science, 325, 840
+Abdo, A. A., Ajello, M., Allafort, A., et al. 2013, ApJS, 208, 17
+Alexov, A., Hessels, J., Mol, J. D., Stappers, B., & van Leeuwen, J. 2010, Astro-
+nomical DataAnalysisSoftware and Systems XIX, 434
+Arias, M., Botteon, A., Bassa, C. G., et al. 2022, Astronomy & Astrophysics,
+667, A71
+Baring, M. G. & Harding, A. K. 2001, ApJ, 547, 929
+Bates, S. D., Lorimer, D. R., & Verbiest, J. P. W. 2013, Monthly Notices of the
+Royal Astronomical Society, 431, 1352
+Bilous, A., Kondratiev, V., Kramer, M., et al. 2016, Astronomy & Astrophysics,
+591, A134
+Bochenek, C. D., Ravi, V., Belov, K. V., et al. 2020, Nature, 587, 59
+Bogdanov, S., Ho, W. C. G., Enoto, T., et al. 2019, arXiv:1902.00144 [astro-ph],
+arXiv: 1902.00144
+Burke-Spolaor, S. 2012, Proceedings of the International Astronomical Union,
+8, 95
+Caleb, M., Heywood, I., Rajwade, K., et al. 2022, Nature Astronomy, 1
+Camilo, F., Ransom, S. M., Halpern, J. P., et al. 2006, Nature, 442, 892
+Chen, J. L. & Wang, H. G. 2014, The Astrophysical Journal Supplement Series,
+215, 11
+Chen, K. & Ruderman, M. 1993, ApJ, 402, 264
+Cheng, K. S., Ruderman, M., & Zhang, L. 2000, The Astrophysical Journal, 537,
+964
+CHIME/FRB Collaboration. 2020, Nature, 587, 54
+Clark, C. J., Wu, J., Pletsch, H. J., et al. 2017, The Astrophysical Journal, 834,
+106, arXiv: 1611.01015
+Coenen, T. 2013, PhD thesis, University of Amsterdam, http://dare.uva.
+nl/en/record/459730
+Coenen, T., van Leeuwen, J., Hessels, J. W. T., et al. 2014, Astronomy & Astro-
+physics, 570, A60
+Connor, L. & van Leeuwen, J. 2018, The Astronomical Journal, 156, 256
+Connor, L., van Leeuwen, J., Oostrum, L. C., et al. 2020, Monthly Notices of the
+Royal Astronomical Society, 499, 4716
+Cordes, J. M. 1978, The Astrophysical Journal, 222, 1006
+Desvignes, G., Kramer, M., Lee, K., et al. 2019, Science, 365, 1013
+Dewey, R. J., Taylor, J. H., Weisberg, J. M., & Stokes, G. H. 1985, ApJ, 294,
+L25
+Fox, D. W., Kaplan, D. L., Kulkarni, S. R., & Frail, D. A. 2001, arXiv:astro-
+ph/0107520
+Article number, page 6 of 7
+
+I. Pastor-Marazuela et al.: Upper limits on radio emission from INSs with LOFAR
+Frail, D. A., Jagannathan, P., Mooley, K. P., & Intema, H. T. 2016, The Astro-
+physical Journal, 829, 119
+Frail, D. A., Kulkarni, S. R., & Bloom, J. S. 1999, Nature, 398, 127
+Gençali, A. A. & Ertan, Ü. 2018, Monthly Notices of the Royal Astronomical
+Society, 481, 244
+Grießmeier, J. M., Smith, D. A., Theureau, G., et al. 2021, A&A, 654, A43
+Haberl, F. 2007, Ap&SS, 308, 181
+Halpern, J. P., Bogdanov, S., & Gotthelf, E. V. 2013, The Astrophysical Journal,
+778, 120
+He, C., Ng, C.-Y., & Kaspi, V. M. 2013, The Astrophysical Journal, 768, 64
+Hessels, J. W. T., Stappers, B. W., Rutledge, R. E., Fox, D. B., & Shevchuk, A. H.
+2007, Astronomy & Astrophysics, 476, 331
+Hewish, A., Bell, S. J., Pilkington, J. D. H., Scott, P. F., & Collins, R. A. 1968,
+Nature, 217, 709
+Hotan, A. W., van Straten, W., & Manchester, R. N. 2004, Publications of the
+Astronomical Society of Australia, 21, 302
+Hurley, K., Li, P., Kouveliotou, C., et al. 1999, The Astrophysical Journal, 510,
+111
+Hurley-Walker, N., Zhang, X., Bahramian, A., et al. 2022, Nature, 601, 526
+Jankowski, F., van Straten, W., Keane, E. F., et al. 2018, Monthly Notices of the
+Royal Astronomical Society, 473, 4436
+Karpova, A., Shternin, P., Zyuzin, D., Danilenko, A., & Shibanov, Y. 2017,
+Monthly Notices of the Royal Astronomical Society, 466, 1757
+Keane, E. F., Kramer, M., Lyne, A. G., Stappers, B. W., & McLaughlin, M. A.
+2011, MNRAS, 415, 3065
+Komesaroﬀ, M. M. 1970, Nature, 225, 612
+Kondratiev, V. I., McLaughlin, M. A., Lorimer, D. R., et al. 2009, The Astro-
+physical Journal, 702, 692
+Kondratiev, V. I., Verbiest, J. P. W., Hessels, J. W. T., et al. 2016, Astronomy &
+Astrophysics, 585, A128
+Kouveliotou, C., Fishman, G. J., Meegan, C. A., et al. 1993, Nature, 362, 728
+Kouveliotou, C., Strohmayer, T., Hurley, K., et al. 1999, The Astrophysical Jour-
+nal, 510, 115
+Lazarus, P., Kaspi, V. M., Champion, D. J., Hessels, J. W. T., & Dib, R. 2012,
+The Astrophysical Journal, 744, 97
+Lorimer, D. R. & Xilouris, K. M. 2000, The Astrophysical Journal, 545, 385
+Maan, Y. 2015, ApJ, 815, 126
+Maan, Y. & Aswathappa, H. A. 2014, Monthly Notices of the Royal Astronomi-
+cal Society, 445, 3221
+Maan, Y., Surnis, M. P., Chandra Joshi, B., & Bagchi, M. 2022a, ApJ, 931, 67
+Maan, Y., van Leeuwen, J., Straal, S., & Pastor-Marazuela, I. 2022b, The As-
+tronomer’s Telegram, 15697, 1
+Malofeev, V. M. & Malov, O. I. 1997, Nature, 389, 697
+Malov, O. I., Malofeev, V. M., Teplykh, D. A., & Logvinenko, S. V. 2015, As-
+tronomy Reports, 59, 183
+Manchester, R. N., Hobbs, G. B., Teoh, A., & Hobbs, M. 2005, The Astronomical
+Journal, 129, 1993
+Mazets, E. P., Golenetskii, S. V., & Guryan, Y. A. 1979, Soviet Astronomy Let-
+ters, 5, 343
+Mereghetti, S., Rigoselli, M., Taverna, R., et al. 2021, ApJ, 922, 253
+Mereghetti, S., Esposito, P., Tiengo, A., et al. 2006, The Astrophysical Journal,
+653, 1423
+Mikhailov, K. & van Leeuwen, J. 2016, Astronomy & Astrophysics, 593, A21
+Morello, V., Keane, E. F., Enoto, T., et al. 2020, MNRAS, 493, 1165
+Muslimov, A. G. & Harding, A. K. 2003, ApJ, 588, 430
+Oostrum, L. C., van Leeuwen, J., Maan, Y., Coenen, T., & Ishwara-Chandra,
+C. H. 2020, MNRAS, 492, 4825
+Pastor-Marazuela, I. 2022, PhD Thesis, University of Amsterdam
+Pastor-Marazuela, I., Connor, L., van Leeuwen, J., et al. 2021, Nature, 596, 505
+Pastor-Marazuela, I., van Leeuwen, J., Bilous, A., et al. 2022, arXiv:2202.08002
+[astro-ph]
+Pierbattista, M., Harding, A. K., Grenier, I. A., et al. 2015, Astronomy & Astro-
+physics, 575, A3
+Pires, A. M., Haberl, F., Zavlin, V. E., et al. 2014, Astronomy & Astrophysics,
+563, A50, arXiv: 1401.7147
+Pitkin, M. 2018, The Journal of Open Source Software, 3, 538
+Pletsch, H. J., Guillemot, L., Allen, B., et al. 2013, The Astrophysical Journal,
+779, L11, arXiv: 1311.6427
+Radhakrishnan, V. & Cooke, D. J. 1969, Astrophysical Letters, 3, 225
+Ransom, S. M. 2001, PhD thesis, Harvard University
+Ray, P. S., Kerr, M., Parent, D., et al. 2011, The Astrophysical Journal Supple-
+ment Series, 194, 17
+Rigoselli, M., Mereghetti, S., Suleimanov, V., et al. 2019, A&A, 627, A69
+Romani, R. W. & Watters, K. P. 2010, The Astrophysical Journal, 714, 810
+Rookyard, S. C., Weltevrede, P., & Johnston, S. 2015, MNRAS, 446, 3367
+Ruderman, M. A. & Sutherland, P. G. 1975, ApJ, 196, 51
+Rutledge, R. E., Fox, D. B., & Shevchuk, A. H. 2008, The Astrophysical Journal,
+672, 1137
+Sanidas, S., Cooper, S., Bassa, C. G., et al. 2019, Astronomy & Astrophysics,
+626, A104
+Shevchuk, A. S. H., Fox, D. B., & Rutledge, R. E. 2009, The Astrophysical
+Journal, 705, 391
+Shitov, Y. P., Pugachev, V. D., & Kutuzov, S. M. 2000, Pulsar Astronomy - 2000
+and Beyond, 202
+Stappers, B. W., Hessels, J. W. T., Alexov, A., et al. 2011, Astronomy & Astro-
+physics, 530, A80
+Szary, A. & van Leeuwen, J. 2017, ApJ, 845, 95
+Szary, A., van Leeuwen, J., Weltevrede, P., & Maan, Y. 2020, The Astrophysical
+Journal, 896, 168
+Tan, C. M., Bassa, C. G., Cooper, S., et al. 2018, ApJ, 866, 54
+van Haarlem, M. P., Wise, M. W., Gunst, A. W., et al. 2013, Astronomy & As-
+trophysics, 556, A2
+van Leeuwen, J. 2014, in The Third Hot-wiring the Transient Universe Workshop
+(HTU-III), Santa Fe, NM, 79
+van Leeuwen, J. & Stappers, B. W. 2010, A&A, 509, 7
+van Leeuwen, J., Kasian, L., Stairs, I. H., et al. 2015, ApJ, 798, 118
+van Leeuwen, J., Kooistra, E., Oostrum, L., et al. 2022, arXiv:2205.12362 [astro-
+ph]
+Voges, W., Aschenbach, B., Boller, T., et al. 1999, Astronomy and Astrophysics,
+349, 389
+Watters, K. P., Romani, R. W., Weltevrede, P., & Johnston, S. 2009, The Astro-
+physical Journal, 695, 1289
+Young, M. D., Manchester, R. N., & Johnston, S. 1999, Nature, 400, 848
+Zane, S., Haberl, F., Israel, G. L., et al. 2011, Monthly Notices of the Royal
+Astronomical Society, 410, 2428
+Article number, page 7 of 7
+
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+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf,len=1212
+page_content='Astronomy & Astrophysics manuscript no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' aanda  ©ESO 2023  January 16, 2023  New upper limits on low-frequency radio emission  from isolated neutron stars with LOFAR  I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' Pastor-Marazuela1, 2, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' Straal3, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' van Leeuwen2, and V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' Kondratiev2  1 Anton Pannekoek Institute for Astronomy, University of Amsterdam, Science Park 904, PO Box 94249, 1090 GE Amsterdam, The  Netherlands  e-mail: ines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='pastormarazuela@uva.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='nl  2 ASTRON, the Netherlands Institute for Radio Astronomy, PO Box 2, 7790 AA Dwingeloo, The Netherlands  3 NYU Abu Dhabi, PO Box 129188, Abu Dhabi, United Arab Emirates  January 16, 2023  ABSTRACT  Neutron stars that show X-ray and γ-ray pulsed emission must, somewhere in the magnetosphere, generate electron-positron pairs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='  Such pairs are also required for radio emission, but then why do a number of these sources appear radio quiet?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' Here, we carried out  a deep radio search towards four such neutron stars that are isolated X-ray/γ-ray pulsars but for which no radio pulsations have been  detected yet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' These sources are 1RXS J141256.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='0+792204 (Calvera), PSR J1958+2846, PSR J1932+1916 and SGR J1907+0919.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='  Searching at lower radio frequencies, where the radio beam is thought to be wider, increases the chances of detecting these sources,  compared to the earlier higher-frequency searches.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' We thus carried a search for periodic and single-pulse radio emission with the  LOFAR radio telescope at 150 MHz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' We used the known periods, and searched a wide range of dispersion measures, as the distances  are not well constrained.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' We did not detect pulsed emission from any of the four sources.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' However, we put very constraining upper  limits on the radio ﬂux density at 150 MHz, of ≲ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='4 mJy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='  Key words.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' Stars: neutron – pulsars: general  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' Introduction  Through their spin and magnetic ﬁeld, neutron stars act as pow-  erful cosmic dynamos that can generate a wide variety of electro-  magnetic emission.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' There thus exist many subclasses of neutron  stars, with diﬀerent observed behavior.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' The evolutionary links  between some of the classes are established, while for others  these connections are currently unknown.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' The largest group in  this varied population is formed by the regular rotation-powered  radio pulsars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' The fast spinning, high magnetic ﬁeld inﬂux to this  group are the young pulsars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' These show a high spin-down en-  ergy loss rate ˙E, and a number of energetic phenomena such as  radio giant pulse (GP) emission.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' The most extreme of these fast-  spinning and/or high-ﬁeld sources could potentially also power  Fast Radio Bursts (FRBs;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' Pastor-Marazuela et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='  On the long-period outskirts of the P- ˙P diagram, slowly-rotating  pulsars (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' Young et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 1999;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' Tan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 2018) and magnetars  (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' Caleb et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 2022;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' Hurley-Walker et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 2022) sometimes  continue to shine.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='  Some neutron stars, however, only shine intermittently at ra-  dio frequencies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' The rotating radio transients (RRATs) burst very  irregularly, and in the P- ˙P diagram most are found near the death  line (Keane et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 2011), between the canonical radio pulsars and  magnetars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' The exact evolutionary connection between RRATs  and the steadily radiating normal pulsars is unclear, but studies  suggest the presence of an evolutionary link between these dif-  ferent classes (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' Burke-Spolaor 2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='  Finally, populations of neutron stars exist that appear to not  emit in radio at all: radio-quiet magnetars such as most anoma-  lous X-ray pulsars (AXPs) and soft gamma repeaters (SGRs),  X-ray dim isolated neutron stars (XDINSs;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' Haberl 2007), and  γ-ray pulsars (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' Abdo et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' These are able to produce  high-energy emission but are often radio quiet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' (Gençali & Er-  tan 2018) proposed RRATs can evolve into XDINSs through a  fallback accretion disk, thus becoming radio quiet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' However, the  magnetar SGR 1935+2154 was recently seen to emit a bright ra-  dio burst bridging the gap in radio luminosities between regular  pulsars and FRBs (CHIME/FRB Collaboration 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' Bochenek  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' Maan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 2022b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' This suggests magnetars could  explain the origin of some, if not all, extragalactic FRBs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='  Potentially, some of these could produce radio emission only  visible at low radio frequencies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' Detections of radio pulsations of  the γ and X-ray pulsar Geminga, PSR J0633+1746, have been  claimed at and below the 100 MHz observing frequency range  (Malofeev & Malov 1997;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' Malov et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 2015;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' Maan 2015), al-  though a very deep search using the low frequency array (LO-  FAR van Haarlem et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 2013) came up empty (Ch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 6 in Coenen  2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' Such low-frequency detections oﬀer an intriguing possi-  bility to better understand the radio emission mechanism of these  enigmatic objects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' Radio detections of a magnetar with LOFAR,  complementary to higher-frequency studies such as Camilo et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='  (2006) and Maan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' (2022a) for XTE J1810−197, could of-  fer insight into emission mechanisms and propagation in ultra-  strong magnetic ﬁelds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='  XDINSs feature periods that are as long as those in magne-  tars, but they display less extreme magnetic ﬁeld strength.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' The  XDINSs form a small group of seven isolated neutron stars that  show thermal emission in the soft X-ray band.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' Since their dis-  covery with ROSAT in the 1990s, several attempts were made  to detect these sources at radio frequencies, but they were un-  successful (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' Kondratiev et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' As those campaigns  operated above 800 MHz, a sensitive lower-frequency search  Article number, page 1 of 7  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='05509v1  [astro-ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='HE]  13 Jan 2023  A&A proofs: manuscript no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' aanda  could be opportune.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' It has been proposed (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' Komesaroﬀ 1970;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='  Cordes 1978) and observed (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' Chen & Wang 2014) that pul-  sar proﬁles are usually narrower at higher frequencies and be-  come broader at lower radio frequencies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' This suggests the radio  emission cone is broader at low frequencies, and sweeps across  a larger fraction of the sky as seen from the pulsar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' Additionally,  radio pulsars often present negative spectral indices, and are thus  brighter at lower frequencies (Bilous et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' If all neutron  star radio beams are broader and brighter at lower frequencies,  chances of detecting radio emission from γ and X-ray Isolated  Neutron Stars (INSs) increase at the lower radio frequencies of-  fered through LOFAR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' The earlier observations that resulted in  non-detections could then have just missed the narrower high-  frequency beam, where the wider lower-frequency beam may, in  contrast, actually enclose Earth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' In that situation, LOFAR could  potentially detect the source.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='  Recently, a number of radio pulsars were discovered that  shared properties with XDINSs and RRATs, such as soft  X-ray thermal emission, a similar position in the P- ˙P dia-  gram, and a short distance to the solar system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' These sources,  PSR J0726−2612 (Rigoselli et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 2019) and PSR J2251−3711  (Morello et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 2020), support the hypothesis that XDINS are in-  deed not intrinsically radio quiet, but have a radio beam pointed  away from us.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' These shared properties could reﬂect a potential  link between the radio and X-ray emitting pulsars with XDINSs  and RRATs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' A ﬁrm low-frequency radio detection of INSs would  thus tie together these observationally distinct populations of  neutron stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='  In this work we present LOFAR observations of four INSs  that brightly pulsate at X-ray or γ-ray energies, but have not been  detected in radio.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' These sources are listed in Section 2, and their  parameters are presented in Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' Targeted sources  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' J1412+7922  The INS 1RXS J141256.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='0+792204, dubbed "Calvera" and here-  after J1412+7922, was ﬁrst detected with ROSAT (Voges et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='  1999) as an X-ray point source, and subsequently with Swift and  Chandra (Rutledge et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 2008;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' Shevchuk et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' X-ray ob-  servations conﬁrmed its neutron star nature through the detection  of P ≃ 59 ms pulsations by Zane et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' (2011), and allowed for  the determination of its spin-down luminosity ˙E ∼ 6 × 1035 erg  s−1, characteristic age τc ≡ P/2 ˙P ∼ 3 × 105 years, and surface  dipole magnetic ﬁeld strength Bs = 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='4×1011 G by Halpern et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='  (2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' Although these values are not unusual for a rotationally-  powered pulsar, the source is not detected in radio (Hessels et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='  2007;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' Zane et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 2011) or γ-rays (Mereghetti et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' The  X-ray emission can be modelled with a two-temperature black  body spectrum (Zane et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 2011), similar to other XDINS (Pires  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' However, J1412+7922 shows a spin period much  faster than typically observed in XDINS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' Since the source is lo-  cated at high galactic latitudes and its inferred distance is rel-  atively low (∼3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='3 kpc;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' Mereghetti et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 2021) the path through  the interstellar medium is not long enough to explain the radio  non-detections by high dispersion measure (DM) or scattering  values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' J1958+2846  Discovered by Abdo et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' (2009) through a blind frequency  search of Fermi-LAT γ-ray data, INS PSR J1958+2846, here-  after J1958+2846, has shown no X-ray or radio continuum emis-  sion counterpart so far (Ray et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 2011;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' Frail et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='  Arecibo observations have put very constraining upper limits of  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='005 mJy at 1510 MHz (Ray et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' Searches for pulsa-  tions from the source using the single international LOFAR sta-  tion FR606 by Grießmeier et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' (2021) also found no periodic  signal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='  The double-peaked pulse proﬁle of J1958+2846 can be inter-  preted as a broad γ-ray beam.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' The earlier higher-frequency radio  non-detections could be due to a narrower radio beam and to an  unfavourable rotation geometry with respect to the line of sight.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='  If the radio beam is indeed wider at lower frequencies, LOFAR  would have higher chances of detecting it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' In that case, a setup  more sensitive than the Grießmeier et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' (2021) single-station  search is required.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='  Modeling by Pierbattista et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' (2015) indicates that the γ-  ray pulse proﬁle of J1958+2846 can be well ﬁtted by One Pole  Caustic emission (OPC, Romani & Watters 2010, Watters et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='  2009) or an Outer Gap model (OG, Cheng et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 2000).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' In both  cases, the γ-rays are generated at high altitudes above the NS  surface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' Each model constrains the geometry of the pulsar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' For  the OPC model, the angle between the rotation and magnetic  axes α = 49◦, while the angle between the observer line-of-sight  and the rotational axis ζ = 85◦.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' The OG model reports similarly  large angles, with the NS equator rotating in the plane that also  contains Earth, and an oblique dipole: α = 64◦, ζ = 90◦.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' If this  model is correct, the low-frequency radio beam would thus need  to be wider than ∼30◦ to encompass the telescope.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' That is un-  commonly wide;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' only 8 out of the 600 pulsars in the ATNF cat-  alogue that are not recycled and have a published 400 MHz ﬂux,  have a duty cycle suggestive of a beam wider than 30% (Manch-  ester et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 2005).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' As such a width is unlikely, a total-intensity  detection would thus suggest to ﬁrst order a geometry where α  and ζ are closer than follows from Pierbattista et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' (2015), even  if that suggestion would only be qualitative.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' Subsequent follow-  up measurements of polarisation properties throughout the pulse,  and ﬁtting these to the rotating vector model (RVM;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' Radhakrish-  nan & Cooke 1969), can quantify allowed geometries to within  a relatively precise combinations of α and ζ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' As a matter of fact,  in a similar study on radio-loud γ-ray pulsars, Rookyard et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='  (2015) already ﬁnd that RVM ﬁts suggest that the magnetic in-  clination angles α are much lower than predicted by the γ-ray  light curve models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' This, in turn, aﬃrms that deep radio searches  can lead to detections even when the γ-ray light curves suggest  the geometry is unfavorable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' J1932+1916  The INS PSR J1932+1916, hereafter J1932+1916, was dis-  covered in Fermi-LAT data through blind searches with the  Einstein@Home volunteer computing system (Clark et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='  2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' J1932+1916 is the youngest and γ-ray brightest among  the four γ-ray pulsars presented from that eﬀort in (Pletsch et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='  2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' The period is 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='21 s, the characteristic age is 35 kyr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' Frail  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' (2016) ﬁnd no continuum 150 MHz source at this position  with GMRT at a ﬂux density upper limit of 27 mJy beam−1, with  1σ errors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' If the ﬂux density they ﬁnd at the position of the pulsar  is in fact the pulsed emission from J1932+1916, then a LOFAR  periodicity search as described here should detect the source at  a S/N of 15 if the duty cycle is 10%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' Karpova et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' (2017) re-  port on a potential pulsar wind nebula (PWN) association from  Swift and Suzaku observations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' However, no X-ray periodicity  searches have been carried out before.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='  Article number, page 2 of 7  I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' Pastor-Marazuela et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' : Upper limits on radio emission from INSs with LOFAR  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' J1907+0919  The Soft Gamma Repeater J1907+0919, also known as SGR  1900+14, was detected through its bursting nature by Mazets  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' (1979).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' Later outbursts were detected in 1992 (Kouveliotou  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 1993), 1998 (Hurley et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 1999) and 2006 (Mereghetti  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 2006).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' The August 1998 outburst allowed the detection of  an X-ray period of ∼ 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='16 s, and thus conﬁrmed the nature of  the source as a magnetar (Hurley et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 1999;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' Kouveliotou et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='  1999).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' Frail et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' (1999) detected a transient radio counterpart  that appeared simultaneous to the 1998 outburst, and they  identiﬁed the radio source as a synchrotron emitting nebula.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='  Shitov et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' (2000) claimed to have found radio pulsations at  111 MHz from four to nine months after the 1998 burst, but the  number of trials involved in the search, the small bandwidth  of the system, and the low S/N of the presented plots, lead us  to conclude the conﬁdence level for these detections is low.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='  No other periodic emission has been found at higher radio  frequencies (Lorimer & Xilouris 2000;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' Fox et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 2001;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' Lazarus  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='  This paper is organised as follows: in Section 3 we explain  how we used LOFAR (van Haarlem et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 2013) to observe the  sources mentioned above;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' in Section 4 we detail the data reduc-  tion procedure, including the periodicity and the single pulse  searches that we carried;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' in Section 5 we present our results,  including the upper limit that we set on the pulsed emission;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' in  Section 6 we discuss the consequences of these non-detections  for the radio-quiet pulsar population, and in Section 7 we give  our conclusions on this work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' Observations  We observed the four sources with the largest possible set of  High Band Antennas (HBAs) that LOFAR can coherently beam  form.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' Each observation thus added 22 HBA Core Stations, cov-  ering 78.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='125 MHz bandwidth in the 110 MHz to 190 MHz  frequency range (centered on 148.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='92 MHz), with 400 channels  of 195 kHz wide.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' The LOFAR beam-forming abilities allow  us to simultaneously observe diﬀerent regions of the sky (van  Leeuwen & Stappers 2010;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' Stappers et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 2011;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' Coenen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='  2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' For our point-source searches of INSs, we used three  beams per observation;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' one beam pointed to the source of in-  terest, one on a nearby known pulsar, and one as a calibrator  blank-sky beam to cross-check potential candidates as possibly  arising from Radio Frequency Interference (RFI).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' We carried out  observations between 16 January 2015 and 15 February 2015  under project ID LC3_0361.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' We integrated for 3 hours on each  of our sources.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' The data was taken in Stokes I mode.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' Since the  periods of the γ-ray pulsars are known, the time resolution of  each observation was chosen such to provide good coverage of  the pulse period, at a sampling time between 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='16−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='3 ms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' The  observation setup is detailed in Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' Data reduction  The data was pre-processed by the LOFAR pulsar pipeline after  each observation (Alexov et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 2010;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' Stappers et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 2011) and  stored on the LOFAR Long Term Archive2 in PSRFITS format  1 After we completed the current manuscript as Pastor-Marazuela  (2022, PhD Thesis, Ch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 2), Arias et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' (2022) posted a pre-print pre-  senting partly the same data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='  2 LTA: https://lta.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='lofar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='eu/  (Hotan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 2004).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' The 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='5 TB of data was then transferred  to one of the nodes of the Apertif real-time FRB search cluster  ARTS (van Leeuwen 2014;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' van Leeuwen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='  We performed a periodicity search as well as a single-pulse  search using Presto3 (Ransom 2001).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' The data was cleaned of  RFI using ﬁrst rfifind, and then removing impulsive and peri-  odic signals at DM=0 pc cm−3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' Next we searched the clean data  for periodic signals and single pulses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' We searched for counter-  parts around the known P and ˙P of each pulsar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' Additionally, we  performed a full blind search in order to look for potential pul-  sars in the same ﬁeld of view, since many new pulsars are found  at low frequencies (Sanidas et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 2019) and chance discover-  ies happen regularly (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', Oostrum et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' Since the DM  of our sources is unknown, we searched over a range of DMs  going from 4 pc cm−3 to 400 pc cm−3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' The DM-distance rela-  tion is not precise enough to warrant a much smaller DM range,  even for sources for which a distance estimate exists;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' and a wider  DM range allows for discovery of other pulsars contained in our  ﬁeld of view.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' The highest DM pulsar detected with LOFAR has  a DM = 217 pc cm−3 (Sanidas et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' We thus searched  up to roughly twice this value to make sure that any detectable  sources were covered.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' We determined the optimal de-dispersion  parameters with DDplan from Presto.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' The sampling time varia-  tion between some of the four observations had a slight impact  on the exact transitions of the step size but generally the data was  de-dispersed in steps of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='01 pc cm−3 up to DM = 100 pc cm−3;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='  then by 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='03 pc cm−3 steps up to 300 pc cm−3 and ﬁnally using  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='05 pc cm−3 steps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='  We manually inspected all candidates down to σ = 4, result-  ing in ∼1400 candidates per beam.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' To verify our observational  setup, we performed the same blind search technique to our test  pulsars B1322+83 and B1933+16, which we detected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' The test  pulsar B1953+29 was not detected because the sampling time of  the observation of J1958+2846 was not adapted to its ∼ 6 ms pe-  riod.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' However, we were able to detect B1952+29 (Hewish et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='  1968) in this same pointing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' Even though it is located at >1◦  from the targeted coordinates, it is bright enough to be visible as  a side-lobe detection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='  The candidates from Presto’s single pulse search were fur-  ther classiﬁed using the deep learning classiﬁcation algorithm  developed by Connor & van Leeuwen (2018), which has been  veriﬁed and successful in the Apertif surveys (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' Connor et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='  2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' Pastor-Marazuela et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' This reduced the number  of candidates signiﬁcantly by sifting out the remaining RFI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' The  remaining candidates were visually inspected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' Results  In our targeted observations we were unable to detect any  plausible astronomical radio pulsations or single pulses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' We  determine new 150 MHz ﬂux upper limits by computing  the sensitivity limits of our observations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' To establish these  sensitivity limits, we apply the radiometer equation adapted to  pulsars, detailed below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' We determine the telescope parameters  that are input to this equation by following the procedure4  described in Kondratiev et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' (2016) and Mikhailov & van  Leeuwen (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' That approach takes into account the system  temperature (including the sky temperature), the projection  eﬀects governing the eﬀective area of the ﬁxed tiles, and the  amount of time and bandwidth removed due to RFI, to produce  3 Presto: https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='cv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='nrao.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='edu/~sransom/presto/  4 https://github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='com/vkond/LOFAR-BF-pulsar-scripts/  blob/master/fluxcal/lofar_fluxcal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='py  Article number, page 3 of 7  A&A proofs: manuscript no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' aanda  Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' Parameters of the observed pulsars and observational setup of the observations in the LC3_036 proposal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' The beam of each observation  was centered in the reported pulsar coordinates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' Listed in the bottom rows are the earlier periodicity and single pulse search limits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' The upper  limits from Frail et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' (2016) described in the main text are period-averaged ﬂux densities and are not listed here.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' The last row lists the limits from  the current work, for S/N=5, with errors of 50% (Bilous et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='  J1412+7922  J1958+2846  J1932+1916  J1907+0919  Right ascension, α (J2000).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
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+page_content='  B1322+83  B1952+29  B1933+16  B1907+10  Periodic ﬂux density (mJy @ GHz) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
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+page_content='41i  <0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
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+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
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+page_content='13  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
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+page_content='73 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
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+page_content='39 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='69  LOFAR single pulse sensitivity S lim,sp (Jy)  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='47 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='73  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='35 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='68  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='20 ± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='84 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='82  Notes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' aBogdanov et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' (2019), bRay et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' (2011), cPletsch et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' (2013), dMereghetti et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' (2006), eHessels et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' (2007), f Zane et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' (2011),  gGrießmeier et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' (2021), hShitov et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' (2000), iLorimer & Xilouris (2000), jLazarus et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' (2012)  the overall observation system-equivalent ﬂux density (SEFD).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='  For the sensitivity limit on the periodic emission we use the  following equation (see.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', Dewey et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 1985):  S lim,p = β  Tsys  G �np ∆ν tobs  × S/Nmin ×  �  W  P − W ,  (1)  where β ≲ 1 is a digitisation factor, Tsys (K) is the system temper-  ature, G (K Jy−1) is the telescope gain, ∆ν (Hz) is the observing  bandwidth, and tobs (s) is the observation time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' P (s) represents  the spin period, while W (s) gives the pulsed width assuming  a pulsar duty cycle of 10%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' To facilitate direct comparison of  the periodic emission limits to values reported in e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', Ray et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='  (2011) and Grießmeier et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' (2021), we use a minimum signal-  to-noise ration S/Nmin = 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' A more conservative option, given  the high number of candidates per beam, would arguably be to  use a limit of S/N=8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' We did, however, review by eye all can-  didates with S/N>4;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' and the reader can easily scale the reported  sensitivity limits to a diﬀerent S/N value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='  The sensitivity limit on the single pulse emission, S lim,sp, is  computed as follows:  S lim,sp = β  Tsys  G �np ∆ν tobs  × S/Nmin ×  �  tobs  W ,  (2)  where all variables are the same as in Equation 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' We searched  for single pulses down to a signal-to-noise ratio S/Nmin = 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='  We report these periodic and single pulse sensitivity limits,  computed at the coordinates of the central beam of each obser-  vation, in Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' Even though all observations are equally long,  the estimated S lim,p values are diﬀerent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' That is mostly due to the  strong dependence of the LOFAR eﬀective area, and hence the  sensitivity, on the elevation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='  In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 1, we compare our upper limits to those established in  previous searches, mostly using the same techniques.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' Our upper  limit on the ﬂux of J1907+0919 is ∼50× deeper than the claimed  1998-1999 detections, at the same 3-m wavelength, with BSA  (Shitov et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 2000).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' Other searches were generally undertaken  at higher frequencies (Hessels et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 2007;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' Zane et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 2011;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' Ray  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 2011;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' Pletsch et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 2013;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' Grießmeier et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' If we  assume that these four pulsars have radio spectra described by  a single power-law S ν ∝ να with a spectral index of α = −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='4  (Bates et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 2013;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' Bilous et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 2016), the upper limits we present  here for J1412+7922 and J1932+1916 are the most stringent so-  far for any search.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' The upper limits on J1958+2846 (Arecibo;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='  Ray et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 2011) and J1907+0919 (GBT;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' Lazarus et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 2012)  are a factor of 2–3 more sensitive than ours.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' However, pulsars  present a broad range of spectral indices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' If we take the mean  ±2σ measured by Jankowski et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' (2018), spectral indices can  vary from −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='7 to −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' The ﬂux upper limits we measure would  be the deepest assuming a −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='7 spectral index, but the shallowest  at −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' Discussion  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' Comparison to previous limits  For J1958+2846 and J1932+1916, we can make a straightfor-  ward relative comparisons between our results presented here  and the existing limit at 150 MHz, from the single-station LO-  FAR campaign by Grießmeier et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' Our 22 Core Sta-  tions are each 1/4th of the area of the FR606 station and are co-  herently combined, leading to a factor  Acore  AFR606 = 22  4 diﬀerence in  area A for the radiometer equation and S lim.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' The integration time  t of 3 h is shorter than the FR606 total of 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='3 h (J1958+2846) and  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='1 h (J1932+1916), leading to a factor  �  tcore  tFR606 =  �  3  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='3 in the ra-  diometer equation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' Other factors such as the sky background and  the inﬂuence of zenith angle on the sensitivity should be mostly  the same for both campaigns.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' Our S lim is thus 22  4  �  3  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='3 = 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='3  times deeper than the Grießmeier et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' (2021) upper limit for  Article number, page 4 of 7  I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' Pastor-Marazuela et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' : Upper limits on radio emission from INSs with LOFAR  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='15  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='4  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='4  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='0  Frequency (GHz)  10−3  10−2  10−1  100  101  102  Flux density (mJy)  J1412+7922  J1958+2846  J1932+1916  J1907+0919  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' Flux density upper limits of this work at 150 MHz (ﬁlled sym-  bols) with S/N = 5 for comparison to earlier searches of the same  sources (empty symbols).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' Solid lines going through our upper limit es-  timates with spectral index α = −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='4 are overlaid to show the scaling of  our sensitivity limits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' Our limits are plotted slightly oﬀset from the 150  MHz observing frequency (dashed line) for better visibility.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' The faded  green marker for SGR J1907+0919 represents the claimed detection  from Shitov et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' (2000).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='  J1958+2846, and 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='7 times for J1932+1916.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' Those factors are  in good agreement with the actual limits listed in Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='  In Bilous et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' (2016), they measured the mean ﬂux den-  sity S mean of 158 pulsars detected with LOFAR, where S lim,p =  S mean × √W/(P − W) = S mean/3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' Compared to those LOFAR  detections, our upper limit on J1412+7922 is deeper than all 158  sources (100%), J1958+2846 is deeper than 156 sources (99%),  J1932+1916 is deeper than 144 sources (93%), and J1907+0919  is deeper than 109 sources (69%).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' The ﬂux upper limits we have  set on each of the sources in our sample are some of the deep-  est compared to other LOFAR radio pulsar detections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' Longer  observing times are thus unlikely to result in a detection or im-  prove our ﬂux upper limits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' Additional follow up would only be  constraining with more sensitive radio telescopes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' Emission angles and intensity  Diﬀerent pulsar emission mechanism models exist that predict  radio and γ-ray emission to be simultaneously formed in the  pulsar magnetosphere.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' The emission sites are not necessarily co-  located, though.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' The periodic radio emission is generally thought  to be formed just above the polar cap.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' The high-energy polar cap  (PC) model next assumes that the γ-ray emission is also pro-  duced near the surface of the NS, and near the magnetic polar  caps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' In the outer magnetosphere emission models, such as the  Outer Gap (OG) or the One Pole Caustic (OPC) models, on the  other hand, the γ-ray emission is produced high up in the mag-  netosphere of the NS, within the extent of the light cylinder.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='  For the sources in our sample, speciﬁc high-energy geome-  try models have only been proposed for J1958+2846 (Pierbat-  tista et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' A detection could have conﬁrmed one of these  (Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' But also for our sample in general, conclusions can  be drawn from the non detections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' The two general high-energy  model classes mentioned above predict diﬀerent, testable beam  widths.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' Our radio non-detections, when attributed to radio beams  that are not wide enough to encompass Earth, favor outer mag-  netospheric models (see, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', Romani & Watters 2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' That is  because in the OG/OPC models, the γ-ray beam (which is de-  tected for our sources) is much broader than the radio beam.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' The  radio beam, being much narrower, is unlikely cut through our  line of sight.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' Such a model class is thus more applicable than  one where the radio and high-energy beam are of similar angu-  lar size, such as the PC model (or, to a lesser extent, the slot  gap model;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' Muslimov & Harding 2003;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' Pierbattista et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='  In that case, detections in both radio and high-energy would be  more often expected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' Our results thus favor OG and OPC models  over PC models for high-energy emission.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='  Note that while it is instructive to discuss the coverage of the  radio pulsar beam in binary terms – it either hits or misses Earth  – this visibility is not that unambiguous in practice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' The beam  edge is not sharp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' In a beam mapping experiment enabled by the  geometric precession in PSR J1906+0745 (van Leeuwen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='  2015), the ﬂux at the edge of the beam is over 100× dimmer  than the peak, but it is still present and detectable (Desvignes  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' Deeper searches thus continue to have value, even  if non-detections at the same frequency already exist.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='  That said, the detection of PSR J1732−3131 only at 327 and  potentially even 34 MHz (Maan & Aswathappa 2014) shows that  emission beam widening (or, possibly equivalently, a steep spec-  tral index) at low frequencies is a real eﬀect, also for γ-ray pul-  sars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' Emission mechanism and evolution  Most models explain the radio quietness of an NS through a  chance beam misalignment, as above.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' It could, of course, also  be a more intrinsic property.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' There are at least two regions in the  P- ˙P diagram where radio emission may be increasingly hard to  generate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='  The ﬁrst parameter space of interest is for sources close to the  radio death line (Chen & Ruderman 1993).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' XDINSs are prefer-  ably found there, which suggests these sources are approach-  ing, in their evolution, a state in which radio emission gener-  ally ceases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' From what we see in normal pulsars, the death line  represents the transition into a state in which electron-positron  pair formation over the polar cap completely ceases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' Once the  pulsar rotates too slowly to generate a large enough potential  drop over the polar cap, required for this formation, the radio  emission turns oﬀ (Ruderman & Sutherland 1975).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' The high-  energy emission also requires pair formation, but these could  occur farther out.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' We note that polar cap pair formation can con-  tinue at longer periods, if the NS surface magnetic ﬁeld is not  a pure dipole.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' With such a decreased curvature radius, the NS  may keep on shining.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' Evidence for such higher-order ﬁelds is  present in a number of pulsars, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', PSR J0815+0939 (Szary  & van Leeuwen 2017) and PSR B1839−04 (Szary et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='  This would also inﬂuence the interpretation of any polarization  information, as the RVM generally assumes a dipole ﬁeld.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='  None of the sources in our sample are close to this death  line (See Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 2), but SGR J1907+0919 is beyond a diﬀerent,  purported boundary: the photon splitting line (Baring & Hard-  ing 2001).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' In pulsars in that second parameter space of inter-  est, where magnetic ﬁelds are stronger than the quantum critical  ﬁeld, of 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='4 × 1013 G (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 2), pair formation cannot compete  with magnetic photon splitting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' Such high-ﬁeld sources could  then be radio quiet but X-ray or γ-ray bright.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' We mark the criti-  cal ﬁeld line for a dipole in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 2, but note, as Baring & Harding  (2001) do, that higher multipoles and general relativistic eﬀects  can subtly change the quiescence limit on a per-source basis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='  That said, given its spindown dipole magnetic ﬁeld strength of  7 × 1014 G, our non-detection of SGR J1907+0919 supports the  existence of this limit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='  Article number, page 5 of 7  A&A proofs: manuscript no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' aanda  Death line  1010 G  1011 G  1012 G  1013 G  Photon splitting line  10−3  10−2  10−1  100  101  Period (s)  10−23  10−21  10−19  10−17  10−15  10−13  10−11  10−9  Period Derivative  Magnetars  Binary  Radio-IR Emission  ”Radio-Quiet”  RRAT  XDINS  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' P − ˙P diagram showing the location of the sources presented in  this work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' All pulsars from the ATNF Pulsar Catalogue (Manchester  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 2005) are shown as grey dots, with diﬀerent pulsar classiﬁca-  tions encircled by diﬀerent symbols.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' The sources discussed in this work  are shown as black stars, from left to right: J1412+7922, J1932+1916,  J1932+1916, and J1907+0919.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' The orange shaded region is delimited  by the death line, while the green shaded region is delimited by the  photon splitting line.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' Plot generated with psrqpy (Pitkin 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' Propagation effects  While the emission beam widening and the negative spectral  index provide potential advantages when searching for pulsars  at low frequencies, some propagation eﬀects such as disper-  sion and scattering intensify there, impeding detection of cer-  tain sources.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' The largest pulsar DM detected with LOFAR is  217 pc cm−3, while many galactic pulsars are known to have  DM>1000 pc cm−3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' Although the sources studied in this work  do not have radio detections and thus no known DM, we can  estimate this DM if a hydrogen column density NH was mea-  sured from soft X-ray detections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' He et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' (2013) ﬁnd a cor-  relation between NH and DM as follows: NH (1020 cm−2) =  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='30+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='13  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='09 DM (pc cm−3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='  While J1958+2846 and J1932+1916 have only been de-  tected in γ-rays, J1412+7922 and J1907+0919 have soft X-  ray detections where NH has been measured.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' For J1907+0919,  Kouveliotou et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' (1999) measured a large NH value of  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='4 − 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='5 × 1022 cm−2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' The correlation suggests a DM of  1100−1800 pc cm−3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' At such a large DM the detection limit of  LOFAR is severly impacted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' Because J1907+0919 is a very slow  rotator, the intra channel dispersion delay still only becomes or  order 10% of the period, which means peridiocity searches could  in principle still detect it;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' but the ﬂux density per bin is of course  much decreased when the pulse is smeared out over 100s of time  bins.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='  In contrast, Shevchuk et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' (2009) reported a measured NH =  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='1 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='9 × 1020 cm−2 for J1412+7922.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' We thus estimate its DM  to be in the range 5–15 pc cm−3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' This low DM would have easily  been detected with LOFAR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' Conclusion  We have conducted deep LOFAR searches of periodic and  single-pulse radio emission from four isolated neutron stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' Al-  though we validated the observational setup with the detection of  the test pulsars, we did not detect any of the four targeted pulsars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='  This can be explained with an intrinsic radio-quietness of these  sources, as was previously proposed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' It could also be caused by  a chance misalignment between the radio beam and the line of  sight.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='  With the new upper limits, we can rule out the hypothesis  that INSs had not been previously detected at radio frequencies  around 1 GHz, because of a steeper spectrum than that of regu-  lar radio pulsars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' Since radio emission from magnetars has been  detected after high energy outbursts (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' Maan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 2022b),  additional radio observations of J1907+0919 if the source reac-  tivates might be successful at detecting single pulse or periodic  emission in the future.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='  Acknowledgements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' This research was supported by the Netherlands Research  School for Astronomy (‘NOVA5-NW3-10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='14’), the European Research  Council under the European Union’s Seventh Framework Programme (FP/2007-  2013)/ERC Grant Agreement No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 617199 (‘ALERT’), and by Vici research pro-  gramme ‘ARGO’ with project number 639.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='043.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='815, ﬁnanced by the Dutch Re-  search Council (NWO).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' We further acknowledge funding from National Aero-  nautics and Space Administration (NASA) grant number NNX17AL74G issued  through the NNH16ZDA001N Astrophysics Data Analysis Program (ADAP) to  SMS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' This paper is based (in part) on data obtained with the International LO-  FAR Telescope (ILT) under project code LC3_036 (PI: van Leeuwen).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' LOFAR  (van Haarlem et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 2013) is the low frequency array designed and constructed  by ASTRON.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' It has observing, data processing, and data storage facilities in  several countries, that are owned by various parties (each with their own fund-  ing sources), and that are collectively operated by the ILT foundation under a  joint scientiﬁc policy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' The ILT resources have beneﬁtted from the following re-  cent major funding sources: CNRS-INSU, Observatoire de Paris and Université  d’Orléans, France;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' BMBF, MIWF-NRW, MPG, Germany;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' Science Foundation  Ireland (SFI), Department of Business, Enterprise and Innovation (DBEI), Ire-  land;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' NWO, The Netherlands;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' The Science and Technology Facilities Council,  UK;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' Ministry of Science and Higher Education, Poland.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='  References  Abdo, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', Ackermann, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', Ajello, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 2009, Science, 325, 840  Abdo, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', Ajello, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', Allafort, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 2013, ApJS, 208, 17  Alexov, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', Hessels, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', Mol, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', Stappers, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', & van Leeuwen, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 2010, Astro-  nomical DataAnalysisSoftware and Systems XIX, 434  Arias, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', Botteon, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', Bassa, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 2022, Astronomy & Astrophysics,  667, A71  Baring, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' & Harding, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 2001, ApJ, 547, 929  Bates, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', Lorimer, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', & Verbiest, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 2013, Monthly Notices of the  Royal Astronomical Society, 431, 1352  Bilous, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', Kondratiev, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', Kramer, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 2016, Astronomy & Astrophysics,  591, A134  Bochenek, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', Ravi, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', Belov, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 2020, Nature, 587, 59  Bogdanov, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', Ho, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', Enoto, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 2019, arXiv:1902.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='00144 [astro-ph],  arXiv: 1902.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='00144  Burke-Spolaor, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 2012, Proceedings of the International Astronomical Union,  8, 95  Caleb, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', Heywood, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', Rajwade, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 2022, Nature Astronomy, 1  Camilo, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', Ransom, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', Halpern, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 2006, Nature, 442, 892  Chen, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' & Wang, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 2014, The Astrophysical Journal Supplement Series,  215, 11  Chen, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' & Ruderman, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 1993, ApJ, 402, 264  Cheng, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', Ruderman, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', & Zhang, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 2000, The Astrophysical Journal, 537,  964  CHIME/FRB Collaboration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 2020, Nature, 587, 54  Clark, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', Wu, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', Pletsch, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 2017, The Astrophysical Journal, 834,  106, arXiv: 1611.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='01015  Coenen, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 2013, PhD thesis, University of Amsterdam, http://dare.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='uva.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='  nl/en/record/459730  Coenen, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', van Leeuwen, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', Hessels, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 2014, Astronomy & Astro-  physics, 570, A60  Connor, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' & van Leeuwen, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 2018, The Astronomical Journal, 156, 256  Connor, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', van Leeuwen, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', Oostrum, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 2020, Monthly Notices of the  Royal Astronomical Society, 499, 4716  Cordes, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 1978, The Astrophysical Journal, 222, 1006  Desvignes, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', Kramer, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', Lee, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 2019, Science, 365, 1013  Dewey, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', Taylor, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', Weisberg, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', & Stokes, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 1985, ApJ, 294,  L25  Fox, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', Kaplan, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', Kulkarni, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', & Frail, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 2001, arXiv:astro-  ph/0107520  Article number, page 6 of 7  I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' Pastor-Marazuela et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' : Upper limits on radio emission from INSs with LOFAR  Frail, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', Jagannathan, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', Mooley, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', & Intema, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 2016, The Astro-  physical Journal, 829, 119  Frail, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', Kulkarni, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', & Bloom, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 1999, Nature, 398, 127  Gençali, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' & Ertan, Ü.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 2018, Monthly Notices of the Royal Astronomical  Society, 481, 244  Grießmeier, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', Smith, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', Theureau, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 2021, A&A, 654, A43  Haberl, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 2007, Ap&SS, 308, 181  Halpern, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', Bogdanov, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', & Gotthelf, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 2013, The Astrophysical Journal,  778, 120  He, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', Ng, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='-Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', & Kaspi, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 2013, The Astrophysical Journal, 768, 64  Hessels, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', Stappers, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', Rutledge, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', Fox, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', & Shevchuk, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='  2007, Astronomy & Astrophysics, 476, 331  Hewish, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', Bell, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', Pilkington, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', Scott, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', & Collins, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 1968,  Nature, 217, 709  Hotan, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', van Straten, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', & Manchester, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 2004, Publications of the  Astronomical Society of Australia, 21, 302  Hurley, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', Li, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', Kouveliotou, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 1999, The Astrophysical Journal, 510,  111  Hurley-Walker, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', Zhang, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', Bahramian, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 2022, Nature, 601, 526  Jankowski, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', van Straten, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', Keane, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 2018, Monthly Notices of the  Royal Astronomical Society, 473, 4436  Karpova, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', Shternin, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', Zyuzin, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', Danilenko, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', & Shibanov, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 2017,  Monthly Notices of the Royal Astronomical Society, 466, 1757  Keane, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', Kramer, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', Lyne, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', Stappers, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', & McLaughlin, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='  2011, MNRAS, 415, 3065  Komesaroﬀ, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 1970, Nature, 225, 612  Kondratiev, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', McLaughlin, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', Lorimer, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 2009, The Astro-  physical Journal, 702, 692  Kondratiev, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', Verbiest, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', Hessels, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 2016, Astronomy &  Astrophysics, 585, A128  Kouveliotou, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', Fishman, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', Meegan, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 1993, Nature, 362, 728  Kouveliotou, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', Strohmayer, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', Hurley, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 1999, The Astrophysical Jour-  nal, 510, 115  Lazarus, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', Kaspi, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', Champion, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', Hessels, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', & Dib, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 2012,  The Astrophysical Journal, 744, 97  Lorimer, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' & Xilouris, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 2000, The Astrophysical Journal, 545, 385  Maan, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 2015, ApJ, 815, 126  Maan, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' & Aswathappa, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 2014, Monthly Notices of the Royal Astronomi-  cal Society, 445, 3221  Maan, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', Surnis, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', Chandra Joshi, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', & Bagchi, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 2022a, ApJ, 931, 67  Maan, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', van Leeuwen, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', Straal, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', & Pastor-Marazuela, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 2022b, The As-  tronomer’s Telegram, 15697, 1  Malofeev, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' & Malov, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 1997, Nature, 389, 697  Malov, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', Malofeev, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', Teplykh, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', & Logvinenko, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 2015, As-  tronomy Reports, 59, 183  Manchester, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', Hobbs, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', Teoh, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', & Hobbs, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 2005, The Astronomical  Journal, 129, 1993  Mazets, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', Golenetskii, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', & Guryan, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 1979, Soviet Astronomy Let-  ters, 5, 343  Mereghetti, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', Rigoselli, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', Taverna, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 2021, ApJ, 922, 253  Mereghetti, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', Esposito, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', Tiengo, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 2006, The Astrophysical Journal,  653, 1423  Mikhailov, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' & van Leeuwen, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 2016, Astronomy & Astrophysics, 593, A21  Morello, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', Keane, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', Enoto, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 2020, MNRAS, 493, 1165  Muslimov, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' & Harding, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 2003, ApJ, 588, 430  Oostrum, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', van Leeuwen, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', Maan, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', Coenen, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', & Ishwara-Chandra,  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 2020, MNRAS, 492, 4825  Pastor-Marazuela, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 2022, PhD Thesis, University of Amsterdam  Pastor-Marazuela, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', Connor, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', van Leeuwen, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 2021, Nature, 596, 505  Pastor-Marazuela, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', van Leeuwen, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', Bilous, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 2022, arXiv:2202.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='08002  [astro-ph]  Pierbattista, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', Harding, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', Grenier, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 2015, Astronomy & Astro-  physics, 575, A3  Pires, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', Haberl, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', Zavlin, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 2014, Astronomy & Astrophysics,  563, A50, arXiv: 1401.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='7147  Pitkin, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 2018, The Journal of Open Source Software, 3, 538  Pletsch, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', Guillemot, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', Allen, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 2013, The Astrophysical Journal,  779, L11, arXiv: 1311.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='6427  Radhakrishnan, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' & Cooke, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 1969, Astrophysical Letters, 3, 225  Ransom, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 2001, PhD thesis, Harvard University  Ray, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', Kerr, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', Parent, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 2011, The Astrophysical Journal Supple-  ment Series, 194, 17  Rigoselli, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', Mereghetti, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', Suleimanov, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 2019, A&A, 627, A69  Romani, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' & Watters, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 2010, The Astrophysical Journal, 714, 810  Rookyard, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', Weltevrede, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', & Johnston, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 2015, MNRAS, 446, 3367  Ruderman, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' & Sutherland, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 1975, ApJ, 196, 51  Rutledge, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', Fox, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', & Shevchuk, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 2008, The Astrophysical Journal,  672, 1137  Sanidas, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', Cooper, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', Bassa, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 2019, Astronomy & Astrophysics,  626, A104  Shevchuk, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', Fox, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', & Rutledge, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 2009, The Astrophysical  Journal, 705, 391  Shitov, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', Pugachev, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', & Kutuzov, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 2000, Pulsar Astronomy - 2000  and Beyond, 202  Stappers, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', Hessels, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', Alexov, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 2011, Astronomy & Astro-  physics, 530, A80  Szary, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' & van Leeuwen, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 2017, ApJ, 845, 95  Szary, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', van Leeuwen, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', Weltevrede, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', & Maan, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 2020, The Astrophysical  Journal, 896, 168  Tan, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', Bassa, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', Cooper, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 2018, ApJ, 866, 54  van Haarlem, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', Wise, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', Gunst, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 2013, Astronomy & As-  trophysics, 556, A2  van Leeuwen, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 2014, in The Third Hot-wiring the Transient Universe Workshop  (HTU-III), Santa Fe, NM, 79  van Leeuwen, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' & Stappers, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 2010, A&A, 509, 7  van Leeuwen, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', Kasian, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', Stairs, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 2015, ApJ, 798, 118  van Leeuwen, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', Kooistra, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', Oostrum, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 2022, arXiv:2205.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content='12362 [astro-  ph]  Voges, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', Aschenbach, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', Boller, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 1999, Astronomy and Astrophysics,  349, 389  Watters, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', Romani, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', Weltevrede, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', & Johnston, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 2009, The Astro-  physical Journal, 695, 1289  Young, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', Manchester, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', & Johnston, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 1999, Nature, 400, 848  Zane, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', Haberl, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', Israel, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
+page_content=' 2011, Monthly Notices of the Royal  Astronomical Society, 410, 2428  Article number, page 7 of 7' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7NE5T4oBgHgl3EQfQA5X/content/2301.05509v1.pdf'}
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+Cross-Model Comparative Loss for Enhancing Neuronal Utility in Language
+Understanding
+YUNCHANG ZHU, Data Intelligence System Research Center, Institute of Computing Technology, CAS; University
+of Chinese Academy of Sciences, China
+LIANG PANG∗, Data Intelligence System Research Center, Institute of Computing Technology, CAS, China
+KANGXI WU, Data Intelligence System Research Center, Institute of Computing Technology, CAS; University of
+Chinese Academy of Sciences, China
+YANYAN LAN, Institute for AI Industry Research, Tsinghua University, China
+HUAWEI SHEN, Data Intelligence System Research Center, Institute of Computing Technology, CAS; University of
+Chinese Academy of Sciences, China
+XUEQI CHENG, Key Lab of Network Data Science and Technology, Institute of Computing Technology, CAS;
+University of Chinese Academy of Sciences, China
+Current natural language understanding (NLU) models have been continuously scaling up, both in terms of model size and input
+context, introducing more hidden and input neurons. While this generally improves performance on average, the extra neurons do
+not yield a consistent improvement for all instances. This is because some hidden neurons are redundant, and the noise mixed in
+input neurons tends to distract the model. Previous work mainly focuses on extrinsically reducing low-utility neurons by additional
+post- or pre-processing, such as network pruning and context selection, to avoid this problem. Beyond that, can we make the model
+reduce redundant parameters and suppress input noise by intrinsically enhancing the utility of each neuron? If a model can efficiently
+utilize neurons, no matter which neurons are ablated (disabled), the ablated submodel should perform no better than the original full
+model. Based on such a comparison principle between models, we propose a cross-model comparative loss for a broad range of tasks.
+Comparative loss is essentially a ranking loss on top of the task-specific losses of the full and ablated models, with the expectation that
+This paper is an extension of the SIGIR 2022 conference paper [71]. The earlier conference paper is limited to solving the query drift problem in
+pseudo-relevance feedback by comparing the retrieval loss using different size feedback sets. However, the comparison principle and comparative loss
+are actually general and task-agnostic. Moreover, in addition to comparing the input of the model, we can also compare the parameters of the model.
+Thus, in this work, we (1) provide a more general and complete formulation of the comparison principle and comparative loss, (2) directly use a unified
+comparative loss as the final loss being optimized, eliminating the need to set a weighting coefficient between the comparative regularization term
+and the task-specific losses, (3) improve the previous comparison method that compares inputs with different context sizes, and propose an alternative
+dropout-based comparison method to improve the utility of the parameters to the model, and (4) apply the comparative loss to more tasks and models
+and empirically demonstrate its universal effectiveness.
+∗Corresponding author
+Authors’ addresses: Yunchang Zhu, Data Intelligence System Research Center, Institute of Computing Technology, CAS; University of Chinese Academy
+of Sciences, Beijing, China, zhuyunchang17s@ict.ac.com; Liang Pang, Data Intelligence System Research Center, Institute of Computing Technology,
+CAS, Beijing, China, pangliang@ict.ac.cn; Kangxi Wu, Data Intelligence System Research Center, Institute of Computing Technology, CAS; University of
+Chinese Academy of Sciences, Beijing, China, wukangxi22s@ict.ac.cn; Yanyan Lan, Institute for AI Industry Research, Tsinghua University, Beijing,
+China, lanyanyan@tsinghua.edu.cn; Huawei Shen, Data Intelligence System Research Center, Institute of Computing Technology, CAS; University of
+Chinese Academy of Sciences, Beijing, China, shenhuawei@ict.ac.cn; Xueqi Cheng, Key Lab of Network Data Science and Technology, Institute of
+Computing Technology, CAS; University of Chinese Academy of Sciences, Beijing, China, cxq@ict.ac.cn.
+Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not
+made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components
+of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to
+redistribute to lists, requires prior specific permission and/or a fee. Request permissions from permissions@acm.org.
+© 2018 Association for Computing Machinery.
+Manuscript submitted to ACM
+Manuscript submitted to ACM
+1
+arXiv:2301.03765v1  [cs.CL]  10 Jan 2023
+
+2
+Zhu and Pang, et al.
+the task-specific loss of the full model is minimal. We demonstrate the universal effectiveness of comparative loss through extensive
+experiments on 14 datasets from 3 distinct NLU tasks based on 4 widely used pretrained language models, and find it particularly
+superior for models with few parameters or long input.
+CCS Concepts: • Information systems → Information retrieval query processing; Retrieval models and ranking; Question
+answering; Clustering and classification.
+Additional Key Words and Phrases: natural language understanding, question answering, pseudo-relevance feedback, loss function
+ACM Reference Format:
+Yunchang Zhu, Liang Pang, Kangxi Wu, Yanyan Lan, Huawei Shen, and Xueqi Cheng. 2018. Cross-Model Comparative Loss for
+Enhancing Neuronal Utility in Language Understanding. ACM Trans. Inf. Syst. 37, 4, Article 111 (August 2018), 27 pages. https:
+//doi.org/XXXXXXX.XXXXXXX
+1
+INTRODUCTION
+Natural language understanding (NLU) has been pushed a remarkable step forward by deep neural models. To further
+enhance the performance of deep models, enlarging model size [7, 8, 33, 51] and input context [6, 32, 61] are two of the
+most conventional and effective ways, where the former introduces more hidden neurons and the latter brings more
+input neurons. Although neural models with more hidden or input neurons have higher accuracy on average, large-scale
+models do not always beat small models. For example, on one hand, many network pruning methods have shown that
+compressed models with significantly reduced parameters (neuron connections) can maintain accuracy [27, 38, 44]
+and even improve generalization [2], [47] find that ablation of neurons can consistently improve performance in
+some specific classes, and [70] empirically demonstrate that larger language models indeed perform worse on a non-
+negligible fraction of instances. These phenomena indicate that some hidden neurons in the currently trained model
+are dispensable or even obstructive. On the other hand, much of the work on question answering [14, 67] and query
+understanding [18, 49, 72] has noted that feeding more contextual information is more likely to distract the model
+and hurt performance. This is not surprising, as more input neurons not only mean more relevant features but are
+also likely to introduce more noise that interferes with the model. Similar to network pruning that cuts out inefficient
+parameters through post-processing, many context selection methods [23, 48, 56, 69] trim off noisy segments from the
+input context by pre-processing. In essence, both network pruning and context selection reduce inefficient hidden or
+input neurons through additional processing. However, apart from extrinsically reducing inefficient neurons, can we
+intrinsically improve the utility of neurons during model training?
+Imagine an ideal efficient1 neural network in which all its neurons should be able to cooperate efficiently to maximize
+the utility of each neuron. If a fraction of the input or hidden neurons in this network are ablated2 (disabling partial input
+context or model parameters), the ablated submodel is not supposed to perform better, even if the ablated neurons are
+noisy. This is because an ideally efficient model should have already suppressed these noises. Following this intuition, we
+can roughly find a comparison principle between the original full model and its ablated model: the fewer neurons
+are ablated in the model, the better the model should perform. During training, we can use task-specific losses
+as a proxy for performance, with lower task-specific losses implying better performance. For example, the task-specific
+loss of the ideal efficient full model (a) in Figure 1 is supposed to be minimal, and if the ablated model (b) is also ideally
+efficient with respect to its restricted parameter space, the task-specific loss of the ablated model (d) is supposed to be
+greater than that of (b) because (d) ablates one more input neuron than (b).
+1In this work, “efficient” refers specifically to the high utility of neurons.
+2The output value of the neuron is set to 0, which is equivalent to all the connection weights to and from this neuron being set to 0.
+Manuscript submitted to ACM
+
+Cross-Model Comparative Loss for Enhancing Neuronal Utility in Language Understanding
+3
+(a)
+(b)
+(c)
+(d)
+Fig. 1. An illustration of a full neural model (a) and its ablated models (b, c, and d), where a hidden neuron is ablated in (b), an input
+neuron is ablated in (c), and (d) additionally ablate another input neuron based on (b). According to the comparison principle, if the
+full model (a) is an ideal efficient model, the comparative relation between the task-specific losses obtained by these models should
+be (a) ≤ (b), (c), (d). If the ablated model (b) is also ideally efficient in its parameter space, then their comparative relation can be
+further written as (a) ≤ (b) ≤ (d). Note that (b, c) and (c, d) are two non-comparable model pairs. This is because the ablated model (c)
+is not a submodel of (b) and (d), and vice versa.
+Noting the gap between the ideal efficient model and reality [48, 70], we aim to ensure this necessity (comparison
+principle) during the training to improve the model’s utilization of neurons. Based on the natural comparison principle
+between models, we propose a cross-model comparative loss to train models without additional manual supervision. In
+general, the comparative loss is a ranking loss on top of multiple task-specific losses. First, these task-specific losses
+are derived from the full neural model and several comparable ablated models whose neurons are ablated to varying
+degrees. Next, the ranking loss is a pairwise hinge loss that penalizes models that have fewer ablated neurons but larger
+task-specific losses. Concretely, if a model with fewer ablated neurons acquires a larger task-specific loss than another
+model with more ablated neurons, then the difference between the task-specific losses of the pair will be taken into
+account in the final comparative loss; otherwise the pair complies with the comparison principle and does not incur any
+training loss. In this way, the comparative loss can drive the order of task-specific losses to be consistent with the order
+of the ablation degrees. Through theoretical derivation, we also show that comparative loss can be viewed as a dynamic
+weighting of multiple task-specific losses, enabling adaptive assignment of weights depending on the performance of
+the full/ablated models.
+The comparability among multiple ablated models is a fundamental prerequisite for comparative loss. As a coun-
+terexample, although the ablated model (c) in Figure 1 ablates less neurons than (d), they are not comparable and so no
+comparative loss can be applied. To make the ablated models comparable with each other, we progressively ablate the
+models. The first ablated model is obtained by performing one ablation on the basis of the full model. If more ablated
+models are needed, in each subsequent ablation step we construct a new ablated model by performing a further ablation
+on top of the ablated model from the previous step, which makes the newly ablated model certainly a comparable
+submodel of the previous ones. We provide two alternative controlled ablation methods for each ablation step, called
+CmpDrop and CmpCrop. CmpDrop ablates hidden neurons by the dropout [30] technique, which is theoretically
+applicable to all dropout-compatible models. While CmpCrop ablates input neurons by cropping extraneous context
+segments and is theoretically applicable to all tasks that contain extraneous content in the input context.
+We apply comparative loss with CmpDrop or/and CmpCrop on 14 datasets from 3 NLU tasks (text classification,
+question answering and query understanding) with distinct prediction types (classification, extraction and ranking) on
+top of 4 widely used pretrained language models [3, 15, 21, 43]. The empirical results demonstrate the effectiveness of
+comparative loss over state-of-the-art baselines, as well as the enhanced utility of parameters and context. Our analysis
+Manuscript submitted to ACM
+
+4
+Zhu and Pang, et al.
+also confirms that comparative losses can indeed more appropriately weight multiple task-specific losses, as indicated
+by our derivation. By exploring different comparison strategies, we observe that comparing the models ablated by
+first CmpCrop and then CmpDrop can bring the greatest improvement. Interestingly, we find that comparative loss
+is particularly effective for models with few parameters or long inputs. This may imply that comparative loss can
+help models with lower capacity to fit the more or longer training samples better, while models with higher capacity
+are inherently prone to fit less data, so comparative loss is less helpful. Moreover, we discover that different ablation
+methods have different effects on training, with CmpDrop helping task-specific loss to decrease to lower levels faster
+and CmpCrop alleviating overfitting to some extent.
+The main contributions can be summarized as follows:
+• We propose comparative loss, a cross-model loss function based on the comparison principle between the full
+model and its ablated models, to improve the neuronal utility without additional human supervision.
+• We progressively ablate the models to make multiple ablated models comparable and present two controlled
+ablation methods based on dropout and context cropping, applicable to a wide range of tasks and models.
+• We theoretically show how comparative loss works and empirically demonstrate its effectiveness through
+experiments on 3 distinct natural language understanding tasks. We release the code and processed data at
+https://github.com/zycdev/CmpLoss.
+2
+PRELIMINARIES
+Before introducing our cross-model comparative loss, we review some of the concepts and notations needed afterward.
+We first introduce typical training methods for the model, followed by formalizations of network pruning and context
+selection methods that can further improve the model performance by removing inefficient inputs or hidden neurons.
+Finally, we elaborate on the concept of ablation, which recurs throughout the paper.
+2.1
+Conventional Training
+Given a training dataset D for a specified task and a neural network 𝑓 parameterized by 𝜽 ∈ R|𝜽 |, the training objective
+for each sample (𝑥,𝑦) ∈ D is to minimize empirical risk
+Lemp(𝑥,𝑦, 𝜽) = 𝐿(𝑦, 𝑓 (𝑥;𝜽)),
+(1)
+where 𝑥 is the input context, 𝑦 in output space Y is the label, and 𝐿 : Y × Y → R≥0 is the task-specific loss function,
+R≥0 denoting the set of non-negative real numbers. In NLU tasks, 𝑥 is typically a sequence of words, while 𝑦 can be a
+single category label for classification [60], or a pair of start and end boundaries for extraction [53, 67], or a sequence of
+relevance levels for ranking [50].
+2.2
+Network Pruning
+After training a neural model 𝑓 (𝑥;𝜽), to reduce memory and computation requirements at test time, network pruning [5]
+entails producing a smaller model 𝑓 (𝑥; 𝒎 ⊙ 𝜽 ′) with similar accuracy through post-hoc processing. Here 𝒎 ∈ {0, 1}|𝜃 |
+is a binary mask that fixes certain pruned parameters to 0 through elementwise product ⊙, and the parameter vector 𝜽 ′
+may be different from 𝜽 because 𝒎 ⊙ 𝜽 ′ is usually retrained from 𝒎 ⊙ 𝜽 to fit the pruned network structure.
+Although pruning is often viewed as a way to compress models, it has also been motivated by the desire to prevent
+overfitting. Pruning systematically removes redundant parameters and neurons that do not significantly contribute
+Manuscript submitted to ACM
+
+Cross-Model Comparative Loss for Enhancing Neuronal Utility in Language Understanding
+5
+to performance and thus have much less prediction variance, which makes us reminiscent of dropout [36], another
+widely used technique to avoid overfitting. Similarly, dropout also uses a mask to disable a fraction (such as 𝑝%) of
+parameters or neurons. The significant difference, though, is that the mask 𝒎 in dropout is randomly sampled from a
+Bernoulli(1 − 𝑝%) distribution, rather than deterministically defined by a criterion (e.g., the bottom 𝑝% of parameters in
+magnitude should be masked) as in pruning. This in turn brings convenience: a model trained with dropout does not
+need to be retrained for a specific mask, because the model’s neurons have already started to learn how to adapt to the
+absence of some neurons in the previous training.
+2.3
+Context Selection
+To eliminate the noisy content in the input context 𝑥 and further improve the model performance, context selection
+selectively crops out a condensed context 𝑥 ′ ⊑ 𝑥 to produce the final model prediction. In general, the model requires
+specialized training to fit the selected context. Therefore, context selection is pre-hoc processing relative to training,
+requiring removing the noise from the training samples in advance. With a slight abuse of notation, here we use 𝑥 ′ ⊑ 𝑥
+to denote that 𝑥 ′ is a condensed subsequence (possibly equal) of 𝑥. In general, 𝑥 ′ is an ordered combination of segments
+of 𝑥, where the segments are usually at the sentence [48], chunk [69], paragraph [14], or document [23, 56] granularity.
+It is worth noting that the selector for segment selection generally requires additional supervised training and needs to
+be run in advance of the prediction, which introduces additional computation overhead.
+2.4
+Ablation
+To assess the contribution of certain components to the overall model, ablation studies investigate model behavior
+by removing or replacing these components in a controlled setting [17]. Here, in the context of machine learning,
+“ablation” refers to the removal of components of the model, which is an analogy to ablative brain surgery (removal of
+components of an organism) in biology [47]. We refer to the model after component removal as the “ablated model”,
+which should continue to work. However, if the removed components are responsible for performance improvement,
+the performance of the ablated model is expected to be worse [24].
+In this paper, we use “ablation” to refer specifically to the removal of some neurons of a neural model, i.e., to set the
+output of some specific neurons to zero. From such a neuronal perspective, network pruning and context selection can
+be viewed as two kinds of ablation, the former removing some low-contributing hidden neurons after training and the
+latter removing some low-information input neurons before training. However, in contrast to ablation studies that aim
+to investigate the role of the ablated neurons, we aim to learn to improve the utility of the ablated neurons.
+3
+METHODLOGY
+The primary motivation of this work is to inherently improve the utility of neurons in NLU models through a cross-model
+training objective, rather than post-hoc network pruning or pre-hoc context selection to eliminate inefficient neurons.
+In the following, we first describe a comparison principle. Then, we propose a novel comparative loss based on the
+corollary of the comparison principle and present how to train models with comparative loss by two controlled ablation
+methods. Finally, we discuss how comparative loss works.
+3.1
+Comparison Principle
+For an ideal efficient model, we believe that all its neurons should be able to work together efficiently to maximize the
+utility of each neuron. This means that each neuron should contribute to the overall model, or at least be harmless,
+Manuscript submitted to ACM
+
+6
+Zhu and Pang, et al.
+because the cooperation of neurons is supposed to eliminate the negative effects of noise that may be produced by
+individual neurons. Thus, if we ablate some neurons, even those that produce noise, due to the missing contribution of
+the ablated neurons, then the ablated submodel should perform no better than the original full model, in other words,
+its task-specific loss should be no smaller than the original. Formally, we formulate this comparative relation as follows.
+Comparison Principle. Suppose 𝑓 (𝑥;𝜽) is an efficient neural model, let 𝑥 ′ ⊏ 𝑥 be the ablated input and 𝜽 ′ = 𝒎 ⊙ 𝜽
+be the ablated parameters. Then, for any subsequence 𝑥 ′ of 𝑥 whose label is still 𝑦, the input-ablated model 𝑓 (𝑥 ′;𝜽) should
+not perform better than the full model 𝑓 (𝑥;𝜽), and for any parameters 𝜽 ′ masked by arbitrary 𝒎, the parameter-ablated
+model 𝑓 (𝑥;𝜽 ′) should not perform better than 𝑓 (𝑥;𝜽), i.e.,
+𝐿(𝑦, 𝑓 (𝑥;𝜽)) ≤ 𝐿(𝑦, 𝑓 (𝑥 ′;𝜽)), ∀𝑥 ′ ⊏ 𝑥 with 𝑔(𝑥 ′) = 𝑦,
+(2)
+𝐿(𝑦, 𝑓 (𝑥;𝜽)) ≤ 𝐿(𝑦, 𝑓 (𝑥;𝜽 ′)), ∀𝜽 ′ = 𝒎 ⊙ 𝜽 with 𝒎 ∈ {0, 1}|𝜽 |,
+(3)
+where 𝑔(𝑥 ′) means the ground-truth output of 𝑥 ′.
+Notably, we restrict the ablated input 𝑥 ′ for comparison to only those subsequences whose ground-truth output
+𝑔(𝑥 ′) remains unchanged, i.e., 𝑔(𝑥 ′) = 𝑔(𝑥) = 𝑦. This is because ablation may remove some key information from the
+original input 𝑥, such as the trigger words in the classification, resulting in an unknown change in the label 𝑦. In this
+case, 𝐿(𝑦, 𝑓 (𝑥 ′;𝜽)) is no longer a correct measure of the task-specific loss of the input-ablated model, and thus cannot
+be compared with the task-specific loss of the original model.
+Intuitively, we justify the above comparison principle of an efficient model in two cases, which we call parameter-
+efficient and input-efficient. For the case of ablating hidden neurons by applying a mask 𝒎 on the parameters 𝜽, similar
+to network pruning and dropout, i.e., 𝜽 ′ = 𝒎 ⊙ 𝜽, since the ablation of hidden neurons is a kind of damage to the
+model, even if the ablated neurons happen to be noise-producing, the parameter-efficient model definitely has zeroed
+out the connection weights from them, so masking them does not result in a gain. For the case of ablating input neurons
+(words) by cropping out a subsequence from the input context 𝑥, i.e., 𝑥 ′ ⊏ 𝑥 3, because while the extra input 𝑥 \ 𝑥 ′ may
+provide more noisy information, there is certainly no more relevant information in 𝑥 ′ than in 𝑥, and the input-efficient
+model 𝑓 (𝑥;𝜽) is able to suppress the noise, 𝑓 (𝑥 ′;𝜽) is impossible to be better than 𝑓 (𝑥;𝜽).
+Further, we can ablate a full model 𝑓 (𝑥 (0);𝜽 (0)) multiple (𝑐) times, but are these ablated models {𝑓 (𝑥 (𝑖);𝜽 (𝑖))}𝑐
+𝑖=1
+comparable to each other? The comparison principle only points out the comparative relation between an efficient
+model and any of its ablated models, and cannot be directly applied to multiple independently ablated models. However,
+if we assume that these ablated models are constructed step by step, i.e., each ablated model 𝑓 (𝑥 (𝑗);𝜽 (𝑗)) is obtained
+by progressively ablating the input (𝑥 (𝑗) ⊏ 𝑥 (𝑗−1)) or parameters (𝜽 (𝑗) = 𝒎(𝑗) ⊙ 𝜽 (𝑗−1)) based on its previous model
+𝑓 (𝑥 (𝑗−1);𝜽 (𝑗−1)), then 𝑓 (𝑥 (𝑗);𝜽 (𝑗)) can be considered as an ablated model of all its ancestor models {𝑓 (𝑥 (𝑖);𝜽 (𝑖))}𝑗−1
+𝑖=0 .
+For simplicity, we abbreviate their task-specific losses as 𝑙 (𝑖) = 𝐿(𝑦, 𝑓 (𝑥 (𝑖);𝜽 (𝑖))). If all {𝑓 (𝑥 (𝑖);𝜽 (𝑖))}𝑐−1
+𝑖=0 are simultane-
+ously assumed to be efficient with respect to their parameter spaces R∥𝒎(𝑖) ∥0 4, we can apply the comparison principle
+to compare the task-specific losses of any two models, i.e., 𝑙 (𝑖) ≤ 𝑙 (𝑗), ∀𝑖 < 𝑗. More formally, we formulate this corollary
+as follows.
+Corollary 3.1. Given a neural model 𝑓 (𝑥 (0);𝜽 (0)) and its multiple progressively ablated models {𝑓 (𝑥 (𝑖);𝜽 (𝑖))}𝑐
+𝑖=1,
+where 𝑥 (𝑖) ⊏ 𝑥 (𝑖−1) or 𝜽 (𝑖) = 𝒎(𝑖) ⊙ 𝜽 (𝑖−1). If 𝑓 (𝑥 (0);𝜽 (0)) is an efficient model in the original parameter space R|𝜽 (0) |,
+3From here on, if not otherwise specified, we default that the ablation of the input context does not change the output label, i.e., 𝑔(𝑥′) = 𝑦.
+4The number of non-zeros (L0 norm) in the mask determines the number of available parameters.
+Manuscript submitted to ACM
+
+Cross-Model Comparative Loss for Enhancing Neuronal Utility in Language Understanding
+7
+efficient
+excepted
+parameter
+-efficient
+input-
+efficient
+extremely 
+efficient
+ERM
+Fig. 2. The Venn diagram for some of the concepts in this paper. The empirical risk minimized (ERM) refers to the minimization
+of Eq. (1), which is a subset of the parameter-efficient (satisfying Eq. (3)). The efficient (intersecting purple region) model in the
+comparison principle, in addition to being parameter-efficient, also needs to be input-efficient (satisfying Eq. (2)). The extremely efficient
+model requires not only the full model to be efficient, but also its progressively ablated models to be efficient, i.e., satisfying Eq. (4) in
+Corollary 3.1. The training objective of the comparative loss Eq. (5) is both extremely efficient and ERM, i.e., the central overlapping
+grid region.
+and all {𝑓 (𝑥 (𝑖);𝜽 (𝑖))}𝑐−1
+𝑖=1 are also efficient models with respect to their parameter spaces R∥𝒎(𝑖) ∥0. Then, their task-specific
+losses should be monotonically non-decreasing with the degrees of ablation, i.e.,
+𝑙 (0) ≤ 𝑙 (1) · · · ≤ 𝑙 (𝑖) · · · ≤ 𝑙 (𝑐).
+(4)
+In brief, the comparison principle and its corollary describe a deserved comparative relation between an efficient
+neural model and its ablated models, i.e., the less ablation, the better the performance. Unfortunately, this natural
+property has been largely ignored before, which motivates us to exploit it to train models that utilize neurons more
+efficiently.
+3.2
+Comparative Loss
+Based on Corollary 3.1, with the objective of ordered comparative relation Eq. (4), we can train an extremely effi-
+cient model, i.e., we expect not only the full model to be efficient, but also its ablated submodels to be efficient with
+respect to their restricted parameter spaces. To measure the difference from the desirable order, we can use pair-
+wise hinge loss [29] to evaluate the ranking of the task-specific losses of the full model and its ablated models, like
+�𝑐−1
+𝑖=0
+�𝑐
+𝑗=𝑖+1 max(0,𝑙 (𝑖) − 𝑙 (𝑗)). However, the order of task-specific losses may happen to coincide with the desirable
+order such that the aforementioned ranking loss may always be zero, so optimizing this ranking loss alone cannot
+guarantee that the full/ablated models are empirical risk minimized (ERM) [57] with respect to their parameter spaces. To
+push these models to be ERM, we introduce a special scalar 𝑏 as the baseline value of the task-specific loss and assume
+that it is derived from a dummy ablated model 𝑓 (𝑥 (𝑐+1);𝜽 (𝑐+1)). The dummy model is set to have the highest degree of
+ablation, and in principle, its task-specific loss 𝑙 (𝑐+1) should be the highest. However, to push the task-specific losses of
+the real models {𝑓 (𝑥 (𝑖), 𝜽 (𝑖))}𝑐
+𝑖=0 down, we usually set 𝑙 (𝑐+1) = 𝑏 to a small value (e.g., 0) and expect all {𝑙 (𝑖)}𝑐
+𝑖=0 to be
+reduced by this target. In this way, our comparative losses can still be written as a pairwise ranking loss, except that on
+Manuscript submitted to ACM
+
+8
+Zhu and Pang, et al.
+Task-specific Loss Function 𝐿(𝑦,𝑦%)
+⋯
+𝑙(#)
+𝑙(%)
+𝑙(%&')
+↑
+𝑏
+𝑙(')
+Task-specific Losses 
+Predictions
+Input Context 𝑥
+Output Label 𝑦
+⋯
+⋯
+𝑓(𝑥 # ;𝜽 # )
+𝑓(𝑥 ' ; 𝜽 ' )
+𝑓(𝑥 % ; 𝜽 % )
+ℒcmp(𝑥, 𝑦; 𝜽)
+Comparative Loss 
+𝑦(#)
+𝑦(')
+𝑦(%)
+Loss Differences
+	Σ
+✂
+✂
+Ablate neurons
+Hinge loss
+Sum
+	Σ
+✂
+Fig. 3. The overview of comparative loss (best viewed in color). Given a data sample (𝑥, 𝑦), conventional training typically feeds the
+input context 𝑥 into the neural model to obtain the prediction 𝑦(0) and then just minimizes the task-specific loss 𝑙 (0). In contrast,
+comparative loss not only progressively ablates the original model to minimize multiple task-specific losses {𝑙 (𝑖) }𝑐
+𝑖=0, but also
+constrains their comparative relation with a pairwise hinge loss.
+top of the 𝑐 + 2 task-specific losses,
+Lcmp(𝑥,𝑦, 𝜽) =
+𝑐∑︁
+𝑖=0
+𝑐+1
+∑︁
+𝑗=𝑖+1
+max �0,𝑙 (𝑖) − 𝑙 (𝑗)�.
+(5)
+Figure 2 visualizes the localization (central grid region) of the expected model of comparative loss, which is both
+ERM and extremely efficient. The extremely efficient is a subset of the efficient, and the efficient is the intersection of the
+input-efficient and parameter-efficient. In this light, comparative loss sets a stricter training objective than ERM. When
+we set 𝑐 and 𝑏 to 0, Eq. (5) can degenerate to Eq. (1). Further, the comparative loss is equivalent to
+∑︁
+𝑙 (𝑖) >𝑏
+𝑙 (𝑖) +
+𝑐−1
+∑︁
+𝑖=0
+𝑐∑︁
+𝑗=𝑖+1
+max �0,𝑙 (𝑖) − 𝑙 (𝑗)�,
+where the first term is to minimize the empirical risk of those not reaching the target 𝑏, and the second term constrains
+the comparative relation to pursue the full model being extremely efficient.
+To train using comparative loss, we first need to obtain several comparable ablated models and task-specific losses.
+As shown in Figure 3, we consider the original model with the input of the entire context as the full model 𝑓 (𝑥 (0);𝜽 (0)).
+According to Corollary 3.1, we progressively perform 𝑐-step ablation based on the full model. At each ablation step,
+we use CmpCrop or CmpDrop to ablate a portion of the input context or parameters based on the ablated model
+of the previous step, which makes each ablated model comparable to its ancestor models. At the 𝑖-th (1 ≤ 𝑖 ≤ 𝑐)
+ablation step, we use CmpCrop or CmpDrop to ablate a small portion of the input or hidden neurons based on the
+Manuscript submitted to ACM
+
+Cross-Model Comparative Loss for Enhancing Neuronal Utility in Language Understanding
+9
+Algorithm 1 Training with Comparative Loss
+Input: Training dataset D, steps of ablation 𝑐, dropout rate 𝑝, baseline value of task-specific loss 𝑏, learning rate 𝜂.
+Output: model parameters 𝜽.
+1: Randomly initialize model parameters 𝜽
+2: while not converged do
+3:
+randomly sample a data pair (𝑥,𝑦) ∼ D
+4:
+𝑥 (0) ← 𝑥, 𝜽 (0) ← 𝜽
+5:
+𝑙 (0) ← 𝐿(𝑦, 𝑓 (𝑥 (0);𝜽 (0)))
+6:
+for 𝑖 ← 1 to 𝑐 do
+7:
+if ablate hidden neurons then
+⊲ ablate model parameters
+8:
+𝜽 (𝑖) ← CmpDrop(𝜽 (𝑖−1), 𝑝)
+9:
+𝑥 (𝑖) ← 𝑥 (𝑖−1)
+10:
+else
+⊲ ablate input context
+11:
+𝑥 (𝑖) ← CmpCrop(𝑥 (𝑖−1))
+12:
+𝜽 (𝑖) ← 𝜽 (𝑖−1)
+13:
+end if
+14:
+calculate the task-specific loss: 𝑙 (𝑖) ← 𝐿(𝑦, 𝑓 (𝑥 (𝑖);𝜽 (𝑖)))
+15:
+end for
+16:
+set the dummy’s task-specific loss: 𝑙 (𝑐+1) ← 𝑏
+17:
+calculate the comparative loss Lcmp(𝑥,𝑦, 𝜽) by Eq. (5)
+18:
+update parameters: 𝜽 ← 𝜽 − 𝜂∇𝜽 Lcmp(𝑥,𝑦, 𝜽)
+19: end while
+model 𝑓 (𝑥 (𝑖−1);𝜽 (𝑖−1)) from the previous step, which makes the newly ablated model 𝑓 (𝑥 (𝑖);𝜽 (𝑖)) comparable to all
+its ancestor models. After all these models have predicted once, we have 𝑐 + 1 comparable task-specific losses. Together
+with 𝑙 (𝑐+1) = 𝑏 from the dummy ablated model, we can calculate the final loss using Eq. (5). Using stochastic gradient
+descent optimization as an example, Algorithm 1 illustrates the training process more formally.
+CmpDrop and CmpCrop in Algorithm 1 are the two alternative ablation methods we present for each ablation step,
+the former for ablating the parameters (hidden neurons) and the latter for ablating the input context (input neurons).
+They both randomly ablate neurons in a controlled manner on top of the previous model, which allows the coverage
+of all potential ablated models without retraining each ablated model. This is because the randomly ablated models
+are jointly trained and adapt to the absence of some neurons during the training process. As for which one to use at
+each ablation step can be specific to the model and task dataset. Ideally, CmpDrop can be used as long as the model is
+dropout compatible, and CmpCrop can be used as long as the input context of the task contains dispensable segments.
+Below we will introduce CmpDrop and CmpCrop in detail.
+3.2.1
+CmpDrop: Ablate Parameters by Dropout. Dropout randomly disables each neuron with probability 𝑝, which
+coincides with our need to randomly ablate hidden neurons. To obtain a model 𝑓 (·;𝜽 (𝑖)) with more ablated parameters,
+instead of simply applying a larger dropout rate on the original model 𝑓 (·;𝜽 (0)), we ablate the surviving neurons
+from the previous ablated model 𝑓 (·;𝜽 (𝑖−1)) with probability 𝑝 consistently. Specifically, the output values of those
+dropped neurons are set to zeros, and the output values of the surviving neurons are scaled by 1/(1 − 𝑝) to ensure
+consistency with the expected output value of a neuron in all full/ablated models [36]. This is equivalent to applying
+a mask with scaling5 𝒎(𝑖) ∈ {0, 1, 1/(1 − 𝑝)}|𝜽 | to the previous parameters 𝜽 (𝑖−1) to obtain the ablated parameters
+5Slightly different from the binary mask in the comparison principle, we incorporate the scaling factors together into the mask in order to still express
+the parameter ablation concisely by 𝜽 (𝑖) = 𝒎(𝑖) ⊙ 𝜽 (𝑖−1).
+Manuscript submitted to ACM
+
+10
+Zhu and Pang, et al.
+𝜽 (𝑖) = 𝒎(𝑖) ⊙ 𝜽 (𝑖−1). Each element in 𝒎(𝑖) corresponds to the scaling factor of each parameter,
+𝑚(𝑖)
+𝑘
+=
+
+
+1,
+if no dropout in 𝜃𝑘’s layer;
+1
+1−𝑝 ,
+if neurons at both ends of 𝜃𝑘 survive;
+0,
+otherwise.
+For the third case in the above equation, once a neuron is newly ablated, all connection parameters from and to it are
+set to zero; in addition, parameters that have been ablated by 𝒎(𝑖−1) are still set to zero.
+In practice, we can leverage the existing dropout to implement it. However, for the comparability of the ablated
+models, we must use the same random seed and the same state of the random number generator in each CmpDrop. In
+this way, assuming that the current ablation step is the 𝑛-th execution of CmpDrop, we can simply run the model with
+the dropout rate of 1 − (1 − 𝑝)𝑛.
+3.2.2
+CmpCrop: Ablate Input by Cropping. Given an input context 𝑥, CmpCrop aims to crop out a condensed context
+𝑥 ′ that does not change the original ground-truth output, i.e. 𝑥 ′ ⊏ 𝑥 and 𝑔(𝑥 ′) = 𝑔(𝑥) = 𝑦. Assume that we know
+the minimum support context 𝑥★ for 𝑥 at training time, i.e., ∀𝑥 ′ ⊒ 𝑥★ 𝑔(𝑥 ′) = 𝑔(𝑥★) and ∀𝑥 ′ ⊏ 𝑥★ 𝑔(𝑥 ′) ≠ 𝑔(𝑥★).
+Then, CmpCrop can produce a streamlined context by randomly cropping out several insignificant segments from the
+non-support context 𝑥 \ 𝑥★. In this way, the trimmed streamlined context is sure to contain the minimum support
+context, so the ground-truth output does not change.
+In practice, to use CmpCrop, we must ensure that enough insignificant segments are set aside in the original context
+𝑥 (0) for cropping. The segments can be of document, paragraph or sentence granularity. For example, in question
+answering, an insignificant segment can be any retrieved paragraph that does not affect the answer to the question. If
+the dataset does not annotate the minimal support context, we can manually inject a few extraneous noise segments
+into 𝑥 (0).
+3.3
+Discussion
+Further deriving Eq. (5), we find that comparative loss can be viewed as a dynamic weighting of multiple task-specific
+losses. Speicially, the loss can be rewrited as follow,
+Lcmp =
+𝑐∑︁
+𝑖=0
+𝑐+1
+∑︁
+𝑗=𝑖+1
+max �0,𝑙 (𝑖) − 𝑙 (𝑗)�
+=
+𝑐∑︁
+𝑖=0
+𝑐+1
+∑︁
+𝑗=𝑖+1
+1𝑙 (𝑖) >𝑙 (𝑗) · 𝑙 (𝑖) −
+𝑐∑︁
+𝑖=0
+𝑐+1
+∑︁
+𝑗=𝑖+1
+1𝑙 (𝑖) >𝑙 (𝑗) · 𝑙 (𝑗)
+=
+𝑐+1
+∑︁
+𝑖=0
+𝑐+1
+∑︁
+𝑗=𝑖+1
+1𝑙 (𝑖) >𝑙 (𝑗) · 𝑙 (𝑖) −
+𝑐+1
+∑︁
+𝑖=1
+𝑖−1
+∑︁
+𝑗=0
+1𝑙 (𝑗) >𝑙 (𝑖) · 𝑙 (𝑖)
+=
+𝑐+1
+∑︁
+𝑖=0
+
+𝑐+1
+∑︁
+𝑗=𝑖+1
+1𝑙 (𝑖) >𝑙 (𝑗) · 𝑙 (𝑖) −
+𝑖−1
+∑︁
+𝑗=0
+1𝑙 (𝑗) >𝑙 (𝑖) · 𝑙 (𝑖)
+
+=
+𝑐+1
+∑︁
+𝑖=0
+∑︁
+𝑗≠𝑖
+CMP(𝑖, 𝑗,𝑙 (𝑖),𝑙 (𝑗)) · 𝑙 (𝑖),
+(6)
+Manuscript submitted to ACM
+
+Cross-Model Comparative Loss for Enhancing Neuronal Utility in Language Understanding
+11
+where 1𝐶 is an indicator function equal to 1 if condition 𝐶 is true and 0 otherwise, and the CMP function determines
+whether model 𝑓 (𝑥 (𝑖);𝜽 (𝑖)) complies with the comparison principle compared to 𝑓 (𝑥 (𝑗);𝜽 (𝑗)) and adjusts the weight
+of 𝑙 (𝑖). There are two cases of non-compliance: for the case where 𝑓 (𝑥 (𝑖);𝜽 (𝑖)) is less ablated (𝑖 < 𝑗) but more loss is
+obtained, we increase the weight of 𝑙 (𝑖); for the case where 𝑓 (𝑥 (𝑖);𝜽 (𝑖)) is more ablated (𝑖 > 𝑗) but less loss is obtained,
+we decrease the weight of 𝑙 (𝑖). Formally, the CMP function can be written as
+CMP(𝑖, 𝑗,𝑙 (𝑖),𝑙 (𝑗)) =
+
+
+1,
+if 𝑖 < 𝑗 and 𝑙 (𝑖) > 𝑙 (𝑗);
+−1,
+if 𝑖 > 𝑗 and 𝑙 (𝑖) < 𝑙 (𝑗);
+0,
+otherwise.
+Here we can notice that for a pair of models that do not conform to the comparison principle, we increase (+1) the
+weight of the task-specific loss of the model that is ablated less and equally decrease (-1) the weight of the loss of
+the model that is ablated more. Thus, let 𝛼 (𝑖) = �
+𝑗≠𝑖 CMP(𝑖, 𝑗,𝑙 (𝑖),𝑙 (𝑗)) denote the weight of 𝑙 (𝑖), then the sum of
+the weights of all task-specific losses (including the dummy one) is 0, i.e., �𝑐
+𝑖=0 𝛼 (𝑖) = −𝛼 (𝑐+1) = �𝑐
+𝑖=0 1𝑙 (𝑖) >𝑏. Since
+𝑙 (𝑐+1) = 𝑏 is a constant, Eq. (6) is also equivalent to �𝑐
+𝑖=0 𝛼 (𝑖)𝑙 (𝑖), i.e., the total weight equals the number of task-specific
+losses worse than the virtual baseline 𝑏, and is adaptively assigned to the 𝑐 + 1 losses according to their performance. In
+this way, poorly performing full/ablated models will be more heavily optimized. And we empirically compare other
+heuristic weighting strategies in §5.1.
+For parameter ablation, in addition to being able to weight each task-specific loss differentially, the comparative loss
+with CmpDrop can also differentially calculate the gradients of the parameters in different parts. According to Eq. (6),
+comparative loss is equal to the sum of all differences of task-specific loss pairs that violate the comparison principle, i.e,
+�
+𝑖<𝑗 ∧𝑙 (𝑖) >𝑙 (𝑗)
+�𝑙 (𝑖) − 𝑙 (𝑗)�, so we can analyze the gradient of comparative loss from the difference of each task-specific
+loss pair. For ease of illustration, we take the original model 𝑓 (𝑥;𝜽) and a model 𝑓 (𝑥 ′;𝜽 ′) whose parameters have been
+ablated 𝑛 times as an example, and other model pairs with different parameters are similar. Assume that the original
+parameters 𝜽 = (𝒖, 𝒗,𝒘) and the ablated parameters 𝜽 ′ = (𝒖′, 𝒗′,𝒘′) = (𝒖, 𝒗/(1 − 𝑝)𝑛, 0), where 𝒖 is the parameters
+from the layers without dropout, 𝒘 is the parameters ablated by 𝑛 times CmpDrop, and 𝒗′ is the scaled parameters
+surviving from 𝑛 times dropout. Then, if their task-specific losses violate the comparison principle, i.e., 𝑙 > 𝑙 ′, the
+gradient of the comparative loss contributed by this model pair is
+∇𝜽 (𝑙 − 𝑙 ′) = (∇𝒖 (𝑙 − 𝑙 ′), ∇𝒗(𝑙 − 𝑙 ′), ∇𝒘𝑙).
+We can see that the comparative loss with respect to 𝒘 is higher than the comparative loss with respect to the other
+parameters. This is intuitive because the model instead performs better after ablating away 𝒘 indicating that the current
+𝒘 is inefficient, so we need to focus on updating 𝒘.
+In addition to the dynamic weighting perspective, comparative loss can also be considered as an “inverse ablation
+study” during training. This is because, in contrast to ablation studies that determine the contribution of removed
+components during validation, comparative loss believes that the ablated neurons should contribute and optimizes
+parameters with this objective.
+For training complexity, given a generally small number of comparisons 𝑐 (i.e., number of ablation steps), the overhead
+of computing the final comparative loss is negligibly small, and the increased computation overhead per update step
+comes mainly from the multiple forward and backward propagations of the models. Specifically, the overhead of a
+Manuscript submitted to ACM
+
+12
+Zhu and Pang, et al.
+training step using comparison loss is 1 + 𝑐 times that of conventional training for the same batch size. For inference
+complexity, however, models trained using comparative loss are the same as conventionally trained models at test time.
+4
+EXPERIMENTS
+To evaluate the effectiveness and generalizability of our approach for natural language understanding, we conduct
+experiments on 3 tasks with representative output types, including classification (8 datasets), extraction (2 datasets),
+and ranking (4 datasets). Among them, the classification task requires predicting a single category for a piece of text or
+a text pair, the extraction task requires predicting a pair of boundary positions to extract the span between the start and
+end boundaries, and the ranking task requires predicting a list of relevance level to rank candidates. Specifically, the
+three distinct tasks are text classification (see §4.1), reading comprehension (extraction, see §4.2), and pseudo-relevance
+feedback (ranking, see §4.3), respectively. We evaluate the comparative loss with just CmpDrop in text classification
+and reading comprehension, the comparative loss with just CmpCrop in reading comprehension and pseudo-relevance
+feedback, and the comparative loss with both CmpDrop and CmpCrop in reading comprehension. For each task, we
+first introduce the dataset used, then present the implementation of our models as well as the baselines, and finally
+show the experimental results.
+Before we start each experiment, we explain some common experimental settings. For the baseline value 𝑏 of the
+task-specific loss in Algorithm 1, we provide two setting options. One is to simply set 𝑏 = 0, which is equivalent to
+setting an unreachable target value for all full/ablated models and thus pushing their task-specific losses to decrease.
+However, this results in the exposure of all training data to the full model and may aggravate overfitting. Therefore, to
+reduce the times the full model is optimized, our second option is to set the baseline value to the task-specific loss of
+the full model, i.e., 𝑏 = 𝑙 (0). In this way, the full model is optimized only when it performs worse than its ablated model.
+In practice, we prefer setting 𝑏 = 0, and change to setting 𝑏 = 𝑙 (0) if we find that the model is prone to overfitting on
+the dataset. For the dropout rate 𝑝 in each CmpDrop, we use the same setting as the baseline models, which is 0.1 in all
+our experiments. For other conventional training hyperparameters, such as batch size and learning rate, we also keep
+the same as the carefully tuned baseline models if not specifically specified. We implement our models and baseline
+models in PyTorch with HuggingFace Transformers [65], and train them on Tesla V100 GPUs with the fixed random
+seed 42. For convenience, in the tables, we use ‘Cmp’ to represent the comparative loss and use ‘Drop’ and ‘Crop’ in
+parentheses to refer to CmpDrop and CmpCrop, respectively.
+4.1
+Classification: Application to Text Classification
+Text classification is a fundamental task in natural language understanding, which aims to assign a predefined category
+to a piece or a group of text. In many text classification datasets, all segments of the input context seem to play an
+important role in the text category and there is almost no annotation of the minimal support context, so it is difficult
+for us to construct an input-ablated model by directly cropping the original input without changing the classification
+label. That is, it is likely to violate the constraint that the label of the ablated input is unchanged in the comparison
+principle, and thus we cannot apply CmpCrop to this task. However, many current neural classification models use
+dropout during training, so in this task, we only validate the comparative loss that uses just CmpDrop.
+4.1.1
+Datasets. The General Language Understanding Evaluation (GLUE) benchmark [60] is a collection of diverse
+natural language understanding tasks. Following [21], we exclude the problematic WNLI set and conduct experiments
+on 8 datasets: (1) Multi-Genre Natural Language Inference (MNLI) [64] is a sentence pair classification task that
+Manuscript submitted to ACM
+
+Cross-Model Comparative Loss for Enhancing Neuronal Utility in Language Understanding
+13
+Table 1. Classification performance on the development sets of GLUE language understanding benchmark.
+Model
+MNLI
+MRPC
+QNLI
+QQP
+RTE
+SST-2
+STS-B
+CoLA
+Average
+BERTbase [21]
+84.3
+85.3
+91.3
+91.1
+69.0
+93.1
+89.4
+63.6
+83.33
++ R-Drop [39]
+85.5
+87.3
+92.0
+91.4
+71.1
+93.0
+89.6
+62.6
+84.06
++ Cmp (𝑐 Drop)
+85.4
+88.5
+92.1
+91.6
+71.8
+93.5
+89.9
+64.6
+84.66
+aims to predict whether the second sentence is an entailment, contradiction, or neutral to the first one. (2) Microsoft
+Research Paraphrase Corpus (MRPC) [22] aims to predict if two sentences in the pair are semantically equivalent.
+(3) Question Natural Language Inference (QNLI) [60] is a binary sentence pair classification task that aims to predict
+whether a sentence contains the correct answer to a question. (4) Quora Question Pairs (QQP) [13] is a binary sentence
+pair classification task that aims to predict whether two questions asked on Quora are semantically equivalent. (5)
+Recognizing Textual Entailment (RTE) [4] is a binary entailment task similar to MNLI, but with much fewer training
+samples. (6) Stanford Sentiment Treebank (SST-2) [55] is a binary sentence sentiment classification task consisting of
+sentences extracted from movie reviews. (7) The Semantic Textual Similarity Benchmark (STS-B) [9] is a sentence pair
+classification task that aims to determine how two sentences are semantically similar. (8) The Corpus of Linguistic
+Acceptability (CoLA) [63] is a binary sentence classification task aimed at judging whether a single English sentence
+conforms to linguistics.
+4.1.2
+Models & Training. Following R-Drop [39], another state-of-the-art training method leveraging dropout, we
+validate our comparative loss on the popular classification models based on pretrained language models (PLMs)6.
+Specifically, we take BERTbase as our backbone to perform finetuning. The task-specific loss is mean squared error
+(MSE) for STS-B and cross-entropy for other datasets. We use different training hyperparameters for each dataset. For
+baseline models and our models trained with comparative loss, we independently select the learning rate within {1e-5,
+2e-5, 3e-5, 4e-5}, warmup rate within {0, 0.1}, the batch size within {16, 24, 32}, and the number of epochs from 2 to 5.
+For our models, we tune the number of ablation steps 𝑐 (i.e., number of CmpDrop) from 1 to 4.
+4.1.3
+Results. We present classification performance in Table 1, where the evaluation metrics are Pearson correlation for
+STS-B, Matthew’s correlation for CoLA, and Accuracy for the others. We can see that our model (+ Cmp) comprehensively
+outperforms the well-tuned baseline BERTbase and achieves an improvement of 1.33 points (on average), which proves
+the effectiveness of comparative loss in classification tasks. Moreover, our model trained with comparative loss also
+outperforms the model trained with state-of-the-art R-Drop [39] by 0.6 points on average, which demonstrates the
+superiority of comparative loss.
+4.2
+Extraction: Application to Reading Comprehension
+Extractive reading comprehension (RC) [42, 53] is an essential technical branch of question answering (QA) [11, 31, 40, 54].
+Given a question and a context, extractive RC aims to extract a span from the context as the predicted answer. Current
+dominant RC models basically use pretrained Transformer [58] architectures, which employ dropout in many layers
+during finetuning. This allows us to use CmpDrop to improve the utility of the model parameters. Additionally, the
+given context is usually lengthy and contains many distracting noise segments, which also allows us to use CmpCrop
+6https://github.com/huggingface/transformers/blob/v4.19.2/examples/pytorch/text-classification/README.md
+Manuscript submitted to ACM
+
+14
+Zhu and Pang, et al.
+Table 2. Question answering performance on the development sets of SQuAD and HotpotQA distractor. The results with † are
+inquired from the authors of its paper.
+Model
+EM
+F1
+SQuAD
+BERTbase [21]
+80.8
+88.5
+BERTbase (our implementation)
+81.1
+88.4
++ Cmp (2 Drop)
+82.5
+89.4
+ELECTRAbase [15]
+84.5
+90.8
+ELECTRAbase (our implementation)
+86.1
+92.3
++ Cmp (2 Drop)
+86.7
+92.9
+HotpotQA
+Longformerbase† [3]
+60.3
+74.3
+Longformerbase(our implementation)
+61.5
+75.2
++ Cmp (1 Drop)
+63.1
+77.0
++ Cmp (1 Crop)
+63.1
+76.8
++ Cmp (1 Crop & 1 Drop)
+63.6
+77.4
+to improve the model’s utilization of the context. Therefore, we intend to verify the effectiveness of comparative loss
+using CmpDrop or/and CmpCrop in this task.
+4.2.1
+Datasets. We evaluate the comparative loss using only CmpDrop on SuQAD [53], which contains 100K single-
+hop questions with 9832 for validation, and HotpotQA [67], which contains 113K multi-hop questions with 7405 for
+validation. For HotpotQA, we consider the distractor setting, where the context of each question contains 10 paragraphs,
+but only 2 of them are useful for answering the question, and the rest 8 are retrieved distracting paragraphs that are
+relevant but do not support the answer. This allows us to evaluate the comparative loss with CmpCrop on HotpotQA
+distractor.
+4.2.2
+Models & Training. We follow simple but effective RC models based on PLMs [3, 15, 21], which take as input
+a concatenation of the question and the context and use a linear layer to predict the start and end positions of the
+answer. And we use cross-entropy of answer boundaries as the task-specific loss function following [21] and use a
+learning rate warmup over the first 10% steps. For SQuAD, we use the popular BERT [21] and ELECTRA [15] with a
+maximum sequence length of 512 as the backbone, both of which have successively achieved top rankings in multiple
+QA benchmarks [52, 53, 67]. We first tune the learning rate in range {1e-5, 3e-5, 5e-5, 8e-5, 1e-4, 2e-4}, batch size in
+{8, 12, 32} and number of epochs in {1, 2, 3} for baseline models. Then, setting 𝑐 = 2, we take these hyperparameters
+along and train our models using the comparative loss with two CmpDrop. For HotpotQA, we use the state-of-the-art
+Longformer [3] with a maximum sequence length of 2048 as the backbone, which is fed with the format <s> [YES]
+[NO] [Q] question </s> [T] title1 [P] paragraph1 · · · [T] title10 [P] paragraph10 </s>. The special
+tokens [YES]/[NO], [Q], [T], and [P] represent yes/no answers and the beginning of questions, titles, and paragraphs,
+respectively. Similarly, we select the learning rate in {1e-5, 3e-5}, batch size in {6, 9, 12} and number of epochs in {3, 5, 8}
+for the baseline model. We then train our models with three comparative losses respectively, the first two applying one
+CmpDrop/CmpCrop (𝑐 = 1), while the third applying one CmpCrop followed by one CmpDrop (𝑐 = 2).
+Manuscript submitted to ACM
+
+Cross-Model Comparative Loss for Enhancing Neuronal Utility in Language Understanding
+15
+Table 3. Retrieval performance on benchmarks built on MS MARCO passage collection. ANCE and uniCOIL are base retrieval
+models, + PRF denotes the PRF baseline model, + Cmp denotes our PRF model trained with the comparative loss of 1 CmpCrop, and
+superscript (𝑘) represents the PRF depth used during testing.
+Model
+MARCO Dev
+MARCO Eval
+TREC DL 2019
+TREC DL 2020
+DL-HARD
+NDCG@10
+MRR@10
+R@1K
+MRR@10
+NDCG@10
+R@1K
+NDCG@10
+R@1K
+NDCG@10
+R@1K
+ANCE [66]
+38.76
+33.01
+95.84
+31.70
+64.76
+75.70
+64.58
+77.64
+33.39
+76.65
++ PRF(3) [68]
+40.10
+34.40
+95.90
+33.00
+68.10
+79.10
+69.50
+81.50
+36.50
+76.10
++ Cmp(3) (1 Crop)
+40.68
+34.84
+96.94
+-
+68.42
+80.10
+69.58
+81.77
+35.61
+79.39
++ Cmp(5) (1 Crop)
+41.01
+35.14
+97.03
+34.17
+69.58
+80.81
+70.44
+82.77
+37.44
+79.55
+uniCOIL [41]
+41.21
+35.13
+95.81
+34.42
+70.09
+82.83
+67.35
+84.42
+35.96
+76.85
++ PRF(3)
+41.76
+35.48
+96.85
+-
+69.42
+83.32
+69.25
+84.44
+36.53
+77.48
++ Cmp(3) (1 Crop)
+42.02
+35.75
+96.91
+35.14
+70.10
+83.58
+69.70
+84.51
+36.90
+77.67
+4.2.3
+Results. Since we focus on extraction here, we only measure the extracted answers using EM (exact match) and
+F1, which is a little different from the official HotpotQA setting that simultaneously evaluates the identification of
+support facts. From Table 2 we can see that our implemented baseline models trained directly using the task-specific loss
+Eq. (1) largely achieve better results than those reported in their original papers. Once trained using comparative loss
+Eq. (5) instead, our models can still significantly outperform these well-tuned baseline models even without re-searching
+the training hyperparameters, demonstrating the effectiveness of comparative loss on the extraction task. Also, the
+consistent improvement based on the three different PLMs demonstrates the model-agnostic nature of comparative loss.
+Furthermore, from the results on HotpotQA we can find that although both CmpDrop and CmpCrop deliver significant
+improvement, CmpCrop + CmpDrop achieves the best results, suggesting that CmpDrop and CmpCrop may bring
+different benefits to the trained models.
+4.3
+Ranking: Application to Pseudo-Relevance Feedback
+Pseudo-relevance feedback (PRF) [1] is an effective query understanding [10] technique to improve ranking accuracy,
+which aims to alleviate the mismatch of linguistic expressions between a query and its potential relevant documents.
+Given an original query 𝑞 and a document collection 𝐶, a base ranking model returns a ranked list 𝐷 = (𝑑1,𝑑2, · · · ,𝑑|𝐷 |).
+Let 𝐷≤𝑘 denote the feedback set containing the top 𝑘 documents, where 𝑘 is usual referred to as the PRF depth. The
+goal of PRF is to reformulate the original query 𝑞 into a new representation 𝑞(𝑘) using the query-relevant information
+in 𝐷≤𝑘, i.e., 𝑞(𝑘) = 𝑓 ((𝑞, 𝐷≤𝑘);𝜽), where 𝑞(𝑘) is expected to yield better ranking results. Although PRF methods do
+usually improve ranking performance on average [16], individual reformulated queries inevitably suffer from query
+drift [49, 72] due to the objectively present noise in the feedback set, causing them to be inferior to the original ones.
+Therefore, we can use comparative loss with CmpCrop to train PRF models to suppress the extra increased noise by
+comparing the effect of queries reformulated using different feedback sets.
+4.3.1
+Datasets. We conduct experiments on MS MARCO passage [50] collection, which consists of 8.8M English
+passages collected from the search results of Bing’s 1M real-world queries. The Train set of MS MARCO contains
+530K queries (about 1.1 relevant passages per query on average), the Dev set contains 6980 queries, and the online
+Eval set contains 6837 queries. Apart from these, we also consider TREC DL 2019 [20], TREC DL 2020 [19], and
+DL-HARD [46], three offline evaluation benchmarks based on the MS MARCO passage collection, which contain 43, 54,
+and 50 fine-grained (relevance grades from 0 to 3) labeled queries, respectively. Among them, DL-HARD [46] is a recent
+evaluation benchmark focusing on complex queries. We use MS MARCO Train set to train models, and evaluate trained
+Manuscript submitted to ACM
+
+16
+Zhu and Pang, et al.
+models on the MS MARCO Dev set to tune hyperparameters and select model checkpoints. The selected models are
+finally evaluated on the online MS MARCO Eval7 and three other offline benchmarks.
+4.3.2
+Models & Training. We carry out PRF experiments on two base retrieval models, ANCE [66] (dense retrieval)
+and uniCOIL [41] (sparse retrieval), respectively. For their PRF models, we do not explicitly modify the query text, but
+directly generate a new query vector for retrieval following the current state-of-the-art method ANCE-PRF [68]. This
+allows us to directly optimize the retrieval of reformulated queries end-to-end with the negative log likelihood of the
+positive document [34] as the task-specific loss:
+𝐿(𝒒(𝑘)) = − log
+𝑒sim(𝒒(𝑘),𝒅+)
+𝑒sim(𝒒(𝑘),𝒅+) + �
+𝑑−∈𝐷− 𝑒sim(𝒒(𝑘),𝒅−) ,
+where 𝒅+ is the vector of a sampled document relevant to 𝑞 and 𝒒(𝑘), and 𝐷− is the collection of negative documents
+for them. Since only vectors of queries are updated8, we mine a lite collection (5.3M for dense retrieval and 3.7M for
+sparse retrieval) containing positive and hard negative documents of all training queries. In this way, for each query,
+all documents in the lite collection except its positive documents can be used as its 𝐷−. In general, our PRF model
+consists of an encoder, a vector projector, and a pooler. First the original query 𝑞 and feedback documents in 𝐷≤𝑘 are
+concatenated in order with [SEP] as separator and input to the encoder to get the contextual embedding of each token.
+Then, the projector maps the contextual embeddings to vectors with the same dimension as the document vectors.
+Finally, all token vectors are pooled into a single query vector. For dense retrieval, the encoder is initialized from
+ANCEFirstP9, the projector is a linear layer, and the pooler applies a layer normalization on the first vector ([CLS]) in the
+sequence, as in the previous work [68]. For sparse retrieval, the encoder and projector are initialized from BERTbase with
+the masked language model head, where the projector is an MLP with GeLU [28] activation and layer normalization,
+and the pooler is composed of a max pooling operation and an L2 normalization10. We finetune PRF baseline models
+for up to 12 epochs with a batch size of 96, a learning rate selected from {2e-5, 1e-5, 5e-6}, and PRF depth 𝑘 randomly
+sampled from 0 to 5 for each query. We then finetune our PRF models using the comparative loss of 𝑐 = 1 CmpCrop for
+up to 6 epochs with a batch size of 48. In this way, the maximum number of training steps for our models remains the
+same as the baseline models, i.e., up to 12 optimizations per original query.
+4.3.3
+Results. We report the official metrics (MRR@10 for MARCO and NDCG@10 for others) and Recall@1K of
+the models on multiple benchmarks in Table 3. In addition to reporting results for the best-performing PRF depths
+(numbers in superscript brackets), for a fair comparison with ANCE-PRF(3) (second row), we also present the results of
+ANCE-PRF + Cmp(3), both of which use the first 3 documents as feedback. We can see that PRF baseline models (+
+PRF) indeed generally outperform their base retrieval models, except that uniCOIL-PRF degrades by 0.67 percentage
+points in NDCG@10 of TREC DL 2019, which reflects the presence of query drift. Our PRF models (+ Cmp) trained with
+comparative loss, however, outperforms their base retrieval model across the board. Under the same use of 3 feedback
+documents, our ANCE-PRF + Cmp also outperforms the published state-of-the-art ANCE-PRF [68] on all metrics except
+NDCG@10 on DL-HARD. Moreover, when 5 feedback documents are used, ANCE-PRF + Cmp achieves a go-ahead over
+ANCE-PRF on NDCG@10 of DL-HARD. For sparse retrieval, our PRF model (+ Cmp) trained with comparative loss also
+7https://microsoft.github.io/MSMARCO-Passage-Ranking-Submissions/leaderboard/
+8The fixed vectors of documents are restored from the index pre-built by https://github.com/castorini/pyserini.
+9https://github.com/microsoft/ANCE
+10We find that L2 normalization helps the model train stably, and it does not change the relevance ranking of documents to a query.
+Manuscript submitted to ACM
+
+Cross-Model Comparative Loss for Enhancing Neuronal Utility in Language Understanding
+17
+Table 4. QA performance on the development set of HotpotQA distractor with different weighting strategies. Cmp refers to Longformer
++ CmpCrop + CmpDrop that adaptively weights multiple task-specific losses through comparative loss. The others are heuristics,
+where AVERAGE assigns the same weights to all task-specific losses, FIRST and SECOND assign weight only to the first or second,
+and MAX dynamically assigns weight only to the largest one.
+Weighting Method
+EM
+F1
+Cmp
+63.6
+77.4
+AVERAGE
+63.4
+77.0
+FIRST
+62.6
+76.2
+SECOND
+61.5
+75.2
+MAX
+63.2
+77.0
+surpasses the strong baseline uniCOIL-PRF implemented following ANCE-PRF. All of these results above demonstrate
+the effectiveness of comparative loss on the ranking task.
+5
+ANALYSIS
+In this section, we further conduct several experiments for a more thorough analysis. First, from the dynamic weighting
+perspective found in §3.3, we examine whether the adaptive weighting of comparative loss is more effective than
+other weighting strategies (§5.1). Next, we try several other comparison strategies to find some guiding experience
+in choosing the number of ablations and ablation methods in practice (§5.2). Then, to confirm the enhancement of
+comparative loss on the utility of hidden and input neurons, we investigate the performance of models with different
+numbers of parameters (§5.3) and context lengths (§5.4). Furthermore, we visualize the loss curves to find the impact
+of the comparative losses with different ablation methods on the task-specific loss (§5.5). Finally, we show the actual
+training overhead of comparative loss in detail (§5.6).
+5.1
+Effect of Weighting Strategy
+To verify the role of comparative loss from the dynamic weighting perspective, we keep all the training settings of
+Longformer + CmpCrop + CmpDrop from the last row of Table 2 unchanged and replace only the weighting strategy of
+task-specific losses with some heuristics. Table 4 shows their performance on the HotpotQA development set. AVERAGE,
+FIRST and SECOND are three static weighting strategies. AVERAGE assigns equal weights to all task-specific losses,
+while FIRST and SECOND assign weight to only the first and second task-specific loss, respectively, i.e., FIRST optimizes
+𝑙 (0) of the full model without dropout and SECOND optimizes 𝑙 (1) of the model with regular dropout rate 𝑝 (equivalent
+to the baseline Longformer in Table 2). MAX is another dynamic weighting strategy that assigns weight to only the
+largest task-specific loss. We can see that dynamic weighting in comparative losses is obviously better than these
+heuristic weighting strategies, which proves that comparative loss can assign weights more appropriately. In addition,
+AVERAGE is better than the latter three strategies that consider only one task-specific loss, indicating that it is beneficial
+to consider multiple task-specific losses. Moreover, although the latter three are all assigned to only one task-specific
+loss, MAX is better than the other two, which indicates that dynamic assignment is better than static assignment.
+Notably, the FIRST that directly optimizes the full model outperforms the SECOND that is trained with dropout,
+suggesting that the inconsistency of dropout between the training and inference stages [73] may indeed lead to
+underfitting of the full model. And the fact that Cmp far outperforms FIRST and SECOND indicates that comparative
+loss can automatically strike a balance between ensuring training-inference consistency and preventing overfitting.
+Manuscript submitted to ACM
+
+18
+Zhu and Pang, et al.
+Table 5. QA performance on the development set of HotpotQA distractor with different comparison strategies. 𝑐 is the number of
+ablation steps. x 2 indicates that an ablation method is repeated twice, and 𝐴 + 𝐵 means that 𝐴 is used followed by 𝐵.
+𝑐
+Ablation Order
+EM
+F1
+1
+CmpDrop
+63.1
+77.0
+CmpCrop
+63.1
+76.8
+2
+CmpDrop x 2
+63.4
+77.1
+CmpCrop x 2
+63.0
+76.7
+CmpDrop + CmpCrop
+63.2
+76.8
+CmpCrop + CmpDrop
+63.6
+77.4
+0
+1
+2
+3
+4
+The number of CmpDrop c
+83.4
+83.6
+83.8
+84.0
+84.2
+Average on GLUE
+BERT + Cmp
+BERT
+Fig. 4. Average results on eight GLUE datasets as the number of ablation steps changes.
+5.2
+Effect of Comparison Strategy
+To study the impact of comparison strategies, i.e., how many ablation steps we should use for comparison and which
+ablation method we should choose at each step, we try a variety of comparison strategies on HopotQA with different
+numbers of comparisons and ablation orders. As shown in Table 5, the results are not significantly further improved
+when we repeat CmpDrop/CmpCrop twice, but the results are further improved when we apply CmpCrop first and
+then CmpDrop. This indicates that comparing multiple models ablated by the same method, i.e., encouraging the model
+be either extremely input-efficient or extremely parameter-efficient, seems to have little effect on the performance of
+the full model, but the successive use of two different ablation methods, i.e., encouraging the model be efficient (both
+input-efficient and parameter-efficient), is helpful. However, applying CmpDrop followed by CmpCrop did not perform
+as well as applying CmpDrop only, suggesting that the order of the ablation methods is important and perhaps the
+ablation should be done in the order of the information flow in the model.
+To further confirm the influence of the number of ablation steps 𝑐, we show in Figure 4 the relationship between
+the model’s Average metric over the eight GLUE datasets and the number of ablations. We can find little difference in
+the average performance of the models trained with different numbers of CmpDrop, with the model trained with one
+Manuscript submitted to ACM
+
+Cross-Model Comparative Loss for Enhancing Neuronal Utility in Language Understanding
+19
+Table 6. Evaluation results of baselines with different model sizes and initializations on the SQuAD development set (EM/F1), and
+relative gains of our models trained using comparative loss with CmpDrop over baselines.
+# Parameter
+BERT
+ELECTRA
+Baseline
+Gain (%)
+Baseline
+Gain (%)
+Tiny: 4M
+41.5/54.4
+2.7/2.0
+-
+-
+Small: 14M
+74.9/83.3
+2.4/1.6
+78.4/86.0
+1.4/1.0
+Medium: 42M
+78.6/86.3
+1.0/0.7
+-
+-
+Base: 110M
+81.1/88.4
+1.7/1.1
+86.1/92.3
+0.7/0.7
+Large: 335M
+84.4/91.0
+0.9/0.7
+89.0/95.0
+0.9/0.2
+CmpDrop performing significantly best mainly because its huge advantage on two of the datasets pulls up the average.
+Therefore, if there is no extreme demand for performance, we usually do not need to tune the hyperparameter 𝑐.
+5.3
+Effect of Model Parameters
+To investigate the impact of model parameters, we explore the application of the comparative loss with CmpDrop on
+different-sized versions of BERT and ELECTRA. From Table 6 we can see that the comparative loss with CmpDrop
+achieves a consistent improvement over the baselines based on these backbone models, which indicates that the
+comparative loss can improve model performance by increasing parameter utility without increasing the number of
+parameters. Moreover, except for the one outlier of BERTMedium, we can roughly find that the less the model parameters,
+the greater the relative gain from comparative loss. This is reasonable because the individual hidden neurons in a model
+with lower capacity play a larger role, so the improvement in the utility of hidden neurons can be more reflected in
+the final performance. Whereas for a model of higher capacity, it is easier to fit less training data, i.e., its task-specific
+loss is already low, so comparative loss has less room to play in reducing task-specific loss further. In addition, we
+observe that the boost to BERT from the comparative loss with CmpDrop is generally higher compared to ELECTRA
+with more complicated pretraining, suggesting that the comparative loss helps the model escape from local optima due
+to parameter initialization.
+5.4
+Effect of Input Context
+To review the utility of the input context (i.e., input neurons) to models, we plot in Figure 5 the performance trends of
+the models using different context sizes. First, in both datasets, our models trained with comparative loss consistently
+outperform the baseline models for all context sizes, indicating that our models are able to utilize input neurons more
+efficiently with equal amounts of input context. Second, this shows that our comparative loss can further improve the
+model performance after streamlining the input with context selection. In addition, we notice that our ANCE-PRF +
+CmpCrop in Figure 5(a) improves retrieval performance as expected as the number of feedback documents increases,
+while ANCE-PRF reaches peak performance at 4 feedback documents and then suffers performance degradation,
+implying that our model is more robust and able to mine and exploit relevant information in the added feedback
+documents. In contrast to PRF, for HotpotQA in Figure 5(b), the performance of all RC models decreases as the number
+of paragraphs increases. This is understandable, since only 2 paragraphs in HotpotQA are supporting facts, and the
+remaining 8 mostly serve as a distraction, so the ideal performance curve can just be a horizontal line that does not drop
+when the paragraph number increases. Interestingly, we find that the degradation of Longformer + CmpDrop (2.7%)
+Manuscript submitted to ACM
+
+20
+Zhu and Pang, et al.
+0
+1
+2
+3
+4
+5
+The number of feedback documents k
+31
+32
+33
+34
+35
+MRR@10
+ANCE
+ANCE-PRF
+ANCE-PRF + Cmp
+(a)
+2
+3
+4
+5
+6
+7
+8
+9
+10
+The number of paragraphs in context
+76
+77
+78
+79
+F1
+Longformer
+Longformer + CmpDrop
+Longformer + CmpCrop
+Longformer + CmpCrop + CmpDrop
+(b)
+Fig. 5. Performance curves using different context sizes. (a) PRF models on MARCO Dev, the horizontal dotted line represents the
+base retrieval model. (b) RC models on HotpotQA Dev.
+Table 7. The robustness index of 𝒒(𝑘) with respect to 𝒒(𝑘−1) on MARCO Dev at each PRF depth 𝑘, where 𝒒(𝑘) and 𝒒(𝑘−1) are
+reformulated query vectors by the PRF model, the latter having one less document in the input context than the former.
+𝑘
+1
+2
+3
+4
+5
+ANCE-PRF
+0.51
+0.54
+0.58
+0.58
+0.61
+ANCE-PRF + Cmp (1 Crop)
+0.54
+0.56
+0.63
+0.63
+0.66
+and Longformer + CmpCrop + CmpDrop (3.0%) from the oracle setting (2 gold paragraphs) to the distractor setting
+(10 paragraphs) is lower than that of the baseline Longformer (3.4%). This suggests that comparative loss can help the
+models suppress the noisy information in the added context. Although Longformer + CmpCrop (3.7%) has a larger
+degradation than Longformer, we believe this is because Longformer + CmpCrop needs to be optimized for various
+numbers of paragraphs, unlike other models without CmpCrop that focus on learning for one input form (i.e., always
+ten paragraphs). However, this variety of input forms makes Longformer + CmpCrop perform better than Longformer +
+CmpDrop when the number of paragraphs is small (≤ 5).
+To further quantitatively demonstrate the help of comparative loss in the robustness of the PRF model to context
+size, we report in Table 7 the robustness indexes [18] of ANCE-PRF + CmpCrop and ANCE-PRF at different numbers of
+feedback documents. The robustness index is defined as 𝑁+−𝑁−
+|𝑄 |
+, where |𝑄| is the total number of evaluated queries and
+𝑁+ and 𝑁− are the number of queries that the PRF model improves or downgrades when one more feedback document
+is used. The value of robustness index is in [-1, 1], and the model with higher robustness index is more robust. We can
+see that the PRF model trained using comparative loss with CmpCrop is significantly more robust than the baseline
+model. Besides, from the gaps in their robustness indexes (only 0.03 or 0.02 for 1 or 2 documents, but 0.05 for more
+documents), we can find that the comparative loss is more helpful for long-form inputs.
+5.5
+Loss Visualization
+To figure out the impact of comparative loss on task-specific loss, we plot the curves of task-specific loss for the full
+model (i.e., 𝑙 (0)) in Figure 6. From Figures 6(a) and 6(b) we can see that with the same batch size, the comparative loss can
+Manuscript submitted to ACM
+
+Cross-Model Comparative Loss for Enhancing Neuronal Utility in Language Understanding
+21
+0
+10000
+20000
+30000
+40000
+Training step
+1
+2
+3
+4
+5
+6
+Task-specific loss of full model
+Longformer
+Longformer + CmpCrop
+Longformer + CmpDrop
+Longformer + CmpCrop + CmpDrop
+(a) Answer extraction loss on HopotQA Train
+0
+10000
+20000
+30000
+40000
+Training step
+19.4
+19.6
+19.8
+20.0
+20.2
+20.4
+20.6
+20.8
+Task-specific loss of full model
+Longformer
+Longformer + CmpCrop
+Longformer + CmpDrop
+Longformer + CmpCrop + CmpDrop
+(b) Answer extraction loss on HopotQA Dev
+0
+10000
+20000
+30000
+40000
+50000
+Training step
+3.5
+4.0
+4.5
+5.0
+5.5
+6.0
+Task-specific loss of full model
+uniCOIL-PRF + CmpCrop
+uniCOIL-PRF
+(c) Retrieval loss on MARCO Train
+0
+10000
+20000
+30000
+40000
+50000
+Training step
+3.75
+3.80
+3.85
+3.90
+3.95
+4.00
+4.05
+4.10
+Task-specific loss of full model
+uniCOIL-PRF + CmpCrop
+uniCOIL-PRF
+(d) Retrieval loss on MARCO Dev
+Fig. 6. Task-specific loss curves for the full model.
+help our models fit better compared to the baseline Longformer. Comparing Longformer + CmpDrop and Longformer +
+CmpCrop, we can find that the training loss of the former is significantly smaller, which indicates that the comparative
+loss with CmpDrop helps the model fit the training data better. Whereas the evaluation loss of Longformer + CmpCrop
+rises less in the later stage, which indicates that the comparative loss with CmpCrop can mitigate the overfitting to
+some extent. Since the number of task-specific losses per sample optimized by comparative loss is 1 + 𝑐 times that of
+conventional training, we also plot the task-specific loss curves for PRF models in Figures 6(c) and 6(d), where the batch
+size of our uniCOIL-PRF + CmpCrop is 1/(1 + 𝑐) of the baseline uniCOIL-PRF. In this way, the number of task-specific
+losses optimized in one batch for our model and the baseline is the same, which helps to further clarify the role of the
+comparative loss with CmpCrop. We can see that while the training loss of our model in Figure 6(c) does not drop as
+low as the baseline, its evaluation loss in Figure 6(d) drops to a lower level and significantly mitigates the overfitting.
+5.6
+Training Efficiency
+We present in Table 8 the performance gain and relative change in training FLOPs of BERTbase + Cmp compared to
+BERTbase, as well as the specific number of comparisons (i.e., number of ablation steps 𝑐) chosen for each dataset. We
+find that the actual overhead of training with comparative loss is usually less than 1 + 𝑐 times that of conventional
+Manuscript submitted to ACM
+
+22
+Zhu and Pang, et al.
+Table 8. Specific settings for the number of ablation steps of BERT + Cmp on each GLUE dataset, as well as the performance gain and
+increase in training computation overhead compared to BERT.
+MNLI
+MRPC
+QNLI
+QQP
+RTE
+SST-2
+STS-B
+CoLA
+𝑐
+3
+1
+4
+2
+1
+2
+4
+4
+Performance (%) ↑
++1.3
++3.8
++0.9
++0.5
++4.1
++0.4
++0.6
++1.6
+FLOPs ↑
+x3.5
+x1.6
+x3.5
+x0.9
+x2.1
+x0.7
+x4.8
+x3.9
+training, and even less than that of conventional training (e.g., on QQP). This is because models trained with comparative
+loss tend to converge earlier than baselines. Combined with the insensitivity of comparative loss to the number of
+comparisons found from Figure 4, we believe that setting 𝑐 to 1 or 2 can lead to effective and fast training when data is
+sufficient.
+6
+RELATED WORK
+In this section, we introduce and discuss some work that has different motivations but is technically relevant to us,
+starting with contrastive learning [37] that learns by comparing, followed by recent training methods that also use
+dropout multiple times.
+6.1
+Contrastive Learning
+Contrastive learning has recently achieved significant success in representation learning in computer vision and natural
+language processing. At its core, contrastive learning aims to learn effective representations by pulling semantically
+similar neighbors together and pushing apart non-neighbors [26]. Instead of learning a signal from individual data
+samples one at a time, it learns by comparing different samples [37]. The comparison is performed between positive
+pairs of similar samples and negative pairs of dissimilar samples. The positive pair must ensure that the two samples
+are similar, which can be constructed either by using supervised similarity annotation or by self-supervision. In self-
+supervised contrastive learning, a positive pair can consist of an original sample and its data augmentation. For example,
+SimCLR [12] in computer vision uses a crop, flip, distortion or rotation of an original image as its similar view, and
+SimCSE [25] in natural language processing applies two dropout masks to an input sentence to create two slightly
+different sentence embeddings that are then used as a positive pair of sentence embeddings. To share more computation
+and save cost, negative pairs usually consist of two dissimilar samples within the same training batch. Although both
+learn through comparison, contrastive learning aims at pursuing alignment and uniformity [62] of representations,
+while our comparative loss aims at pursuing orderliness of the task-specific losses of the full model and its ablated
+model. Moreover, as the lexical meaning suggests, contrastive learning only classifies the relationship (i.e., similar or
+dissimilar) between two data samples in a binary manner, whereas our comparative loss compares multiple full/ablated
+models by ranking. However, these two are not in conflict, and our comparative loss can be used over the contrastive
+losses that served as task-specific losses.
+6.2
+Dropout-based Comparison
+Dropout is a family of stochastic techniques used in neural network training or inference that have attracted extensive
+research interest and are widely used in practice. The standard dropout [30] aims to avoid overfitting of the network by
+reducing the co-adaptation of neurons, where the outputs of individual neurons only provide useful information in
+Manuscript submitted to ACM
+
+Cross-Model Comparative Loss for Enhancing Neuronal Utility in Language Understanding
+23
+combination with other neuron outputs. After this, a line of research focused on improving the standard dropout by
+employing other strategies for dropping neurons, such as dropconnect [59] and variational dropout [35].
+A line of research that is relevant to us is the use of dropout multiple times in training. SimCSE [25] forwards the
+model twice with different dropout masks of the same rate and uses a contrastive loss to constrain the distribution of
+model outputs in the representation space. A possible side effect of dropout revealed by the existing literature [45, 73]
+is the non-negligible inconsistency between the training and inference stages of the model, i.e., the submodels are
+optimized during training, but the full model without dropout is used during inference. To address this inconsistency,
+R-Drop [39] forward runs the model multiple times with different dropout masks to obtain multiple predicted probability
+distributions and applies KL-divergence on them to constrain their consistency. Unlike their multiple dropout masks that
+are sampled independently, the multiple dropout rates are increasing and the masks are progressive in our CmpDrop,
+with the subsequent mask obtained by further randomly discarding elements based on the previous one. In addition, we
+impose constraints on the task-specific losses at the end rather than on the representations and probabilities upstream.
+Notably, the full model is also optimized in due time when trained using the comparative loss with CmpDrop, which
+we argue is important to mitigate the inconsistency between training and inference. This is because, while dropout
+avoids co-adaptation of neurons, it also weakens the cooperation between neurons (§5.1 gives some empirical support).
+In particular, in cases where all neurons are involved, the full model trained with dropout has not been taught how to
+make them work together efficiently and thus cannot be fully exploited during testing. Surprisingly, our comparative
+loss with CmpDrop can balance between promoting the cooperation of neurons and preventing their co-adaptation.
+7
+CONCLUSION
+In this paper, we propose cross-model comparative loss, a simple task-agnostic loss function, to improve the utility of
+neurons in NLU models. Comparative loss is essentially a ranking loss based on the comparison principle between
+the full model and its ablated models, with the expectation that the less ablation there is, the smaller the task-specific
+loss. To ensure comparability among multiple ablated models, we progressively ablate the models and provide two
+controlled ablation methods based on dropout and context cropping, applicable to a wide range of tasks and models.
+We show theoretically how comparative loss works, suggesting that it can adaptively assign weights to multiple
+task-specific losses. Extensive experiments and analysis on 14 datasets from 3 distinct NLU tasks demonstrate the
+universal effectiveness of comparative loss. Interestingly, our analysis confirms that comparative loss can indeed assign
+weights more appropriately, and finds that comparative loss is particularly effective for models with few parameters or
+long input.
+In the future, we would like to apply comparative loss in other domains, such as natural language generation
+and computer vision, and explore its applications on other model architectures beyond Transformer. It could also be
+interesting to explore the application of comparative loss on top of self-supervised losses (e.g., contrastive loss) during
+pretraining. For training costs, how to reduce the overhead by reusing more shared computations is a direction worth
+exploring. Further, more advanced ablation methods in training, such as dropconnect [59] rather than standard dropout
+and adversarial rather than stochastic, may deserve future research efforts.
+REFERENCES
+[1] R. Attar and A. S. Fraenkel. 1977. Local Feedback in Full-Text Retrieval Systems. J. ACM 24, 3 (July 1977), 397–417. https://doi.org/10.1145/322017.
+322021
+[2] Brian Bartoldson, Ari Morcos, Adrian Barbu, and Gordon Erlebacher. 2020. The Generalization-Stability Tradeoff In Neural Network Pruning. In
+Advances in Neural Information Processing Systems, Vol. 33. Curran Associates, Inc., 20852–20864. https://proceedings.neurips.cc/paper/2020/hash/
+Manuscript submitted to ACM
+
+24
+Zhu and Pang, et al.
+ef2ee09ea9551de88bc11fd7eeea93b0-Abstract.html
+[3] Iz Beltagy, Matthew E. Peters, and Arman Cohan. 2020. Longformer: The Long-Document Transformer. https://doi.org/10.48550/arXiv.2004.05150
+arXiv:2004.05150
+[4] Luisa Bentivogli, Peter Clark, Ido Dagan, and Danilo Giampiccolo. 2009. The Fifth PASCAL Recognizing Textual Entailment Challenge.. In TAC.
+[5] Davis Blalock, Jose Javier Gonzalez Ortiz, Jonathan Frankle, and John Guttag. 2020. What Is the State of Neural Network Pruning? Proceedings
+of Machine Learning and Systems 2 (March 2020), 129–146. https://proceedings.mlsys.org/paper/2020/hash/d2ddea18f00665ce8623e36bd4e3c7c5-
+Abstract.html
+[6] Sebastian Borgeaud, Arthur Mensch, Jordan Hoffmann, Trevor Cai, Eliza Rutherford, Katie Millican, George Bm Van Den Driessche, Jean-Baptiste
+Lespiau, Bogdan Damoc, Aidan Clark, Diego De Las Casas, Aurelia Guy, Jacob Menick, Roman Ring, Tom Hennigan, Saffron Huang, Loren Maggiore,
+Chris Jones, Albin Cassirer, Andy Brock, Michela Paganini, Geoffrey Irving, Oriol Vinyals, Simon Osindero, Karen Simonyan, Jack Rae, Erich Elsen,
+and Laurent Sifre. 2022. Improving Language Models by Retrieving from Trillions of Tokens. In Proceedings of the 39th International Conference on
+Machine Learning. PMLR, 2206–2240. https://proceedings.mlr.press/v162/borgeaud22a.html
+[7] Tom Brown, Benjamin Mann, Nick Ryder, Melanie Subbiah, Jared D Kaplan, Prafulla Dhariwal, Arvind Neelakantan, Pranav Shyam, Girish
+Sastry, Amanda Askell, Sandhini Agarwal, Ariel Herbert-Voss, Gretchen Krueger, Tom Henighan, Rewon Child, Aditya Ramesh, Daniel Ziegler,
+Jeffrey Wu, Clemens Winter, Chris Hesse, Mark Chen, Eric Sigler, Mateusz Litwin, Scott Gray, Benjamin Chess, Jack Clark, Christopher Berner,
+Sam McCandlish, Alec Radford, Ilya Sutskever, and Dario Amodei. 2020. Language Models Are Few-Shot Learners. In Proceedings of the 34th
+International Conference on Neural Information Processing Systems, Vol. 33. Curran Associates, Inc., Red Hook, NY, USA, 1877–1901.
+https:
+//papers.nips.cc/paper/2020/hash/1457c0d6bfcb4967418bfb8ac142f64a-Abstract.html
+[8] Alon Brutzkus and Amir Globerson. 2019. Why Do Larger Models Generalize Better? A Theoretical Perspective via the XOR Problem. In Proceedings
+of the 36th International Conference on Machine Learning. PMLR, 822–830. https://proceedings.mlr.press/v97/brutzkus19b.html
+[9] Daniel Cer, Mona Diab, Eneko Agirre, Iñigo Lopez-Gazpio, and Lucia Specia. 2017. SemEval-2017 Task 1: Semantic Textual Similarity Multilingual
+and Crosslingual Focused Evaluation. In Proceedings of the 11th International Workshop on Semantic Evaluation (SemEval-2017). Association for
+Computational Linguistics, Vancouver, Canada, 1–14. https://doi.org/10.18653/v1/S17-2001
+[10] Yi Chang and Hongbo Deng. 2020. Query understanding for search engines. Springer.
+[11] Danqi Chen. 2018. Neural Reading Comprehension and Beyond. Stanford University.
+[12] Ting Chen, Simon Kornblith, Mohammad Norouzi, and Geoffrey Hinton. 2020. A Simple Framework for Contrastive Learning of Visual Representa-
+tions. In Proceedings of the 37th International Conference on Machine Learning. PMLR, 1597–1607. https://proceedings.mlr.press/v119/chen20j.html
+[13] Zihan Chen, Hongbo Zhang, Xiaoji Zhang, and Leqi Zhao. 2018. Quora question pairs. https://www.kaggle.com/c/quora-question-pairs
+[14] Christopher Clark and Matt Gardner. 2018. Simple and Effective Multi-Paragraph Reading Comprehension. In Proceedings of the 56th Annual Meeting
+of the Association for Computational Linguistics (Volume 1: Long Papers). Association for Computational Linguistics, Melbourne, Australia, 845–855.
+https://doi.org/10.18653/v1/P18-1078
+[15] Kevin Clark, Minh-Thang Luong, Quoc V. Le, and Christopher D. Manning. 2020. ELECTRA: Pre-training Text Encoders as Discriminators Rather
+Than Generators. In International Conference on Learning Representations. https://openreview.net/forum?id=r1xMH1BtvB
+[16] Stéphane Clinchant and Eric Gaussier. 2013. A Theoretical Analysis of Pseudo-Relevance Feedback Models. In Proceedings of the 2013 Conference on the
+Theory of Information Retrieval (ICTIR ’13). Association for Computing Machinery, New York, NY, USA, 6–13. https://doi.org/10.1145/2499178.2499179
+[17] Paul R. Cohen and Adele E. Howe. 1988. How Evaluation Guides AI Research: The Message Still Counts More than the Medium. AI Magazine 9, 4
+(Dec. 1988), 35–35. https://doi.org/10.1609/aimag.v9i4.952
+[18] Kevyn Collins-Thompson. 2009. Reducing the Risk of Query Expansion via Robust Constrained Optimization. In Proceedings of the 18th ACM
+Conference on Information and Knowledge Management (CIKM ’09). Association for Computing Machinery, New York, NY, USA, 837–846. https:
+//doi.org/10.1145/1645953.1646059
+[19] Nick Craswell, Bhaskar Mitra, Emine Yilmaz, and Daniel Campos. 2021. Overview of the TREC 2020 Deep Learning Track. arXiv:2102.07662 [cs]
+(Feb. 2021). arXiv:2102.07662 http://arxiv.org/abs/2102.07662
+[20] Nick Craswell, Bhaskar Mitra, Emine Yilmaz, Daniel Campos, and Ellen M. Voorhees. 2020. Overview of the TREC 2019 Deep Learning Track.
+arXiv:2003.07820 [cs] (March 2020). arXiv:2003.07820 http://arxiv.org/abs/2003.07820
+[21] Jacob Devlin, Ming-Wei Chang, Kenton Lee, and Kristina Toutanova. 2019. BERT: Pre-training of Deep Bidirectional Transformers for Language
+Understanding. In Proceedings of the 2019 Conference of the North American Chapter of the Association for Computational Linguistics: Human
+Language Technologies, Volume 1 (Long and Short Papers). Association for Computational Linguistics, Minneapolis, Minnesota, 4171–4186. https:
+//doi.org/10.18653/v1/N19-1423
+[22] William B. Dolan and Chris Brockett. 2005. Automatically Constructing a Corpus of Sentential Paraphrases. In Proceedings of the Third International
+Workshop on Paraphrasing (IWP2005). https://aclanthology.org/I05-5002
+[23] Dheeru Dua, Cicero Nogueira dos Santos, Patrick Ng, Ben Athiwaratkun, Bing Xiang, Matt Gardner, and Sameer Singh. 2021. Generative Context Pair
+Selection for Multi-hop Question Answering. In Proceedings of the 2021 Conference on Empirical Methods in Natural Language Processing. Association
+for Computational Linguistics, Online and Punta Cana, Dominican Republic, 7009–7015. https://doi.org/10.18653/v1/2021.emnlp-main.561
+[24] Stella Frank, Emanuele Bugliarello, and Desmond Elliott. 2021. Vision-and-Language or Vision-for-Language? On Cross-Modal Influence in
+Multimodal Transformers. In Proceedings of the 2021 Conference on Empirical Methods in Natural Language Processing. Association for Computational
+Linguistics, Online and Punta Cana, Dominican Republic, 9847–9857. https://doi.org/10.18653/v1/2021.emnlp-main.775
+Manuscript submitted to ACM
+
+Cross-Model Comparative Loss for Enhancing Neuronal Utility in Language Understanding
+25
+[25] Tianyu Gao, Xingcheng Yao, and Danqi Chen. 2021. SimCSE: Simple Contrastive Learning of Sentence Embeddings. In Proceedings of the 2021
+Conference on Empirical Methods in Natural Language Processing. Association for Computational Linguistics, Online and Punta Cana, Dominican
+Republic, 6894–6910. https://doi.org/10.18653/v1/2021.emnlp-main.552
+[26] Raia Hadsell, Sumit Chopra, and Yann LeCun. 2006. Dimensionality reduction by learning an invariant mapping. In 2006 IEEE Computer Society
+Conference on Computer Vision and Pattern Recognition (CVPR’06), Vol. 2. IEEE, 1735–1742.
+[27] Song Han, Jeff Pool, John Tran, and William Dally. 2015. Learning Both Weights and Connections for Efficient Neural Network. In Advances in
+Neural Information Processing Systems, Vol. 28. Curran Associates, Inc. https://papers.nips.cc/paper/2015/hash/ae0eb3eed39d2bcef4622b2499a05fe6-
+Abstract.html
+[28] Dan Hendrycks and Kevin Gimpel. 2016. Gaussian error linear units (gelus). arXiv preprint arXiv:1606.08415 (2016).
+[29] Ralf Herbrich, Thore Graepel, and Klaus Obermayer. 2000. Large Margin Rank Boundaries for Ordinal Regression. Advances in large margin
+classifiers 88, 2 (2000), 115–132.
+[30] Geoffrey E. Hinton, Nitish Srivastava, Alex Krizhevsky, Ilya Sutskever, and Ruslan R. Salakhutdinov. 2012. Improving Neural Networks by Preventing
+Co-Adaptation of Feature Detectors. https://doi.org/10.48550/arXiv.1207.0580 arXiv:1207.0580
+[31] L. Hirschman and R. Gaizauskas. 2001. Natural Language Question Answering: The View from Here. Natural Language Engineering 7, 4 (Dec. 2001),
+275–300. https://doi.org/10.1017/S1351324901002807
+[32] Gautier Izacard, Patrick Lewis, Maria Lomeli, Lucas Hosseini, Fabio Petroni, Timo Schick, Jane Dwivedi-Yu, Armand Joulin, Sebastian Riedel, and
+Edouard Grave. 2022. Few-Shot Learning with Retrieval Augmented Language Models. https://doi.org/10.48550/arXiv.2208.03299 arXiv:2208.03299
+[33] Jared Kaplan, Sam McCandlish, Tom Henighan, Tom B. Brown, Benjamin Chess, Rewon Child, Scott Gray, Alec Radford, Jeffrey Wu, and Dario
+Amodei. 2020. Scaling Laws for Neural Language Models. https://doi.org/10.48550/arXiv.2001.08361 arXiv:2001.08361
+[34] Vladimir Karpukhin, Barlas Oguz, Sewon Min, Patrick Lewis, Ledell Wu, Sergey Edunov, Danqi Chen, and Wen-tau Yih. 2020. Dense Passage
+Retrieval for Open-Domain Question Answering. In Proceedings of the 2020 Conference on Empirical Methods in Natural Language Processing (EMNLP).
+Association for Computational Linguistics, Online, 6769–6781. https://doi.org/10.18653/v1/2020.emnlp-main.550
+[35] Durk P Kingma, Tim Salimans, and Max Welling. 2015. Variational Dropout and the Local Reparameterization Trick. In Advances in Neural Information
+Processing Systems, Vol. 28. Curran Associates, Inc. https://papers.nips.cc/paper/2015/hash/bc7316929fe1545bf0b98d114ee3ecb8-Abstract.html
+[36] Alex Labach, Hojjat Salehinejad, and Shahrokh Valaee. 2019. Survey of Dropout Methods for Deep Neural Networks. https://doi.org/10.48550/arXiv.
+1904.13310 arXiv:1904.13310
+[37] Phuc H. Le-Khac, Graham Healy, and Alan F. Smeaton. 2020. Contrastive Representation Learning: A Framework and Review. IEEE Access 8 (2020),
+193907–193934. https://doi.org/10.1109/ACCESS.2020.3031549
+[38] Yann LeCun, John Denker, and Sara Solla. 1989. Optimal Brain Damage. In Advances in Neural Information Processing Systems, Vol. 2. Morgan-
+Kaufmann. https://papers.nips.cc/paper/1989/hash/6c9882bbac1c7093bd25041881277658-Abstract.html
+[39] xiaobo liang, Lijun Wu, Juntao Li, Yue Wang, Qi Meng, Tao Qin, Wei Chen, Min Zhang, and Tie-Yan Liu. 2021. R-Drop: Regularized Dropout for
+Neural Networks. In Advances in Neural Information Processing Systems, Vol. 34. Curran Associates, Inc., 10890–10905. https://proceedings.neurips.
+cc/paper/2021/hash/5a66b9200f29ac3fa0ae244cc2a51b39-Abstract.html
+[40] Jimmy Lin. 2002. The Web as a Resource for Question Answering: Perspectives and Challenges. In Proceedings of the Third International Conference
+on Language Resources and Evaluation (LREC’02). European Language Resources Association (ELRA), Las Palmas, Canary Islands - Spain. http:
+//www.lrec-conf.org/proceedings/lrec2002/pdf/85.pdf
+[41] Jimmy Lin and Xueguang Ma. 2021. A Few Brief Notes on DeepImpact, COIL, and a Conceptual Framework for Information Retrieval Techniques.
+arXiv:2106.14807 [cs] (June 2021). arXiv:2106.14807 http://arxiv.org/abs/2106.14807
+[42] Shanshan Liu, Xin Zhang, Sheng Zhang, Hui Wang, and Weiming Zhang. 2019. Neural Machine Reading Comprehension: Methods and Trends.
+Applied Sciences 9, 18 (Jan. 2019), 3698. https://doi.org/10.3390/app9183698
+[43] Yinhan Liu, Myle Ott, Naman Goyal, Jingfei Du, Mandar Joshi, Danqi Chen, Omer Levy, Mike Lewis, Luke Zettlemoyer, and Veselin Stoyanov. 2019.
+RoBERTa: A Robustly Optimized BERT Pretraining Approach. arXiv:1907.11692 [cs] (July 2019). arXiv:1907.11692 http://arxiv.org/abs/1907.11692
+[44] Zhuang Liu, Jianguo Li, Zhiqiang Shen, Gao Huang, Shoumeng Yan, and Changshui Zhang. 2017. Learning Efficient Convolutional Networks
+through Network Slimming. In 2017 IEEE International Conference on Computer Vision (ICCV). 2755–2763. https://doi.org/10.1109/ICCV.2017.298
+[45] Xuezhe Ma, Yingkai Gao, Zhiting Hu, Yaoliang Yu, Yuntian Deng, and Eduard Hovy. 2016. Dropout with expectation-linear regularization. arXiv
+preprint arXiv:1609.08017 (2016).
+[46] Iain Mackie, Jeffrey Dalton, and Andrew Yates. 2021. How Deep Is Your Learning: The DL-HARD Annotated Deep Learning Dataset. In Proceedings
+of the 44th International ACM SIGIR Conference on Research and Development in Information Retrieval. Association for Computing Machinery, New
+York, NY, USA, 2335–2341. https://doi.org/10.1145/3404835.3463262
+[47] Richard Meyes, Melanie Lu, Constantin Waubert de Puiseau, and Tobias Meisen. 2019. Ablation Studies in Artificial Neural Networks.
+https:
+//doi.org/10.48550/arXiv.1901.08644 arXiv:1901.08644
+[48] Sewon Min, Victor Zhong, Richard Socher, and Caiming Xiong. 2018. Efficient and Robust Question Answering from Minimal Context over
+Documents. In Proceedings of the 56th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers). Association for
+Computational Linguistics, Melbourne, Australia, 1725–1735. https://doi.org/10.18653/v1/P18-1160
+[49] Mandar Mitra, Amit Singhal, and Chris Buckley. 1998. Improving Automatic Query Expansion. In Proceedings of the 21st Annual International ACM
+SIGIR Conference on Research and Development in Information Retrieval (SIGIR ’98). Association for Computing Machinery, New York, NY, USA,
+Manuscript submitted to ACM
+
+26
+Zhu and Pang, et al.
+206–214. https://doi.org/10.1145/290941.290995
+[50] Tri Nguyen, Mir Rosenberg, Xia Song, Jianfeng Gao, Saurabh Tiwary, Rangan Majumder, and Li Deng. 2016. MS MARCO: A Human Generated
+Machine Reading Comprehension Dataset. In CoCo@ NIPS.
+[51] Colin Raffel, Noam Shazeer, Adam Roberts, Katherine Lee, Sharan Narang, Michael Matena, Yanqi Zhou, Wei Li, and Peter J. Liu. 2020. Exploring
+the Limits of Transfer Learning with a Unified Text-to-Text Transformer. Journal of Machine Learning Research 21, 140 (2020), 1–67.
+http:
+//jmlr.org/papers/v21/20-074.html
+[52] Pranav Rajpurkar, Robin Jia, and Percy Liang. 2018. Know What You Don’t Know: Unanswerable Questions for SQuAD. In Proceedings of the 56th
+Annual Meeting of the Association for Computational Linguistics (Volume 2: Short Papers). Association for Computational Linguistics, Melbourne,
+Australia, 784–789. https://doi.org/10.18653/v1/P18-2124
+[53] Pranav Rajpurkar, Jian Zhang, Konstantin Lopyrev, and Percy Liang. 2016. SQuAD: 100,000+ Questions for Machine Comprehension of Text. In
+Proceedings of the 2016 Conference on Empirical Methods in Natural Language Processing. Association for Computational Linguistics, Austin, Texas,
+2383–2392. https://doi.org/10.18653/v1/D16-1264
+[54] Pedro Rodriguez and Jordan Boyd-Graber. 2021. Evaluation Paradigms in Question Answering. In Proceedings of the 2021 Conference on Empirical
+Methods in Natural Language Processing. Association for Computational Linguistics, Online and Punta Cana, Dominican Republic, 9630–9642.
+https://doi.org/10.18653/v1/2021.emnlp-main.758
+[55] Richard Socher, Alex Perelygin, Jean Wu, Jason Chuang, Christopher D Manning, Andrew Y Ng, and Christopher Potts. 2013. Recursive deep models
+for semantic compositionality over a sentiment treebank. In Proceedings of the 2013 conference on empirical methods in natural language processing.
+1631–1642.
+[56] Ming Tu, Kevin Huang, Guangtao Wang, Jing Huang, Xiaodong He, and Bowen Zhou. 2020. Select, Answer and Explain: Interpretable Multi-
+Hop Reading Comprehension over Multiple Documents. In Proceedings of the AAAI Conference on Artificial Intelligence, Vol. 34. 9073–9080.
+https://doi.org/10.1609/aaai.v34i05.6441
+[57] Vladimir Vapnik. 1991. Principles of risk minimization for learning theory. Advances in neural information processing systems 4 (1991).
+[58] Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones, Aidan N Gomez, Łukasz Kaiser, and Illia Polosukhin. 2017. Attention Is
+All You Need. In Advances in Neural Information Processing Systems, Vol. 30. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2017/
+hash/3f5ee243547dee91fbd053c1c4a845aa-Abstract.html
+[59] Li Wan, Matthew Zeiler, Sixin Zhang, Yann Le Cun, and Rob Fergus. 2013. Regularization of Neural Networks Using DropConnect. In Proceedings of
+the 30th International Conference on Machine Learning. PMLR, 1058–1066. https://proceedings.mlr.press/v28/wan13.html
+[60] Alex Wang, Amanpreet Singh, Julian Michael, Felix Hill, Omer Levy, and Samuel R. Bowman. 2019. GLUE: A Multi-Task Benchmark and Analysis
+Platform for Natural Language Understanding. In International Conference on Learning Representations. https://openreview.net/forum?id=rJ4km2R5t7
+[61] Shuohang Wang, Yichong Xu, Yuwei Fang, Yang Liu, Siqi Sun, Ruochen Xu, Chenguang Zhu, and Michael Zeng. 2022. Training Data Is More
+Valuable than You Think: A Simple and Effective Method by Retrieving from Training Data. In Proceedings of the 60th Annual Meeting of the
+Association for Computational Linguistics (Volume 1: Long Papers). Association for Computational Linguistics, Dublin, Ireland, 3170–3179. https:
+//doi.org/10.18653/v1/2022.acl-long.226
+[62] Tongzhou Wang and Phillip Isola. 2020. Understanding Contrastive Representation Learning through Alignment and Uniformity on the Hypersphere.
+In Proceedings of the 37th International Conference on Machine Learning. PMLR, 9929–9939. https://proceedings.mlr.press/v119/wang20k.html
+[63] Alex Warstadt, Amanpreet Singh, and Samuel R Bowman. 2019. Neural network acceptability judgments. Transactions of the Association for
+Computational Linguistics 7 (2019), 625–641.
+[64] Adina Williams, Nikita Nangia, and Samuel Bowman. 2018. A Broad-Coverage Challenge Corpus for Sentence Understanding through Inference. In
+Proceedings of the 2018 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies,
+Volume 1 (Long Papers). Association for Computational Linguistics, New Orleans, Louisiana, 1112–1122. https://doi.org/10.18653/v1/N18-1101
+[65] Thomas Wolf, Lysandre Debut, Victor Sanh, Julien Chaumond, Clement Delangue, Anthony Moi, Pierric Cistac, Tim Rault, Remi Louf, Morgan
+Funtowicz, Joe Davison, Sam Shleifer, Patrick von Platen, Clara Ma, Yacine Jernite, Julien Plu, Canwen Xu, Teven Le Scao, Sylvain Gugger, Mariama
+Drame, Quentin Lhoest, and Alexander Rush. 2020. Transformers: State-of-the-Art Natural Language Processing. In Proceedings of the 2020
+Conference on Empirical Methods in Natural Language Processing: System Demonstrations. Association for Computational Linguistics, Online, 38–45.
+https://doi.org/10.18653/v1/2020.emnlp-demos.6
+[66] Lee Xiong, Chenyan Xiong, Ye Li, Kwok-Fung Tang, Jialin Liu, Paul N. Bennett, Junaid Ahmed, and Arnold Overwijk. 2020. Approximate
+Nearest Neighbor Negative Contrastive Learning for Dense Text Retrieval. In International Conference on Learning Representations.
+https:
+//openreview.net/forum?id=zeFrfgyZln
+[67] Zhilin Yang, Peng Qi, Saizheng Zhang, Yoshua Bengio, William Cohen, Ruslan Salakhutdinov, and Christopher D. Manning. 2018. HotpotQA: A
+Dataset for Diverse, Explainable Multi-hop Question Answering. In Proceedings of the 2018 Conference on Empirical Methods in Natural Language
+Processing. Association for Computational Linguistics, 2369–2380. https://doi.org/10.18653/v1/D18-1259
+[68] HongChien Yu, Chenyan Xiong, and Jamie Callan. 2021. Improving Query Representations for Dense Retrieval with Pseudo Relevance Feedback. In
+Proceedings of the 30th ACM International Conference on Information & Knowledge Management (CIKM ’21). Association for Computing Machinery,
+New York, NY, USA, 3592–3596. https://doi.org/10.1145/3459637.3482124
+[69] Zhi Zheng, Kai Hui, Ben He, Xianpei Han, Le Sun, and Andrew Yates. 2020. BERT-QE: Contextualized Query Expansion for Document Re-
+ranking. In Findings of the Association for Computational Linguistics: EMNLP 2020. Association for Computational Linguistics, Online, 4718–4728.
+Manuscript submitted to ACM
+
+Cross-Model Comparative Loss for Enhancing Neuronal Utility in Language Understanding
+27
+https://doi.org/10.18653/v1/2020.findings-emnlp.424
+[70] Ruiqi Zhong, Dhruba Ghosh, Dan Klein, and Jacob Steinhardt. 2021. Are Larger Pretrained Language Models Uniformly Better? Comparing
+Performance at the Instance Level. In Findings of the Association for Computational Linguistics: ACL-IJCNLP 2021. Association for Computational
+Linguistics, Online, 3813–3827. https://doi.org/10.18653/v1/2021.findings-acl.334
+[71] Yunchang Zhu, Liang Pang, Yanyan Lan, Huawei Shen, and Xueqi Cheng. 2022. LoL: A Comparative Regularization Loss over Query Reformulation
+Losses for Pseudo-Relevance Feedback. In Proceedings of the 45th International ACM SIGIR Conference on Research and Development in Information
+Retrieval (SIGIR ’22). Association for Computing Machinery, New York, NY, USA, 825–836. https://doi.org/10.1145/3477495.3532017
+[72] Liron Zighelnic and Oren Kurland. 2008. Query-Drift Prevention for Robust Query Expansion. In Proceedings of the 31st Annual International ACM
+SIGIR Conference on Research and Development in Information Retrieval (SIGIR ’08). Association for Computing Machinery, New York, NY, USA,
+825–826. https://doi.org/10.1145/1390334.1390524
+[73] Konrad Zolna, Devansh Arpit, Dendi Suhubdy, and Yoshua Bengio. 2017. Fraternal dropout. arXiv preprint arXiv:1711.00066 (2017).
+Manuscript submitted to ACM
+
diff --git a/9NE2T4oBgHgl3EQfQAZl/content/tmp_files/load_file.txt b/9NE2T4oBgHgl3EQfQAZl/content/tmp_files/load_file.txt
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+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf,len=1526
+page_content='Cross-Model Comparative Loss for Enhancing Neuronal Utility in Language  Understanding  YUNCHANG ZHU, Data Intelligence System Research Center, Institute of Computing Technology, CAS;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' University  of Chinese Academy of Sciences, China  LIANG PANG∗, Data Intelligence System Research Center, Institute of Computing Technology, CAS, China  KANGXI WU, Data Intelligence System Research Center, Institute of Computing Technology, CAS;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' University of  Chinese Academy of Sciences, China  YANYAN LAN, Institute for AI Industry Research, Tsinghua University, China  HUAWEI SHEN, Data Intelligence System Research Center, Institute of Computing Technology, CAS;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' University of  Chinese Academy of Sciences, China  XUEQI CHENG, Key Lab of Network Data Science and Technology, Institute of Computing Technology, CAS;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  University of Chinese Academy of Sciences, China  Current natural language understanding (NLU) models have been continuously scaling up, both in terms of model size and input  context, introducing more hidden and input neurons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' While this generally improves performance on average, the extra neurons do  not yield a consistent improvement for all instances.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' This is because some hidden neurons are redundant, and the noise mixed in  input neurons tends to distract the model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' Previous work mainly focuses on extrinsically reducing low-utility neurons by additional  post- or pre-processing, such as network pruning and context selection, to avoid this problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' Beyond that, can we make the model  reduce redundant parameters and suppress input noise by intrinsically enhancing the utility of each neuron?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' If a model can efficiently  utilize neurons, no matter which neurons are ablated (disabled), the ablated submodel should perform no better than the original full  model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' Based on such a comparison principle between models, we propose a cross-model comparative loss for a broad range of tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  Comparative loss is essentially a ranking loss on top of the task-specific losses of the full and ablated models, with the expectation that  This paper is an extension of the SIGIR 2022 conference paper [71].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' The earlier conference paper is limited to solving the query drift problem in  pseudo-relevance feedback by comparing the retrieval loss using different size feedback sets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' However, the comparison principle and comparative loss  are actually general and task-agnostic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' Moreover, in addition to comparing the input of the model, we can also compare the parameters of the model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  Thus,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' in this work,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' we (1) provide a more general and complete formulation of the comparison principle and comparative loss,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' (2) directly use a unified  comparative loss as the final loss being optimized,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' eliminating the need to set a weighting coefficient between the comparative regularization term  and the task-specific losses,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' (3) improve the previous comparison method that compares inputs with different context sizes,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' and propose an alternative  dropout-based comparison method to improve the utility of the parameters to the model,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' and (4) apply the comparative loss to more tasks and models  and empirically demonstrate its universal effectiveness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  ∗Corresponding author  Authors’ addresses: Yunchang Zhu, Data Intelligence System Research Center, Institute of Computing Technology, CAS;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' University of Chinese Academy  of Sciences, Beijing, China, zhuyunchang17s@ict.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='ac.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='com;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' Liang Pang, Data Intelligence System Research Center, Institute of Computing Technology,  CAS, Beijing, China, pangliang@ict.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='ac.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='cn;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' Kangxi Wu, Data Intelligence System Research Center, Institute of Computing Technology, CAS;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' University of  Chinese Academy of Sciences, Beijing, China, wukangxi22s@ict.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='ac.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='cn;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' Yanyan Lan, Institute for AI Industry Research, Tsinghua University, Beijing,  China, lanyanyan@tsinghua.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='edu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='cn;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' Huawei Shen, Data Intelligence System Research Center, Institute of Computing Technology, CAS;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' University of  Chinese Academy of Sciences, Beijing, China, shenhuawei@ict.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='ac.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='cn;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' Xueqi Cheng, Key Lab of Network Data Science and Technology, Institute of  Computing Technology, CAS;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' University of Chinese Academy of Sciences, Beijing, China, cxq@ict.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='ac.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='cn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not  made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' Copyrights for components  of this work owned by others than ACM must be honored.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' Abstracting with credit is permitted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' To copy otherwise, or republish, to post on servers or to  redistribute to lists, requires prior specific permission and/or a fee.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' Request permissions from permissions@acm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='org.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  © 2018 Association for Computing Machinery.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  Manuscript submitted to ACM  Manuscript submitted to ACM  1  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='03765v1  [cs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='CL]  10 Jan 2023  2  Zhu and Pang, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  the task-specific loss of the full model is minimal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' We demonstrate the universal effectiveness of comparative loss through extensive  experiments on 14 datasets from 3 distinct NLU tasks based on 4 widely used pretrained language models, and find it particularly  superior for models with few parameters or long input.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  CCS Concepts: • Information systems → Information retrieval query processing;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' Retrieval models and ranking;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' Question  answering;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' Clustering and classification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  Additional Key Words and Phrases: natural language understanding, question answering, pseudo-relevance feedback, loss function  ACM Reference Format:  Yunchang Zhu, Liang Pang, Kangxi Wu, Yanyan Lan, Huawei Shen, and Xueqi Cheng.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' Cross-Model Comparative Loss for  Enhancing Neuronal Utility in Language Understanding.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' ACM Trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' Inf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' Syst.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' 37, 4, Article 111 (August 2018), 27 pages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' https:  //doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='org/XXXXXXX.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='XXXXXXX  1  INTRODUCTION  Natural language understanding (NLU) has been pushed a remarkable step forward by deep neural models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' To further  enhance the performance of deep models, enlarging model size [7, 8, 33, 51] and input context [6, 32, 61] are two of the  most conventional and effective ways, where the former introduces more hidden neurons and the latter brings more  input neurons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' Although neural models with more hidden or input neurons have higher accuracy on average, large-scale  models do not always beat small models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' For example, on one hand, many network pruning methods have shown that  compressed models with significantly reduced parameters (neuron connections) can maintain accuracy [27, 38, 44]  and even improve generalization [2], [47] find that ablation of neurons can consistently improve performance in  some specific classes, and [70] empirically demonstrate that larger language models indeed perform worse on a non-  negligible fraction of instances.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' These phenomena indicate that some hidden neurons in the currently trained model  are dispensable or even obstructive.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' On the other hand, much of the work on question answering [14, 67] and query  understanding [18, 49, 72] has noted that feeding more contextual information is more likely to distract the model  and hurt performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' This is not surprising, as more input neurons not only mean more relevant features but are  also likely to introduce more noise that interferes with the model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' Similar to network pruning that cuts out inefficient  parameters through post-processing, many context selection methods [23, 48, 56, 69] trim off noisy segments from the  input context by pre-processing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' In essence, both network pruning and context selection reduce inefficient hidden or  input neurons through additional processing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' However, apart from extrinsically reducing inefficient neurons, can we  intrinsically improve the utility of neurons during model training?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  Imagine an ideal efficient1 neural network in which all its neurons should be able to cooperate efficiently to maximize  the utility of each neuron.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' If a fraction of the input or hidden neurons in this network are ablated2 (disabling partial input  context or model parameters), the ablated submodel is not supposed to perform better, even if the ablated neurons are  noisy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' This is because an ideally efficient model should have already suppressed these noises.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' Following this intuition, we  can roughly find a comparison principle between the original full model and its ablated model: the fewer neurons  are ablated in the model, the better the model should perform.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' During training, we can use task-specific losses  as a proxy for performance, with lower task-specific losses implying better performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' For example, the task-specific  loss of the ideal efficient full model (a) in Figure 1 is supposed to be minimal, and if the ablated model (b) is also ideally  efficient with respect to its restricted parameter space, the task-specific loss of the ablated model (d) is supposed to be  greater than that of (b) because (d) ablates one more input neuron than (b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  1In this work, “efficient” refers specifically to the high utility of neurons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  2The output value of the neuron is set to 0, which is equivalent to all the connection weights to and from this neuron being set to 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  Manuscript submitted to ACM  Cross-Model Comparative Loss for Enhancing Neuronal Utility in Language Understanding  3  (a)  (b)  (c)  (d)  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' An illustration of a full neural model (a) and its ablated models (b, c, and d), where a hidden neuron is ablated in (b), an input  neuron is ablated in (c), and (d) additionally ablate another input neuron based on (b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' According to the comparison principle, if the  full model (a) is an ideal efficient model, the comparative relation between the task-specific losses obtained by these models should  be (a) ≤ (b), (c), (d).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' If the ablated model (b) is also ideally efficient in its parameter space, then their comparative relation can be  further written as (a) ≤ (b) ≤ (d).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' Note that (b, c) and (c, d) are two non-comparable model pairs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' This is because the ablated model (c)  is not a submodel of (b) and (d), and vice versa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  Noting the gap between the ideal efficient model and reality [48, 70], we aim to ensure this necessity (comparison  principle) during the training to improve the model’s utilization of neurons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' Based on the natural comparison principle  between models, we propose a cross-model comparative loss to train models without additional manual supervision.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' In  general, the comparative loss is a ranking loss on top of multiple task-specific losses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' First, these task-specific losses  are derived from the full neural model and several comparable ablated models whose neurons are ablated to varying  degrees.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' Next, the ranking loss is a pairwise hinge loss that penalizes models that have fewer ablated neurons but larger  task-specific losses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' Concretely, if a model with fewer ablated neurons acquires a larger task-specific loss than another  model with more ablated neurons, then the difference between the task-specific losses of the pair will be taken into  account in the final comparative loss;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' otherwise the pair complies with the comparison principle and does not incur any  training loss.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' In this way, the comparative loss can drive the order of task-specific losses to be consistent with the order  of the ablation degrees.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' Through theoretical derivation, we also show that comparative loss can be viewed as a dynamic  weighting of multiple task-specific losses, enabling adaptive assignment of weights depending on the performance of  the full/ablated models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  The comparability among multiple ablated models is a fundamental prerequisite for comparative loss.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' As a coun-  terexample, although the ablated model (c) in Figure 1 ablates less neurons than (d), they are not comparable and so no  comparative loss can be applied.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' To make the ablated models comparable with each other, we progressively ablate the  models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' The first ablated model is obtained by performing one ablation on the basis of the full model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' If more ablated  models are needed, in each subsequent ablation step we construct a new ablated model by performing a further ablation  on top of the ablated model from the previous step, which makes the newly ablated model certainly a comparable  submodel of the previous ones.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' We provide two alternative controlled ablation methods for each ablation step, called  CmpDrop and CmpCrop.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' CmpDrop ablates hidden neurons by the dropout [30] technique, which is theoretically  applicable to all dropout-compatible models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' While CmpCrop ablates input neurons by cropping extraneous context  segments and is theoretically applicable to all tasks that contain extraneous content in the input context.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  We apply comparative loss with CmpDrop or/and CmpCrop on 14 datasets from 3 NLU tasks (text classification,  question answering and query understanding) with distinct prediction types (classification, extraction and ranking) on  top of 4 widely used pretrained language models [3, 15, 21, 43].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' The empirical results demonstrate the effectiveness of  comparative loss over state-of-the-art baselines, as well as the enhanced utility of parameters and context.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' Our analysis  Manuscript submitted to ACM  4  Zhu and Pang, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  also confirms that comparative losses can indeed more appropriately weight multiple task-specific losses, as indicated  by our derivation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' By exploring different comparison strategies, we observe that comparing the models ablated by  first CmpCrop and then CmpDrop can bring the greatest improvement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' Interestingly, we find that comparative loss  is particularly effective for models with few parameters or long inputs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' This may imply that comparative loss can  help models with lower capacity to fit the more or longer training samples better, while models with higher capacity  are inherently prone to fit less data, so comparative loss is less helpful.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' Moreover, we discover that different ablation  methods have different effects on training, with CmpDrop helping task-specific loss to decrease to lower levels faster  and CmpCrop alleviating overfitting to some extent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  The main contributions can be summarized as follows:  We propose comparative loss, a cross-model loss function based on the comparison principle between the full  model and its ablated models, to improve the neuronal utility without additional human supervision.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  We progressively ablate the models to make multiple ablated models comparable and present two controlled  ablation methods based on dropout and context cropping, applicable to a wide range of tasks and models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  We theoretically show how comparative loss works and empirically demonstrate its effectiveness through  experiments on 3 distinct natural language understanding tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' We release the code and processed data at  https://github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='com/zycdev/CmpLoss.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  2  PRELIMINARIES  Before introducing our cross-model comparative loss, we review some of the concepts and notations needed afterward.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  We first introduce typical training methods for the model, followed by formalizations of network pruning and context  selection methods that can further improve the model performance by removing inefficient inputs or hidden neurons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  Finally, we elaborate on the concept of ablation, which recurs throughout the paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='1  Conventional Training  Given a training dataset D for a specified task and a neural network 𝑓 parameterized by 𝜽 ∈ R|𝜽 |, the training objective  for each sample (𝑥,𝑦) ∈ D is to minimize empirical risk  Lemp(𝑥,𝑦, 𝜽) = 𝐿(𝑦, 𝑓 (𝑥;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='𝜽)),  (1)  where 𝑥 is the input context, 𝑦 in output space Y is the label, and 𝐿 : Y × Y → R≥0 is the task-specific loss function,  R≥0 denoting the set of non-negative real numbers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' In NLU tasks, 𝑥 is typically a sequence of words, while 𝑦 can be a  single category label for classification [60], or a pair of start and end boundaries for extraction [53, 67], or a sequence of  relevance levels for ranking [50].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='2  Network Pruning  After training a neural model 𝑓 (𝑥;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='𝜽), to reduce memory and computation requirements at test time, network pruning [5]  entails producing a smaller model 𝑓 (𝑥;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' 𝒎 ⊙ 𝜽 ′) with similar accuracy through post-hoc processing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' Here 𝒎 ∈ {0, 1}|𝜃 |  is a binary mask that fixes certain pruned parameters to 0 through elementwise product ⊙, and the parameter vector 𝜽 ′  may be different from 𝜽 because 𝒎 ⊙ 𝜽 ′ is usually retrained from 𝒎 ⊙ 𝜽 to fit the pruned network structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  Although pruning is often viewed as a way to compress models, it has also been motivated by the desire to prevent  overfitting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' Pruning systematically removes redundant parameters and neurons that do not significantly contribute  Manuscript submitted to ACM  Cross-Model Comparative Loss for Enhancing Neuronal Utility in Language Understanding  5  to performance and thus have much less prediction variance, which makes us reminiscent of dropout [36], another  widely used technique to avoid overfitting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' Similarly, dropout also uses a mask to disable a fraction (such as 𝑝%) of  parameters or neurons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' The significant difference, though, is that the mask 𝒎 in dropout is randomly sampled from a  Bernoulli(1 − 𝑝%) distribution, rather than deterministically defined by a criterion (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=', the bottom 𝑝% of parameters in  magnitude should be masked) as in pruning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' This in turn brings convenience: a model trained with dropout does not  need to be retrained for a specific mask, because the model’s neurons have already started to learn how to adapt to the  absence of some neurons in the previous training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='3  Context Selection  To eliminate the noisy content in the input context 𝑥 and further improve the model performance, context selection  selectively crops out a condensed context 𝑥 ′ ⊑ 𝑥 to produce the final model prediction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' In general, the model requires  specialized training to fit the selected context.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' Therefore, context selection is pre-hoc processing relative to training,  requiring removing the noise from the training samples in advance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' With a slight abuse of notation, here we use 𝑥 ′ ⊑ 𝑥  to denote that 𝑥 ′ is a condensed subsequence (possibly equal) of 𝑥.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' In general, 𝑥 ′ is an ordered combination of segments  of 𝑥, where the segments are usually at the sentence [48], chunk [69], paragraph [14], or document [23, 56] granularity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  It is worth noting that the selector for segment selection generally requires additional supervised training and needs to  be run in advance of the prediction, which introduces additional computation overhead.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='4  Ablation  To assess the contribution of certain components to the overall model, ablation studies investigate model behavior  by removing or replacing these components in a controlled setting [17].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' Here, in the context of machine learning,  “ablation” refers to the removal of components of the model, which is an analogy to ablative brain surgery (removal of  components of an organism) in biology [47].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' We refer to the model after component removal as the “ablated model”,  which should continue to work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' However, if the removed components are responsible for performance improvement,  the performance of the ablated model is expected to be worse [24].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  In this paper, we use “ablation” to refer specifically to the removal of some neurons of a neural model, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=', to set the  output of some specific neurons to zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' From such a neuronal perspective, network pruning and context selection can  be viewed as two kinds of ablation, the former removing some low-contributing hidden neurons after training and the  latter removing some low-information input neurons before training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' However, in contrast to ablation studies that aim  to investigate the role of the ablated neurons, we aim to learn to improve the utility of the ablated neurons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  3  METHODLOGY  The primary motivation of this work is to inherently improve the utility of neurons in NLU models through a cross-model  training objective, rather than post-hoc network pruning or pre-hoc context selection to eliminate inefficient neurons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  In the following, we first describe a comparison principle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' Then, we propose a novel comparative loss based on the  corollary of the comparison principle and present how to train models with comparative loss by two controlled ablation  methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' Finally, we discuss how comparative loss works.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='1  Comparison Principle  For an ideal efficient model, we believe that all its neurons should be able to work together efficiently to maximize the  utility of each neuron.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' This means that each neuron should contribute to the overall model, or at least be harmless,  Manuscript submitted to ACM  6  Zhu and Pang, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  because the cooperation of neurons is supposed to eliminate the negative effects of noise that may be produced by  individual neurons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' Thus, if we ablate some neurons, even those that produce noise, due to the missing contribution of  the ablated neurons, then the ablated submodel should perform no better than the original full model, in other words,  its task-specific loss should be no smaller than the original.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' Formally, we formulate this comparative relation as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  Comparison Principle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' Suppose 𝑓 (𝑥;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='𝜽) is an efficient neural model, let 𝑥 ′ ⊏ 𝑥 be the ablated input and 𝜽 ′ = 𝒎 ⊙ 𝜽  be the ablated parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' Then, for any subsequence 𝑥 ′ of 𝑥 whose label is still 𝑦, the input-ablated model 𝑓 (𝑥 ′;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='𝜽) should  not perform better than the full model 𝑓 (𝑥;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='𝜽), and for any parameters 𝜽 ′ masked by arbitrary 𝒎, the parameter-ablated  model 𝑓 (𝑥;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='𝜽 ′) should not perform better than 𝑓 (𝑥;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='𝜽), i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=',  𝐿(𝑦, 𝑓 (𝑥;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='𝜽)) ≤ 𝐿(𝑦, 𝑓 (𝑥 ′;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='𝜽)), ∀𝑥 ′ ⊏ 𝑥 with 𝑔(𝑥 ′) = 𝑦,  (2)  𝐿(𝑦, 𝑓 (𝑥;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='𝜽)) ≤ 𝐿(𝑦, 𝑓 (𝑥;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='𝜽 ′)), ∀𝜽 ′ = 𝒎 ⊙ 𝜽 with 𝒎 ∈ {0, 1}|𝜽 |,  (3)  where 𝑔(𝑥 ′) means the ground-truth output of 𝑥 ′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  Notably, we restrict the ablated input 𝑥 ′ for comparison to only those subsequences whose ground-truth output  𝑔(𝑥 ′) remains unchanged, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=', 𝑔(𝑥 ′) = 𝑔(𝑥) = 𝑦.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' This is because ablation may remove some key information from the  original input 𝑥, such as the trigger words in the classification, resulting in an unknown change in the label 𝑦.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' In this  case, 𝐿(𝑦, 𝑓 (𝑥 ′;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='𝜽)) is no longer a correct measure of the task-specific loss of the input-ablated model, and thus cannot  be compared with the task-specific loss of the original model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  Intuitively, we justify the above comparison principle of an efficient model in two cases, which we call parameter-  efficient and input-efficient.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' For the case of ablating hidden neurons by applying a mask 𝒎 on the parameters 𝜽, similar  to network pruning and dropout, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=', 𝜽 ′ = 𝒎 ⊙ 𝜽, since the ablation of hidden neurons is a kind of damage to the  model, even if the ablated neurons happen to be noise-producing, the parameter-efficient model definitely has zeroed  out the connection weights from them, so masking them does not result in a gain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' For the case of ablating input neurons  (words) by cropping out a subsequence from the input context 𝑥, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=', 𝑥 ′ ⊏ 𝑥 3, because while the extra input 𝑥 \\ 𝑥 ′ may  provide more noisy information, there is certainly no more relevant information in 𝑥 ′ than in 𝑥, and the input-efficient  model 𝑓 (𝑥;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='𝜽) is able to suppress the noise, 𝑓 (𝑥 ′;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='𝜽) is impossible to be better than 𝑓 (𝑥;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='𝜽).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  Further, we can ablate a full model 𝑓 (𝑥 (0);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='𝜽 (0)) multiple (𝑐) times, but are these ablated models {𝑓 (𝑥 (𝑖);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='𝜽 (𝑖))}𝑐  𝑖=1  comparable to each other?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' The comparison principle only points out the comparative relation between an efficient  model and any of its ablated models, and cannot be directly applied to multiple independently ablated models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' However,  if we assume that these ablated models are constructed step by step, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=', each ablated model 𝑓 (𝑥 (𝑗);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='𝜽 (𝑗)) is obtained  by progressively ablating the input (𝑥 (𝑗) ⊏ 𝑥 (𝑗−1)) or parameters (𝜽 (𝑗) = 𝒎(𝑗) ⊙ 𝜽 (𝑗−1)) based on its previous model  𝑓 (𝑥 (𝑗−1);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='𝜽 (𝑗−1)), then 𝑓 (𝑥 (𝑗);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='𝜽 (𝑗)) can be considered as an ablated model of all its ancestor models {𝑓 (𝑥 (𝑖);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='𝜽 (𝑖))}𝑗−1  𝑖=0 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  For simplicity, we abbreviate their task-specific losses as 𝑙 (𝑖) = 𝐿(𝑦, 𝑓 (𝑥 (𝑖);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='𝜽 (𝑖))).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' If all {𝑓 (𝑥 (𝑖);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='𝜽 (𝑖))}𝑐−1  𝑖=0 are simultane-  ously assumed to be efficient with respect to their parameter spaces R∥𝒎(𝑖) ∥0 4, we can apply the comparison principle  to compare the task-specific losses of any two models, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=', 𝑙 (𝑖) ≤ 𝑙 (𝑗), ∀𝑖 < 𝑗.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' More formally, we formulate this corollary  as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  Corollary 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' Given a neural model 𝑓 (𝑥 (0);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='𝜽 (0)) and its multiple progressively ablated models {𝑓 (𝑥 (𝑖);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='𝜽 (𝑖))}𝑐  𝑖=1,  where 𝑥 (𝑖) ⊏ 𝑥 (𝑖−1) or 𝜽 (𝑖) = 𝒎(𝑖) ⊙ 𝜽 (𝑖−1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' If 𝑓 (𝑥 (0);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='𝜽 (0)) is an efficient model in the original parameter space R|𝜽 (0) |,  3From here on, if not otherwise specified, we default that the ablation of the input context does not change the output label, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=', 𝑔(𝑥′) = 𝑦.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  4The number of non-zeros (L0 norm) in the mask determines the number of available parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  Manuscript submitted to ACM  Cross-Model Comparative Loss for Enhancing Neuronal Utility in Language Understanding  7  efficient  excepted  parameter  efficient  input-  efficient  extremely  efficient  ERM  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' The Venn diagram for some of the concepts in this paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' The empirical risk minimized (ERM) refers to the minimization  of Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' (1), which is a subset of the parameter-efficient (satisfying Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' (3)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' The efficient (intersecting purple region) model in the  comparison principle, in addition to being parameter-efficient, also needs to be input-efficient (satisfying Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' (2)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' The extremely efficient  model requires not only the full model to be efficient, but also its progressively ablated models to be efficient, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=', satisfying Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' (4) in  Corollary 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' The training objective of the comparative loss Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' (5) is both extremely efficient and ERM, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=', the central overlapping  grid region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  and all {𝑓 (𝑥 (𝑖);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='𝜽 (𝑖))}𝑐−1  𝑖=1 are also efficient models with respect to their parameter spaces R∥𝒎(𝑖) ∥0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' Then, their task-specific  losses should be monotonically non-decreasing with the degrees of ablation, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=',  𝑙 (0) ≤ 𝑙 (1) · · · ≤ 𝑙 (𝑖) · · · ≤ 𝑙 (𝑐).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  (4)  In brief, the comparison principle and its corollary describe a deserved comparative relation between an efficient  neural model and its ablated models, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=', the less ablation, the better the performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' Unfortunately, this natural  property has been largely ignored before, which motivates us to exploit it to train models that utilize neurons more  efficiently.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='2  Comparative Loss  Based on Corollary 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='1, with the objective of ordered comparative relation Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' (4), we can train an extremely effi-  cient model, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=', we expect not only the full model to be efficient, but also its ablated submodels to be efficient with  respect to their restricted parameter spaces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' To measure the difference from the desirable order, we can use pair-  wise hinge loss [29] to evaluate the ranking of the task-specific losses of the full model and its ablated models, like  �𝑐−1  𝑖=0  �𝑐  𝑗=𝑖+1 max(0,𝑙 (𝑖) − 𝑙 (𝑗)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' However, the order of task-specific losses may happen to coincide with the desirable  order such that the aforementioned ranking loss may always be zero, so optimizing this ranking loss alone cannot  guarantee that the full/ablated models are empirical risk minimized (ERM) [57] with respect to their parameter spaces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' To  push these models to be ERM, we introduce a special scalar 𝑏 as the baseline value of the task-specific loss and assume  that it is derived from a dummy ablated model 𝑓 (𝑥 (𝑐+1);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='𝜽 (𝑐+1)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' The dummy model is set to have the highest degree of  ablation, and in principle, its task-specific loss 𝑙 (𝑐+1) should be the highest.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' However, to push the task-specific losses of  the real models {𝑓 (𝑥 (𝑖), 𝜽 (𝑖))}𝑐  𝑖=0 down, we usually set 𝑙 (𝑐+1) = 𝑏 to a small value (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=', 0) and expect all {𝑙 (𝑖)}𝑐  𝑖=0 to be  reduced by this target.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' In this way, our comparative losses can still be written as a pairwise ranking loss, except that on  Manuscript submitted to ACM  8  Zhu and Pang, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content="  Task-specific Loss Function 𝐿(𝑦,𝑦%)  ⋯  𝑙(#)  𝑙(%)  𝑙(%&')  ↑  𝑏  𝑙(')  Task-specific Losses  Predictions  Input Context 𝑥  Output Label 𝑦  ⋯  ⋯  𝑓(𝑥 # ;" metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content="𝜽 # )  𝑓(𝑥 ' ;" metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=" 𝜽 ' )  𝑓(𝑥 % ;" metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' 𝜽 % )  ℒcmp(𝑥, 𝑦;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=" 𝜽)  Comparative Loss  𝑦(#)  𝑦(')  𝑦(%)  Loss Differences  Σ  ✂  ✂  Ablate neurons  Hinge loss  Sum  Σ  ✂  Fig." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' The overview of comparative loss (best viewed in color).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' Given a data sample (𝑥, 𝑦), conventional training typically feeds the  input context 𝑥 into the neural model to obtain the prediction 𝑦(0) and then just minimizes the task-specific loss 𝑙 (0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' In contrast,  comparative loss not only progressively ablates the original model to minimize multiple task-specific losses {𝑙 (𝑖) }𝑐  𝑖=0, but also  constrains their comparative relation with a pairwise hinge loss.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  top of the 𝑐 + 2 task-specific losses,  Lcmp(𝑥,𝑦, 𝜽) =  𝑐∑︁  𝑖=0  𝑐+1  ∑︁  𝑗=𝑖+1  max �0,𝑙 (𝑖) − 𝑙 (𝑗)�.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  (5)  Figure 2 visualizes the localization (central grid region) of the expected model of comparative loss, which is both  ERM and extremely efficient.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' The extremely efficient is a subset of the efficient, and the efficient is the intersection of the  input-efficient and parameter-efficient.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' In this light, comparative loss sets a stricter training objective than ERM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' When  we set 𝑐 and 𝑏 to 0, Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' (5) can degenerate to Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' (1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' Further, the comparative loss is equivalent to  ∑︁  𝑙 (𝑖) >𝑏  𝑙 (𝑖) +  𝑐−1  ∑︁  𝑖=0  𝑐∑︁  𝑗=𝑖+1  max �0,𝑙 (𝑖) − 𝑙 (𝑗)�,  where the first term is to minimize the empirical risk of those not reaching the target 𝑏, and the second term constrains  the comparative relation to pursue the full model being extremely efficient.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  To train using comparative loss, we first need to obtain several comparable ablated models and task-specific losses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  As shown in Figure 3, we consider the original model with the input of the entire context as the full model 𝑓 (𝑥 (0);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='𝜽 (0)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  According to Corollary 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='1, we progressively perform 𝑐-step ablation based on the full model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' At each ablation step,  we use CmpCrop or CmpDrop to ablate a portion of the input context or parameters based on the ablated model  of the previous step, which makes each ablated model comparable to its ancestor models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' At the 𝑖-th (1 ≤ 𝑖 ≤ 𝑐)  ablation step, we use CmpCrop or CmpDrop to ablate a small portion of the input or hidden neurons based on the  Manuscript submitted to ACM  Cross-Model Comparative Loss for Enhancing Neuronal Utility in Language Understanding  9  Algorithm 1 Training with Comparative Loss  Input: Training dataset D, steps of ablation 𝑐, dropout rate 𝑝, baseline value of task-specific loss 𝑏, learning rate 𝜂.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  Output: model parameters 𝜽.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  1: Randomly initialize model parameters 𝜽  2: while not converged do  3:  randomly sample a data pair (𝑥,𝑦) ∼ D  4:  𝑥 (0) ← 𝑥, 𝜽 (0) ← 𝜽  5:  𝑙 (0) ← 𝐿(𝑦, 𝑓 (𝑥 (0);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='𝜽 (0)))  6:  for 𝑖 ← 1 to 𝑐 do  7:  if ablate hidden neurons then  ⊲ ablate model parameters  8:  𝜽 (𝑖) ← CmpDrop(𝜽 (𝑖−1), 𝑝)  9:  𝑥 (𝑖) ← 𝑥 (𝑖−1)  10:  else  ⊲ ablate input context  11:  𝑥 (𝑖) ← CmpCrop(𝑥 (𝑖−1))  12:  𝜽 (𝑖) ← 𝜽 (𝑖−1)  13:  end if  14:  calculate the task-specific loss: 𝑙 (𝑖) ← 𝐿(𝑦, 𝑓 (𝑥 (𝑖);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='𝜽 (𝑖)))  15:  end for  16:  set the dummy’s task-specific loss: 𝑙 (𝑐+1) ← 𝑏  17:  calculate the comparative loss Lcmp(𝑥,𝑦, 𝜽) by Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' (5)  18:  update parameters: 𝜽 ← 𝜽 − 𝜂∇𝜽 Lcmp(𝑥,𝑦, 𝜽)  19: end while  model 𝑓 (𝑥 (𝑖−1);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='𝜽 (𝑖−1)) from the previous step, which makes the newly ablated model 𝑓 (𝑥 (𝑖);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='𝜽 (𝑖)) comparable to all  its ancestor models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' After all these models have predicted once, we have 𝑐 + 1 comparable task-specific losses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' Together  with 𝑙 (𝑐+1) = 𝑏 from the dummy ablated model, we can calculate the final loss using Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' (5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' Using stochastic gradient  descent optimization as an example, Algorithm 1 illustrates the training process more formally.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  CmpDrop and CmpCrop in Algorithm 1 are the two alternative ablation methods we present for each ablation step,  the former for ablating the parameters (hidden neurons) and the latter for ablating the input context (input neurons).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  They both randomly ablate neurons in a controlled manner on top of the previous model, which allows the coverage  of all potential ablated models without retraining each ablated model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' This is because the randomly ablated models  are jointly trained and adapt to the absence of some neurons during the training process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' As for which one to use at  each ablation step can be specific to the model and task dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' Ideally, CmpDrop can be used as long as the model is  dropout compatible, and CmpCrop can be used as long as the input context of the task contains dispensable segments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  Below we will introduce CmpDrop and CmpCrop in detail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='1  CmpDrop: Ablate Parameters by Dropout.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' Dropout randomly disables each neuron with probability 𝑝, which  coincides with our need to randomly ablate hidden neurons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' To obtain a model 𝑓 (·;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='𝜽 (𝑖)) with more ablated parameters,  instead of simply applying a larger dropout rate on the original model 𝑓 (·;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='𝜽 (0)), we ablate the surviving neurons  from the previous ablated model 𝑓 (·;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='𝜽 (𝑖−1)) with probability 𝑝 consistently.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' Specifically, the output values of those  dropped neurons are set to zeros, and the output values of the surviving neurons are scaled by 1/(1 − 𝑝) to ensure  consistency with the expected output value of a neuron in all full/ablated models [36].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' This is equivalent to applying  a mask with scaling5 𝒎(𝑖) ∈ {0, 1, 1/(1 − 𝑝)}|𝜽 | to the previous parameters 𝜽 (𝑖−1) to obtain the ablated parameters  5Slightly different from the binary mask in the comparison principle, we incorporate the scaling factors together into the mask in order to still express  the parameter ablation concisely by 𝜽 (𝑖) = 𝒎(𝑖) ⊙ 𝜽 (𝑖−1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  Manuscript submitted to ACM  10  Zhu and Pang, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  𝜽 (𝑖) = 𝒎(𝑖) ⊙ 𝜽 (𝑖−1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' Each element in 𝒎(𝑖) corresponds to the scaling factor of each parameter,  𝑚(𝑖)  𝑘  =  \uf8f1\uf8f4\uf8f4\uf8f4\uf8f4\uf8f4\uf8f2  \uf8f4\uf8f4\uf8f4\uf8f4\uf8f4\uf8f3  1,  if no dropout in 𝜃𝑘’s layer;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  1  1−𝑝 ,  if neurons at both ends of 𝜃𝑘 survive;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  0,  otherwise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  For the third case in the above equation, once a neuron is newly ablated, all connection parameters from and to it are  set to zero;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' in addition, parameters that have been ablated by 𝒎(𝑖−1) are still set to zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  In practice, we can leverage the existing dropout to implement it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' However, for the comparability of the ablated  models, we must use the same random seed and the same state of the random number generator in each CmpDrop.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' In  this way, assuming that the current ablation step is the 𝑛-th execution of CmpDrop, we can simply run the model with  the dropout rate of 1 − (1 − 𝑝)𝑛.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='2  CmpCrop: Ablate Input by Cropping.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' Given an input context 𝑥, CmpCrop aims to crop out a condensed context  𝑥 ′ that does not change the original ground-truth output, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' 𝑥 ′ ⊏ 𝑥 and 𝑔(𝑥 ′) = 𝑔(𝑥) = 𝑦.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' Assume that we know  the minimum support context 𝑥★ for 𝑥 at training time, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=', ∀𝑥 ′ ⊒ 𝑥★ 𝑔(𝑥 ′) = 𝑔(𝑥★) and ∀𝑥 ′ ⊏ 𝑥★ 𝑔(𝑥 ′) ≠ 𝑔(𝑥★).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  Then, CmpCrop can produce a streamlined context by randomly cropping out several insignificant segments from the  non-support context 𝑥 \\ 𝑥★.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' In this way, the trimmed streamlined context is sure to contain the minimum support  context, so the ground-truth output does not change.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  In practice, to use CmpCrop, we must ensure that enough insignificant segments are set aside in the original context  𝑥 (0) for cropping.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' The segments can be of document, paragraph or sentence granularity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' For example, in question  answering, an insignificant segment can be any retrieved paragraph that does not affect the answer to the question.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' If  the dataset does not annotate the minimal support context, we can manually inject a few extraneous noise segments  into 𝑥 (0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='3  Discussion  Further deriving Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' (5), we find that comparative loss can be viewed as a dynamic weighting of multiple task-specific  losses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' Speicially,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' the loss can be rewrited as follow,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  Lcmp =  𝑐∑︁  𝑖=0  𝑐+1  ∑︁  𝑗=𝑖+1  max �0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='𝑙 (𝑖) − 𝑙 (𝑗)�  =  𝑐∑︁  𝑖=0  𝑐+1  ∑︁  𝑗=𝑖+1  1𝑙 (𝑖) >𝑙 (𝑗) · 𝑙 (𝑖) −  𝑐∑︁  𝑖=0  𝑐+1  ∑︁  𝑗=𝑖+1  1𝑙 (𝑖) >𝑙 (𝑗) · 𝑙 (𝑗)  =  𝑐+1  ∑︁  𝑖=0  𝑐+1  ∑︁  𝑗=𝑖+1  1𝑙 (𝑖) >𝑙 (𝑗) · 𝑙 (𝑖) −  𝑐+1  ∑︁  𝑖=1  𝑖−1  ∑︁  𝑗=0  1𝑙 (𝑗) >𝑙 (𝑖) · 𝑙 (𝑖)  =  𝑐+1  ∑︁  𝑖=0  \uf8ee\uf8ef\uf8ef\uf8ef\uf8ef\uf8f0  𝑐+1  ∑︁  𝑗=𝑖+1  1𝑙 (𝑖) >𝑙 (𝑗) · 𝑙 (𝑖) −  𝑖−1  ∑︁  𝑗=0  1𝑙 (𝑗) >𝑙 (𝑖) · 𝑙 (𝑖)  \uf8f9\uf8fa\uf8fa\uf8fa\uf8fa\uf8fb  =  𝑐+1  ∑︁  𝑖=0  ∑︁  𝑗≠𝑖  CMP(𝑖,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' 𝑗,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='𝑙 (𝑖),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='𝑙 (𝑗)) · 𝑙 (𝑖),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  (6)  Manuscript submitted to ACM  Cross-Model Comparative Loss for Enhancing Neuronal Utility in Language Understanding  11  where 1𝐶 is an indicator function equal to 1 if condition 𝐶 is true and 0 otherwise,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' and the CMP function determines  whether model 𝑓 (𝑥 (𝑖);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='𝜽 (𝑖)) complies with the comparison principle compared to 𝑓 (𝑥 (𝑗);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='𝜽 (𝑗)) and adjusts the weight  of 𝑙 (𝑖).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' There are two cases of non-compliance: for the case where 𝑓 (𝑥 (𝑖);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='𝜽 (𝑖)) is less ablated (𝑖 < 𝑗) but more loss is  obtained, we increase the weight of 𝑙 (𝑖);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' for the case where 𝑓 (𝑥 (𝑖);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='𝜽 (𝑖)) is more ablated (𝑖 > 𝑗) but less loss is obtained,  we decrease the weight of 𝑙 (𝑖).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' Formally, the CMP function can be written as  CMP(𝑖, 𝑗,𝑙 (𝑖),𝑙 (𝑗)) =  \uf8f1\uf8f4\uf8f4\uf8f4\uf8f4\uf8f4\uf8f2  \uf8f4\uf8f4\uf8f4\uf8f4\uf8f4\uf8f3  1,  if 𝑖 < 𝑗 and 𝑙 (𝑖) > 𝑙 (𝑗);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  −1,  if 𝑖 > 𝑗 and 𝑙 (𝑖) < 𝑙 (𝑗);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  0,  otherwise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  Here we can notice that for a pair of models that do not conform to the comparison principle, we increase (+1) the  weight of the task-specific loss of the model that is ablated less and equally decrease (-1) the weight of the loss of  the model that is ablated more.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' Thus, let 𝛼 (𝑖) = �  𝑗≠𝑖 CMP(𝑖, 𝑗,𝑙 (𝑖),𝑙 (𝑗)) denote the weight of 𝑙 (𝑖), then the sum of  the weights of all task-specific losses (including the dummy one) is 0, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=', �𝑐  𝑖=0 𝛼 (𝑖) = −𝛼 (𝑐+1) = �𝑐  𝑖=0 1𝑙 (𝑖) >𝑏.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' Since  𝑙 (𝑐+1) = 𝑏 is a constant, Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' (6) is also equivalent to �𝑐  𝑖=0 𝛼 (𝑖)𝑙 (𝑖), i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=', the total weight equals the number of task-specific  losses worse than the virtual baseline 𝑏, and is adaptively assigned to the 𝑐 + 1 losses according to their performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' In  this way, poorly performing full/ablated models will be more heavily optimized.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' And we empirically compare other  heuristic weighting strategies in §5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  For parameter ablation, in addition to being able to weight each task-specific loss differentially, the comparative loss  with CmpDrop can also differentially calculate the gradients of the parameters in different parts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' According to Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' (6),  comparative loss is equal to the sum of all differences of task-specific loss pairs that violate the comparison principle, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='e,  �  𝑖<𝑗 ∧𝑙 (𝑖) >𝑙 (𝑗)  �𝑙 (𝑖) − 𝑙 (𝑗)�, so we can analyze the gradient of comparative loss from the difference of each task-specific  loss pair.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' For ease of illustration, we take the original model 𝑓 (𝑥;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='𝜽) and a model 𝑓 (𝑥 ′;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='𝜽 ′) whose parameters have been  ablated 𝑛 times as an example, and other model pairs with different parameters are similar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' Assume that the original  parameters 𝜽 = (𝒖, 𝒗,𝒘) and the ablated parameters 𝜽 ′ = (𝒖′, 𝒗′,𝒘′) = (𝒖, 𝒗/(1 − 𝑝)𝑛, 0), where 𝒖 is the parameters  from the layers without dropout, 𝒘 is the parameters ablated by 𝑛 times CmpDrop, and 𝒗′ is the scaled parameters  surviving from 𝑛 times dropout.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' Then, if their task-specific losses violate the comparison principle, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=', 𝑙 > 𝑙 ′, the  gradient of the comparative loss contributed by this model pair is  ∇𝜽 (𝑙 − 𝑙 ′) = (∇𝒖 (𝑙 − 𝑙 ′), ∇𝒗(𝑙 − 𝑙 ′), ∇𝒘𝑙).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  We can see that the comparative loss with respect to 𝒘 is higher than the comparative loss with respect to the other  parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' This is intuitive because the model instead performs better after ablating away 𝒘 indicating that the current  𝒘 is inefficient, so we need to focus on updating 𝒘.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  In addition to the dynamic weighting perspective, comparative loss can also be considered as an “inverse ablation  study” during training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' This is because, in contrast to ablation studies that determine the contribution of removed  components during validation, comparative loss believes that the ablated neurons should contribute and optimizes  parameters with this objective.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  For training complexity, given a generally small number of comparisons 𝑐 (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=', number of ablation steps), the overhead  of computing the final comparative loss is negligibly small, and the increased computation overhead per update step  comes mainly from the multiple forward and backward propagations of the models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' Specifically, the overhead of a  Manuscript submitted to ACM  12  Zhu and Pang, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  training step using comparison loss is 1 + 𝑐 times that of conventional training for the same batch size.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' For inference  complexity, however, models trained using comparative loss are the same as conventionally trained models at test time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  4  EXPERIMENTS  To evaluate the effectiveness and generalizability of our approach for natural language understanding, we conduct  experiments on 3 tasks with representative output types, including classification (8 datasets), extraction (2 datasets),  and ranking (4 datasets).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' Among them, the classification task requires predicting a single category for a piece of text or  a text pair, the extraction task requires predicting a pair of boundary positions to extract the span between the start and  end boundaries, and the ranking task requires predicting a list of relevance level to rank candidates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' Specifically, the  three distinct tasks are text classification (see §4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='1), reading comprehension (extraction, see §4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='2), and pseudo-relevance  feedback (ranking, see §4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='3), respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' We evaluate the comparative loss with just CmpDrop in text classification  and reading comprehension, the comparative loss with just CmpCrop in reading comprehension and pseudo-relevance  feedback, and the comparative loss with both CmpDrop and CmpCrop in reading comprehension.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' For each task, we  first introduce the dataset used, then present the implementation of our models as well as the baselines, and finally  show the experimental results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  Before we start each experiment, we explain some common experimental settings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' For the baseline value 𝑏 of the  task-specific loss in Algorithm 1, we provide two setting options.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' One is to simply set 𝑏 = 0, which is equivalent to  setting an unreachable target value for all full/ablated models and thus pushing their task-specific losses to decrease.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  However, this results in the exposure of all training data to the full model and may aggravate overfitting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' Therefore, to  reduce the times the full model is optimized, our second option is to set the baseline value to the task-specific loss of  the full model, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=', 𝑏 = 𝑙 (0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' In this way, the full model is optimized only when it performs worse than its ablated model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  In practice, we prefer setting 𝑏 = 0, and change to setting 𝑏 = 𝑙 (0) if we find that the model is prone to overfitting on  the dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' For the dropout rate 𝑝 in each CmpDrop, we use the same setting as the baseline models, which is 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='1 in all  our experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' For other conventional training hyperparameters, such as batch size and learning rate, we also keep  the same as the carefully tuned baseline models if not specifically specified.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' We implement our models and baseline  models in PyTorch with HuggingFace Transformers [65], and train them on Tesla V100 GPUs with the fixed random  seed 42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' For convenience, in the tables, we use ‘Cmp’ to represent the comparative loss and use ‘Drop’ and ‘Crop’ in  parentheses to refer to CmpDrop and CmpCrop, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='1  Classification: Application to Text Classification  Text classification is a fundamental task in natural language understanding, which aims to assign a predefined category  to a piece or a group of text.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' In many text classification datasets, all segments of the input context seem to play an  important role in the text category and there is almost no annotation of the minimal support context, so it is difficult  for us to construct an input-ablated model by directly cropping the original input without changing the classification  label.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' That is, it is likely to violate the constraint that the label of the ablated input is unchanged in the comparison  principle, and thus we cannot apply CmpCrop to this task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' However, many current neural classification models use  dropout during training, so in this task, we only validate the comparative loss that uses just CmpDrop.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='1  Datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' The General Language Understanding Evaluation (GLUE) benchmark [60] is a collection of diverse  natural language understanding tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' Following [21], we exclude the problematic WNLI set and conduct experiments  on 8 datasets: (1) Multi-Genre Natural Language Inference (MNLI) [64] is a sentence pair classification task that  Manuscript submitted to ACM  Cross-Model Comparative Loss for Enhancing Neuronal Utility in Language Understanding  13  Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' Classification performance on the development sets of GLUE language understanding benchmark.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  Model  MNLI  MRPC  QNLI  QQP  RTE  SST-2  STS-B  CoLA  Average  BERTbase [21]  84.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='3  85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='3  91.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='3  91.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='1  69.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='0  93.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='1  89.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='4  63.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='6  83.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='33  + R-Drop [39]  85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='5  87.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='3  92.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='0  91.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='4  71.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='1  93.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='0  89.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='6  62.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='6  84.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='06  + Cmp (𝑐 Drop)  85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='4  88.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='5  92.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='1  91.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='6  71.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='8  93.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='5  89.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='9  64.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='6  84.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='66  aims to predict whether the second sentence is an entailment, contradiction, or neutral to the first one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' (2) Microsoft  Research Paraphrase Corpus (MRPC) [22] aims to predict if two sentences in the pair are semantically equivalent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  (3) Question Natural Language Inference (QNLI) [60] is a binary sentence pair classification task that aims to predict  whether a sentence contains the correct answer to a question.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' (4) Quora Question Pairs (QQP) [13] is a binary sentence  pair classification task that aims to predict whether two questions asked on Quora are semantically equivalent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' (5)  Recognizing Textual Entailment (RTE) [4] is a binary entailment task similar to MNLI, but with much fewer training  samples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' (6) Stanford Sentiment Treebank (SST-2) [55] is a binary sentence sentiment classification task consisting of  sentences extracted from movie reviews.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' (7) The Semantic Textual Similarity Benchmark (STS-B) [9] is a sentence pair  classification task that aims to determine how two sentences are semantically similar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' (8) The Corpus of Linguistic  Acceptability (CoLA) [63] is a binary sentence classification task aimed at judging whether a single English sentence  conforms to linguistics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='2  Models & Training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' Following R-Drop [39], another state-of-the-art training method leveraging dropout, we  validate our comparative loss on the popular classification models based on pretrained language models (PLMs)6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  Specifically, we take BERTbase as our backbone to perform finetuning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' The task-specific loss is mean squared error  (MSE) for STS-B and cross-entropy for other datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' We use different training hyperparameters for each dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' For  baseline models and our models trained with comparative loss, we independently select the learning rate within {1e-5,  2e-5, 3e-5, 4e-5}, warmup rate within {0, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='1}, the batch size within {16, 24, 32}, and the number of epochs from 2 to 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  For our models, we tune the number of ablation steps 𝑐 (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=', number of CmpDrop) from 1 to 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='3  Results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' We present classification performance in Table 1, where the evaluation metrics are Pearson correlation for  STS-B, Matthew’s correlation for CoLA, and Accuracy for the others.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' We can see that our model (+ Cmp) comprehensively  outperforms the well-tuned baseline BERTbase and achieves an improvement of 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='33 points (on average), which proves  the effectiveness of comparative loss in classification tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' Moreover, our model trained with comparative loss also  outperforms the model trained with state-of-the-art R-Drop [39] by 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='6 points on average, which demonstrates the  superiority of comparative loss.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='2  Extraction: Application to Reading Comprehension  Extractive reading comprehension (RC) [42, 53] is an essential technical branch of question answering (QA) [11, 31, 40, 54].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  Given a question and a context, extractive RC aims to extract a span from the context as the predicted answer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' Current  dominant RC models basically use pretrained Transformer [58] architectures, which employ dropout in many layers  during finetuning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' This allows us to use CmpDrop to improve the utility of the model parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' Additionally, the  given context is usually lengthy and contains many distracting noise segments, which also allows us to use CmpCrop  6https://github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='com/huggingface/transformers/blob/v4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='2/examples/pytorch/text-classification/README.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='md  Manuscript submitted to ACM  14  Zhu and Pang, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  Table 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' Question answering performance on the development sets of SQuAD and HotpotQA distractor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' The results with † are  inquired from the authors of its paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  Model  EM  F1  SQuAD  BERTbase [21]  80.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='8  88.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='5  BERTbase (our implementation)  81.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='1  88.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='4  + Cmp (2 Drop)  82.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='5  89.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='4  ELECTRAbase [15]  84.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='5  90.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='8  ELECTRAbase (our implementation)  86.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='1  92.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='3  + Cmp (2 Drop)  86.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='7  92.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='9  HotpotQA  Longformerbase† [3]  60.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='3  74.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='3  Longformerbase(our implementation)  61.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='5  75.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='2  + Cmp (1 Drop)  63.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='1  77.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='0  + Cmp (1 Crop)  63.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='1  76.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='8  + Cmp (1 Crop & 1 Drop)  63.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='6  77.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='4  to improve the model’s utilization of the context.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' Therefore, we intend to verify the effectiveness of comparative loss  using CmpDrop or/and CmpCrop in this task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='1  Datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' We evaluate the comparative loss using only CmpDrop on SuQAD [53], which contains 100K single-  hop questions with 9832 for validation, and HotpotQA [67], which contains 113K multi-hop questions with 7405 for  validation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' For HotpotQA, we consider the distractor setting, where the context of each question contains 10 paragraphs,  but only 2 of them are useful for answering the question, and the rest 8 are retrieved distracting paragraphs that are  relevant but do not support the answer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' This allows us to evaluate the comparative loss with CmpCrop on HotpotQA  distractor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='2  Models & Training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' We follow simple but effective RC models based on PLMs [3, 15, 21], which take as input  a concatenation of the question and the context and use a linear layer to predict the start and end positions of the  answer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' And we use cross-entropy of answer boundaries as the task-specific loss function following [21] and use a  learning rate warmup over the first 10% steps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' For SQuAD, we use the popular BERT [21] and ELECTRA [15] with a  maximum sequence length of 512 as the backbone, both of which have successively achieved top rankings in multiple  QA benchmarks [52, 53, 67].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' We first tune the learning rate in range {1e-5, 3e-5, 5e-5, 8e-5, 1e-4, 2e-4}, batch size in  {8, 12, 32} and number of epochs in {1, 2, 3} for baseline models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' Then, setting 𝑐 = 2, we take these hyperparameters  along and train our models using the comparative loss with two CmpDrop.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' For HotpotQA, we use the state-of-the-art  Longformer [3] with a maximum sequence length of 2048 as the backbone, which is fed with the format <s> [YES]  [NO] [Q] question </s> [T] title1 [P] paragraph1 · · · [T] title10 [P] paragraph10 </s>.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' The special  tokens [YES]/[NO], [Q], [T], and [P] represent yes/no answers and the beginning of questions, titles, and paragraphs,  respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' Similarly, we select the learning rate in {1e-5, 3e-5}, batch size in {6, 9, 12} and number of epochs in {3, 5, 8}  for the baseline model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' We then train our models with three comparative losses respectively, the first two applying one  CmpDrop/CmpCrop (𝑐 = 1), while the third applying one CmpCrop followed by one CmpDrop (𝑐 = 2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  Manuscript submitted to ACM  Cross-Model Comparative Loss for Enhancing Neuronal Utility in Language Understanding  15  Table 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' Retrieval performance on benchmarks built on MS MARCO passage collection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' ANCE and uniCOIL are base retrieval  models, + PRF denotes the PRF baseline model, + Cmp denotes our PRF model trained with the comparative loss of 1 CmpCrop, and  superscript (𝑘) represents the PRF depth used during testing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  Model  MARCO Dev  MARCO Eval  TREC DL 2019  TREC DL 2020  DL-HARD  NDCG@10  MRR@10  R@1K  MRR@10  NDCG@10  R@1K  NDCG@10  R@1K  NDCG@10  R@1K  ANCE [66]  38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
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+page_content='70  64.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='76  75.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='70  64.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='58  77.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='64  33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='39  76.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='65  + PRF(3) [68]  40.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='10  34.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='40  95.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='90  33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='00  68.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
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+page_content='10  + Cmp(3) (1 Crop)  40.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
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+page_content='94 68.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='42  80.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='10  69.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='58  81.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
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+page_content='61  79.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='39  + Cmp(5) (1 Crop)  41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
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+page_content='03  34.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
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+page_content='58  80.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
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+page_content='55  uniCOIL [41]  41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
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+page_content='85  + PRF(3)  41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='76  35.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
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+page_content='85 69.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
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+page_content='48  + Cmp(3) (1 Crop)  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
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+page_content='10  83.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='58  69.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='70  84.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='51  36.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='90  77.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='67  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='3  Results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' Since we focus on extraction here, we only measure the extracted answers using EM (exact match) and  F1, which is a little different from the official HotpotQA setting that simultaneously evaluates the identification of  support facts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' From Table 2 we can see that our implemented baseline models trained directly using the task-specific loss  Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' (1) largely achieve better results than those reported in their original papers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' Once trained using comparative loss  Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' (5) instead, our models can still significantly outperform these well-tuned baseline models even without re-searching  the training hyperparameters, demonstrating the effectiveness of comparative loss on the extraction task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' Also, the  consistent improvement based on the three different PLMs demonstrates the model-agnostic nature of comparative loss.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  Furthermore, from the results on HotpotQA we can find that although both CmpDrop and CmpCrop deliver significant  improvement, CmpCrop + CmpDrop achieves the best results, suggesting that CmpDrop and CmpCrop may bring  different benefits to the trained models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='3  Ranking: Application to Pseudo-Relevance Feedback  Pseudo-relevance feedback (PRF) [1] is an effective query understanding [10] technique to improve ranking accuracy,  which aims to alleviate the mismatch of linguistic expressions between a query and its potential relevant documents.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  Given an original query 𝑞 and a document collection 𝐶, a base ranking model returns a ranked list 𝐷 = (𝑑1,𝑑2, · · · ,𝑑|𝐷 |).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  Let 𝐷≤𝑘 denote the feedback set containing the top 𝑘 documents, where 𝑘 is usual referred to as the PRF depth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' The  goal of PRF is to reformulate the original query 𝑞 into a new representation 𝑞(𝑘) using the query-relevant information  in 𝐷≤𝑘, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=', 𝑞(𝑘) = 𝑓 ((𝑞, 𝐷≤𝑘);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='𝜽), where 𝑞(𝑘) is expected to yield better ranking results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' Although PRF methods do  usually improve ranking performance on average [16], individual reformulated queries inevitably suffer from query  drift [49, 72] due to the objectively present noise in the feedback set, causing them to be inferior to the original ones.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  Therefore, we can use comparative loss with CmpCrop to train PRF models to suppress the extra increased noise by  comparing the effect of queries reformulated using different feedback sets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='1  Datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' We conduct experiments on MS MARCO passage [50] collection, which consists of 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='8M English  passages collected from the search results of Bing’s 1M real-world queries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' The Train set of MS MARCO contains  530K queries (about 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='1 relevant passages per query on average), the Dev set contains 6980 queries, and the online  Eval set contains 6837 queries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' Apart from these, we also consider TREC DL 2019 [20], TREC DL 2020 [19], and  DL-HARD [46], three offline evaluation benchmarks based on the MS MARCO passage collection, which contain 43, 54,  and 50 fine-grained (relevance grades from 0 to 3) labeled queries, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' Among them, DL-HARD [46] is a recent  evaluation benchmark focusing on complex queries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' We use MS MARCO Train set to train models, and evaluate trained  Manuscript submitted to ACM  16  Zhu and Pang, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  models on the MS MARCO Dev set to tune hyperparameters and select model checkpoints.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' The selected models are  finally evaluated on the online MS MARCO Eval7 and three other offline benchmarks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='2  Models & Training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' We carry out PRF experiments on two base retrieval models, ANCE [66] (dense retrieval)  and uniCOIL [41] (sparse retrieval), respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' For their PRF models, we do not explicitly modify the query text, but  directly generate a new query vector for retrieval following the current state-of-the-art method ANCE-PRF [68].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' This  allows us to directly optimize the retrieval of reformulated queries end-to-end with the negative log likelihood of the  positive document [34] as the task-specific loss:  𝐿(𝒒(𝑘)) = − log  𝑒sim(𝒒(𝑘),𝒅+)  𝑒sim(𝒒(𝑘),𝒅+) + �  𝑑−∈𝐷− 𝑒sim(𝒒(𝑘),𝒅−) ,  where 𝒅+ is the vector of a sampled document relevant to 𝑞 and 𝒒(𝑘), and 𝐷− is the collection of negative documents  for them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' Since only vectors of queries are updated8, we mine a lite collection (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='3M for dense retrieval and 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='7M for  sparse retrieval) containing positive and hard negative documents of all training queries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' In this way, for each query,  all documents in the lite collection except its positive documents can be used as its 𝐷−.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' In general, our PRF model  consists of an encoder, a vector projector, and a pooler.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' First the original query 𝑞 and feedback documents in 𝐷≤𝑘 are  concatenated in order with [SEP] as separator and input to the encoder to get the contextual embedding of each token.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  Then, the projector maps the contextual embeddings to vectors with the same dimension as the document vectors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  Finally, all token vectors are pooled into a single query vector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' For dense retrieval, the encoder is initialized from  ANCEFirstP9, the projector is a linear layer, and the pooler applies a layer normalization on the first vector ([CLS]) in the  sequence, as in the previous work [68].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' For sparse retrieval, the encoder and projector are initialized from BERTbase with  the masked language model head, where the projector is an MLP with GeLU [28] activation and layer normalization,  and the pooler is composed of a max pooling operation and an L2 normalization10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' We finetune PRF baseline models  for up to 12 epochs with a batch size of 96, a learning rate selected from {2e-5, 1e-5, 5e-6}, and PRF depth 𝑘 randomly  sampled from 0 to 5 for each query.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' We then finetune our PRF models using the comparative loss of 𝑐 = 1 CmpCrop for  up to 6 epochs with a batch size of 48.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' In this way, the maximum number of training steps for our models remains the  same as the baseline models, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=', up to 12 optimizations per original query.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='3  Results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' We report the official metrics (MRR@10 for MARCO and NDCG@10 for others) and Recall@1K of  the models on multiple benchmarks in Table 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' In addition to reporting results for the best-performing PRF depths  (numbers in superscript brackets), for a fair comparison with ANCE-PRF(3) (second row), we also present the results of  ANCE-PRF + Cmp(3), both of which use the first 3 documents as feedback.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' We can see that PRF baseline models (+  PRF) indeed generally outperform their base retrieval models, except that uniCOIL-PRF degrades by 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='67 percentage  points in NDCG@10 of TREC DL 2019, which reflects the presence of query drift.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' Our PRF models (+ Cmp) trained with  comparative loss, however, outperforms their base retrieval model across the board.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' Under the same use of 3 feedback  documents, our ANCE-PRF + Cmp also outperforms the published state-of-the-art ANCE-PRF [68] on all metrics except  NDCG@10 on DL-HARD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' Moreover, when 5 feedback documents are used, ANCE-PRF + Cmp achieves a go-ahead over  ANCE-PRF on NDCG@10 of DL-HARD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' For sparse retrieval, our PRF model (+ Cmp) trained with comparative loss also  7https://microsoft.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='io/MSMARCO-Passage-Ranking-Submissions/leaderboard/  8The fixed vectors of documents are restored from the index pre-built by https://github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='com/castorini/pyserini.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  9https://github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='com/microsoft/ANCE  10We find that L2 normalization helps the model train stably, and it does not change the relevance ranking of documents to a query.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  Manuscript submitted to ACM  Cross-Model Comparative Loss for Enhancing Neuronal Utility in Language Understanding  17  Table 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' QA performance on the development set of HotpotQA distractor with different weighting strategies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' Cmp refers to Longformer  + CmpCrop + CmpDrop that adaptively weights multiple task-specific losses through comparative loss.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' The others are heuristics,  where AVERAGE assigns the same weights to all task-specific losses, FIRST and SECOND assign weight only to the first or second,  and MAX dynamically assigns weight only to the largest one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  Weighting Method  EM  F1  Cmp  63.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='6  77.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='4  AVERAGE  63.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='4  77.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='0  FIRST  62.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='6  76.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='2  SECOND  61.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='5  75.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='2  MAX  63.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='2  77.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='0  surpasses the strong baseline uniCOIL-PRF implemented following ANCE-PRF.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' All of these results above demonstrate  the effectiveness of comparative loss on the ranking task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  5  ANALYSIS  In this section, we further conduct several experiments for a more thorough analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' First, from the dynamic weighting  perspective found in §3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='3, we examine whether the adaptive weighting of comparative loss is more effective than  other weighting strategies (§5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' Next, we try several other comparison strategies to find some guiding experience  in choosing the number of ablations and ablation methods in practice (§5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' Then, to confirm the enhancement of  comparative loss on the utility of hidden and input neurons, we investigate the performance of models with different  numbers of parameters (§5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='3) and context lengths (§5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' Furthermore, we visualize the loss curves to find the impact  of the comparative losses with different ablation methods on the task-specific loss (§5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' Finally, we show the actual  training overhead of comparative loss in detail (§5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='1  Effect of Weighting Strategy  To verify the role of comparative loss from the dynamic weighting perspective, we keep all the training settings of  Longformer + CmpCrop + CmpDrop from the last row of Table 2 unchanged and replace only the weighting strategy of  task-specific losses with some heuristics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' Table 4 shows their performance on the HotpotQA development set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' AVERAGE,  FIRST and SECOND are three static weighting strategies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' AVERAGE assigns equal weights to all task-specific losses,  while FIRST and SECOND assign weight to only the first and second task-specific loss, respectively, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=', FIRST optimizes  𝑙 (0) of the full model without dropout and SECOND optimizes 𝑙 (1) of the model with regular dropout rate 𝑝 (equivalent  to the baseline Longformer in Table 2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' MAX is another dynamic weighting strategy that assigns weight to only the  largest task-specific loss.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' We can see that dynamic weighting in comparative losses is obviously better than these  heuristic weighting strategies, which proves that comparative loss can assign weights more appropriately.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' In addition,  AVERAGE is better than the latter three strategies that consider only one task-specific loss, indicating that it is beneficial  to consider multiple task-specific losses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' Moreover, although the latter three are all assigned to only one task-specific  loss, MAX is better than the other two, which indicates that dynamic assignment is better than static assignment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  Notably, the FIRST that directly optimizes the full model outperforms the SECOND that is trained with dropout,  suggesting that the inconsistency of dropout between the training and inference stages [73] may indeed lead to  underfitting of the full model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' And the fact that Cmp far outperforms FIRST and SECOND indicates that comparative  loss can automatically strike a balance between ensuring training-inference consistency and preventing overfitting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  Manuscript submitted to ACM  18  Zhu and Pang, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  Table 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' QA performance on the development set of HotpotQA distractor with different comparison strategies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' 𝑐 is the number of  ablation steps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' x 2 indicates that an ablation method is repeated twice, and 𝐴 + 𝐵 means that 𝐴 is used followed by 𝐵.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  𝑐  Ablation Order  EM  F1  1  CmpDrop  63.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='1  77.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='0  CmpCrop  63.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='1  76.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='8  2  CmpDrop x 2  63.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='4  77.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='1  CmpCrop x 2  63.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='0  76.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='7  CmpDrop + CmpCrop  63.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='2  76.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='8  CmpCrop + CmpDrop  63.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='6  77.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='4  0  1  2  3  4  The number of CmpDrop c  83.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='4  83.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='6  83.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='8  84.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='0  84.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='2  Average on GLUE  BERT + Cmp  BERT  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' Average results on eight GLUE datasets as the number of ablation steps changes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='2  Effect of Comparison Strategy  To study the impact of comparison strategies, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=', how many ablation steps we should use for comparison and which  ablation method we should choose at each step, we try a variety of comparison strategies on HopotQA with different  numbers of comparisons and ablation orders.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' As shown in Table 5, the results are not significantly further improved  when we repeat CmpDrop/CmpCrop twice, but the results are further improved when we apply CmpCrop first and  then CmpDrop.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' This indicates that comparing multiple models ablated by the same method, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=', encouraging the model  be either extremely input-efficient or extremely parameter-efficient, seems to have little effect on the performance of  the full model, but the successive use of two different ablation methods, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=', encouraging the model be efficient (both  input-efficient and parameter-efficient), is helpful.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' However, applying CmpDrop followed by CmpCrop did not perform  as well as applying CmpDrop only, suggesting that the order of the ablation methods is important and perhaps the  ablation should be done in the order of the information flow in the model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  To further confirm the influence of the number of ablation steps 𝑐, we show in Figure 4 the relationship between  the model’s Average metric over the eight GLUE datasets and the number of ablations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' We can find little difference in  the average performance of the models trained with different numbers of CmpDrop, with the model trained with one  Manuscript submitted to ACM  Cross-Model Comparative Loss for Enhancing Neuronal Utility in Language Understanding  19  Table 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' Evaluation results of baselines with different model sizes and initializations on the SQuAD development set (EM/F1), and  relative gains of our models trained using comparative loss with CmpDrop over baselines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  # Parameter  BERT  ELECTRA  Baseline  Gain (%)  Baseline  Gain (%)  Tiny: 4M  41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='5/54.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='4  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='7/2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='0 Small: 14M  74.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='9/83.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='3  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='4/1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='6  78.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='4/86.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='4/1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='0  Medium: 42M  78.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='6/86.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='3  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='0/0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='7 Base: 110M  81.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='1/88.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='4  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='7/1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='1  86.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='1/92.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='7/0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='7  Large: 335M  84.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='4/91.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='9/0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='7  89.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='0/95.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='9/0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='2  CmpDrop performing significantly best mainly because its huge advantage on two of the datasets pulls up the average.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  Therefore, if there is no extreme demand for performance, we usually do not need to tune the hyperparameter 𝑐.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='3  Effect of Model Parameters  To investigate the impact of model parameters, we explore the application of the comparative loss with CmpDrop on  different-sized versions of BERT and ELECTRA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' From Table 6 we can see that the comparative loss with CmpDrop  achieves a consistent improvement over the baselines based on these backbone models, which indicates that the  comparative loss can improve model performance by increasing parameter utility without increasing the number of  parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' Moreover, except for the one outlier of BERTMedium, we can roughly find that the less the model parameters,  the greater the relative gain from comparative loss.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' This is reasonable because the individual hidden neurons in a model  with lower capacity play a larger role, so the improvement in the utility of hidden neurons can be more reflected in  the final performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' Whereas for a model of higher capacity, it is easier to fit less training data, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=', its task-specific  loss is already low, so comparative loss has less room to play in reducing task-specific loss further.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' In addition, we  observe that the boost to BERT from the comparative loss with CmpDrop is generally higher compared to ELECTRA  with more complicated pretraining, suggesting that the comparative loss helps the model escape from local optima due  to parameter initialization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='4  Effect of Input Context  To review the utility of the input context (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=', input neurons) to models, we plot in Figure 5 the performance trends of  the models using different context sizes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' First, in both datasets, our models trained with comparative loss consistently  outperform the baseline models for all context sizes, indicating that our models are able to utilize input neurons more  efficiently with equal amounts of input context.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' Second, this shows that our comparative loss can further improve the  model performance after streamlining the input with context selection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' In addition, we notice that our ANCE-PRF +  CmpCrop in Figure 5(a) improves retrieval performance as expected as the number of feedback documents increases,  while ANCE-PRF reaches peak performance at 4 feedback documents and then suffers performance degradation,  implying that our model is more robust and able to mine and exploit relevant information in the added feedback  documents.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' In contrast to PRF, for HotpotQA in Figure 5(b), the performance of all RC models decreases as the number  of paragraphs increases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' This is understandable, since only 2 paragraphs in HotpotQA are supporting facts, and the  remaining 8 mostly serve as a distraction, so the ideal performance curve can just be a horizontal line that does not drop  when the paragraph number increases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' Interestingly, we find that the degradation of Longformer + CmpDrop (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='7%)  Manuscript submitted to ACM  20  Zhu and Pang, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  0  1  2  3  4  5  The number of feedback documents k  31  32  33  34  35  MRR@10  ANCE  ANCE-PRF  ANCE-PRF + Cmp  (a)  2  3  4  5  6  7  8  9  10  The number of paragraphs in context  76  77  78  79  F1  Longformer  Longformer + CmpDrop  Longformer + CmpCrop  Longformer + CmpCrop + CmpDrop  (b)  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' Performance curves using different context sizes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' (a) PRF models on MARCO Dev, the horizontal dotted line represents the  base retrieval model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' (b) RC models on HotpotQA Dev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  Table 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' The robustness index of 𝒒(𝑘) with respect to 𝒒(𝑘−1) on MARCO Dev at each PRF depth 𝑘, where 𝒒(𝑘) and 𝒒(𝑘−1) are  reformulated query vectors by the PRF model, the latter having one less document in the input context than the former.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  𝑘  1  2  3  4  5  ANCE-PRF  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='51  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='54  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='58  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='58  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='61  ANCE-PRF + Cmp (1 Crop)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='54  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='56  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='63  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='63  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='66  and Longformer + CmpCrop + CmpDrop (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='0%) from the oracle setting (2 gold paragraphs) to the distractor setting  (10 paragraphs) is lower than that of the baseline Longformer (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='4%).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' This suggests that comparative loss can help the  models suppress the noisy information in the added context.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' Although Longformer + CmpCrop (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='7%) has a larger  degradation than Longformer, we believe this is because Longformer + CmpCrop needs to be optimized for various  numbers of paragraphs, unlike other models without CmpCrop that focus on learning for one input form (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=', always  ten paragraphs).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' However, this variety of input forms makes Longformer + CmpCrop perform better than Longformer +  CmpDrop when the number of paragraphs is small (≤ 5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  To further quantitatively demonstrate the help of comparative loss in the robustness of the PRF model to context  size, we report in Table 7 the robustness indexes [18] of ANCE-PRF + CmpCrop and ANCE-PRF at different numbers of  feedback documents.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' The robustness index is defined as 𝑁+−𝑁−  |𝑄 |  , where |𝑄| is the total number of evaluated queries and  𝑁+ and 𝑁− are the number of queries that the PRF model improves or downgrades when one more feedback document  is used.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' The value of robustness index is in [-1, 1], and the model with higher robustness index is more robust.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' We can  see that the PRF model trained using comparative loss with CmpCrop is significantly more robust than the baseline  model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' Besides, from the gaps in their robustness indexes (only 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='03 or 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='02 for 1 or 2 documents, but 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='05 for more  documents), we can find that the comparative loss is more helpful for long-form inputs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='5  Loss Visualization  To figure out the impact of comparative loss on task-specific loss, we plot the curves of task-specific loss for the full  model (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=', 𝑙 (0)) in Figure 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' From Figures 6(a) and 6(b) we can see that with the same batch size, the comparative loss can  Manuscript submitted to ACM  Cross-Model Comparative Loss for Enhancing Neuronal Utility in Language Understanding  21  0  10000  20000  30000  40000  Training step  1  2  3  4  5  6  Task-specific loss of full model  Longformer  Longformer + CmpCrop  Longformer + CmpDrop  Longformer + CmpCrop + CmpDrop  (a) Answer extraction loss on HopotQA Train  0  10000  20000  30000  40000  Training step  19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='4  19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='6  19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='8  20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='0  20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='2  20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='4  20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='6  20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='8  Task-specific loss of full model  Longformer  Longformer + CmpCrop  Longformer + CmpDrop  Longformer + CmpCrop + CmpDrop  (b) Answer extraction loss on HopotQA Dev  0  10000  20000  30000  40000  50000  Training step  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='5  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='0  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='5  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='0  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='5  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='0  Task-specific loss of full model  uniCOIL-PRF + CmpCrop  uniCOIL-PRF  (c) Retrieval loss on MARCO Train  0  10000  20000  30000  40000  50000  Training step  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='75  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='80  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='85  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='90  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='95  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='00  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='05  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='10  Task-specific loss of full model  uniCOIL-PRF + CmpCrop  uniCOIL-PRF  (d) Retrieval loss on MARCO Dev  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' Task-specific loss curves for the full model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  help our models fit better compared to the baseline Longformer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' Comparing Longformer + CmpDrop and Longformer +  CmpCrop, we can find that the training loss of the former is significantly smaller, which indicates that the comparative  loss with CmpDrop helps the model fit the training data better.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' Whereas the evaluation loss of Longformer + CmpCrop  rises less in the later stage, which indicates that the comparative loss with CmpCrop can mitigate the overfitting to  some extent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' Since the number of task-specific losses per sample optimized by comparative loss is 1 + 𝑐 times that of  conventional training, we also plot the task-specific loss curves for PRF models in Figures 6(c) and 6(d), where the batch  size of our uniCOIL-PRF + CmpCrop is 1/(1 + 𝑐) of the baseline uniCOIL-PRF.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' In this way, the number of task-specific  losses optimized in one batch for our model and the baseline is the same, which helps to further clarify the role of the  comparative loss with CmpCrop.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' We can see that while the training loss of our model in Figure 6(c) does not drop as  low as the baseline, its evaluation loss in Figure 6(d) drops to a lower level and significantly mitigates the overfitting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='6  Training Efficiency  We present in Table 8 the performance gain and relative change in training FLOPs of BERTbase + Cmp compared to  BERTbase, as well as the specific number of comparisons (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=', number of ablation steps 𝑐) chosen for each dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' We  find that the actual overhead of training with comparative loss is usually less than 1 + 𝑐 times that of conventional  Manuscript submitted to ACM  22  Zhu and Pang, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  Table 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' Specific settings for the number of ablation steps of BERT + Cmp on each GLUE dataset, as well as the performance gain and  increase in training computation overhead compared to BERT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  MNLI  MRPC  QNLI  QQP  RTE  SST-2  STS-B  CoLA  𝑐  3  1  4  2  1  2  4  4  Performance (%) ↑  +1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='3  +3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='8  +0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='9  +0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='5  +4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='1  +0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='4  +0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='6  +1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='6  FLOPs ↑  x3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='5  x1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='6  x3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='5  x0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='9  x2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='1  x0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='7  x4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='8  x3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='9  training, and even less than that of conventional training (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=', on QQP).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' This is because models trained with comparative  loss tend to converge earlier than baselines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' Combined with the insensitivity of comparative loss to the number of  comparisons found from Figure 4, we believe that setting 𝑐 to 1 or 2 can lead to effective and fast training when data is  sufficient.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  6  RELATED WORK  In this section, we introduce and discuss some work that has different motivations but is technically relevant to us,  starting with contrastive learning [37] that learns by comparing, followed by recent training methods that also use  dropout multiple times.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='1  Contrastive Learning  Contrastive learning has recently achieved significant success in representation learning in computer vision and natural  language processing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' At its core, contrastive learning aims to learn effective representations by pulling semantically  similar neighbors together and pushing apart non-neighbors [26].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' Instead of learning a signal from individual data  samples one at a time, it learns by comparing different samples [37].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' The comparison is performed between positive  pairs of similar samples and negative pairs of dissimilar samples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' The positive pair must ensure that the two samples  are similar, which can be constructed either by using supervised similarity annotation or by self-supervision.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' In self-  supervised contrastive learning, a positive pair can consist of an original sample and its data augmentation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' For example,  SimCLR [12] in computer vision uses a crop, flip, distortion or rotation of an original image as its similar view, and  SimCSE [25] in natural language processing applies two dropout masks to an input sentence to create two slightly  different sentence embeddings that are then used as a positive pair of sentence embeddings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' To share more computation  and save cost, negative pairs usually consist of two dissimilar samples within the same training batch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' Although both  learn through comparison, contrastive learning aims at pursuing alignment and uniformity [62] of representations,  while our comparative loss aims at pursuing orderliness of the task-specific losses of the full model and its ablated  model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' Moreover, as the lexical meaning suggests, contrastive learning only classifies the relationship (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=', similar or  dissimilar) between two data samples in a binary manner, whereas our comparative loss compares multiple full/ablated  models by ranking.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' However, these two are not in conflict, and our comparative loss can be used over the contrastive  losses that served as task-specific losses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='2  Dropout-based Comparison  Dropout is a family of stochastic techniques used in neural network training or inference that have attracted extensive  research interest and are widely used in practice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' The standard dropout [30] aims to avoid overfitting of the network by  reducing the co-adaptation of neurons, where the outputs of individual neurons only provide useful information in  Manuscript submitted to ACM  Cross-Model Comparative Loss for Enhancing Neuronal Utility in Language Understanding  23  combination with other neuron outputs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' After this, a line of research focused on improving the standard dropout by  employing other strategies for dropping neurons, such as dropconnect [59] and variational dropout [35].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  A line of research that is relevant to us is the use of dropout multiple times in training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' SimCSE [25] forwards the  model twice with different dropout masks of the same rate and uses a contrastive loss to constrain the distribution of  model outputs in the representation space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' A possible side effect of dropout revealed by the existing literature [45, 73]  is the non-negligible inconsistency between the training and inference stages of the model, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=', the submodels are  optimized during training, but the full model without dropout is used during inference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' To address this inconsistency,  R-Drop [39] forward runs the model multiple times with different dropout masks to obtain multiple predicted probability  distributions and applies KL-divergence on them to constrain their consistency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' Unlike their multiple dropout masks that  are sampled independently, the multiple dropout rates are increasing and the masks are progressive in our CmpDrop,  with the subsequent mask obtained by further randomly discarding elements based on the previous one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' In addition, we  impose constraints on the task-specific losses at the end rather than on the representations and probabilities upstream.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  Notably, the full model is also optimized in due time when trained using the comparative loss with CmpDrop, which  we argue is important to mitigate the inconsistency between training and inference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' This is because, while dropout  avoids co-adaptation of neurons, it also weakens the cooperation between neurons (§5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='1 gives some empirical support).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  In particular, in cases where all neurons are involved, the full model trained with dropout has not been taught how to  make them work together efficiently and thus cannot be fully exploited during testing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' Surprisingly, our comparative  loss with CmpDrop can balance between promoting the cooperation of neurons and preventing their co-adaptation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  7  CONCLUSION  In this paper, we propose cross-model comparative loss, a simple task-agnostic loss function, to improve the utility of  neurons in NLU models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' Comparative loss is essentially a ranking loss based on the comparison principle between  the full model and its ablated models, with the expectation that the less ablation there is, the smaller the task-specific  loss.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' To ensure comparability among multiple ablated models, we progressively ablate the models and provide two  controlled ablation methods based on dropout and context cropping, applicable to a wide range of tasks and models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  We show theoretically how comparative loss works, suggesting that it can adaptively assign weights to multiple  task-specific losses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' Extensive experiments and analysis on 14 datasets from 3 distinct NLU tasks demonstrate the  universal effectiveness of comparative loss.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' Interestingly, our analysis confirms that comparative loss can indeed assign  weights more appropriately, and finds that comparative loss is particularly effective for models with few parameters or  long input.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  In the future, we would like to apply comparative loss in other domains, such as natural language generation  and computer vision, and explore its applications on other model architectures beyond Transformer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' It could also be  interesting to explore the application of comparative loss on top of self-supervised losses (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=', contrastive loss) during  pretraining.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' For training costs, how to reduce the overhead by reusing more shared computations is a direction worth  exploring.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' Further, more advanced ablation methods in training, such as dropconnect [59] rather than standard dropout  and adversarial rather than stochastic, may deserve future research efforts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  REFERENCES  [1] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' Attar and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' Fraenkel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' 1977.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' Local Feedback in Full-Text Retrieval Systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' ACM 24, 3 (July 1977), 397–417.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='1145/322017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  322021  [2] Brian Bartoldson, Ari Morcos, Adrian Barbu, and Gordon Erlebacher.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' The Generalization-Stability Tradeoff In Neural Network Pruning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' In  Advances in Neural Information Processing Systems, Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' 33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' Curran Associates, Inc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=', 20852–20864.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' https://proceedings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='neurips.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='cc/paper/2020/hash/  Manuscript submitted to ACM  24  Zhu and Pang, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  ef2ee09ea9551de88bc11fd7eeea93b0-Abstract.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='html  [3] Iz Beltagy, Matthew E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' Peters, and Arman Cohan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' Longformer: The Long-Document Transformer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='48550/arXiv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='2004.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='05150  arXiv:2004.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='05150  [4] Luisa Bentivogli, Peter Clark, Ido Dagan, and Danilo Giampiccolo.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' 2009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' The Fifth PASCAL Recognizing Textual Entailment Challenge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='. In TAC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  [5] Davis Blalock, Jose Javier Gonzalez Ortiz, Jonathan Frankle, and John Guttag.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' What Is the State of Neural Network Pruning?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' Proceedings  of Machine Learning and Systems 2 (March 2020), 129–146.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
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+page_content='html  [6] Sebastian Borgeaud, Arthur Mensch, Jordan Hoffmann, Trevor Cai, Eliza Rutherford, Katie Millican, George Bm Van Den Driessche, Jean-Baptiste  Lespiau, Bogdan Damoc, Aidan Clark, Diego De Las Casas, Aurelia Guy, Jacob Menick, Roman Ring, Tom Hennigan, Saffron Huang, Loren Maggiore,  Chris Jones, Albin Cassirer, Andy Brock, Michela Paganini, Geoffrey Irving, Oriol Vinyals, Simon Osindero, Karen Simonyan, Jack Rae, Erich Elsen,  and Laurent Sifre.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
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+page_content=' https://proceedings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
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+page_content='html  [7] Tom Brown, Benjamin Mann, Nick Ryder, Melanie Subbiah, Jared D Kaplan, Prafulla Dhariwal, Arvind Neelakantan, Pranav Shyam, Girish  Sastry, Amanda Askell, Sandhini Agarwal, Ariel Herbert-Voss, Gretchen Krueger, Tom Henighan, Rewon Child, Aditya Ramesh, Daniel Ziegler,  Jeffrey Wu, Clemens Winter, Chris Hesse, Mark Chen, Eric Sigler, Mateusz Litwin, Scott Gray, Benjamin Chess, Jack Clark, Christopher Berner,  Sam McCandlish, Alec Radford, Ilya Sutskever, and Dario Amodei.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' Language Models Are Few-Shot Learners.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' In Proceedings of the 34th  International Conference on Neural Information Processing Systems, Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' 33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' Curran Associates, Inc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=', Red Hook, NY, USA, 1877–1901.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  https:  //papers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='nips.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='cc/paper/2020/hash/1457c0d6bfcb4967418bfb8ac142f64a-Abstract.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='html  [8] Alon Brutzkus and Amir Globerson.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' Why Do Larger Models Generalize Better?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
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+page_content='561  [24] Stella Frank, Emanuele Bugliarello, and Desmond Elliott.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
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+page_content='552  [26] Raia Hadsell, Sumit Chopra, and Yann LeCun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
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+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
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+page_content='  [27] Song Han, Jeff Pool, John Tran, and William Dally.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
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+page_content=' In Advances in  Neural Information Processing Systems, Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' 28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
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+page_content='html  [28] Dan Hendrycks and Kevin Gimpel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' Gaussian error linear units (gelus).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' arXiv preprint arXiv:1606.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='08415 (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  [29] Ralf Herbrich, Thore Graepel, and Klaus Obermayer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' 2000.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' Large Margin Rank Boundaries for Ordinal Regression.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' Advances in large margin  classifiers 88, 2 (2000), 115–132.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  [30] Geoffrey E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' Hinton, Nitish Srivastava, Alex Krizhevsky, Ilya Sutskever, and Ruslan R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' Salakhutdinov.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' 2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' Improving Neural Networks by Preventing  Co-Adaptation of Feature Detectors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
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+page_content='0580  [31] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' Hirschman and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' Gaizauskas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' 2001.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
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+page_content=' Natural Language Engineering 7, 4 (Dec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' 2001),  275–300.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
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+page_content='1017/S1351324901002807  [32] Gautier Izacard, Patrick Lewis, Maria Lomeli, Lucas Hosseini, Fabio Petroni, Timo Schick, Jane Dwivedi-Yu, Armand Joulin, Sebastian Riedel, and  Edouard Grave.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
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+page_content='03299  [33] Jared Kaplan, Sam McCandlish, Tom Henighan, Tom B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
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+page_content=' Scaling Laws for Neural Language Models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
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+page_content='08361 arXiv:2001.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='08361  [34] Vladimir Karpukhin, Barlas Oguz, Sewon Min, Patrick Lewis, Ledell Wu, Sergey Edunov, Danqi Chen, and Wen-tau Yih.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
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+page_content=' Dense Passage  Retrieval for Open-Domain Question Answering.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' In Proceedings of the 2020 Conference on Empirical Methods in Natural Language Processing (EMNLP).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  Association for Computational Linguistics, Online, 6769–6781.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
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+page_content='550  [35] Durk P Kingma, Tim Salimans, and Max Welling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
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+page_content=' Variational Dropout and the Local Reparameterization Trick.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' In Advances in Neural Information  Processing Systems, Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' 28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
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+page_content=' https://papers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='nips.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='cc/paper/2015/hash/bc7316929fe1545bf0b98d114ee3ecb8-Abstract.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='html  [36] Alex Labach, Hojjat Salehinejad, and Shahrokh Valaee.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
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+page_content=' Survey of Dropout Methods for Deep Neural Networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
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+page_content='  1904.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='13310 arXiv:1904.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='13310  [37] Phuc H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' Le-Khac, Graham Healy, and Alan F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
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+page_content=' IEEE Access 8 (2020),  193907–193934.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
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+page_content=' arXiv:1907.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
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+page_content='11692  [44] Zhuang Liu, Jianguo Li, Zhiqiang Shen, Gao Huang, Shoumeng Yan, and Changshui Zhang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
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+page_content=' 2755–2763.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
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+page_content='298  [45] Xuezhe Ma, Yingkai Gao, Zhiting Hu, Yaoliang Yu, Yuntian Deng, and Eduard Hovy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
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+page_content='08017 (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  [46] Iain Mackie, Jeffrey Dalton, and Andrew Yates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
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+page_content='08644  [48] Sewon Min, Victor Zhong, Richard Socher, and Caiming Xiong.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
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+page_content='18653/v1/P18-1160  [49] Mandar Mitra, Amit Singhal, and Chris Buckley.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
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+page_content='290995  [50] Tri Nguyen, Mir Rosenberg, Xia Song, Jianfeng Gao, Saurabh Tiwary, Rangan Majumder, and Li Deng.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
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+page_content='  [51] Colin Raffel, Noam Shazeer, Adam Roberts, Katherine Lee, Sharan Narang, Michael Matena, Yanqi Zhou, Wei Li, and Peter J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
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+page_content=' 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' HotpotQA: A  Dataset for Diverse, Explainable Multi-hop Question Answering.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' In Proceedings of the 2018 Conference on Empirical Methods in Natural Language  Processing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' Association for Computational Linguistics, 2369–2380.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='18653/v1/D18-1259  [68] HongChien Yu, Chenyan Xiong, and Jamie Callan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' Improving Query Representations for Dense Retrieval with Pseudo Relevance Feedback.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' In  Proceedings of the 30th ACM International Conference on Information & Knowledge Management (CIKM ’21).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' Association for Computing Machinery,  New York, NY, USA, 3592–3596.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='1145/3459637.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='3482124  [69] Zhi Zheng, Kai Hui, Ben He, Xianpei Han, Le Sun, and Andrew Yates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' BERT-QE: Contextualized Query Expansion for Document Re-  ranking.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' In Findings of the Association for Computational Linguistics: EMNLP 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' Association for Computational Linguistics, Online, 4718–4728.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  Manuscript submitted to ACM  Cross-Model Comparative Loss for Enhancing Neuronal Utility in Language Understanding  27  https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='18653/v1/2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='findings-emnlp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='424  [70] Ruiqi Zhong, Dhruba Ghosh, Dan Klein, and Jacob Steinhardt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' Are Larger Pretrained Language Models Uniformly Better?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' Comparing  Performance at the Instance Level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' In Findings of the Association for Computational Linguistics: ACL-IJCNLP 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' Association for Computational  Linguistics, Online, 3813–3827.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='18653/v1/2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='findings-acl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='334  [71] Yunchang Zhu, Liang Pang, Yanyan Lan, Huawei Shen, and Xueqi Cheng.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' LoL: A Comparative Regularization Loss over Query Reformulation  Losses for Pseudo-Relevance Feedback.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' In Proceedings of the 45th International ACM SIGIR Conference on Research and Development in Information  Retrieval (SIGIR ’22).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' Association for Computing Machinery, New York, NY, USA, 825–836.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='1145/3477495.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='3532017  [72] Liron Zighelnic and Oren Kurland.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' 2008.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' Query-Drift Prevention for Robust Query Expansion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' In Proceedings of the 31st Annual International ACM  SIGIR Conference on Research and Development in Information Retrieval (SIGIR ’08).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' Association for Computing Machinery, New York, NY, USA,  825–826.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='1145/1390334.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='1390524  [73] Konrad Zolna, Devansh Arpit, Dendi Suhubdy, and Yoshua Bengio.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' Fraternal dropout.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content=' arXiv preprint arXiv:1711.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='00066 (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
+page_content='  Manuscript submitted to ACM' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9NE2T4oBgHgl3EQfQAZl/content/2301.03765v1.pdf'}
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+Under review
+LEVERAGING THE THIRD DIMENSION
+IN CONTRASTIVE LEARNING
+Sumukh K Aithal 1, Anirudh Goyal 1, 4, Alex Lamb 2, Yoshua Bengio 1, Michael Mozer 3
+1 Mila, Universit´e de Montr´eal, 2 Microsoft Research, NYC, 3 Google Research, Brain Team
+4 DeepMind
+ABSTRACT
+Self-Supervised Learning (SSL) methods operate on unlabeled data to learn robust
+representations useful for downstream tasks. Most SSL methods rely on augmen-
+tations obtained by transforming the 2D image pixel map. These augmentations
+ignore the fact that biological vision takes place in an immersive three-dimensional,
+temporally contiguous environment, and that low-level biological vision relies
+heavily on depth cues. Using a signal provided by a pretrained state-of-the-art
+monocular RGB-to-depth model (the Depth Prediction Transformer, Ranftl et
+al., 2021), we explore two distinct approaches to incorporating depth signals into
+the SSL framework. First, we evaluate contrastive learning using an RGB+depth
+input representation. Second, we use the depth signal to generate novel views
+from slightly different camera positions, thereby producing a 3D augmentation
+for contrastive learning. We evaluate these two approaches on three different SSL
+methods—BYOL, SimSiam, and SwAV—using ImageNette (10 class subset of
+ImageNet), ImageNet-100 and ImageNet-1k datasets. We ﬁnd that both approaches
+to incorporating depth signals improve the robustness and generalization of the
+baseline SSL methods, though the ﬁrst approach (with depth-channel concatena-
+tion) is superior. For instance, BYOL with the additional depth channel leads
+to an increase in downstream classiﬁcation accuracy from 85.3% to 88.0% on
+ImageNette and 84.1% to 87.0% on ImageNet-C.
+1
+INTRODUCTION
+Biological vision systems evolved in and interact with a three-dimensional world. As an individual
+moves through the environment, the relative distance of objects is indicated by rich signals extracted
+by the visual system, from motion parallax to binocular disparity to occlusion cues. These signals play
+a role in early development to bootstrap an infant’s ability to perceive objects in visual scenes (Spelke,
+1990; Spelke & Kinzler, 2007) and to reason about physical interactions between objects (Baillargeon,
+2004). In the mature visual system, features predictive of occlusion and three-dimensional structure
+are extracted early and in parallel in the visual processing stream (Enns & Rensink, 1990; 1991), and
+early vision uses monocular cues to rapidly complete partially-occluded objects (Rensink & Enns,
+1998) and binocular cues to guide attention (Nakayama & Silverman, 1986). In short, biological
+vision systems are designed to leverage the three-dimensional structure of the environment.
+In contrast, machine vision systems typically consider a 2D RGB image or a sequence of 2D RGB
+frames to be the relevant signal. Depth is considered as the end product of vision, not a signal that
+can be exploited to improve visual information processing. Given the bias in favor of end-to-end
+models, researchers might suppose that if depth were a useful signal, an end-to-end computer vision
+system would infer depth. Indeed, it’s easy to imagine the advantages of depth processing integrated
+into the visual information processing stream. For example, if foreground objects are segmented from
+the background scene, neural networks would not make the errors they often do by using short-cut
+features to classify (e.g., misclassifying a cow at the beach as a whale) (Geirhos et al., 2020).
+In this work, we take seriously the insight from biological vision that depth signals are extracted
+early in the processing stream, and we explore how depth signals might support computer vision. We
+assume the availability of a depth signal by using an existing state-of-the-art monocular RGB-to-depth
+extraction model, the Dense Prediction Transformer (DPT) (Ranftl et al., 2021).
+1
+arXiv:2301.11790v1  [cs.CV]  27 Jan 2023
+
+Under review
+Augmentation
+Contrastive 
+Self-Supervised 
+Learning Method
+Depth 
+Estimation
+Depth 
+Estimation
+R
+G
+B
++
+D
+R
+G
+B
++
+D
+Figure 1: Improving Self-Supervised Learning by concatenating an input channel with estimated
+depth to the RGB input. Depth is estimated from both an original image and an augmentation, and
+the resulting 4-channel inputs are used to produce the representation. Incorporating the depth channel
+improves downstream accuracy in a variety of SSL techniques, with the largest improvements on
+challenging corrupted benchmarks. (Teaser results are shown. Complete results in Tables 1, 2, 3)
+We focus on using the additional depth information for self-supervised representation learning. SSL
+aims to learn effective representations from unlabelled data that will be useful for downstream tasks
+(Chen et al., 2020a). We investigate two speciﬁc hypotheses. First, we consider directly appending
+the depth channel to the RGB and then use the RGB+D input directly in contrastive learning (Fig. 1).
+Second, we consider synthesizing novel image views from the RGB+D representation using a recent
+method, AdaMPI (Han et al., 2022) and treating these synthetic views as image augmentations for
+contrastive learning (Fig. 2).
+Prior work has explored the beneﬁt of depth signals in supervised learning for speciﬁc tasks like
+object detection and semantic segmentation (Cao et al., 2016; Hoyer et al., 2021; Song et al., 2021;
+Seichter et al., 2021). Here, we pursue a similar approach in contrastive learning, where the goal is to
+learn robust, universal representations that support downstream tasks. To the best of our knowledge,
+only one previous paper has explored the use of depth for contrastive learning (Tian et al., 2020). In
+their case, ground truth depth was used and it was considered as one of many distinct “views” of the
+world. We summarize our contributions below:
+• Motivated by biological vision systems, we propose two distinct approaches to improving SSL
+using a (noisy) depth signal extracted from a monocular RGB image. First, we concatenate the
+derived depth map and the image and pass the four-channel RGB+D input to the SSL method.
+Second, we use a single-view view synthesis method that utilizes the depth map as input to generate
+novel 3D views and provides them as augmentations for contrastive learning.
+• We show that both of these approaches improve the performance of three different contrastive
+learning methods (BYOL, SimSiam, and SwAV) on ImageNette, ImageNet-100 and large-scale
+ImageNet-1k datasets. Our approaches can be integrated into any contrastive learning framework
+without incurring any signiﬁcant computational cost and trained with the same hyperparameters
+as the base contrastive method. We achieve a 2.8% gain in the performance of BYOL with the
+addition of depth channel on ImageNette dataset.
+• Both approaches also yield representations that are more robust to image corruptions than the
+baseline SSL methods, as reﬂected in performance on ImageNet-C and ImageNet-3DCC. On the
+large-scale ImageNet-100 dataset, SimSiam+Depth outperforms base SimSiam model by 4% in
+terms of corruption robustness.
+2
+RELATED WORK
+Self-Supervised Learning. The goal of self-supervised learning based methods is to learn a universal
+representation that can generalize to various downstream tasks. Earlier work on SSL relied on
+handcrafted pretext tasks like rotation (Gidaris et al., 2018), colorization (Zhang et al., 2016) and
+jigsaw (Noroozi & Favaro, 2016). Recently, most of the state-of-the-art methods in SSL are based on
+2
+
+Results on ImageNette
+100
+BYOL
+BYOL+Depth
+Accuracy (in %)
+90
+80
+70
+60
+Top-1 Acc
+IN-C
+IN-3DCCResults on ImageNet-100
+90
+SimSiam
+80
+SimSiam+Depth
+(%
+Accuracy (in 
+70
+60
+50
+40
+30
+Top-1 Acc
+IN-C
+IN-3DCCUnder review
+Single-View View Synthesis 
+Contrastive 
+Self-Supervised 
+Learning Method
+Augmentation
+Augmentation
+Sample one of K Views
+Figure 2: Novel views can be synthesized from a single image by using the estimated depth channel,
+which can be used as additional augmentations across a variety of contrastive self-supervised learning
+techniques. These improve results, especially on benchmarks with image corruptions. (Result
+highlights are shown. Complete results in Tables 1, 2, 3
+contrastive representation learning. The goal of contrastive representation learning is to make the
+representations between two augmented views of the scene similar and also to make representations
+of views of different scenes dissimilar.
+SimCLR (Chen et al., 2020b) showed that augmentations play a key role in contrastive learning and
+the set of augmentations proposed in the work showed that contrastive learning can perform really
+well on large-scale datasets like ImageNet. BYOL (Grill et al., 2020) is one of the ﬁrst contrastive
+learning based methods without negative pairs. BYOL is trained with two networks that have the
+same architecture: an online network and a target network. From an image, two augmented views
+are generated; one is routed to the online network, the other to the target network. The model learns
+by predicting the output of the one view from the other view. SwAV (Caron et al., 2020) is an
+online clustering based method that compares cluster assignments from multiple views. The cluster
+assignments (or code) from one augmented view of the image is predicted from the other augmented
+view. SimSiam (Chen & He, 2021) explores the role of Siamese networks in contrastive learning.
+SimSiam is an conceptually simple method as it does not require a BYOL-like momentum encoder or
+a SwAV-like clustering mechanism.
+Contrastive Multiview Coding (CMC) Tian et al. (2020) proposes a framework for multiview con-
+trastive learning that maximizes the mutual information between views of the same scenes. Each
+view can be an additional sensory signal like depth, optical ﬂow, or surface normals. CMC is closely
+related to our work but differs in two primary ways. First, CMC considers depth as a separate view
+and applies a mutual information maximization loss across multiple views; in contrast, we either
+concatenate the estimated depth information to the RGB input or generate 3D realistic views using
+the depth signal. Second, CMC considers only ground truth depth maps whereas we show that depth
+maps estimated from RGB are also quite helpful.
+Monocular Depth Estimation in Computer Vision. Monocular depth estimation is a pixel-level
+task that aims to predict the distance of every pixel from the camera using a single image. Though
+monocular depth estimation is a highly ill-posed problem, deep learning based techniques have been
+shown to perform extremely well on this task. A few works (Eitel et al., 2015; Cao et al., 2016; Hoyer
+et al., 2021; Song et al., 2021; Seichter et al., 2021) have explored the beneﬁts of depth estimation
+for semantic segmentation and object detection. Cao et al. (2016) were one of the ﬁrst efforts to
+perform a detailed analysis showing that augmenting the RGB input with estimated depth map can
+signiﬁcantly improve the performance on object detection and segmentation tasks. A multi-task
+training procedure of predicting the depth signal along with the semantic label was also proposed
+in Cao et al. (2016). RGB-D segmentation with ground truth depth maps was shown to be superior
+compared to standard RGB segmentation (Seichter et al., 2021). Hoyer et al. (2021) proposed to
+use self-supervised depth estimation as an auxiliary task for semantic segmentation. Multimodal
+Estimated-Depth Uniﬁcation with Self-Attention (MEDUSA) Song et al. (2021) incorporated inferred
+depth maps with RGB images in a multimodal transformer for object detection tasks. With limited
+analysis on CIFAR-10, He (2017) showed that estimated depth maps aid image classiﬁcation.
+3
+
+Results on ImageNette
+100
+BYOL
+BYOL+3DViewS
+Accuracy (in %)
+90
+80
+70
+60
+Top-1 Acc
+IN-C
+IN-3DCCResults on ImageNet-100
+90
+SimSiam
+80
+SimSiam+3DViews
+(%
+Accuracy (in 
+70
+60
+50
+40
+30
+Top-1 Acc
+IN-C
+IN-3DCCUnder review
+Most prior works that utilize depth information do so with the objective of improving certain tasks
+like object detection or semantic segmentation. To the best of our knowledge, ours is the ﬁrst work
+that focuses speciﬁcally on using an estimated depth signal to enhance contrastive learning. The deep
+encoder obtained from contrastive learning can then be used for various downstream tasks like object
+detection or image classiﬁcation.
+3
+DEPTH IN CONTRASTIVE LEARNING
+We propose two general methods of incorporating depth information into any SSL framework. Both
+of these methods, which we describe in detail shortly, assume the availability of a depth signal.
+We obtain this signal from an off-the-shelf pretrained Monocular Depth Estimation model. We
+generate depth maps for every RGB image in our data set using the state-of-the-art Dense Prediction
+Transformer (DPT) Ranftl et al. (2021) trained for the monocular depth estimation task. DPT is trained
+on a large training dataset with 1.4 million images and leverages the power of Vision Transformers.
+DPT outperforms other monocular depth estimation methods by a signiﬁcant margin. It has been
+shown that DPT can accurately predict depth maps for in-the-wild images Han et al. (2022). We treat
+the availability of these depth maps for contrastive learning as being similar to the availability that
+people have to extract depth cues via binocular disparity, motion parallax, or occlusion.
+(a) Original Image
+(b) Estimated Depth Map
+(c) Cropped Image
+(d) Estimated Depth Map
+Figure 3: Despite two images of a church (Imagenette) being quite similar visually, the presence of
+a tree occluding the church is a strong hint that the church is in the background, resulting in a very
+different depth map.
+3.1
+CONCATENATING A DEPTH CHANNEL TO THE INPUT
+We analyze the effect of concatenating a depth channel to the RGB image as a means of providing a
+richer input. This four-channel input is then fed through the model backbone. As we argued earlier,
+ample evidence suggests that cues to the three dimensional structure of the world are critical in the
+course of human development (e.g., learning about objects and their relationships), and these cues
+are available to biological systems early in the visual processing stream and are very likely used
+to segment the world into objects. Consequently, we hypothesize that a depth channel will support
+improved representations in contrastive learning.
+We anticipate that the depth channel might particularly assist the model when an image is corrupted,
+occluded, or viewed from an unusual perspective (Fig. 3). Depth might also be helpful in low-light
+environments where surface features of an object may not be clearly visible. This is quite important
+in safety critical applications like autonomous driving. The conjecture that depth cues will support
+interpretation of corrupted images is far from obvious because when the depth estimation method
+is applied to a corrupted image, the resulting depth maps are less than accurate (see Fig. 6 and
+7). We conduct evaluations using two corruption-robustness benchmarks to determine whether the
+depth signal extracted yields representations that on balance improve accuracy in a downstream
+classiﬁcation task. Sample visualizations of the images and their depth map can be found in App. C.
+As Figure 1 depicts, our proposed method processes each image and each augmentation of an
+image through the DPT depth extractor. However, in accord with practice in SSL, we sample a new
+augmentation on each training step and the computational cost of running DPT on every augmentation
+in every batch is high. To avoid this high cost of training, we perform a one-time computation of depth
+4
+
+Under review
+maps for every image in the dataset and use this cached map in training for the original image, but we
+also transform it for the augmentation. This transformation works as follows. First, an augmentation
+is chosen from the set of augmentations deﬁned by the base SSL method, and the RGB image is
+transformed according to this augmentation. For the depth map, only the corresponding Random
+Crop and Horizontal Flip transforms (i.e., dilation, translation, and rotations) are applied. The
+resulting depth map for the augmentation is cheap to compute, but it has a stronger correspondence
+to the original image’s depth map than one might expect had the depth map been computed for the
+augmentation by DPT. To address the possibility that the SSL method might come to rely too heavily
+on the depth map, we incorporated the notion of depth dropout.
+With depth dropout, the depth channel of any original image or augmentation is cleared (set to 0)
+with probability p, independently decided for each image or augmentation. When depth dropout is
+integrated with a SSL method, it prevents the SSL method from becoming too dependent on the depth
+signal by reducing the reliability of that signal. Consider a method like BYOL, whose objective is to
+predict the representations of one view from the other. With depth dropout, the objective is much
+more challenging. Since the depth channel is dropped out in some views, the network has to learn to
+predict the representations of a view with a depth signal using a view without depth. This leads to the
+model capturing additional 3D structure about the input without any signiﬁcant computation cost.
+At evaluation, every image in the evaluation set is processed by DPT; the short cut of remapping the
+depth channel from the original image to the augmentation was used only during training.
+3.2
+3D VIEWS WITH ADAMPI
+We now discuss our second method of incorporating depth information in contrastive SSL methods.
+This method is motivated by the fact that humans have two eyes and binocular vision requires us
+to match up the different views of the world seen by each eye. Because each eye has a subtlely
+different perspective, the images impinging on the retina are slightly different. The brain integrates
+the two images by determining the correspondence between regions from each eye. This stereo
+correspondence helps people in understanding and representing the 3D scene. We introduce this idea
+into Self-Supervised Learning with the help of Single-View View Synthesis methods.
+Single-View View Synthesis (Tucker & Snavely, 2020) is an extreme version of the view synthesis
+problem that takes single image as the input and renders images of the scene from new viewpoints. The
+task of view synthesis requires a deep understanding of the objects, scene geometry and appearance.
+Most of the methods proposed for this task make use of multiplane-image (MPI) representation
+(Tucker & Snavely, 2020; Li et al., 2021; Han et al., 2022). MPI consists of N fronto-parallel RGBα
+planes arranged at increasing depths. MINE (Li et al., 2021) introduced the idea of Neural Radiance
+Fields (Mildenhall et al., 2020) into the MPI to perform novel view synthesis with a single image.
+These single-view view synthesis methods have a wide ranging applications in Augmented and
+Virtual Reality as they allow the viewer to interact with the photos.
+Recently, a lot of single-view view synthesis methods have been using layered depth representations
+(Shih et al., 2020; Jampani et al., 2021). These methods have been shown to generalize well on the
+unseen real world images. As mentioned in Section 3.1, monocular depth estimation models like DPT
+(Ranftl et al., 2021) are used when depth maps are not available. AdaMPI (Han et al., 2022) is one
+such recently proposed method that aims to generate novel views for in-the-wild images. AdaMPI
+introduces two novel modules, a plane adjustment network and a color prediction network to adapt to
+diverse scenes. Results show that AdaMPI outperforms MINE and other single image view synthesis
+methods in terms of quality of the synthesized images. We use AdaMPI for all of the experiments in
+our paper, given the quality of synthesized images generated by AdaMPI.
+At inference, AdaMPI takes an RGB image, depth (estimated from the monocular depth estimation
+model), and the target view to be rendered. The single-view view synthesis model then generates a
+multiplane-image representation of the scene. This representation can then be easily used to transform
+the image in the source view to the target view. More details about AdaMPI is present in App. B.
+In a nutshell, AdaMPI generates a “3D photo” of a given scene given a single input. In a way, it can
+be claimed that an image can be “brought to life” by generating the same image from another camera
+viewpoint (Kopf et al., 2019). We propose to use the views generated by AdaMPI as augmentations
+for SSL methods (Fig. 2). The synthesized views captures the 3D scene and generates realistic
+5
+
+Under review
+Table 1: Results on ImageNette Dataset show consistently improved robustness from explicitly
+leveraging depth estimation. Additionally, the depth channel approach consistently outperforms the
+3D view augmentation approach.
+Method
+kNN
+Top-1 Acc.
+ImageNet-C
+ImageNet-3DCC
+BYOL (Grill et al., 2020)
+85.71
+85.27
+84.13
+83.68
++ Depth (p = 0.5)
+88.56
+88.03
+87.00
+86.68
++ 3D Views
+87.01
+87.42
+85.75
+85.86
+SimSiam (Chen & He, 2021)
+85.10
+85.76
+84.08
+84.16
++ Depth (p = 0.5)
+86.52
+87.41
+85.13
+85.08
++ 3D Views
+85.94
+87.62
+83.87
+84.37
+SwAV (Caron et al., 2020)
+89.63
+91.08
+75.31
+82.05
++ Depth (p = 0.5)
+89.20
+90.85
+83.80
+85.02
+augmentations that help the model learn better representations. These augmentations are meant to
+reﬂect the type of subtle shifts in perspective obtained from the two eyes or from minor head or body
+movements.
+Augmentations are a key ingredient in contrastive learning methods (Chen et al., 2020a). Modifying
+the strength of augmentations or removing certain augmentations leads to signiﬁcant drop in the
+performance of contrastive methods (Chen et al., 2020a; Grill et al., 2020; Zhang & Ma, 2022). Most
+of these augmentations can be considered as ”2D” as they make changes in the image either by
+cropping the image or applying color jitter. On the other hand, the generated 3D views are quite
+diverse as they bring in another dimension to the contrastive setup. Moreover, they can be combined
+with the existing set of augmentations to achieve the best performance.
+The synthesized views as augmentations allow the model to virtually interact with the 3D world.
+For every training sample, we generate k views synthesized from the camera in the range of x-axis
+range, y-axis range and z-axis range. The x-axis range essentially refers to the shift in the x-axis
+from the position of the original camera. The synthesis of the 3D Views is computed only once for
+the training dataset in an ofﬂine manner. Out of the total k views per sample, we sample one view at
+every training step and use it for training. We tried two techniques to augment the synthesized views.
+First, we applied the augmentations of the base SSL method on top of the synthesized view. Second,
+we applied the base SSL augmentations with a probability of q or we used the synthesized view (with
+Random Crop and Flip) with a probability of 1-q. Full details can be found in the Appendix.
+The range of novel camera views generated by the single-view view synthesis method can be
+controlled by the user. It is possible to speciﬁcally control the x-axis shift, y-axis shift and z-axis
+shift (zoom) during the generation of the novel views. The quality of generated images degrades
+when the novel view to be generated is far from the current position of the camera. This is expected
+because it is not feasible to generate a complete 360-degree view of the scene by using a single image.
+In practice, we observe certain artifacts in the image when views far away from the current position
+of the camera. Additional details can be found in App. A and App. D.
+4
+EXPERIMENTAL RESULTS
+We show results with the addition of depth channel and 3D Views with various SSL methods on
+ImageNette, ImageNet-100 and ImageNet-1k datasets. We also measure the corruption robustness of
+these models by evaluating the performance of these models on ImageNet-C and ImageNet-3DCC.
+4.1
+EXPERIMENTAL SETUP
+ImageNette: is a 10 class subset of ImageNet (Deng et al., 2009) that consists of 9469 images for
+training and 2425 images for testing. We use the 160px version of the dataset for all the experiments
+and train the models with an image size of 128.
+6
+
+Under review
+Table 2: Results on ImageNet-100 Dataset indicates that both addition of the depth channel and 3D
+Views leads to a gain in corruption robustness performance.
+Method
+kNN
+Top-1 Acc.
+ImageNet-C
+ImageNet-3DCC
+BYOL (Grill et al., 2020)
+74.24
+80.74
+47.15
+53.69
++ Depth (p = 0.3)
+74.66
+80.24
+50.17
+55.55
++ 3D Views
+73.42
+80.16
+48.15
+54.88
+SimSiam (Chen & He, 2021)
+67.56
+76.00
+44.39
+50.44
++ Depth (p = 0.2)
+70.90
+76.54
+48.30
+52.93
++ 3D Views
+68.08
+76.40
+45.78
+52.17
+ImageNet-100: is a 100 class subset of ImageNet (Deng et al., 2009) consisting of 126689 training
+images and 5000 validation images. We use the same classes as in (Tian et al., 2020) and train all
+models with image size of 224.
+ImageNet-1k: consists of 1000 classes with 1.2 million training images and 50000 validation images.
+ImageNet-C (IN-C) (Hendrycks & Dietterich, 2019): ImageNet-C dataset is a benchmark to evaluate
+the robustness of the model to common corruptions. It consists of 15 types of algorithmically
+generated corruptions including weather corruptions, noise corruptions and blur corruptions with
+different severity. Refer to Fig. 6 for a visual depiction of the images corrupted with Gaussian Noise.
+ImageNet-3DCC (IN-3DCC) (Kar et al., 2022): ImageNet-3DCC consists of realistic 3D corruptions
+like camera motion, occlusions, weather to name a few. The 3D realistic corruptions are generated
+using the estimated depth map and improves upon the corruptions in ImageNet-C. Some examples of
+these corruptions include XY-Motion Blur, Near Focus, Flash, Fog3D to name a few.
+Experimental Details. We use a ResNet-18 (He et al., 2016) backbone for all our experiments
+except the ImageNet-1k dataset where we use ResNet-50 architecture as used in Chen & He (2021).
+For the pretraining stage, the network is trained using the SGD optimizer with a momentum of 0.9
+and batch size of 256. The ImageNette experiments are trained with a learning rate of 0.06 for
+800 epochs whereas the ImageNet-100 experiments are trained with a learning rate of 0.2 for 200
+epochs. We implement our methods in PyTorch 1.11 (Paszke et al., 2019) and use Weights and Biases
+(Biewald, 2020) to track the experiments. We refer to the lightly (Susmelj et al., 2020) benchmark
+for ImageNette experiments and solo-learn (da Costa et al., 2022) benchmark for ImageNet-100
+experiments. We follow the commonly used linear evaluation protocol to evaluate the representations
+learned by the SSL method. For linear evaluation, we use SGD optimizer with a momentum of 0.9
+and train the network for 100 epochs. For the ImageNette+3D Views experiments, we apply base
+SSL augmentation on top of the synthesized views at every training step. For the ImageNet-100+3D
+Views experiments, we apply the base SSL augmentations with a probability of 0.5. Additional
+experimental details is present in the App. A.
+4.2
+RESULTS ON IMAGENETTE
+Table 1 shows the beneﬁt of incorporating depth with any SSL method on the ImageNette dataset. We
+use the k-nearest neighbor (kNN) classiﬁer and Top-1 Acc from the linear evaluation performance
+to evaluate the learned representation of the SSL method. It can be seen that the addition of depth
+improves the accuracy of BYOL, SimSiam and SwAV. BYOL+Depth indicates that the model is
+trained with depth map with the depth dropout. BYOL+Depth improves upon the Top-1 accuracy
+of BYOL by 2.8% along with a 3% increase in the ImageNet-C and ImageNet-3DCC performance.
+This clearly demonstrates the role of depth information in corrupted images.
+We observe a signiﬁcant 8.5% increase in the ImageNet-C with SwAV+Depth over the base SwAV.
+On a closer look, it can be seen that the addition of depth channel results in high robustness to
+noise-based perturbations and blur-based perturbations. For instance, the accuracy on the Motion Blur
+corruption increases from 70.32% with SwAV to 86.88% with SwAV+Depth. And the performance
+on Gaussian Noise corruption increases from 69.76% to 84.56% with the addition of depth channel.
+BYOL + 3D Views indicates that the views synthesized by AdaMPI are used as augmentations in the
+contrastive learning setup. We show that proposed 3D Views leads to a gain in accuracy with both
+7
+
+Under review
+Table 3: Results on ImageNet-1k dataset (ResNet-50) illustrates the role of depth channel and 3D
+Views in self-supervised learning methods on large-scale datasets.
+Method
+Epochs
+Top-1 Acc.
+ImageNet-C
+ImageNet-3DCC
+SimSiam (Chen & He, 2021)
+800
+71.70
+36.45
+43.32
++ Depth (p = 0.2)
+800
+71.30
+38.23
+45.11
+SimSiam (Chen & He, 2021)
+100
+68.10
+32.99
+38.94
++ 3D Views
+100
+68.08
+34.43
+40.71
+BYOL and SimSiam. This indicates that the diversity in the augmentations due to the 3D Views helps
+the model capture a better representation of the world. We also observe a decent gain in accuracy on
+IN-C and IN-3DCC with 3D views compared to the baseline BYOL.
+4.3
+RESULTS ON IMAGENET-100
+Table 2 summarizes the results on the large-scale ImageNet-100 with BYOL and SimSiam. We ﬁnd
+that most of the observations on the ImageNette datasets also hold true in the ImageNet-100 datasets.
+Though the increase in the Top-1 Accuracy with the inclusion of depth is minimal, we observe that
+performance on ImageNet-C and ImageNet-3DCC increases notably. With SimSiam, we notice a
+3.9% increase in ImageNet-C accuracy and a 2.5% increase in ImageNet-3DCC accuracy just by
+the addition of depth channel. These results emphasize the role of the proposed depth channel with
+dropout in contrastive learning.
+We observe that the proposed method of incorporating 3D views outperforms the base SSL method
+on the ImageNet-100 dataset, primarily in the corruption benchmarks. On a detailed look at the
+performance of each corruption, we observe that the 3D Views improves the performance of 3D
+based corruptions by more than 2.5%. (Refer Table 5)
+4.4
+RESULTS ON IMAGENET-1K
+Table 3 shows results on the large scale ImageNet dataset with 1000 classes. We achieve comparable
+Top-1 accuracy with both Depth and 3D Views. Since the training set is large, the additional inductive
+bias is ineffective for the in-distribution test set but useful for out-of-distribution samples. We observe
+signiﬁcant accuracy boosts in classiﬁcation of corrupted images: 1.5% for ImageNet-C and 1.8% for
+ImageNet-3DCC. These results indicate that our observations scale up to ImageNet-1k dataset and
+further strengthens the argument about the role of depth channel and 3D Views in SSL methods.
+5
+DISCUSSION
+Depth Dropout. Table 4 shows the ablation of probability of Depth dropout (p) on the ImageNette
+dataset with BYOL. The inﬂuence of using the depth dropout can also be understood with these
+results. It can be observed that without depth dropout (p = 0.0), the performance of the model
+is signiﬁcantly lower than the baseline BYOL, as the network learns to focus solely on the depth
+channel. We ﬁnd that p = 0.2 leads to the highest Top-1 Accuracy but p = 0.5 achieves the best
+performance on the ImageNet-C and ImageNet-3DCC. As the depth dropout increases (p = 0.8), the
+performance gets closer to the base SSL method as the model completely ignores the depth channel.
+What happens when depth is not available during inference? In this ablation, we examine the
+importance of depth signal at inference. Given a model trained with depth information, we analyze
+what happens when we set the depth to 0 at inference. Table 7 reports these results on ImageNette
+dataset with BYOL. Interestingly, we ﬁnd that even with the absence of depth information, the
+accuracy of the model is higher than the baseline BYOL. This indicates that the model has implicitly
+learned some depth signal and captured better representations. It can also be seen that the performance
+on IN-3DCC is 1.5% higher than BYOL. Furthermore, we observe that the addition of depth map
+improves the performance on all the benchmarks. This further highlights our message that depth
+signal is a useful signal in learning a robust model.
+8
+
+Under review
+10
+15
+20
+25
+30
+35
+40
+45
+50
+Number of Views
+85.75
+86.00
+86.25
+86.50
+86.75
+87.00
+87.25
+87.50
+Accuracy (in %)
+Number of generated 3D views
+SimSiam (Baseline)
+Figure 4: As the number of 3D
+views increases, the performance of
+the SSL method increases with very
+limited increase in performance.
+Method
+Top-1 Acc.
+IN-C
+IN-3DCC
+BYOL (Grill et al., 2020)
+85.27
+84.13
+83.68
++ Depth (p = 0.0)
+84.38
+72.64
+73.68
++ Depth (p = 0.2)
+89.05
+85.93
+85.33
++ Depth (p = 0.5)
+88.03
+87.00
+86.68
++ Depth (p = 0.8)
+86.57
+85.38
+85.60
+Table 4: Ablation of Depth Dropout hyperparameter (p). A
+large dropout (p = 0.8) leads to the model ignoring the depth
+signal and a low (or zero) depth dropout leads to model
+relying only on depth signal.
+Table 5: Results on ImageNet-100 Corruptions show that while use of 3D view augmentations
+provides a larger improvement on 3D corruptions, the improvements from using depth channel are
+more consistent on a wide range of corruptions. Detailed results in App. E.
+Method
+IN-C
+Noise
+Blur
+Weather
+Digital
+IN-3DCC
+3D
+Misc
+BYOL (Grill et al., 2020)
+47.15
+36.69
+38.95
+49.57
+59.33
+53.69
+54.53
+51.16
++ Depth (p = 0.3)
+50.17
+42.36
+40.66
+51.88
+62.17
+55.55
+55.85
+54.65
++ 3D Views
+48.15
+34.50
+43.06
+50.16
+60.14
+54.88
+56.56
+49.81
+SimSiam (Chen & He, 2021)
+44.39
+36.20
+36.11
+45.24
+55.86
+50.44
+51.32
+47.83
++ Depth (p = 0.2)
+48.30
+41.90
+38.40
+49.76
+59.84
+52.93
+53.16
+52.25
++ 3D Views
+45.78
+35.00
+40.42
+46.20
+57.14
+52.17
+53.69
+47.63
+Number of Views generated by AdaMPI. Figure 4 investigates the impact of the number of
+generated 3D views on the performance of SimSiam (ImageNette). We observe that as the number of
+views increases, the Top-1 Accuracy increases although the gains are quite minimal. It must be noted
+that even with 10 views, the SimSiam+3D Views outperforms the baseline SimSiam by 1.5%.
+Which corruptions improve due to depth and 3D Views? A detailed analysis of the performance
+of the methods on various type of corruptions is reported in Table 5. We report the average on different
+categories of corruptions to understand the role of various corruptions on the overall performance.
+For ImageNet-C (IN-C), we divide the corruptions into 4 groups: Noise, Blur, Weather and Digital.
+ImageNet-3DCC is split up into two categories based on whether they make use of 3D information.
+We observe that the depth channel leads to a massive 5.7% average gain on the noise corruptions
+and 3.4% increase in digital corruptions over the baseline. The use of 3D Views in SSL results in
+a notable 4.2% improvement on the Blur corruptions over the base SSL method. As expected, the
+performance on 3D Corruptions with the 3D Views is much higher than standard SSL method and
+slightly higher than the method that uses depth channel. More results can be found in App. E.
+Table 6: Ablation on Range of synthesized views generated
+by AdaMPI. Results are shown on ImageNette dataset.
+Method
+Top-1 Acc.
+IN-C
+IN-3DCC
+BYOL (Grill et al., 2020)
+85.27
+84.13
+83.68
++ 3D Views (x = 0.1; y = 0.1)
+86.09
+83.33
+83.63
++ 3D Views (x = 0.4; y = 0.4)
+87.87
+84.78
+85.22
++ 3D Views (x = 0.5; y = 0.5)
+88.08
+85.07
+85.33
++ 3D Views (x = 0.8; y = 0.8)
+87.49
+82.47
+84.35
++ 3D Views (x = 1.0; y = 1.0)
+86.34
+80.81
+83.30
+Range
+of
+Views
+generated
+by
+AdaMPI. The range of 3D Views
+generated by AdaMPI play a huge
+role in the performance of the SSL
+method. Table 6 summarizes the ef-
+fects of moving the target camera on
+the learned representations on Ima-
+geNette dataset. x denotes the amount
+by which the x-axis is moved and y de-
+notes the same for y-axis. We observe
+that a very small change in viewing
+direction (x = 0.1; y = 0.1) does not
+boost the performance very much. As x and y get larger, the quality of generated images also de-
+creases. Thus, a large change in the viewing direction leads to artifacts which hurts the performance.
+9
+
+Under review
+Table 7: These results on ImageNette show that
+the model is robust to the absence of depth signal
+and that estimated depth improves the corruption
+robustness and linear evaluation performance.
+Method
+Top-1 Acc.
+IN-C
+IN-3DCC
+BYOL (Grill et al., 2020)
+85.27
+84.13
+83.68
++ Depth (p = 0.5)
+88.03
+87.00
+86.68
+Depth = 0 at inference
+86.80
+84.95
+85.21
+Table 8: Comparison of two Single-View View
+Synthesis Methods for generating 3D Views on
+ImageNette dataset. Higher quality views leads
+to higher performance.
+Method
+Top-1 Acc.
+IN-C
+IN-3DCC
+BYOL (Grill et al., 2020)
+85.27
+84.13
+83.68
++ 3D Views (MINE)
+87.49
+84.47
+83.93
++ 3D Views (AdaMPI)
+88.08
+85.07
+85.33
+This can be clearly observed in Table 6 where we see a drop in accuracy as the x and y increases
+from 0.5 to 1.0.
+Quality of Synthesized Views. In this ablation, we investigate how the quality of the synthesized
+views affects the representations learnt by Self-Supervised methods. We compare two different
+methods to generate 3D Views of the image namely MINE (Li et al., 2021) and AdaMPI (Han et al.,
+2022). The quantitative and qualitative results shown in Han et al. (2022) indicate that AdaMPI
+generates superior quality images compared to MINE. Table 8 reports the results on ImageNette with
+BYOL comparing the 3D Views synthesized by MINE and AdaMPI methods. We observe that the
+method with 3D Views generated by AdaMPI outperforms the method with 3D Views generated
+by MINE. This is a clear indication that as the quality of 3D view synthesis methods improves, the
+accuracy of the SSL methods with 3D views increases as well.
+6
+CONCLUSION
+In this work, we propose two distinct approaches to improving SSL using a (noisy) depth signal
+extracted from a monocular RGB image. Our results on ImageNette, ImageNet-100 and ImageNet-
+1k datasets with a range of SSL methods (BYOL, SimSiam and SwAV) show that both proposed
+approaches outperform the baseline SSL on test accuracy and corruption robustness. Further, our
+approaches can be integrated into any SSL method to boost performance. We close with several
+critical directions for future research. First, given that our two approaches are complementary
+and compatible, we might evaluate the two approaches in combination. Second, is depth dropout
+necessary when depth extraction with DPT can be run on every augmentation on every training step?
+Third, one might explore the idea of synthesizing views in Single-View View Synthesis methods with
+the goal of maximizing the performance (Ge et al., 2022) or develop better methods to utilize the 3D
+Views.
+REFERENCES
+R. Baillargeon. Infants’ reasoning about hidden objects: evidence for event-general and event-
+speciﬁc expectations. Developmental science, 7(4):391–414, 2004. doi: https://doi.org/10.1111/j.
+1467-7687.2004.00357.
+Lukas Biewald. Experiment tracking with weights and biases, 2020. URL https://www.wandb.
+com/. Software available from wandb.com.
+Yuanzhouhan Cao, Chunhua Shen, and Heng Tao Shen. Exploiting depth from single monocular
+images for object detection and semantic segmentation. IEEE Transactions on Image Processing,
+26(2):836–846, 2016.
+Mathilde Caron, Ishan Misra, Julien Mairal, Priya Goyal, Piotr Bojanowski, and Armand Joulin.
+Unsupervised learning of visual features by contrasting cluster assignments. Advances in Neural
+Information Processing Systems, 33:9912–9924, 2020.
+Ting Chen, Simon Kornblith, Mohammad Norouzi, and Geoffrey Hinton. A simple framework for
+contrastive learning of visual representations. In International conference on machine learning, pp.
+1597–1607. PMLR, 2020a.
+Xinlei Chen and Kaiming He. Exploring simple siamese representation learning. In Proceedings of
+the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp. 15750–15758, 2021.
+10
+
+Under review
+Xinlei Chen, Haoqi Fan, Ross Girshick, and Kaiming He. Improved baselines with momentum
+contrastive learning. arXiv preprint arXiv:2003.04297, 2020b.
+Victor Guilherme Turrisi da Costa, Enrico Fini, Moin Nabi, Nicu Sebe, and Elisa Ricci. solo-learn: A
+library of self-supervised methods for visual representation learning. Journal of Machine Learning
+Research, 23(56):1–6, 2022. URL http://jmlr.org/papers/v23/21-1155.html.
+Jia Deng, Wei Dong, Richard Socher, Li-Jia Li, Kai Li, and Li Fei-Fei. Imagenet: A large-scale
+hierarchical image database. In 2009 IEEE conference on computer vision and pattern recognition,
+pp. 248–255. Ieee, 2009.
+Andreas Eitel, Jost Tobias Springenberg, Luciano Spinello, Martin Riedmiller, and Wolfram Burgard.
+Multimodal deep learning for robust rgb-d object recognition. In 2015 IEEE/RSJ International
+Conference on Intelligent Robots and Systems (IROS), pp. 681–687. IEEE, 2015.
+J. T. Enns and R. A. Rensink. Preattentive recovery of three-dimensional orientation from line
+drawings. Psychological Review, 3(98):335–351, 1991. doi: https://doi.org/10.1037/0033-295X.
+98.3.335.
+James Enns and Ronald Rensink. Sensitivity to three-dimensional orientation in visual search.
+Psychological Science, 1:323–326, 09 1990. doi: 10.1111/j.1467-9280.1990.tb00227.x.
+Yunhao Ge, Harkirat Behl, Jiashu Xu, Suriya Gunasekar, Neel Joshi, Yale Song, Xin Wang, Laurent
+Itti, and Vibhav Vineet. Neural-sim: Learning to generate training data with nerf. arXiv preprint
+arXiv:2207.11368, 2022.
+Robert Geirhos, J¨orn-Henrik Jacobsen, Claudio Michaelis, Richard Zemel, Wieland Brendel, Matthias
+Bethge, and Felix A. Wichmann. Shortcut learning in deep neural networks. Nature Machine
+Intelligence, 2(11):665–673, nov 2020. doi: 10.1038/s42256-020-00257-z.
+Spyros Gidaris, Praveer Singh, and Nikos Komodakis. Unsupervised representation learning by
+predicting image rotations. arXiv preprint arXiv:1803.07728, 2018.
+Jean-Bastien Grill, Florian Strub, Florent Altch´e, Corentin Tallec, Pierre Richemond, Elena
+Buchatskaya, Carl Doersch, Bernardo Avila Pires, Zhaohan Guo, Mohammad Gheshlaghi Azar,
+et al. Bootstrap your own latent-a new approach to self-supervised learning. Advances in neural
+information processing systems, 33:21271–21284, 2020.
+Yuxuan Han, Ruicheng Wang, and Jiaolong Yang. Single-view view synthesis in the wild with
+learned adaptive multiplane images. In ACM SIGGRAPH, 2022.
+Richard Hartley and Andrew Zisserman. Multiple View Geometry in Computer Vision. Cambridge
+University Press, 2004.
+Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun. Deep residual learning for image
+recognition. In Proceedings of the IEEE conference on computer vision and pattern recognition,
+pp. 770–778, 2016.
+Yihui He. Estimated depth map helps image classiﬁcation. arXiv preprint arXiv:1709.07077, 2017.
+Dan Hendrycks and Thomas Dietterich. Benchmarking neural network robustness to common corrup-
+tions and perturbations. Proceedings of the International Conference on Learning Representations,
+2019.
+Lukas Hoyer, Dengxin Dai, Yuhua Chen, Adrian Koring, Suman Saha, and Luc Van Gool. Three
+ways to improve semantic segmentation with self-supervised depth estimation. In Proceedings of
+the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp. 11130–11140, 2021.
+Sergey Ioffe and Christian Szegedy. Batch normalization: Accelerating deep network training by
+reducing internal covariate shift. In International conference on machine learning, pp. 448–456.
+PMLR, 2015.
+11
+
+Under review
+Varun Jampani, Huiwen Chang, Kyle Sargent, Abhishek Kar, Richard Tucker, Michael Krainin,
+Dominik Kaeser, William T Freeman, David Salesin, Brian Curless, et al. Slide: Single image
+3d photography with soft layering and depth-aware inpainting. In Proceedings of the IEEE/CVF
+International Conference on Computer Vision, pp. 12518–12527, 2021.
+James T Kajiya and Brian P Von Herzen. Ray tracing volume densities. ACM SIGGRAPH computer
+graphics, 18(3):165–174, 1984.
+O˘guzhan Fatih Kar, Teresa Yeo, Andrei Atanov, and Amir Zamir. 3d common corruptions and data
+augmentation. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern
+Recognition, pp. 18963–18974, 2022.
+Diederik P Kingma and Jimmy Ba. Adam: A method for stochastic optimization. arXiv preprint
+arXiv:1412.6980, 2014.
+Johannes Kopf, Suhib Alsisan, Francis Ge, Yangming Chong, Kevin Matzen, Ocean Quigley, Josh
+Patterson, Jossie Tirado, Shu Wu, and Michael F Cohen. Practical 3d photography. In Proceedings
+of CVPR Workshops, volume 1, 2019.
+Jiaxin Li, Zijian Feng, Qi She, Henghui Ding, Changhu Wang, and Gim Hee Lee. Mine: Towards
+continuous depth mpi with nerf for novel view synthesis. In Proceedings of the IEEE/CVF
+International Conference on Computer Vision, pp. 12578–12588, 2021.
+Ben Mildenhall, Pratul P Srinivasan, Matthew Tancik, Jonathan T Barron, Ravi Ramamoorthi, and
+Ren Ng. Nerf: Representing scenes as neural radiance ﬁelds for view synthesis. In European
+conference on computer vision, pp. 405–421. Springer, 2020.
+Vinod Nair and Geoffrey E Hinton. Rectiﬁed linear units improve restricted boltzmann machines. In
+Icml, 2010.
+K. Nakayama and G. H. Silverman. Serial and parallel processing of visual feature conjunctions.
+Nature, 320:264–265, 1986.
+Mehdi Noroozi and Paolo Favaro. Unsupervised learning of visual representations by solving jigsaw
+puzzles. In European conference on computer vision, pp. 69–84. Springer, 2016.
+Adam Paszke, Sam Gross, Francisco Massa, Adam Lerer, James Bradbury, Gregory Chanan,
+Trevor Killeen, Zeming Lin, Natalia Gimelshein, Luca Antiga, Alban Desmaison, Andreas
+Kopf, Edward Yang, Zachary DeVito, Martin Raison, Alykhan Tejani, Sasank Chilamkurthy,
+Benoit Steiner, Lu Fang, Junjie Bai, and Soumith Chintala. Pytorch: An imperative style, high-
+performance deep learning library. In H. Wallach, H. Larochelle, A. Beygelzimer, F. d'Alch´e-Buc,
+E. Fox, and R. Garnett (eds.), Advances in Neural Information Processing Systems 32, pp.
+8024–8035. Curran Associates, Inc., 2019. URL http://papers.neurips.cc/paper/
+9015-pytorch-an-imperative-style-high-performance-deep-learning-library.
+pdf.
+Ren´e Ranftl, Alexey Bochkovskiy, and Vladlen Koltun. Vision transformers for dense prediction. In
+Proceedings of the IEEE/CVF International Conference on Computer Vision, pp. 12179–12188,
+2021.
+Ronald Rensink and James Enns. Early completion of occluded objects. Vision Research, 38:
+2489–2505, 09 1998. doi: 10.1016/S0042-6989(98)00051-0.
+Daniel Seichter, Mona K¨ohler, Benjamin Lewandowski, Tim Wengefeld, and Horst-Michael Gross.
+Efﬁcient rgb-d semantic segmentation for indoor scene analysis. In 2021 IEEE International
+Conference on Robotics and Automation (ICRA), pp. 13525–13531. IEEE, 2021.
+Meng-Li Shih, Shih-Yang Su, Johannes Kopf, and Jia-Bin Huang. 3d photography using context-
+aware layered depth inpainting. In Proceedings of the IEEE/CVF Conference on Computer Vision
+and Pattern Recognition, pp. 8028–8038, 2020.
+Hwanjun Song, Eunyoung Kim, Varun Jampan, Deqing Sun, Jae-Gil Lee, and Ming-Hsuan Yang.
+Exploiting scene depth for object detection with multimodal transformers. In 32nd British Machine
+Vision Conference, pp. 1–14. British Machine Vision Association (BMVA), 2021.
+12
+
+Under review
+E. S. Spelke. Principles of object perception. Cognitive Science, 14:29–56, 1990.
+Elizabeth S Spelke and Katherine D Kinzler. Core knowledge. Developmental Science, 10(1):89–96,
+2007.
+Igor Susmelj, Matthias Heller, Philipp Wirth, Jeremy Prescott, Malte Ebner, and et al. Lightly.
+GitHub. Note: https://github.com/lightly-ai/lightly, 2020.
+Yonglong Tian, Dilip Krishnan, and Phillip Isola. Contrastive multiview coding. In European
+conference on computer vision, pp. 776–794. Springer, 2020.
+Richard Tucker and Noah Snavely. Single-view view synthesis with multiplane images. In Proceed-
+ings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp. 551–560,
+2020.
+Junbo Zhang and Kaisheng Ma. Rethinking the augmentation module in contrastive learning:
+Learning hierarchical augmentation invariance with expanded views. In Proceedings of the
+IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp. 16650–16659, 2022.
+Richard Zhang, Phillip Isola, and Alexei A Efros. Colorful image colorization. In European
+conference on computer vision, pp. 649–666. Springer, 2016.
+Jinghao Zhou, Chen Wei, Huiyu Wang, Wei Shen, Cihang Xie, Alan Yuille, and Tao Kong. ibot:
+Image bert pre-training with online tokenizer. arXiv preprint arXiv:2111.07832, 2021.
+13
+
+Under review
+A
+EXPERIMENTAL DETAILS
+We discuss the detailed experimental setup to allow reproducibility of the results.
+Pretraining:
+BYOL: The architecture of the online and target networks in BYOL consists of three components:
+encoder, projector and predictor. We use ResNet-18 (He et al., 2016) implementation available in
+torchvision as our encoder. The Prediction Network in BYOL is a Multi-Layer Perceptron (MLP) that
+consists of a linear layer with an output dimension of 4096, followed by Batch Normalization (Ioffe
+& Szegedy, 2015), ReLU (Nair & Hinton, 2010) and a ﬁnal linear layer with a dimension of 256.
+We use the same augmentations as in lightly benchmark which uses a slightly modiﬁed version of
+augmentations used in SimCLR (Chen et al., 2020b). The network is trained with an SGD Optimizer
+with a momentum of 0.9 and a weight decay of 0.0005. A batch size of 256 is used and the network
+is trained for a total of 800 epochs with a cosine annealing scheduler.
+For ImageNet-100, we use the ResNet-18 encoder and train the network using an SGD optimizer
+with a momentum of 0.9 and a weight decay of 0.0001. We use the set of augmentations in solo-
+learn benchmark in our experiments. The model is trained for 200 epochs with a batch size of 256.
+The architecture of the prediction head is same as the one used in ImageNette but with the output
+dimension of the linear layer set to 8192.
+SimSiam We follow the same optimization hyperparameters as in BYOL for the ImageNette dataset.
+The architecture of the projection head is a 3-layer MLP with Batch Normalization and ReLU applied
+to each layer. (The output layer does not have ReLU). The prediction head is a 2-layer MLP with a
+hidden dimension of 512. We refer to the ofﬁcial implementation of SimSiam 1 for the ImageNet-1k
+experiments.
+SwAV: For SwAV, we use the Adam optimizer (Kingma & Ba, 2014) with a learning rate of 0.001
+and weight decay of 0.000001. The number of code vectors (or prototypes) is set to 3K with 128
+dimensions. The projection head is a 2-layer MLP with a hidden layer dimension of 2048 and an
+output dimension of 128. SwAV also introduced the idea of multi-crop where a single input image
+is transformed into 2 global views and V local views. 6 local views are used in our ImageNette
+experiments.
+Linear Probing:
+For linear probing, we choose the model with the highest validation kNN accuracy and freeze the
+representations. We then train a linear layer using SGD with momentum optimizer for 100 epochs.
+We do a grid search on {0.2, 0.5, 0.8, 5.0} and report the best accuracy of the best performing
+model. This is commonly followed in the SSL literature (Zhou et al., 2021). We use the standard
+set of augmentations which includes Random Resized Crop and Horizontal Flip for training. For
+ImageNet-100, we observe that a higher learning rate seems to help and we do a grid search on
+{0.5, 0.8, 5.0, 30.0}. In most of the experiments, we observe that using the learning rate of 30.0
+yields the best-performing model.
+Depth Prediction Transformer
+We refer to the ofﬁcial implementation of the DPT 2 to compute the depth maps. The weights of the
+best-performing monocular depth estimation model i.e, DPT-Large, is used for the calculation of the
+depth maps. We use the relative depth maps generated by the DPT model.
+AdaMPI:
+We refer to the ofﬁcial implementation of AdaMPI 3 paper to compute the 3D Views. The depth maps
+generated by DPT are fed as input to the AdaMPI. We generate 50 views per sample. A pretrained
+AdaMPI model with 64 MPI planes is used in our experiments.
+For the ImageNette experiments, we apply base SSL augmentations on top of the generated AdaMPI
+at every training step. We did a grid search on a set of generated views and selected the best
+1https://github.com/facebookresearch/simsiam
+2https://github.com/isl-org/DPT
+3https://github.com/yxuhan/AdaMPI
+14
+
+Under review
+performing model. For both BYOL and SimSiam x = 0.4; y = 0.4 and z = 0.0 was used to generate
+3D Views.
+For ImageNet-100, we apply the base SSL augmentations with a probability of 0.5 and use the
+synthesized views with a probability of 0.5. We use the views synthesized with x = 0.2; y = 0.2 and z
+= 0.2.
+For ImageNet-100 experiments, we use Automatic Mixed Precision training to speed up the training.
+All the ImageNette experiments are run on RTX 8000 GPUs while the ImageNet-100 experiments are
+run on A100 GPUs. We are thankful to the authors of DPT (Ranftl et al., 2021) and AdaMPI (Han
+et al., 2022) for publicly releasing the code and pretrained weights. We will also release the code and
+pretrained weights to enable reproducible research.
+B
+ADAMPI
+This section explains about how AdaMPI renders new views. The notation and content of this section
+is heavily derived from Han et al. (2022) and Li et al. (2021).
+Consider a pixel coordinate in a image as [x, y], the camera intrinsic matrix K, camera rotation matrix
+R, camera translation matrix t. A Multiplane image (MPI) is a layered representation that consists of
+N fronto-parallel RGBα planes arranged in the increasing order of depth.
+The ﬁrst step in rendering a novel view to ﬁnd the correspondence between the source pixel coordinates
+[xs, ys]T and target pixel coordinates [xt, yt]T . This can be done by using the homography function
+(Hartley & Zisserman, 2004) as shown by the equation below.
+�xs, ys, 1�⊤ ∼ K
+�
+R − tn⊤
+di
+�
+K−1 �xt, yt, 1�⊤ ,
+(1)
+where, n = [0, 0, 1]⊤ is the normal vector of the fronto-parallel plane in the source view. Equation 1
+essentially maps the correspondence between source and target pixel coordinate at a particular MPI
+plane.
+The plane projections at the target plane c′
+di(xt, yt) = c′
+di(xs, ys) and σ′
+di(xt, yt) = σ′
+di(xs, ys).
+Volume rendering (Li et al., 2021; Kajiya & Von Herzen, 1984; Mildenhall et al., 2020) and Alpha
+compositing can then be used to render the image.
+AdaMPI has two major components, a planar adjustment network and color prediction network. In
+previous works Tucker & Snavely (2020), the di was usually ﬁxed. However, in AdaMPI, the planar
+adjustment predicts di and each MPI plane at correct depth. The color prediction network takes this
+adjusted depth planes and predicts the color and density at each plane. For additional details, we refer
+the reader to Han et al. (2022).
+C
+VISUALIZATION OF DEPTH MAPS
+In this section, we show sample visualization of the depth map generated by the DPT model. Figure
+5 shows some sample visualization of the original image and the corresponding depth maps. The
+impact of corrupted images on the estimated depth maps is shown in Fig. 7. It can be seen that high
+severity in Gaussian Noise distorts the estimated depth maps signiﬁcantly.
+In Figure 3, we show the impact of occlusion on the estimated depth map. Fig 3a contains a tree
+in front of it and thus it looks like the Church building has a low depth (It is far away). When we
+just crop the image and remove the trees (Fig. 3c), it can clearly seen how the estimated depth maps
+changes drastically (Fig. 3d).
+D
+VISUALIZATION OF 3D VIEWS
+We refer the reader to the supplementary zip ﬁle for some sample videos and images of synthesized
+views from AdaMPI.
+15
+
+Under review
+(a) Original Image
+(b) Estimated Depth Map
+(c) Original Image
+(d) Estimated Depth Map
+Figure 5: Visualization of Depth Maps of Images from the ImageNette dataset
+(a) Severity = 1
+(b) Severity = 2
+(c) Severity = 3
+(d) Severity = 4
+(e) Severity = 5
+Figure 6: Visualization of Images corrupted by Gaussian Noise (from ImageNet-C dataset)
+(a) Severity = 1
+(b) Severity = 2
+(c) Severity = 3
+(d) Severity = 4
+(e) Severity = 5
+Figure 7: Visualization of Depth Maps of Images corrupted by Gaussian Noise
+16
+
+Under review
+Table 9: Different Augmentations on top of 3D Views.
+Method
+Top-1 Acc.
+IN-C
+IN-3DCC
+BYOL (Grill et al., 2020)
+85.27
+84.13
+83.68
++ 3D Views (Base SSL Aug)
+88.08
+85.07
+85.33
++ 3D Views (Minimal Aug)
+83.54
+68.69
+72.26
+Table 10: Results on ImageNet-100 Noise Corruptions (IN-C). It can be clearly seen that the
+concatenation of the depth channel signiﬁcantly improves the performance on noise based corruptions
+(by 8% in the case of Impulse noise). On the other hand, the introduction 3D Views hurts the
+performance on noise based corruptions.
+Method
+IN-C
+Gaussian Noise
+Shot Noise
+Impulse Noise
+Speckle Noise
+BYOL (Grill et al., 2020)
+47.15
+37.08
+36.00
+28.31
+45.36
++ Depth (p = 0.3)
+50.17
+41.79
+40.37
+36.98
+50.30
++ 3D Views
+48.15
+34.25
+33.25
+27.04
+43.46
+SimSiam (Chen & He, 2021)
+44.39
+36.51
+34.48
+30.80
+43.00
++ Depth (p = 0.2)
+48.30
+41.36
+39.98
+36.99
+49.29
++ 3D Views
+45.78
+34.85
+33.66
+28.86
+42.61
+E
+ADDITIONAL RESULTS
+What happens when the base SSL augmentations are not applied on 3D Views? Table 9 analyzes
+the role of augmentations applied on top of the synthesized 3D Views. ”Base SSL Aug” refers to
+applying the same augmentations as the base SSL method, whereas ”Minimal Aug” means that only
+Random Resized Crop and Horizontal Flip are used as augmentations. With 3D Views, even without
+the sophisticated augmentations, the model’s linear evaluation performance is close to baseline BYOL
+trained with heavy augmentations.
+Table 10 and 11 summarize the results on Noise Based Corruptions and Blur Corruptions respectively.
+Table 12 and 13 reports the results on Weather based and Digital Corruptions respectively.
+Table 14 and Table 15 report the performance of corruptions in ImageNet-3DCC dataset.
+Table 11: Results on ImageNet-100 Blur Corruptions (IN-C). Both the depth channel and 3D Views
+method improve the accuracy on blur based corruptions. The introduction of the 3D Views helps the
+model capture the 3D structure more easily and thus is highly robust to blur based corruptions.
+Method
+IN-C
+Defocus Blur
+Glass Blur
+Motion Blur
+Zoom Blur
+Gaussian Blur
+BYOL (Grill et al., 2020)
+47.15
+40.77
+33.37
+37.03
+37.76
+46.30
++ Depth (p = 0.3)
+50.17
+40.21
+36.89
+38.50
+41.55
+46.16
++ 3D Views
+48.15
+45.21
+37.32
+39.98
+42.13
+50.70
+SimSiam (Chen & He, 2021)
+44.39
+36.84
+30.92
+34.72
+35.32
+42.76
++ Depth (p = 0.2)
+48.30
+37.34
+34.94
+37.64
+39.17
+42.92
++ 3D Views
+45.78
+40.58
+35.21
+39.19
+41.40
+45.72
+17
+
+Under review
+Table 12: Results on ImageNet-100 Weather Corruptions (IN-C). The proposed method with the
+incorporation of depth channel results in a large increase on the performance of weather-corrupted
+images.
+Method
+IN-C
+Snow
+Frost
+Fog
+Brightness
+BYOL (Grill et al., 2020)
+47.15
+35.93
+41.79
+46.84
+73.71
++ Depth (p = 0.3)
+50.17
+40.15
+46.46
+46.48
+74.42
++ 3D Views
+48.15
+38.43
+42.48
+45.99
+73.72
+SimSiam (Chen & He, 2021)
+44.39
+32.78
+38.62
+40.10
+69.48
++ Depth (p = 0.2)
+48.30
+38.84
+44.11
+45.81
+70.78
++ 3D Views
+45.78
+35.20
+38.86
+41.45
+69.3
+Table 13: Results on ImageNet-100 Digital Corruptions (IN-C). Combining the depth channel with
+the input improves the performance of all kinds of digital corruptions whereas we observe that
+3D Views improves the accuracy on some corruptions and the performance degrades with some
+corruptions.
+Method
+IN-C
+Elastic
+Contrast
+Pixelate
+Saturate
+Spatter
+JPEG
+BYOL (Grill et al., 2020)
+47.15
+53.32
+50.57
+65.94
+71.92
+51.02
+63.22
++ Depth (p = 0.3)
+50.17
+58.50
+51.62
+69.10
+72.55
+54.98
+66.26
++ 3D Views
+48.15
+58.74
+50.32
+66.73
+69.79
+51.26
+63.97
+SimSiam (Chen & He, 2021)
+44.39
+50.32
+49.28
+60.91
+69.44
+47.25
+57.94
++ Depth (p = 0.2)
+48.30
+55.37
+49.95
+66.08
+69.54
+53.33
+64.14
++ 3D Views
+45.78
+54.65
+47.69
+62.50
+68.17
+47.38
+62.48
+Table 14: Results on ImageNet-100 3D Corruptions (Subset of ImageNet-3DCC). Both the proposed
+methods improve upon the base SSL method in terms of the 3D Corruptions with the 3D Views being
+the best of the three.
+Method
+IN-3DCC
+Far Focus
+Flash
+Low Light
+Near Focus
+XY-Motion Blur
+Z Motion Blur
+BYOL (Grill et al., 2020)
+53.69
+59.09
+47.85
+53.98
+64.84
+31.12
+36.22
++ Depth (p = 0.3)
+55.55
+60.42
+50.24
+57.37
+65.18
+34.28
+42.04
++ 3D Views
+54.88
+61.39
+49.36
+53.98
+66.75
+34.73
+41.82
+SimSiam (Chen & He, 2021)
+50.44
+55.31
+44.82
+48.51
+61.67
+28.93
+34.34
++ Depth (p = 0.2)
+52.93
+58.78
+47.16
+52.76
+62.61
+32.62
+39.93
++ 3D Views
+52.17
+57.24
+45.94
+48.88
+63.27
+34.10
+42.29
+Table 15: Results on ImageNet-100 3D Corruptions (Subset of IN-3DCC). Depth Channel improves
+upon the performance of non-3D corruptions like Iso-Noise and Color Quant.
+Method
+IN-3DCC
+Fog3D
+Iso-Noise
+Color Quant
+Bit Error
+BYOL (Grill et al., 2020)
+53.69
+51.68
+33.36
+66.15
+51.78
++ Depth (p = 0.3)
+55.55
+50.64
+39.15
+67.44
+52.09
++ 3D Views
+54.88
+51.55
+29.82
+65.64
+52.30
+SimSiam (Chen & He, 2021)
+50.44
+48.26
+32.56
+62.42
+48.69
++ Depth (p = 0.2)
+52.93
+48.24
+39.53
+64.46
+49.30
++ 3D Views
+52.17
+48.83
+30.87
+63.13
+48.72
+18
+
diff --git a/AtFKT4oBgHgl3EQfWC5j/content/tmp_files/load_file.txt b/AtFKT4oBgHgl3EQfWC5j/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..8aa2994ed8df34655e94b93cb8a81e679c152c61
--- /dev/null
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@@ -0,0 +1,1293 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf,len=1292
+page_content='Under review  LEVERAGING THE THIRD DIMENSION  IN CONTRASTIVE LEARNING  Sumukh K Aithal 1, Anirudh Goyal 1, 4, Alex Lamb 2, Yoshua Bengio 1, Michael Mozer 3  1 Mila, Universit´e de Montr´eal, 2 Microsoft Research, NYC, 3 Google Research, Brain Team  4 DeepMind  ABSTRACT  Self-Supervised Learning (SSL) methods operate on unlabeled data to learn robust  representations useful for downstream tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' Most SSL methods rely on augmen-  tations obtained by transforming the 2D image pixel map.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' These augmentations  ignore the fact that biological vision takes place in an immersive three-dimensional,  temporally contiguous environment, and that low-level biological vision relies  heavily on depth cues.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' Using a signal provided by a pretrained state-of-the-art  monocular RGB-to-depth model (the Depth Prediction Transformer, Ranftl et  al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=', 2021), we explore two distinct approaches to incorporating depth signals into  the SSL framework.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' First, we evaluate contrastive learning using an RGB+depth  input representation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' Second, we use the depth signal to generate novel views  from slightly different camera positions, thereby producing a 3D augmentation  for contrastive learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' We evaluate these two approaches on three different SSL  methods—BYOL, SimSiam, and SwAV—using ImageNette (10 class subset of  ImageNet), ImageNet-100 and ImageNet-1k datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' We ﬁnd that both approaches  to incorporating depth signals improve the robustness and generalization of the  baseline SSL methods, though the ﬁrst approach (with depth-channel concatena-  tion) is superior.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' For instance, BYOL with the additional depth channel leads  to an increase in downstream classiﬁcation accuracy from 85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='3% to 88.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='0% on  ImageNette and 84.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='1% to 87.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='0% on ImageNet-C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  1  INTRODUCTION  Biological vision systems evolved in and interact with a three-dimensional world.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' As an individual  moves through the environment, the relative distance of objects is indicated by rich signals extracted  by the visual system, from motion parallax to binocular disparity to occlusion cues.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' These signals play  a role in early development to bootstrap an infant’s ability to perceive objects in visual scenes (Spelke,  1990;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' Spelke & Kinzler, 2007) and to reason about physical interactions between objects (Baillargeon,  2004).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' In the mature visual system, features predictive of occlusion and three-dimensional structure  are extracted early and in parallel in the visual processing stream (Enns & Rensink, 1990;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' 1991), and  early vision uses monocular cues to rapidly complete partially-occluded objects (Rensink & Enns,  1998) and binocular cues to guide attention (Nakayama & Silverman, 1986).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' In short, biological  vision systems are designed to leverage the three-dimensional structure of the environment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  In contrast, machine vision systems typically consider a 2D RGB image or a sequence of 2D RGB  frames to be the relevant signal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' Depth is considered as the end product of vision, not a signal that  can be exploited to improve visual information processing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' Given the bias in favor of end-to-end  models, researchers might suppose that if depth were a useful signal, an end-to-end computer vision  system would infer depth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' Indeed, it’s easy to imagine the advantages of depth processing integrated  into the visual information processing stream.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' For example, if foreground objects are segmented from  the background scene, neural networks would not make the errors they often do by using short-cut  features to classify (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=', misclassifying a cow at the beach as a whale) (Geirhos et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=', 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  In this work, we take seriously the insight from biological vision that depth signals are extracted  early in the processing stream, and we explore how depth signals might support computer vision.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' We  assume the availability of a depth signal by using an existing state-of-the-art monocular RGB-to-depth  extraction model, the Dense Prediction Transformer (DPT) (Ranftl et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=', 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  1  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='11790v1  [cs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='CV]  27 Jan 2023  Under review  Augmentation  Contrastive  Self-Supervised  Learning Method  Depth  Estimation  Depth  Estimation  R  G  B  +  D  R  G  B  +  D  Figure 1: Improving Self-Supervised Learning by concatenating an input channel with estimated  depth to the RGB input.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' Depth is estimated from both an original image and an augmentation, and  the resulting 4-channel inputs are used to produce the representation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' Incorporating the depth channel  improves downstream accuracy in a variety of SSL techniques, with the largest improvements on  challenging corrupted benchmarks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' (Teaser results are shown.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' Complete results in Tables 1, 2, 3)  We focus on using the additional depth information for self-supervised representation learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' SSL  aims to learn effective representations from unlabelled data that will be useful for downstream tasks  (Chen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=', 2020a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' We investigate two speciﬁc hypotheses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' First, we consider directly appending  the depth channel to the RGB and then use the RGB+D input directly in contrastive learning (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  Second, we consider synthesizing novel image views from the RGB+D representation using a recent  method, AdaMPI (Han et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=', 2022) and treating these synthetic views as image augmentations for  contrastive learning (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' 2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  Prior work has explored the beneﬁt of depth signals in supervised learning for speciﬁc tasks like  object detection and semantic segmentation (Cao et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=', 2016;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' Hoyer et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=', 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' Song et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=', 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  Seichter et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=', 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' Here, we pursue a similar approach in contrastive learning, where the goal is to  learn robust, universal representations that support downstream tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' To the best of our knowledge,  only one previous paper has explored the use of depth for contrastive learning (Tian et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=', 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' In  their case, ground truth depth was used and it was considered as one of many distinct “views” of the  world.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' We summarize our contributions below:  Motivated by biological vision systems, we propose two distinct approaches to improving SSL  using a (noisy) depth signal extracted from a monocular RGB image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' First, we concatenate the  derived depth map and the image and pass the four-channel RGB+D input to the SSL method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  Second, we use a single-view view synthesis method that utilizes the depth map as input to generate  novel 3D views and provides them as augmentations for contrastive learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  We show that both of these approaches improve the performance of three different contrastive  learning methods (BYOL, SimSiam, and SwAV) on ImageNette, ImageNet-100 and large-scale  ImageNet-1k datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' Our approaches can be integrated into any contrastive learning framework  without incurring any signiﬁcant computational cost and trained with the same hyperparameters  as the base contrastive method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' We achieve a 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='8% gain in the performance of BYOL with the  addition of depth channel on ImageNette dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  Both approaches also yield representations that are more robust to image corruptions than the  baseline SSL methods, as reﬂected in performance on ImageNet-C and ImageNet-3DCC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' On the  large-scale ImageNet-100 dataset, SimSiam+Depth outperforms base SimSiam model by 4% in  terms of corruption robustness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  2  RELATED WORK  Self-Supervised Learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' The goal of self-supervised learning based methods is to learn a universal  representation that can generalize to various downstream tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' Earlier work on SSL relied on  handcrafted pretext tasks like rotation (Gidaris et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=', 2018), colorization (Zhang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=', 2016) and  jigsaw (Noroozi & Favaro, 2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' Recently,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' most of the state-of-the-art methods in SSL are based on  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='Results on ImageNette  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='100  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='BYOL  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='BYOL+Depth  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='Accuracy (in %)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='90  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='80  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='70  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='60  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='Top-1 Acc  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='IN-C  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='IN-3DCCResults on ImageNet-100  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='90  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='SimSiam  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='80  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='SimSiam+Depth  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='(%  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='Accuracy (in  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='70  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='60  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='50  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='40  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='30  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='Top-1 Acc  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='IN-C  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='IN-3DCCUnder review  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='Single-View View Synthesis  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='Contrastive  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='Self-Supervised  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='Learning Method  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='Augmentation  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='Augmentation  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='Sample one of K Views  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='Figure 2: Novel views can be synthesized from a single image by using the estimated depth channel,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  which can be used as additional augmentations across a variety of contrastive self-supervised learning  techniques.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' These improve results, especially on benchmarks with image corruptions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' (Result  highlights are shown.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' Complete results in Tables 1, 2, 3  contrastive representation learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' The goal of contrastive representation learning is to make the  representations between two augmented views of the scene similar and also to make representations  of views of different scenes dissimilar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  SimCLR (Chen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=', 2020b) showed that augmentations play a key role in contrastive learning and  the set of augmentations proposed in the work showed that contrastive learning can perform really  well on large-scale datasets like ImageNet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' BYOL (Grill et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=', 2020) is one of the ﬁrst contrastive  learning based methods without negative pairs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' BYOL is trained with two networks that have the  same architecture: an online network and a target network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' From an image, two augmented views  are generated;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' one is routed to the online network, the other to the target network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' The model learns  by predicting the output of the one view from the other view.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' SwAV (Caron et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=', 2020) is an  online clustering based method that compares cluster assignments from multiple views.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' The cluster  assignments (or code) from one augmented view of the image is predicted from the other augmented  view.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' SimSiam (Chen & He, 2021) explores the role of Siamese networks in contrastive learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  SimSiam is an conceptually simple method as it does not require a BYOL-like momentum encoder or  a SwAV-like clustering mechanism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  Contrastive Multiview Coding (CMC) Tian et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' (2020) proposes a framework for multiview con-  trastive learning that maximizes the mutual information between views of the same scenes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' Each  view can be an additional sensory signal like depth, optical ﬂow, or surface normals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' CMC is closely  related to our work but differs in two primary ways.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' First, CMC considers depth as a separate view  and applies a mutual information maximization loss across multiple views;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' in contrast, we either  concatenate the estimated depth information to the RGB input or generate 3D realistic views using  the depth signal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' Second, CMC considers only ground truth depth maps whereas we show that depth  maps estimated from RGB are also quite helpful.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  Monocular Depth Estimation in Computer Vision.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' Monocular depth estimation is a pixel-level  task that aims to predict the distance of every pixel from the camera using a single image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' Though  monocular depth estimation is a highly ill-posed problem, deep learning based techniques have been  shown to perform extremely well on this task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' A few works (Eitel et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=', 2015;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' Cao et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=', 2016;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' Hoyer  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=', 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' Song et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=', 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' Seichter et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=', 2021) have explored the beneﬁts of depth estimation  for semantic segmentation and object detection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' Cao et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' (2016) were one of the ﬁrst efforts to  perform a detailed analysis showing that augmenting the RGB input with estimated depth map can  signiﬁcantly improve the performance on object detection and segmentation tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' A multi-task  training procedure of predicting the depth signal along with the semantic label was also proposed  in Cao et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' RGB-D segmentation with ground truth depth maps was shown to be superior  compared to standard RGB segmentation (Seichter et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=', 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' Hoyer et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' (2021) proposed to  use self-supervised depth estimation as an auxiliary task for semantic segmentation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' Multimodal  Estimated-Depth Uniﬁcation with Self-Attention (MEDUSA) Song et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' (2021) incorporated inferred  depth maps with RGB images in a multimodal transformer for object detection tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' With limited  analysis on CIFAR-10, He (2017) showed that estimated depth maps aid image classiﬁcation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  3  Results on ImageNette  100  BYOL  BYOL+3DViewS  Accuracy (in %)  90  80  70  60  Top-1 Acc  IN-C  IN-3DCCResults on ImageNet-100  90  SimSiam  80  SimSiam+3DViews  (%  Accuracy (in  70  60  50  40  30  Top-1 Acc  IN-C  IN-3DCCUnder review  Most prior works that utilize depth information do so with the objective of improving certain tasks  like object detection or semantic segmentation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' To the best of our knowledge, ours is the ﬁrst work  that focuses speciﬁcally on using an estimated depth signal to enhance contrastive learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' The deep  encoder obtained from contrastive learning can then be used for various downstream tasks like object  detection or image classiﬁcation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  3  DEPTH IN CONTRASTIVE LEARNING  We propose two general methods of incorporating depth information into any SSL framework.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' Both  of these methods, which we describe in detail shortly, assume the availability of a depth signal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  We obtain this signal from an off-the-shelf pretrained Monocular Depth Estimation model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' We  generate depth maps for every RGB image in our data set using the state-of-the-art Dense Prediction  Transformer (DPT) Ranftl et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' (2021) trained for the monocular depth estimation task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' DPT is trained  on a large training dataset with 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='4 million images and leverages the power of Vision Transformers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  DPT outperforms other monocular depth estimation methods by a signiﬁcant margin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' It has been  shown that DPT can accurately predict depth maps for in-the-wild images Han et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' We treat  the availability of these depth maps for contrastive learning as being similar to the availability that  people have to extract depth cues via binocular disparity, motion parallax, or occlusion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  (a) Original Image  (b) Estimated Depth Map  (c) Cropped Image  (d) Estimated Depth Map  Figure 3: Despite two images of a church (Imagenette) being quite similar visually, the presence of  a tree occluding the church is a strong hint that the church is in the background, resulting in a very  different depth map.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='1  CONCATENATING A DEPTH CHANNEL TO THE INPUT  We analyze the effect of concatenating a depth channel to the RGB image as a means of providing a  richer input.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' This four-channel input is then fed through the model backbone.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' As we argued earlier,  ample evidence suggests that cues to the three dimensional structure of the world are critical in the  course of human development (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=', learning about objects and their relationships), and these cues  are available to biological systems early in the visual processing stream and are very likely used  to segment the world into objects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' Consequently, we hypothesize that a depth channel will support  improved representations in contrastive learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  We anticipate that the depth channel might particularly assist the model when an image is corrupted,  occluded, or viewed from an unusual perspective (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' 3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' Depth might also be helpful in low-light  environments where surface features of an object may not be clearly visible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' This is quite important  in safety critical applications like autonomous driving.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' The conjecture that depth cues will support  interpretation of corrupted images is far from obvious because when the depth estimation method  is applied to a corrupted image, the resulting depth maps are less than accurate (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' 6 and  7).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' We conduct evaluations using two corruption-robustness benchmarks to determine whether the  depth signal extracted yields representations that on balance improve accuracy in a downstream  classiﬁcation task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' Sample visualizations of the images and their depth map can be found in App.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  As Figure 1 depicts, our proposed method processes each image and each augmentation of an  image through the DPT depth extractor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' However, in accord with practice in SSL, we sample a new  augmentation on each training step and the computational cost of running DPT on every augmentation  in every batch is high.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' To avoid this high cost of training, we perform a one-time computation of depth  4  Under review  maps for every image in the dataset and use this cached map in training for the original image, but we  also transform it for the augmentation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' This transformation works as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' First, an augmentation  is chosen from the set of augmentations deﬁned by the base SSL method, and the RGB image is  transformed according to this augmentation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' For the depth map, only the corresponding Random  Crop and Horizontal Flip transforms (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=', dilation, translation, and rotations) are applied.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' The  resulting depth map for the augmentation is cheap to compute, but it has a stronger correspondence  to the original image’s depth map than one might expect had the depth map been computed for the  augmentation by DPT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' To address the possibility that the SSL method might come to rely too heavily  on the depth map, we incorporated the notion of depth dropout.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  With depth dropout, the depth channel of any original image or augmentation is cleared (set to 0)  with probability p, independently decided for each image or augmentation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' When depth dropout is  integrated with a SSL method, it prevents the SSL method from becoming too dependent on the depth  signal by reducing the reliability of that signal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' Consider a method like BYOL, whose objective is to  predict the representations of one view from the other.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' With depth dropout, the objective is much  more challenging.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' Since the depth channel is dropped out in some views, the network has to learn to  predict the representations of a view with a depth signal using a view without depth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' This leads to the  model capturing additional 3D structure about the input without any signiﬁcant computation cost.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  At evaluation, every image in the evaluation set is processed by DPT;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' the short cut of remapping the  depth channel from the original image to the augmentation was used only during training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='2  3D VIEWS WITH ADAMPI  We now discuss our second method of incorporating depth information in contrastive SSL methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  This method is motivated by the fact that humans have two eyes and binocular vision requires us  to match up the different views of the world seen by each eye.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' Because each eye has a subtlely  different perspective, the images impinging on the retina are slightly different.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' The brain integrates  the two images by determining the correspondence between regions from each eye.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' This stereo  correspondence helps people in understanding and representing the 3D scene.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' We introduce this idea  into Self-Supervised Learning with the help of Single-View View Synthesis methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  Single-View View Synthesis (Tucker & Snavely, 2020) is an extreme version of the view synthesis  problem that takes single image as the input and renders images of the scene from new viewpoints.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' The  task of view synthesis requires a deep understanding of the objects, scene geometry and appearance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  Most of the methods proposed for this task make use of multiplane-image (MPI) representation  (Tucker & Snavely, 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' Li et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=', 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' Han et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=', 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' MPI consists of N fronto-parallel RGBα  planes arranged at increasing depths.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' MINE (Li et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=', 2021) introduced the idea of Neural Radiance  Fields (Mildenhall et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=', 2020) into the MPI to perform novel view synthesis with a single image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  These single-view view synthesis methods have a wide ranging applications in Augmented and  Virtual Reality as they allow the viewer to interact with the photos.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  Recently, a lot of single-view view synthesis methods have been using layered depth representations  (Shih et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=', 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' Jampani et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=', 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' These methods have been shown to generalize well on the  unseen real world images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' As mentioned in Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='1, monocular depth estimation models like DPT  (Ranftl et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=', 2021) are used when depth maps are not available.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' AdaMPI (Han et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=', 2022) is one  such recently proposed method that aims to generate novel views for in-the-wild images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' AdaMPI  introduces two novel modules, a plane adjustment network and a color prediction network to adapt to  diverse scenes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' Results show that AdaMPI outperforms MINE and other single image view synthesis  methods in terms of quality of the synthesized images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' We use AdaMPI for all of the experiments in  our paper, given the quality of synthesized images generated by AdaMPI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  At inference, AdaMPI takes an RGB image, depth (estimated from the monocular depth estimation  model), and the target view to be rendered.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' The single-view view synthesis model then generates a  multiplane-image representation of the scene.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' This representation can then be easily used to transform  the image in the source view to the target view.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' More details about AdaMPI is present in App.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  In a nutshell, AdaMPI generates a “3D photo” of a given scene given a single input.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' In a way, it can  be claimed that an image can be “brought to life” by generating the same image from another camera  viewpoint (Kopf et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=', 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' We propose to use the views generated by AdaMPI as augmentations  for SSL methods (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' 2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' The synthesized views captures the 3D scene and generates realistic  5  Under review  Table 1: Results on ImageNette Dataset show consistently improved robustness from explicitly  leveraging depth estimation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' Additionally, the depth channel approach consistently outperforms the  3D view augmentation approach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  Method  kNN  Top-1 Acc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  ImageNet-C  ImageNet-3DCC  BYOL (Grill et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=', 2020)  85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='71  85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='27  84.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='13  83.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='68  + Depth (p = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='5)  88.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='56  88.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='03  87.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='00  86.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='68  + 3D Views  87.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='01  87.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='42  85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='75  85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='86  SimSiam (Chen & He, 2021)  85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='10  85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='76  84.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='08  84.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='16  + Depth (p = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='5)  86.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='52  87.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='41  85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='13  85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='08  + 3D Views  85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='94  87.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='62  83.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='87  84.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='37  SwAV (Caron et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=', 2020)  89.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='63  91.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='08  75.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='31  82.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='05  + Depth (p = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='5)  89.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='20  90.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='85  83.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='80  85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='02  augmentations that help the model learn better representations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' These augmentations are meant to  reﬂect the type of subtle shifts in perspective obtained from the two eyes or from minor head or body  movements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  Augmentations are a key ingredient in contrastive learning methods (Chen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=', 2020a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' Modifying  the strength of augmentations or removing certain augmentations leads to signiﬁcant drop in the  performance of contrastive methods (Chen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=', 2020a;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' Grill et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=', 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' Zhang & Ma, 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' Most  of these augmentations can be considered as ”2D” as they make changes in the image either by  cropping the image or applying color jitter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' On the other hand, the generated 3D views are quite  diverse as they bring in another dimension to the contrastive setup.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' Moreover, they can be combined  with the existing set of augmentations to achieve the best performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  The synthesized views as augmentations allow the model to virtually interact with the 3D world.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  For every training sample, we generate k views synthesized from the camera in the range of x-axis  range, y-axis range and z-axis range.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' The x-axis range essentially refers to the shift in the x-axis  from the position of the original camera.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' The synthesis of the 3D Views is computed only once for  the training dataset in an ofﬂine manner.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' Out of the total k views per sample, we sample one view at  every training step and use it for training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' We tried two techniques to augment the synthesized views.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  First, we applied the augmentations of the base SSL method on top of the synthesized view.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' Second,  we applied the base SSL augmentations with a probability of q or we used the synthesized view (with  Random Crop and Flip) with a probability of 1-q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' Full details can be found in the Appendix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  The range of novel camera views generated by the single-view view synthesis method can be  controlled by the user.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' It is possible to speciﬁcally control the x-axis shift, y-axis shift and z-axis  shift (zoom) during the generation of the novel views.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' The quality of generated images degrades  when the novel view to be generated is far from the current position of the camera.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' This is expected  because it is not feasible to generate a complete 360-degree view of the scene by using a single image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  In practice, we observe certain artifacts in the image when views far away from the current position  of the camera.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' Additional details can be found in App.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' A and App.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  4  EXPERIMENTAL RESULTS  We show results with the addition of depth channel and 3D Views with various SSL methods on  ImageNette, ImageNet-100 and ImageNet-1k datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' We also measure the corruption robustness of  these models by evaluating the performance of these models on ImageNet-C and ImageNet-3DCC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='1  EXPERIMENTAL SETUP  ImageNette: is a 10 class subset of ImageNet (Deng et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=', 2009) that consists of 9469 images for  training and 2425 images for testing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' We use the 160px version of the dataset for all the experiments  and train the models with an image size of 128.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  6  Under review  Table 2: Results on ImageNet-100 Dataset indicates that both addition of the depth channel and 3D  Views leads to a gain in corruption robustness performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  Method  kNN  Top-1 Acc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  ImageNet-C  ImageNet-3DCC  BYOL (Grill et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=', 2020)  74.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='24  80.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='74  47.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='15  53.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='69  + Depth (p = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='3)  74.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='66  80.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='24  50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='17  55.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='55  + 3D Views  73.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='42  80.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='16  48.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='15  54.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='88  SimSiam (Chen & He, 2021)  67.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='56  76.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='00  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='39  50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='44  + Depth (p = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='2)  70.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='90  76.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='54  48.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='30  52.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='93  + 3D Views  68.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='08  76.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='40  45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='78  52.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='17  ImageNet-100: is a 100 class subset of ImageNet (Deng et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=', 2009) consisting of 126689 training  images and 5000 validation images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' We use the same classes as in (Tian et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=', 2020) and train all  models with image size of 224.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  ImageNet-1k: consists of 1000 classes with 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='2 million training images and 50000 validation images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  ImageNet-C (IN-C) (Hendrycks & Dietterich, 2019): ImageNet-C dataset is a benchmark to evaluate  the robustness of the model to common corruptions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' It consists of 15 types of algorithmically  generated corruptions including weather corruptions, noise corruptions and blur corruptions with  different severity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' Refer to Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' 6 for a visual depiction of the images corrupted with Gaussian Noise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  ImageNet-3DCC (IN-3DCC) (Kar et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=', 2022): ImageNet-3DCC consists of realistic 3D corruptions  like camera motion, occlusions, weather to name a few.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' The 3D realistic corruptions are generated  using the estimated depth map and improves upon the corruptions in ImageNet-C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' Some examples of  these corruptions include XY-Motion Blur, Near Focus, Flash, Fog3D to name a few.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  Experimental Details.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' We use a ResNet-18 (He et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=', 2016) backbone for all our experiments  except the ImageNet-1k dataset where we use ResNet-50 architecture as used in Chen & He (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  For the pretraining stage, the network is trained using the SGD optimizer with a momentum of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='9  and batch size of 256.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' The ImageNette experiments are trained with a learning rate of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='06 for  800 epochs whereas the ImageNet-100 experiments are trained with a learning rate of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='2 for 200  epochs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' We implement our methods in PyTorch 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='11 (Paszke et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=', 2019) and use Weights and Biases  (Biewald, 2020) to track the experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' We refer to the lightly (Susmelj et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=', 2020) benchmark  for ImageNette experiments and solo-learn (da Costa et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=', 2022) benchmark for ImageNet-100  experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' We follow the commonly used linear evaluation protocol to evaluate the representations  learned by the SSL method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' For linear evaluation, we use SGD optimizer with a momentum of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='9  and train the network for 100 epochs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' For the ImageNette+3D Views experiments, we apply base  SSL augmentation on top of the synthesized views at every training step.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' For the ImageNet-100+3D  Views experiments, we apply the base SSL augmentations with a probability of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' Additional  experimental details is present in the App.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='2  RESULTS ON IMAGENETTE  Table 1 shows the beneﬁt of incorporating depth with any SSL method on the ImageNette dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' We  use the k-nearest neighbor (kNN) classiﬁer and Top-1 Acc from the linear evaluation performance  to evaluate the learned representation of the SSL method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' It can be seen that the addition of depth  improves the accuracy of BYOL, SimSiam and SwAV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' BYOL+Depth indicates that the model is  trained with depth map with the depth dropout.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' BYOL+Depth improves upon the Top-1 accuracy  of BYOL by 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='8% along with a 3% increase in the ImageNet-C and ImageNet-3DCC performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  This clearly demonstrates the role of depth information in corrupted images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  We observe a signiﬁcant 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='5% increase in the ImageNet-C with SwAV+Depth over the base SwAV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  On a closer look, it can be seen that the addition of depth channel results in high robustness to  noise-based perturbations and blur-based perturbations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' For instance, the accuracy on the Motion Blur  corruption increases from 70.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='32% with SwAV to 86.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='88% with SwAV+Depth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' And the performance  on Gaussian Noise corruption increases from 69.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='76% to 84.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='56% with the addition of depth channel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  BYOL + 3D Views indicates that the views synthesized by AdaMPI are used as augmentations in the  contrastive learning setup.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' We show that proposed 3D Views leads to a gain in accuracy with both  7  Under review  Table 3: Results on ImageNet-1k dataset (ResNet-50) illustrates the role of depth channel and 3D  Views in self-supervised learning methods on large-scale datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  Method  Epochs  Top-1 Acc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  ImageNet-C  ImageNet-3DCC  SimSiam (Chen & He, 2021)  800  71.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='70  36.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='45  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='32  + Depth (p = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='2)  800  71.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='30  38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='23  45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='11  SimSiam (Chen & He, 2021)  100  68.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='10  32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='99  38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='94  + 3D Views  100  68.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='08  34.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='43  40.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='71  BYOL and SimSiam.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' This indicates that the diversity in the augmentations due to the 3D Views helps  the model capture a better representation of the world.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' We also observe a decent gain in accuracy on  IN-C and IN-3DCC with 3D views compared to the baseline BYOL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='3  RESULTS ON IMAGENET-100  Table 2 summarizes the results on the large-scale ImageNet-100 with BYOL and SimSiam.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' We ﬁnd  that most of the observations on the ImageNette datasets also hold true in the ImageNet-100 datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  Though the increase in the Top-1 Accuracy with the inclusion of depth is minimal, we observe that  performance on ImageNet-C and ImageNet-3DCC increases notably.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' With SimSiam, we notice a  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='9% increase in ImageNet-C accuracy and a 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='5% increase in ImageNet-3DCC accuracy just by  the addition of depth channel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' These results emphasize the role of the proposed depth channel with  dropout in contrastive learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  We observe that the proposed method of incorporating 3D views outperforms the base SSL method  on the ImageNet-100 dataset, primarily in the corruption benchmarks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' On a detailed look at the  performance of each corruption, we observe that the 3D Views improves the performance of 3D  based corruptions by more than 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='5%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' (Refer Table 5)  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='4  RESULTS ON IMAGENET-1K  Table 3 shows results on the large scale ImageNet dataset with 1000 classes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' We achieve comparable  Top-1 accuracy with both Depth and 3D Views.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' Since the training set is large, the additional inductive  bias is ineffective for the in-distribution test set but useful for out-of-distribution samples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' We observe  signiﬁcant accuracy boosts in classiﬁcation of corrupted images: 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='5% for ImageNet-C and 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='8% for  ImageNet-3DCC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' These results indicate that our observations scale up to ImageNet-1k dataset and  further strengthens the argument about the role of depth channel and 3D Views in SSL methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  5  DISCUSSION  Depth Dropout.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' Table 4 shows the ablation of probability of Depth dropout (p) on the ImageNette  dataset with BYOL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' The inﬂuence of using the depth dropout can also be understood with these  results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' It can be observed that without depth dropout (p = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='0), the performance of the model  is signiﬁcantly lower than the baseline BYOL, as the network learns to focus solely on the depth  channel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' We ﬁnd that p = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='2 leads to the highest Top-1 Accuracy but p = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='5 achieves the best  performance on the ImageNet-C and ImageNet-3DCC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' As the depth dropout increases (p = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='8), the  performance gets closer to the base SSL method as the model completely ignores the depth channel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  What happens when depth is not available during inference?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' In this ablation, we examine the  importance of depth signal at inference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' Given a model trained with depth information, we analyze  what happens when we set the depth to 0 at inference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' Table 7 reports these results on ImageNette  dataset with BYOL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' Interestingly, we ﬁnd that even with the absence of depth information, the  accuracy of the model is higher than the baseline BYOL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' This indicates that the model has implicitly  learned some depth signal and captured better representations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' It can also be seen that the performance  on IN-3DCC is 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='5% higher than BYOL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' Furthermore, we observe that the addition of depth map  improves the performance on all the benchmarks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' This further highlights our message that depth  signal is a useful signal in learning a robust model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  8  Under review  10  15  20  25  30  35  40  45  50  Number of Views  85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='75  86.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='00  86.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='25  86.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='50  86.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='75  87.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='00  87.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='25  87.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='50  Accuracy (in %)  Number of generated 3D views  SimSiam (Baseline)  Figure 4: As the number of 3D  views increases, the performance of  the SSL method increases with very  limited increase in performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  Method  Top-1 Acc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  IN-C  IN-3DCC  BYOL (Grill et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=', 2020)  85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='27  84.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='13  83.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='68  + Depth (p = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='0)  84.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='38  72.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='64  73.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='68  + Depth (p = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='2)  89.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='05  85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='93  85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='33  + Depth (p = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='5)  88.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='03  87.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='00  86.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='68  + Depth (p = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='8)  86.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='57  85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='38  85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='60  Table 4: Ablation of Depth Dropout hyperparameter (p).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' A  large dropout (p = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='8) leads to the model ignoring the depth  signal and a low (or zero) depth dropout leads to model  relying only on depth signal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  Table 5: Results on ImageNet-100 Corruptions show that while use of 3D view augmentations  provides a larger improvement on 3D corruptions, the improvements from using depth channel are  more consistent on a wide range of corruptions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' Detailed results in App.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  Method  IN-C  Noise  Blur  Weather  Digital  IN-3DCC  3D  Misc  BYOL (Grill et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=', 2020)  47.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='15  36.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='69  38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='95  49.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='57  59.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='33  53.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='69  54.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='53  51.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='16  + Depth (p = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='3)  50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='17  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='36  40.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='66  51.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='88  62.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='17  55.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='55  55.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='85  54.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='65  + 3D Views  48.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='15  34.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='50  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='06  50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='16  60.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='14  54.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='88  56.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='56  49.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='81  SimSiam (Chen & He, 2021)  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='39  36.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='20  36.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='11  45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='24  55.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='86  50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='44  51.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='32  47.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='83  + Depth (p = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='2)  48.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='30  41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='90  38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='40  49.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='76  59.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='84  52.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='93  53.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='16  52.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='25  + 3D Views  45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='78  35.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='00  40.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='42  46.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='20  57.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='14  52.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='17  53.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='69  47.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='63  Number of Views generated by AdaMPI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' Figure 4 investigates the impact of the number of  generated 3D views on the performance of SimSiam (ImageNette).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' We observe that as the number of  views increases, the Top-1 Accuracy increases although the gains are quite minimal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' It must be noted  that even with 10 views, the SimSiam+3D Views outperforms the baseline SimSiam by 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='5%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  Which corruptions improve due to depth and 3D Views?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' A detailed analysis of the performance  of the methods on various type of corruptions is reported in Table 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' We report the average on different  categories of corruptions to understand the role of various corruptions on the overall performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  For ImageNet-C (IN-C), we divide the corruptions into 4 groups: Noise, Blur, Weather and Digital.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  ImageNet-3DCC is split up into two categories based on whether they make use of 3D information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  We observe that the depth channel leads to a massive 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='7% average gain on the noise corruptions  and 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='4% increase in digital corruptions over the baseline.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' The use of 3D Views in SSL results in  a notable 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='2% improvement on the Blur corruptions over the base SSL method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' As expected, the  performance on 3D Corruptions with the 3D Views is much higher than standard SSL method and  slightly higher than the method that uses depth channel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' More results can be found in App.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  Table 6: Ablation on Range of synthesized views generated  by AdaMPI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' Results are shown on ImageNette dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  Method  Top-1 Acc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  IN-C  IN-3DCC  BYOL (Grill et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=', 2020)  85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='27  84.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='13  83.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='68  + 3D Views (x = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' y = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='1)  86.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='09  83.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='33  83.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='63  + 3D Views (x = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='4;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' y = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='4)  87.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='87  84.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='78  85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='22  + 3D Views (x = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='5;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' y = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='5)  88.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='08  85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='07  85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='33  + 3D Views (x = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='8;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' y = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='8)  87.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='49  82.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='47  84.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='35  + 3D Views (x = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' y = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='0)  86.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='34  80.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='81  83.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='30  Range  of  Views  generated  by  AdaMPI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' The range of 3D Views  generated by AdaMPI play a huge  role in the performance of the SSL  method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' Table 6 summarizes the ef-  fects of moving the target camera on  the learned representations on Ima-  geNette dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' x denotes the amount  by which the x-axis is moved and y de-  notes the same for y-axis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' We observe  that a very small change in viewing  direction (x = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' y = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='1) does not  boost the performance very much.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' As x and y get larger, the quality of generated images also de-  creases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' Thus, a large change in the viewing direction leads to artifacts which hurts the performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  9  Under review  Table 7: These results on ImageNette show that  the model is robust to the absence of depth signal  and that estimated depth improves the corruption  robustness and linear evaluation performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  Method  Top-1 Acc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  IN-C  IN-3DCC  BYOL (Grill et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=', 2020)  85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='27  84.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='13  83.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='68  + Depth (p = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='5)  88.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='03  87.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='00  86.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='68  Depth = 0 at inference  86.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='80  84.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='95  85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='21  Table 8: Comparison of two Single-View View  Synthesis Methods for generating 3D Views on  ImageNette dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' Higher quality views leads  to higher performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  Method  Top-1 Acc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  IN-C  IN-3DCC  BYOL (Grill et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=', 2020)  85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='27  84.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='13  83.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='68  + 3D Views (MINE)  87.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='49  84.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='47  83.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='93  + 3D Views (AdaMPI)  88.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='08  85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='07  85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='33  This can be clearly observed in Table 6 where we see a drop in accuracy as the x and y increases  from 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='5 to 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  Quality of Synthesized Views.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' In this ablation, we investigate how the quality of the synthesized  views affects the representations learnt by Self-Supervised methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' We compare two different  methods to generate 3D Views of the image namely MINE (Li et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=', 2021) and AdaMPI (Han et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=',  2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' The quantitative and qualitative results shown in Han et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' (2022) indicate that AdaMPI  generates superior quality images compared to MINE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' Table 8 reports the results on ImageNette with  BYOL comparing the 3D Views synthesized by MINE and AdaMPI methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' We observe that the  method with 3D Views generated by AdaMPI outperforms the method with 3D Views generated  by MINE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' This is a clear indication that as the quality of 3D view synthesis methods improves, the  accuracy of the SSL methods with 3D views increases as well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  6  CONCLUSION  In this work, we propose two distinct approaches to improving SSL using a (noisy) depth signal  extracted from a monocular RGB image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' Our results on ImageNette, ImageNet-100 and ImageNet-  1k datasets with a range of SSL methods (BYOL, SimSiam and SwAV) show that both proposed  approaches outperform the baseline SSL on test accuracy and corruption robustness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' Further, our  approaches can be integrated into any SSL method to boost performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' We close with several  critical directions for future research.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' First, given that our two approaches are complementary  and compatible, we might evaluate the two approaches in combination.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' Second, is depth dropout  necessary when depth extraction with DPT can be run on every augmentation on every training step?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  Third, one might explore the idea of synthesizing views in Single-View View Synthesis methods with  the goal of maximizing the performance (Ge et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=', 2022) or develop better methods to utilize the 3D  Views.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  REFERENCES  R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' Baillargeon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' Infants’ reasoning about hidden objects: evidence for event-general and event-  speciﬁc expectations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' Developmental science, 7(4):391–414, 2004.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' doi: https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='1111/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  1467-7687.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='2004.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='00357.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  Lukas Biewald.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' Experiment tracking with weights and biases, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' URL https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='wandb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  com/.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' Software available from wandb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='com.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  Yuanzhouhan Cao, Chunhua Shen, and Heng Tao Shen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' Exploiting depth from single monocular  images for object detection and semantic segmentation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' IEEE Transactions on Image Processing,  26(2):836–846, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  Mathilde Caron, Ishan Misra, Julien Mairal, Priya Goyal, Piotr Bojanowski, and Armand Joulin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  Unsupervised learning of visual features by contrasting cluster assignments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' Advances in Neural  Information Processing Systems, 33:9912–9924, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  Ting Chen, Simon Kornblith, Mohammad Norouzi, and Geoffrey Hinton.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' A simple framework for  contrastive learning of visual representations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' In International conference on machine learning, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  1597–1607.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' PMLR, 2020a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  Xinlei Chen and Kaiming He.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' Exploring simple siamese representation learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' In Proceedings of  the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' 15750–15758, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  10  Under review  Xinlei Chen, Haoqi Fan, Ross Girshick, and Kaiming He.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' Improved baselines with momentum  contrastive learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' arXiv preprint arXiv:2003.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='04297, 2020b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  Victor Guilherme Turrisi da Costa, Enrico Fini, Moin Nabi, Nicu Sebe, and Elisa Ricci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' solo-learn: A  library of self-supervised methods for visual representation learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' Journal of Machine Learning  Research, 23(56):1–6, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' URL http://jmlr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='org/papers/v23/21-1155.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='html.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  Jia Deng, Wei Dong, Richard Socher, Li-Jia Li, Kai Li, and Li Fei-Fei.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' Imagenet: A large-scale  hierarchical image database.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' In 2009 IEEE conference on computer vision and pattern recognition,  pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' 248–255.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' Ieee, 2009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  Andreas Eitel, Jost Tobias Springenberg, Luciano Spinello, Martin Riedmiller, and Wolfram Burgard.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  Multimodal deep learning for robust rgb-d object recognition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' In 2015 IEEE/RSJ International  Conference on Intelligent Robots and Systems (IROS), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' 681–687.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' IEEE, 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' Enns and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' Rensink.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' Preattentive recovery of three-dimensional orientation from line  drawings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' Psychological Review, 3(98):335–351, 1991.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' doi: https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='1037/0033-295X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  98.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='335.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  James Enns and Ronald Rensink.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' Sensitivity to three-dimensional orientation in visual search.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  Psychological Science, 1:323–326, 09 1990.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='1111/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='1467-9280.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='1990.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='tb00227.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='x.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  Yunhao Ge, Harkirat Behl, Jiashu Xu, Suriya Gunasekar, Neel Joshi, Yale Song, Xin Wang, Laurent  Itti, and Vibhav Vineet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' Neural-sim: Learning to generate training data with nerf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' arXiv preprint  arXiv:2207.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='11368, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  Robert Geirhos, J¨orn-Henrik Jacobsen, Claudio Michaelis, Richard Zemel, Wieland Brendel, Matthias  Bethge, and Felix A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' Wichmann.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' Shortcut learning in deep neural networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' Nature Machine  Intelligence, 2(11):665–673, nov 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='1038/s42256-020-00257-z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  Spyros Gidaris, Praveer Singh, and Nikos Komodakis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' Unsupervised representation learning by  predicting image rotations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' arXiv preprint arXiv:1803.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='07728, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  Jean-Bastien Grill, Florian Strub, Florent Altch´e, Corentin Tallec, Pierre Richemond, Elena  Buchatskaya, Carl Doersch, Bernardo Avila Pires, Zhaohan Guo, Mohammad Gheshlaghi Azar,  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' Bootstrap your own latent-a new approach to self-supervised learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' Advances in neural  information processing systems, 33:21271–21284, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  Yuxuan Han, Ruicheng Wang, and Jiaolong Yang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' Single-view view synthesis in the wild with  learned adaptive multiplane images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' In ACM SIGGRAPH, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  Richard Hartley and Andrew Zisserman.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' Multiple View Geometry in Computer Vision.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' Cambridge  University Press, 2004.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' Deep residual learning for image  recognition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' In Proceedings of the IEEE conference on computer vision and pattern recognition,  pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' 770–778, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  Yihui He.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' Estimated depth map helps image classiﬁcation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' arXiv preprint arXiv:1709.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='07077, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  Dan Hendrycks and Thomas Dietterich.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' Benchmarking neural network robustness to common corrup-  tions and perturbations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' Proceedings of the International Conference on Learning Representations,  2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  Lukas Hoyer, Dengxin Dai, Yuhua Chen, Adrian Koring, Suman Saha, and Luc Van Gool.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' Three  ways to improve semantic segmentation with self-supervised depth estimation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' In Proceedings of  the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' 11130–11140, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  Sergey Ioffe and Christian Szegedy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' Batch normalization: Accelerating deep network training by  reducing internal covariate shift.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' In International conference on machine learning, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' 448–456.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  PMLR, 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  11  Under review  Varun Jampani, Huiwen Chang, Kyle Sargent, Abhishek Kar, Richard Tucker, Michael Krainin,  Dominik Kaeser, William T Freeman, David Salesin, Brian Curless, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' Slide: Single image  3d photography with soft layering and depth-aware inpainting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' In Proceedings of the IEEE/CVF  International Conference on Computer Vision, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' 12518–12527, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  James T Kajiya and Brian P Von Herzen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' Ray tracing volume densities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' ACM SIGGRAPH computer  graphics, 18(3):165–174, 1984.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  O˘guzhan Fatih Kar, Teresa Yeo, Andrei Atanov, and Amir Zamir.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' 3d common corruptions and data  augmentation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern  Recognition, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' 18963–18974, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  Diederik P Kingma and Jimmy Ba.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' Adam: A method for stochastic optimization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' arXiv preprint  arXiv:1412.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='6980, 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  Johannes Kopf, Suhib Alsisan, Francis Ge, Yangming Chong, Kevin Matzen, Ocean Quigley, Josh  Patterson, Jossie Tirado, Shu Wu, and Michael F Cohen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' Practical 3d photography.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' In Proceedings  of CVPR Workshops, volume 1, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  Jiaxin Li, Zijian Feng, Qi She, Henghui Ding, Changhu Wang, and Gim Hee Lee.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' Mine: Towards  continuous depth mpi with nerf for novel view synthesis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' In Proceedings of the IEEE/CVF  International Conference on Computer Vision, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' 12578–12588, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  Ben Mildenhall, Pratul P Srinivasan, Matthew Tancik, Jonathan T Barron, Ravi Ramamoorthi, and  Ren Ng.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' Nerf: Representing scenes as neural radiance ﬁelds for view synthesis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' In European  conference on computer vision, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' 405–421.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' Springer, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  Vinod Nair and Geoffrey E Hinton.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' Rectiﬁed linear units improve restricted boltzmann machines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' In  Icml, 2010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' Nakayama and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' Silverman.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' Serial and parallel processing of visual feature conjunctions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  Nature, 320:264–265, 1986.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  Mehdi Noroozi and Paolo Favaro.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' Unsupervised learning of visual representations by solving jigsaw  puzzles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' In European conference on computer vision, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' 69–84.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' Springer, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  Adam Paszke, Sam Gross, Francisco Massa, Adam Lerer, James Bradbury, Gregory Chanan,  Trevor Killeen, Zeming Lin, Natalia Gimelshein, Luca Antiga, Alban Desmaison, Andreas  Kopf, Edward Yang, Zachary DeVito, Martin Raison, Alykhan Tejani, Sasank Chilamkurthy,  Benoit Steiner, Lu Fang, Junjie Bai, and Soumith Chintala.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' Pytorch: An imperative style, high-  performance deep learning library.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' In H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' Wallach, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' Larochelle, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' Beygelzimer, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=" d'Alch´e-Buc,  E." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' Fox, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' Garnett (eds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' ), Advances in Neural Information Processing Systems 32, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  8024–8035.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' Curran Associates, Inc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=', 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' URL http://papers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='neurips.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='cc/paper/  9015-pytorch-an-imperative-style-high-performance-deep-learning-library.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  pdf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  Ren´e Ranftl, Alexey Bochkovskiy, and Vladlen Koltun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' Vision transformers for dense prediction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' In  Proceedings of the IEEE/CVF International Conference on Computer Vision, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' 12179–12188,  2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  Ronald Rensink and James Enns.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' Early completion of occluded objects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' Vision Research, 38:  2489–2505, 09 1998.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='1016/S0042-6989(98)00051-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  Daniel Seichter, Mona K¨ohler, Benjamin Lewandowski, Tim Wengefeld, and Horst-Michael Gross.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  Efﬁcient rgb-d semantic segmentation for indoor scene analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' In 2021 IEEE International  Conference on Robotics and Automation (ICRA), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' 13525–13531.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' IEEE, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  Meng-Li Shih, Shih-Yang Su, Johannes Kopf, and Jia-Bin Huang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' 3d photography using context-  aware layered depth inpainting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' In Proceedings of the IEEE/CVF Conference on Computer Vision  and Pattern Recognition, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' 8028–8038, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  Hwanjun Song, Eunyoung Kim, Varun Jampan, Deqing Sun, Jae-Gil Lee, and Ming-Hsuan Yang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  Exploiting scene depth for object detection with multimodal transformers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' In 32nd British Machine  Vision Conference, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' 1–14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' British Machine Vision Association (BMVA), 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  12  Under review  E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' Spelke.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' Principles of object perception.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' Cognitive Science, 14:29–56, 1990.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  Elizabeth S Spelke and Katherine D Kinzler.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' Core knowledge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' Developmental Science, 10(1):89–96,  2007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  Igor Susmelj, Matthias Heller, Philipp Wirth, Jeremy Prescott, Malte Ebner, and et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' Lightly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  GitHub.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' Note: https://github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='com/lightly-ai/lightly, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  Yonglong Tian, Dilip Krishnan, and Phillip Isola.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' Contrastive multiview coding.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' In European  conference on computer vision, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' 776–794.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' Springer, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  Richard Tucker and Noah Snavely.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' Single-view view synthesis with multiplane images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' In Proceed-  ings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' 551–560,  2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  Junbo Zhang and Kaisheng Ma.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' Rethinking the augmentation module in contrastive learning:  Learning hierarchical augmentation invariance with expanded views.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' In Proceedings of the  IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' 16650–16659, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  Richard Zhang, Phillip Isola, and Alexei A Efros.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' Colorful image colorization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' In European  conference on computer vision, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' 649–666.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' Springer, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  Jinghao Zhou, Chen Wei, Huiyu Wang, Wei Shen, Cihang Xie, Alan Yuille, and Tao Kong.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' ibot:  Image bert pre-training with online tokenizer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' arXiv preprint arXiv:2111.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='07832, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  13  Under review  A  EXPERIMENTAL DETAILS  We discuss the detailed experimental setup to allow reproducibility of the results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  Pretraining:  BYOL: The architecture of the online and target networks in BYOL consists of three components:  encoder, projector and predictor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' We use ResNet-18 (He et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=', 2016) implementation available in  torchvision as our encoder.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' The Prediction Network in BYOL is a Multi-Layer Perceptron (MLP) that  consists of a linear layer with an output dimension of 4096, followed by Batch Normalization (Ioffe  & Szegedy, 2015), ReLU (Nair & Hinton, 2010) and a ﬁnal linear layer with a dimension of 256.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  We use the same augmentations as in lightly benchmark which uses a slightly modiﬁed version of  augmentations used in SimCLR (Chen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=', 2020b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' The network is trained with an SGD Optimizer  with a momentum of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='9 and a weight decay of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='0005.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' A batch size of 256 is used and the network  is trained for a total of 800 epochs with a cosine annealing scheduler.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  For ImageNet-100, we use the ResNet-18 encoder and train the network using an SGD optimizer  with a momentum of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='9 and a weight decay of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='0001.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' We use the set of augmentations in solo-  learn benchmark in our experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' The model is trained for 200 epochs with a batch size of 256.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  The architecture of the prediction head is same as the one used in ImageNette but with the output  dimension of the linear layer set to 8192.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  SimSiam We follow the same optimization hyperparameters as in BYOL for the ImageNette dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  The architecture of the projection head is a 3-layer MLP with Batch Normalization and ReLU applied  to each layer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' (The output layer does not have ReLU).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' The prediction head is a 2-layer MLP with a  hidden dimension of 512.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' We refer to the ofﬁcial implementation of SimSiam 1 for the ImageNet-1k  experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  SwAV: For SwAV, we use the Adam optimizer (Kingma & Ba, 2014) with a learning rate of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='001  and weight decay of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='000001.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' The number of code vectors (or prototypes) is set to 3K with 128  dimensions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' The projection head is a 2-layer MLP with a hidden layer dimension of 2048 and an  output dimension of 128.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' SwAV also introduced the idea of multi-crop where a single input image  is transformed into 2 global views and V local views.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' 6 local views are used in our ImageNette  experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  Linear Probing:  For linear probing, we choose the model with the highest validation kNN accuracy and freeze the  representations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' We then train a linear layer using SGD with momentum optimizer for 100 epochs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  We do a grid search on {0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='2, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='5, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='8, 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='0} and report the best accuracy of the best performing  model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' This is commonly followed in the SSL literature (Zhou et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=', 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' We use the standard  set of augmentations which includes Random Resized Crop and Horizontal Flip for training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' For  ImageNet-100, we observe that a higher learning rate seems to help and we do a grid search on  {0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='5, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='8, 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='0, 30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='0}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' In most of the experiments, we observe that using the learning rate of 30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='0  yields the best-performing model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  Depth Prediction Transformer  We refer to the ofﬁcial implementation of the DPT 2 to compute the depth maps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' The weights of the  best-performing monocular depth estimation model i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='e, DPT-Large, is used for the calculation of the  depth maps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' We use the relative depth maps generated by the DPT model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  AdaMPI:  We refer to the ofﬁcial implementation of AdaMPI 3 paper to compute the 3D Views.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' The depth maps  generated by DPT are fed as input to the AdaMPI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' We generate 50 views per sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' A pretrained  AdaMPI model with 64 MPI planes is used in our experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  For the ImageNette experiments, we apply base SSL augmentations on top of the generated AdaMPI  at every training step.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' We did a grid search on a set of generated views and selected the best  1https://github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='com/facebookresearch/simsiam  2https://github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='com/isl-org/DPT  3https://github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='com/yxuhan/AdaMPI  14  Under review  performing model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' For both BYOL and SimSiam x = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='4;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' y = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='4 and z = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='0 was used to generate  3D Views.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  For ImageNet-100, we apply the base SSL augmentations with a probability of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='5 and use the  synthesized views with a probability of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' We use the views synthesized with x = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' y = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='2 and z  = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  For ImageNet-100 experiments, we use Automatic Mixed Precision training to speed up the training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  All the ImageNette experiments are run on RTX 8000 GPUs while the ImageNet-100 experiments are  run on A100 GPUs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' We are thankful to the authors of DPT (Ranftl et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=', 2021) and AdaMPI (Han  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=', 2022) for publicly releasing the code and pretrained weights.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' We will also release the code and  pretrained weights to enable reproducible research.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  B  ADAMPI  This section explains about how AdaMPI renders new views.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' The notation and content of this section  is heavily derived from Han et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' (2022) and Li et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  Consider a pixel coordinate in a image as [x, y], the camera intrinsic matrix K, camera rotation matrix  R, camera translation matrix t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' A Multiplane image (MPI) is a layered representation that consists of  N fronto-parallel RGBα planes arranged in the increasing order of depth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  The ﬁrst step in rendering a novel view to ﬁnd the correspondence between the source pixel coordinates  [xs, ys]T and target pixel coordinates [xt, yt]T .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' This can be done by using the homography function  (Hartley & Zisserman, 2004) as shown by the equation below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  �xs, ys, 1�⊤ ∼ K  �  R − tn⊤  di  �  K−1 �xt, yt, 1�⊤ ,  (1)  where, n = [0, 0, 1]⊤ is the normal vector of the fronto-parallel plane in the source view.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' Equation 1  essentially maps the correspondence between source and target pixel coordinate at a particular MPI  plane.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  The plane projections at the target plane c′  di(xt, yt) = c′  di(xs, ys) and σ′  di(xt, yt) = σ′  di(xs, ys).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  Volume rendering (Li et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=', 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' Kajiya & Von Herzen, 1984;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' Mildenhall et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=', 2020) and Alpha  compositing can then be used to render the image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  AdaMPI has two major components, a planar adjustment network and color prediction network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' In  previous works Tucker & Snavely (2020), the di was usually ﬁxed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' However, in AdaMPI, the planar  adjustment predicts di and each MPI plane at correct depth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' The color prediction network takes this  adjusted depth planes and predicts the color and density at each plane.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' For additional details, we refer  the reader to Han et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  C  VISUALIZATION OF DEPTH MAPS  In this section, we show sample visualization of the depth map generated by the DPT model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' Figure  5 shows some sample visualization of the original image and the corresponding depth maps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' The  impact of corrupted images on the estimated depth maps is shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' It can be seen that high  severity in Gaussian Noise distorts the estimated depth maps signiﬁcantly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  In Figure 3, we show the impact of occlusion on the estimated depth map.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' Fig 3a contains a tree  in front of it and thus it looks like the Church building has a low depth (It is far away).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' When we  just crop the image and remove the trees (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' 3c), it can clearly seen how the estimated depth maps  changes drastically (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' 3d).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  D  VISUALIZATION OF 3D VIEWS  We refer the reader to the supplementary zip ﬁle for some sample videos and images of synthesized  views from AdaMPI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='Under review  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='(a) Original Image  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='(b) Estimated Depth Map  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='(c) Original Image  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='(d) Estimated Depth Map  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='Figure 5: Visualization of Depth Maps of Images from the ImageNette dataset  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='(a) Severity = 1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='(b) Severity = 2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='(c) Severity = 3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='(d) Severity = 4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='(e) Severity = 5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='Figure 6: Visualization of Images corrupted by Gaussian Noise (from ImageNet-C dataset)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='(a) Severity = 1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='(b) Severity = 2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='(c) Severity = 3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='(d) Severity = 4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='(e) Severity = 5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='Figure 7: Visualization of Depth Maps of Images corrupted by Gaussian Noise  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='16  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='Under review  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='Table 9: Different Augmentations on top of 3D Views.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  Method  Top-1 Acc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  IN-C  IN-3DCC  BYOL (Grill et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=', 2020)  85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='27  84.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='13  83.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='68  + 3D Views (Base SSL Aug)  88.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='08  85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='07  85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='33  + 3D Views (Minimal Aug)  83.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='54  68.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='69  72.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='26  Table 10: Results on ImageNet-100 Noise Corruptions (IN-C).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' It can be clearly seen that the  concatenation of the depth channel signiﬁcantly improves the performance on noise based corruptions  (by 8% in the case of Impulse noise).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' On the other hand, the introduction 3D Views hurts the  performance on noise based corruptions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  Method  IN-C  Gaussian Noise  Shot Noise  Impulse Noise  Speckle Noise  BYOL (Grill et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=', 2020)  47.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='15  37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='08  36.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='00  28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='31  45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='36  + Depth (p = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='3)  50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='17  41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='79  40.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='37  36.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='98  50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='30  + 3D Views  48.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='15  34.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='25  33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='25  27.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='04  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='46  SimSiam (Chen & He, 2021)  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='39  36.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='51  34.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='48  30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='80  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='00  + Depth (p = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='2)  48.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='30  41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='36  39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='98  36.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='99  49.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='29  + 3D Views  45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='78  34.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='85  33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='66  28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='86  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='61  E  ADDITIONAL RESULTS  What happens when the base SSL augmentations are not applied on 3D Views?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' Table 9 analyzes  the role of augmentations applied on top of the synthesized 3D Views.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' ”Base SSL Aug” refers to  applying the same augmentations as the base SSL method, whereas ”Minimal Aug” means that only  Random Resized Crop and Horizontal Flip are used as augmentations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' With 3D Views, even without  the sophisticated augmentations, the model’s linear evaluation performance is close to baseline BYOL  trained with heavy augmentations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  Table 10 and 11 summarize the results on Noise Based Corruptions and Blur Corruptions respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  Table 12 and 13 reports the results on Weather based and Digital Corruptions respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  Table 14 and Table 15 report the performance of corruptions in ImageNet-3DCC dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  Table 11: Results on ImageNet-100 Blur Corruptions (IN-C).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' Both the depth channel and 3D Views  method improve the accuracy on blur based corruptions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' The introduction of the 3D Views helps the  model capture the 3D structure more easily and thus is highly robust to blur based corruptions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  Method  IN-C  Defocus Blur  Glass Blur  Motion Blur  Zoom Blur  Gaussian Blur  BYOL (Grill et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=', 2020)  47.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='15  40.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='77  33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='37  37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='03  37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='76  46.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='30  + Depth (p = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='3)  50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='17  40.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='21  36.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='89  38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='50  41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='55  46.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='16  + 3D Views  48.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='15  45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='21  37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='32  39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='98  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='13  50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='70  SimSiam (Chen & He, 2021)  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='39  36.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='84  30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='92  34.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='72  35.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='32  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='76  + Depth (p = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='2)  48.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='30  37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='34  34.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='94  37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='64  39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='17  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='92  + 3D Views  45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='78  40.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='58  35.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='21  39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='19  41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='40  45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='72  17  Under review  Table 12: Results on ImageNet-100 Weather Corruptions (IN-C).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' The proposed method with the  incorporation of depth channel results in a large increase on the performance of weather-corrupted  images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  Method  IN-C  Snow  Frost  Fog  Brightness  BYOL (Grill et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=', 2020)  47.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='15  35.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='93  41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='79  46.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='84  73.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='71  + Depth (p = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='3)  50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='17  40.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='15  46.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='46  46.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='48  74.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='42  + 3D Views  48.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='15  38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='43  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='48  45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='99  73.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='72  SimSiam (Chen & He, 2021)  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='39  32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='78  38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='62  40.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='10  69.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='48  + Depth (p = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='2)  48.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='30  38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='84  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='11  45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='81  70.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='78  + 3D Views  45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='78  35.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='20  38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='86  41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='45  69.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='3  Table 13: Results on ImageNet-100 Digital Corruptions (IN-C).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=' Combining the depth channel with  the input improves the performance of all kinds of digital corruptions whereas we observe that  3D Views improves the accuracy on some corruptions and the performance degrades with some  corruptions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='  Method  IN-C  Elastic  Contrast  Pixelate  Saturate  Spatter  JPEG  BYOL (Grill et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content=', 2020)  47.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='15  53.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='32  50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='57  65.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='94  71.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='92  51.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='02  63.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='22  + Depth (p = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='3)  50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='17  58.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='50  51.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='62  69.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='10  72.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='55  54.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='98  66.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='26  + 3D Views  48.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='15  58.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='74  50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='32  66.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='73  69.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='79  51.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='26  63.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='97  SimSiam (Chen & He, 2021)  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
+page_content='39  50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
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+page_content='28  60.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFKT4oBgHgl3EQfWC5j/content/2301.11790v1.pdf'}
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+arXiv:2301.03329v1  [cs.CG]  9 Jan 2023
+Sparse Geometric Set Systems and the Beck-Fiala Conjecture
+Kunal Dutta ∗ 1 and Arijit Ghosh ∗ 2
+1Faculty of Mathematics, Informatics, and Mechanics, University of Warsaw, Poland.
+email: K.Dutta@mimuw.edu.pl
+2Indian Statistical Institute, Kolkata, India email: arijitiitkgpster@gmail.com
+Abstract
+We investigate the combinatorial discrepancy of geometric set systems having bounded
+shallow cell complexity in the Beck-Fiala setting, where each point belongs to at most t
+ranges. For set systems with shallow cell complexity ψ(m, k) = g(m)kc, where (i) g(m) =
+o(mε) for any ε ∈ (0, 1], (ii) ψ is non-decreasing in m, and (iii) c > 0 is independent of m
+and k, we get a discrepancy bound of
+O
+���
+log n + (tcg(n))
+1
+1+c
+�
+log n
+�
+.
+For t = ω(log2 n), in several cases, such as for set systems of points and half-planes / disks
+/ pseudo-disks in R2, points and orthants in R3 etc., these bounds are o(
+√
+t), which veriﬁes
+(and improves upon) the conjectured bound of Beck and Fiala (Disc. Appl. Math., 1981).
+Our bounds are obtained by showing the existence of matchings with low crossing number,
+using the multiplicative weights update method of Welzl (SoCG, 1988), together with the
+recent bound of Mustafa (Disc. Comp. Geom., 2015) on shallow packings of set systems in
+terms of their shallow cell complexity. For set systems of shallow cell complexity ψ(m, k) =
+mc1g(m)kc, we obtain matchings with crossing number at most
+O
+�
+(nc1g(n)tc)
+1
+1+c1+c
+�
+.
+These are of independent interest.
+1
+Introduction
+Given a set system (X, R) with ground set X and a collection R ⊂ 2X of subsets of X, the
+combinatorial discrepancy of the system is given by
+disc(R) :=
+min
+χ:X→{±1} max
+S∈R
+�����
+�
+i∈S
+χ(i)
+����� ,
+that is, the maximum imbalance over all sets in R, minimized over all possible 2-partitions of X.
+Using the incidence matrix A of the system (X, R), an equivalent linear algebraic formulation
+– the vector balancing problem can be stated as
+disc(A) :=
+min
+x∈{−1,1}n ∥Ax∥∞.
+∗Supported by the Polish NCN-SONATA Grant no.
+2019/35/D/ST6/04525 (Probabilistic tools for high-
+dimensional geometric inference, topological data analysis and large-scale networks).
+1
+
+For a given class of set systems, the problem of discrepancy minimization seeks to establish
+bounds on the discrepancy of systems in the class, as a function of the size of the ground set, or
+other parameters. Besides its inherent interest, discrepancy minimization has many applications
+in several areas of mathematics as well as computer science and related subjects [13, 30].
+Beck-Fiala and Komlos Conjectures
+In their seminal work which initiated the use of the
+term “discrepancy” as well as the study of the discrepancy of set systems, Beck and Fiala [10]
+showed that any set system where each element belongs to at most t sets, has discrepancy at
+most 2t−1. They conjectured that this bound could be improved to O
+�√
+t
+�
+. In linear algebraic
+terms, the closely related generalization known as the Komlos conjecture, states that for a real
+matrix with ℓ2 norm of each column at most 1, the discrepancy is O(1). Despite signiﬁcant
+progress in partial results and understanding of discrepancy theory in the last 4 decades, these
+tantalizing conjectures have remained open.
+Early and Recent Progress
+Since the seminal results of Beck and Fiala, much progress has
+been made toward resolving the Beck-Fiala and Komlos conjectures. Early breakthroughs in
+the area include those of Spencer [39] and Gluskin [22] who showed that the Komlos conjecture
+holds for t = Θ(n). Later Srinivasan [40] and Banaszczyk [3] proved bounds for general t. The
+latter’s bound of 5√t log n remains the best current result on the Komlos conjecture.
+The above bounds were non-constructive and it was even conjectured that eﬃcient algo-
+rithms to construct colorings with the promised discrepancy bounds, did not exist. However in
+a major breakthrough, Bansal [4] gave an eﬃcient algorithm to construct a coloring matching
+Spencer’s discrepancy bounds for |R| = Θ(n). This has been followed by a large number of
+recent results, both algorithmic and non-algorithmic, for upper and lower bounds, as well as
+many applications and generalizations, see [28, 5, 6, 16, 27, 37, 7].
+Geometric Set Systems
+The discrepancy of set systems with a geometric interpretation,
+such as for example of points and half-planes in R2 and R3 or points and disks in R2, has
+been of signiﬁcant theoretical and practical importance, as it relates to several areas like com-
+putational geometry, statistical and machine learning, algorithmic analysis, database theory,
+etc. [30, 25, 26]. Questions such as Tu´snady’s problem have been studied since the early years
+of discrepancy theory [9, 11]. Other notable results include those of points and projective planes
+(Spencer [1]), primal systems of bounded VC dimension (Matouˇsek [29]), systems of bounded
+dual VC dimension, etc.(Matouˇsek-Welzl-Wernisch [32]).
+More recently Ezra [21] proposed the notion of size-sensitive discrepancy, and further asked
+about the discrepancy of geometric set systems with bounded degree. Using the packing and
+chaining framework of Dutta, Ezra and Ghosh [17], together with the partial coloring based
+algorithm of Lovett-Meka (or a similar algorithm), it is comparatively straightforward to obtain
+bounds of O
+�
+t1/4 · log n
+�
+for points and half-planes in R2. To some extent, this setting has
+been considered in the unpublished work [20], but the bounds have an extra √log log t log n
+factor (as in the above example) which stems from using the partial coloring approach and a
+suboptimal assignment of parameters. 1 To the best of our knowledge, other than the above-
+mentioned unpublished drafts, there are no published or publicly available works which consider
+the question of geometric set systems with bounded degree of elements. However interesting
+questions remain to be asked for such systems. For example it seemed interesting to ask if the
+O
+�
+t1/4 log n
+�
+bound for points and half-planes in the Beck-Fiala setting, can be improved to
+O
+�
+t1/4√log n
+�
+or better, using (for instance) the algorithmic frameworks of Bansal and others.
+1Moreover these bounds do not appear in the published version.
+2
+
+Union and Shallow Cell Complexity
+Set systems with low union complexity or shallow
+cell complexity constitute a fairly general class and include several important cases such as
+points and half-spaces in R2 and R3, points and (pseudo)disks in R2 and several others (see, for
+example [36, Chapter 4]). Moreover, since dual systems of low union complexity also have low
+shallow cell complexity of the corresponding primal systems (e.g. [35]), they have been studied
+in a series of works e.g. [14, 41, 12, 8, 34, 18, 19] where better bounds have been obtained for
+them for several structures of interest, such as unweighted and weighted epsilon nets, epsilon
+approximations, relative approximations, ǫ-brackets, combinatorial Macbeath regions, etc.
+Our Contribution
+We investigate the discrepancy of geometric set systems with linear or near-linear shallow cell
+complexity, and each element belonging to at most t sets, where t is a given parameter inde-
+pendent of n. Our discrepancy bounds are stated below.
+Theorem 1. Let (X, R) be a set system with shallow cell complexity ψ(m, k) = g(m)kc, where
+g(m) = o(mε) for every ε ∈ (0, 1), is a non-decreasing function of m and c > 0 is a constant
+independent of n and k, and each element of X belongs to at most t sets of R.
+Then the
+discrepancy of (X, R) is at most
+O
+���
+log n + (tcg(n))
+1
+1+c
+�
+log n
+�
+.
+In particular, for the following families of set systems with degree at most t, the discrepancy is
+bounded as below.
+1. Points and half-planes in R2: O
+��
+(log n + t1/2) log n
+�
+.
+2. Points and homothets of a convex body in R2: O
+��
+(log n + t1/2) log n
+�
+.
+3. Points and disks in R2: O
+��
+(log n + t1/2) log n
+�
+.
+4. Points and pseudodisks in R2: O
+��
+(log n + t1/2) log n
+�
+.
+5. Points and α-fat triangles in R2: O
+��
+(log n + (t · log∗ n)1/2) log n
+�
+.
+6. Points and objects with linear union complexity: O
+��
+(log n + t1/2) log n
+�
+.
+7. Points and locally γ-fat semi-algebraic objects in R2 with bounded description complexity:
+O
+��
+(log n + t1/2 · 2O(log∗ n)) log n
+�
+.
+8. Points and half-spaces in R3: O
+��
+(log n + t2/3) log n
+�
+.
+9. Points and orthants in R2 and R3: O
+��
+(log n + t1/2) log n
+�
+.
+These bounds match or improve the known, as well as the conjectured general bounds for
+systems of bounded degree. For instance, for set systems of points and half-planes in R2, we
+get the bound of
+O
+���
+log n +
+√
+t
+�
+log n
+�1/2�
+,
+which is O
+�√
+t
+�
+for t = Ω(log n).
+For t = ω
+�
+log2 n
+�
+, we have √log n = o(t1/4), so the
+O
+�
+t1/4√log n
+�
+bound improves upon the conjectured O
+�√
+t
+�
+bound of Beck and Fiala. Thus,
+3
+
+they give much better bounds even without using the random walk based framework and intri-
+cate analysis of many recent discrepancy minimization algorithms e.g. [28, 6, 38].
+More generally, we get the following corollary of Theorem 1.
+Corollary 2. The Beck-Fiala conjecture holds for the following set systems having maximum
+degree t, with the given constraints on t.
+1. Points and half-planes in R2: t = Ω
+�
+log2 n
+�
+.
+2. Points and homothets of a convex body in R2: t = Ω
+�
+log2 n
+�
+.
+3. Points and disks in R2: t = Ω
+�
+log2 n
+�
+.
+4. Points and pseudodisks in R2: t = Ω
+�
+log2 n
+�
+.
+5. Points and α-fat triangles in R2: t = Ω
+�
+log2 n log∗ n
+�
+.
+6. Points and objects with linear union complexity: t = Ω
+�
+log2 n
+�
+.
+7. Points and locally γ-fat semi-algebraic objects in R2 with bounded description complexity:
+t = Ω
+�
+2O(log∗ n)) log2 n
+�
+.
+8. Points and half-spaces in R3: t = Ω
+�
+log3 n
+�
+.
+9. Points and orthants in R2 and R3: t = Ω
+�
+log2 n
+�
+.
+Our techniques are based upon showing the existence of matchings with low crossing number
+using the well-known multiplicative weights update method of Welzl [42], together with the
+shallow packing bound of Mustafa [33] and Dutta, Ezra and Ghosh [17]. These crossing number
+bounds, which are of independent interest, are as below.
+Theorem 3. Let (X, R) be an n-point set system, with |R| ≥ n, generated by intersections of
+X with a class of objects having dual shatter dimension at most d and shallow cell complexity
+ψ(m, k) = mc1 · g(m)kc, where c1, c ≥ 0 are independent of m and k, and g(m) is a non-
+decreasing function of m such that g(m) = o(mε) for every ε ∈ (0, 1). Further, let (X, R) have
+the property that each point of X belongs to at most t sets. Then there exists a matching of the
+points of X, with crossing number at most
+O
+�
+(nc1tcg(n))
+1
+1+c1+c
+�
+.
+In particular, if c1 = 0, then the crossing number is at most
+O
+�
+(tcg(n))
+1
+1+c
+�
+.
+Corollary 4. For the following set systems (X, R) with each element of X belonging to at most
+t members of R, there exist matchings with the following bounds on the crossing number.
+1. Points and half-planes in R2: O
+�
+log n +
+√
+t
+�
+.
+2. Points and homothets of a convex body in R2: O
+�
+log n +
+√
+t
+�
+.
+3. Points and disks in R2: O
+�
+log n +
+√
+t
+�
+.
+4. Points and pseudodisks in R2: O
+�
+log n +
+√
+t
+�
+.
+5. Points and α-fat triangles in R2: O
+�
+log n +
+�
+t · log∗ n
+�
+.
+4
+
+6. Points and objects with linear union complexity: O
+�
+log n +
+√
+t
+�
+.
+7. Points and locally γ-fat semi-algebraic objects in R2 with bounded description complexity:
+O
+�
+log n +
+√
+t · 2O(log∗ n)
+�
+.
+8. Points and half-spaces in R3: O
+�
+log n + t2/3�
+.
+9. Points and orthants in R2 and R3: O
+�
+log n + t1/2�
+.
+The proofs of our results are in Section 3. While our discrepancy and crossing number bounds
+are not diﬃcult to obtain, we believe they are important, as they demonstrate cases of non-
+random (and non-smoothed) natural set systems which verify or improve upon the Beck-Fiala
+conjecture. Further, these bounds are much stronger than the bounds for general set systems
+of bounded VC dimension or shallow cell complexity (without the degree bound), which are
+known to be tight [31]. It should be noted that merely using low shallow complexity cannot
+improve the bound on the crossing number, as the tightness results in [31] hold for systems in
+2 and 3 dimensions. Matchings (or spanning paths or trees) with low crossing number are of
+wide interest, as they are used in a number of applications [30, 15].
+2
+Preliminaries
+The projection of a set system (X, R) on to a subset Y ⊂ X of the ground set is denoted by
+R|Y := {R ∩ Y | R ∈ R}.
+A primal set system has a ground set P of points in Rd and subsets given by all possible
+intersections with a class G of geometric objects in Rd, that is the set system (P, G|P ). A dual set
+system given a (ﬁnite) collection G of geometric objects is given by (G, G|Rd), that is, equivalence
+classes of points of Rd under intersection with objects in G.
+The notion of shallow cell complexity has found many applications in Computational Ge-
+ometry, including improved bounds on ε-nets and related structures (see e.g. [35]).
+Deﬁnition 5 (Shallow-cell Complexity). A set system (X, R) has shallow-cell complexity ψ(·, ·)
+if for any Y ⊆ X, the number of subsets in R|Y of size l is at most |Y | · ψ(|Y |, l).
+In this paper, we shall throughout work with set systems whose shallow cell complexity is
+given by
+ψ(l, k)
+=
+lc1g(l)kc,
+(1)
+where c1, c > 0 are constants independent of l, k, and g(l) = o(lε) for every ε ∈ (0, 1].
+Deﬁnition 6 (Union Complexity). A set of m geometric objects O has union complexity f(m)
+if the number of faces of all dimensions in the union of the members of O, is at most f(m).
+It is known (see e.g. [35]) that set systems formed by intersections of points with objects
+having union complexity f(.), have shallow cell complexity at most f(m/k) · k2.
+A central lemma for set systems of bounded shallow cell complexity, is the Shallow Packing
+Lemma of [17, 33]. To state the lemma, ﬁrst we need to deﬁne shallow packings.
+Deﬁnition 7 (Shallow Packing). Let (X, R) be a set system, and δ and k be positive integers.
+A subset of ranges P ⊆ R is a k-shallow δ-packing or (k, δ)-packing, if any pair of ranges in
+P have symmetric diﬀerence greater than δ, and for all R ∈ P we have |R ∩ X| ≤ k.
+5
+
+Now follows the Shallow Packing Lemma of Mustafa [33], which gives optimal bounds for
+shallow packings of set systems, in terms of their shallow cell complexity.
+Theorem 8 (Shallow Packing Lemma, Mustafa [33]). Let (X, R) be a set system with |X| = n
+and shallow cell complexity ϕR. If the VC dimension of (X, R) is at most d0, and (X, R) is a
+k-shallow δ-packing then
+24d0n
+δ
+· ϕR
+�4d0n
+δ
+, 12d0k
+δ
+�
+≤ Cd0
+n
+δ ψ
+�n
+δ , k
+δ
+�
+,
+where Cd0 is a constant independent of n and δ.
+Finally, we deﬁne the notions of crossing number and partitions with low crossing number,
+which are central to this paper.
+Deﬁnition 9 (Crossing Number; Partitions with Low Crossing Number). A range S ∈ R is
+crossed by a pair of elements of X, {x, y} if |{x, y} ∩ X| = 1. Given a partition of the universe
+X into pairs Π = ({xi, yi})n/2
+i=1 with {xi, yi} ∩ {xj, yj} = ∅ for i ̸= j, and �
+i≥1{xi, yi} = X, the
+crossing number of Π is the maximum number of pairs of Π which cross any given range of R.
+3
+Well-Behaved Dual Systems
+In this section, we prove our theorems and corollaries. We begin with the proof of Theorem 1.
+The proof follows immediately from the statements of Theorem 3 and Corollary 4, with the
+following additional lemma, which gives a bound on the discrepancy of an arbitrary set system,
+in terms of the crossing number of a perfect matching of the elements. The ﬁrst statement in
+the lemma is an easy observation, while the second statement is well-known (see e.g. Chapter
+5 [30]).
+Lemma 10. Let (X, R) be a set system, |X| even, with degree bounded by t and having a
+matching with crossing number at most N. Then the discrepancy of (X, R) is at most
+O
+�
+min
+�
+N,
+�
+N · log |R|
+��
+= O
+��
+N · log |R|
+�
+.
+Proof. It is easy to see that the discrepancy is at most N: just take an arbitrary coloring where
+each vertex of matched pair of vertices, is given opposite colors. The discrepancy of a set S ∈ R
+is at most the number of pairs that have exactly one vertex in S. This is at most the crossing
+number, i.e. N.
+To see that the discrepancy is at most O
+��
+N log |R|
+�
+, consider a random coloring which
+ensure that in every matched pair, opposite colors are assigned to the vertices in the pair. Now
+for any set S ∈ R, the expected discrepancy of S is zero, and the variance of the discrepancy
+of S is at most the number of pairs which cross S, i.e. at most the crossing number N. Now
+applying Chernoﬀ bounds, allowing for a maximum deviation of O
+��
+N log |R|
+�
+, and taking a
+union bound over all sets of R, we get the statement of the lemma.
+For the proof of Theorem 3, we shall need the following lemma, which guarantees the
+existence of a pair of points which cross a small number of ranges.
+Lemma 11 (Short Edge Lemma). Assume the setting of Theorem 3. Then for any set or
+multiset of ranges T ⊆ R, there exist points x, y ∈ X, such that the edge {x, y} is crossed by at
+most δ ranges, where δ is the maximum value satisfying
+n
+≤
+Cd0
+|T|
+δ · ψ
+�|T|
+δ , t
+δ
+�
+,
+where Cd0 is a constant that depends only on d0.
+6
+
+Proof. For each point x ∈ X, deﬁne the set of ranges Dx := {S ∈ T
+:
+x ∈ S}.
+Let
+D := {Dx : x ∈ X} be the collection of sets of ranges so formed. Then for any pair of points
+x, y ∈ X, the symmetric diﬀerence Dx∆Dy is the set of ranges which are crossed by the pair
+{x, y}. The shallow cell complexity of the system D is at most the union complexity of the dual
+set system given by T. Let δ denote the minimum symmetric diﬀerence between any pair of
+sets in D. If there exists a pair {x, y} such that Dx = Dy, then we are done, since δ = 0 for this
+pair. Otherwise, observe that by deﬁnition, D is a δ-packing. Since every element of (X, R)
+belongs to at most t ranges, the maximum size of any set in D is t. Thus, we can apply the
+Shallow Packing Lemma 8 to bound the size of the δ-packing. We get
+n
+=
+|D|
+≤
+Cd0
+|T|
+δ · ψ
+�|T|
+δ , t
+δ
+�
+.
+where Cd0 is a constant that depends only on d0.
+We will now give the proof of Theorem 3.
+Theorem 12 (Restatement of Theorem 3). Let (X, R) be an n-point set system, with |R| ≥ n,
+generated by intersections of X with a class of objects having dual shatter dimension at most d
+and shallow cell complexity ψ(m, k) = mc1 · g(m)kc, where c1, c ≥ 0 are independent of m and
+k, and g(m) is a non-decreasing function of m such that g(m) = o(mε) for every ε ∈ (0, 1).
+Further, let (X, R) have the property that each point of X belongs to at most t sets. Then there
+exists a matching of the points of X, with crossing number at most
+O
+�
+(nc1tcg(n))
+1
+1+c1+c
+�
+.
+In particular, if c1 = 0, then the crossing number is at most
+O
+�
+(tcg(n))
+1
+1+c
+�
+.
+Proof. We shall construct the matching by picking pairs of points sequentially, in a greedy
+manner. Each time, we shall choose a pair of points that crosses the least number of ranges.
+However, instead of looking at the number of ranges crossed by a given pair, we shall do a
+weighted counting, in which we shall assign a weight to each range and look to choose the pair
+that minimizes the weight of the ranges that it crosses. The weight of a range S ∈ R will be
+a function of the number of pairs already selected, which cross S. This will force the selection
+of edges which do not cross the ranges that have already been crossed several times, thus our
+strategy will tend to favour low crossing number with respect to the already selected edges.
+Initially, we assign each range a weight of 1. After the i-th pair has been chosen, for a
+given range S ∈ R let cS(i) denote the number of already selected pairs, which cross i. Then
+the weight of S is given by wi(S) = 2cS(i). The weight of any subset of ranges S ⊆ R is the
+sum of the weights of the ranges in S. At each step, we greedily pick a pair that crosses the
+least number of weighted ranges of R, where the weights have been updated at the end of the
+previous step. At the end of the i-th step, let Ti denote the multiset obtained R by replacing
+each range S ∈ R with wi(S) copies of S. Note that wi(R) = |Ti|, where the cardinality of Ti
+refers to the weighted cardinality.
+By the Short Edge Lemma 11, we have
+n
+≤
+|Ti|1+c1
+δ1+c1+c g(|Ti|/δ)tc
+≤
+wi(R)1+c1
+δ1+c1+c g(wi(R))tc.
+7
+
+Therefore, there exists a pair of points in
+X \ {x1, y1, x2, y2, . . . , xi, yi},
+which cross at most δ ranges, where δ is the maximum value satisfying
+δ ≤
+�|Ti|1+c1
+n
+g(|T|)tc
+�1/(1+c1+c)
+.
+We choose this pair {xi+1, yi+1} to be the (i + 1)-st edge of the matching. Let Ri+1 denote the
+ranges of R that are crossed by the pair {xi+1, yi+1}. The weight of the system R after the
+(i + 1)-st step, will therefore be
+wi+1(R)
+=
+wi(R) − wi(Ri+1) + wi+1(Ri+1).
+Now since the crossing number of the ranges in R increased by 1 after choosing {x, y}, therefore
+by the deﬁnition of the weight function, their weights double after the (i + 1)-st step, that is,
+wi+1(Ri+1) = 2wi(Ri+1).
+Thus we get
+wi+1(R)
+=
+wi(R) − wi(Ri+1) + 2wi(Ri+1)
+=
+wi(R)
+�
+1 + wi(Ri+1)
+wi(R)
+�
+.
+(2)
+Noting that |Ri+1| ≤ δ by our choice of the pair {xi+1, yi+1}, we get
+wi(Ri+1)
+≤
+C ·
+�
+wi(R)1+c1tc ·
+�g(wi(R))
+n − 2i
+��1/(1+c1+c)
+.
+Now substituting in the recurrence relation (2) for the weight of R, gives
+wi+1(R)
+≤
+wi(R)
+�
+1 + wi(Ri+1)
+wi(R)
+�
+=
+wi(R)
+�
+1 +
+�
+tc
+(n − 2i) · g(wi(R))
+wi(R)c
+�
+1
+1+c1+c
+�
+.
+Since by deﬁnition g(n) = o(nε) for every ε ∈ (0, 1] and we assumed c is constant, therefore the
+ratio g(wi(R))
+wi(R)c
+is maximized when wi(R) is the minimum, i.e. w0(R), or |R|. Further, by our
+assumption that |R| ≥ n, the ratio becomes at most g(n)
+nc . Thus we get
+wn/2(R)
+≤
+w0(R)
+n/2−1
+�
+i=1
+�
+1 +
+�
+tcg(n))
+(n − 2i)nc
+�
+1
+1+c1+c
+�
+≤
+|R|
+n/2−1
+�
+i=1
+�
+1 +
+�
+tcg(n)
+(n − 2i)nc
+�
+1
+1+c1+c
+�
+.
+Taking logarithms with respect to both sides, we get
+log wn/2(R)
+≤
+log |R| + O
+
+
+�� t
+n
+�c
+g(n)
+�
+1
+1+c1+c n/2−1
+�
+i=1
+1
+(n − 2i)1/(1+c1+c)
+
+
+≤
+log |R| + O
+�
+(tcg(n))
+1
+1+c1+c nc1/(1+c1+c)�
+=
+log |R| + O
+�
+(nc1tcg(n))
+1
+1+c1+c
+�
+.
+(3)
+8
+
+Here in the second inequality above, we have used the fact that
+n/2−1
+�
+i=1
+1
+(n − 2i)
+1
+1+c1+c
+≤ n1−
+1
+1+c1+c .
+Finally, let cmax := maxS∈R cS(n/2) denote the maximum number of crossings over all sets
+S ∈ R. We have
+cmax = max
+S∈R log wn/2(S) ≤ log wn/2(R).
+By Equation (3), this is at most
+log |R| + O
+�
+(nc1tcg(n))1/(1+c1+c)�
+.
+Since the VC dimension of the system is bounded (in fact, substituting k = n in the shallow cell
+complexity, we see that the VC dimension is at most 2+ c1 + c), we get that log |R| = O(log n),
+since the number of ranges is polynomial in the size of the universe X.
+This completes the proof of the theorem.
+It only remains to prove Corollary 4. The corollary follows immediately from known bounds
+on the shallow cell complexity and the union complexity of various geometric set systems. These
+bounds are given in the table below.
+Proof of Corollary 4. The proof of the corollary follows by applying the shallow cell complexity
+functions in the table below, to the result of Theorem 3. These bounds can be found in [18]
+and [36][see the list in Chapter 4.3] and the references therein. We also recommend the survey [2]
+for the interested reader. The bounds for orthants was proved in [24].
+Objects
+mψ(m, k)
+Intervals in R
+m.
+Half-spaces in R2
+mk.
+Homothets of a convex body in R2
+mk.
+Disks in R2
+mk.
+Pseudodisks in R2
+mk.
+α-fat triangles in R2
+mk log∗ m
+k + mk log2 α.
+Locally γ-fat semi-algebraic objects
+mk2O(log∗ m).
+with bounded description complexity in R2
+Objects with union complexity mφ(m)
+mφ(m/k)k.
+Halfspaces in R3
+mk.
+Orthants in R2 and R3
+mk.
+Table 1: Shallow-cell complexity bounds for diﬀerent geometric set systems.
+4
+Conclusion
+We have shown improved discrepancy bounds in set systems with near-linear shallow cell com-
+plexity, under the condition that each point belongs to a bounded number of sets. Though
+algorithmic considerations are not the focus of our paper, these are now brieﬂy discussed. In
+order to obtain a low-discrepancy coloring, we need to compute a matching with low crossing
+number. Such algorithms have been studied by several authors e.g. [42, 43, 23, 15]. For our
+9
+
+purposes, it suﬃces to use the original algorithm of Welzl, which uses at most O(n3t) time in
+our case. We note that the faster algorithms of Csikos and Mustafa [15] as well as Har-Peled [23]
+give matchings with slightly worse bounds on the crossing number (by a logarithmic factor in
+n), which results in a corresponding increase in the discrepancy.
+References
+[1] Coloring the Projective Plane. Discrete Mathematics, 73(1):213–220, 1988.
+[2] P. K. Agarwal, J. Pach, and M. Sharir. State of the Union (of Geometric Objects): A Re-
+view. In J. Goodman, J. Pach, and R. Pollack, editors, Computational Geometry: Twenty
+Years Later, pages 9–48. American Mathematical Society, 2008.
+[3] W. Banaszczyk. Balancing vectors and Gaussian measures of n-dimensional convex bodies.
+Random Struct. Algorithms, 12(4):351–360, 1998.
+[4] N. Bansal. Constructive Algorithms for Discrepancy Minimization. In FOCS, pages 3–10,
+2010.
+[5] N. Bansal, D. Dadush, and S. Garg.
+An Algorithm for Koml´os Conjecture Matching
+Banaszczyk’s Bound. In FOCS, pages 788–799, 2016.
+[6] N. Bansal and S. Garg. Algorithmic Discrepancy Beyond Partial Coloring. In STOC 2017:
+Proceedings of the 49th Annual ACM SIGACT Symposium on Theory of Computing, pages
+914–926, 2017.
+[7] Nikhil Bansal, Daniel Dadush, Shashwat Garg, and Shachar Lovett. The Gram-Schmidt
+Walk: A Cure for the Banaszczyk Blues. In Proceedings of the 50th Annual ACM SIGACT
+Symposium on Theory of Computing, STOC, page 587–597, 2018.
+[8] Nikhil
+Bansal
+and
+Kirk
+Pruhs.
+Weighted
+geometric
+set
+multi-cover
+via
+quasi-uniform
+sampling.
+J.
+Comput.
+Geom.,
+7(1):221–236,
+2016.
+URL:
+https://doi.org/10.20382/jocg.v7i1a11, doi:10.20382/jocg.v7i1a11.
+[9] J. Beck. Balanced two-colorings of ﬁnite sets in the square I. Combinatorica, 1(4):327–335,
+1981.
+[10] J. Beck and T. Fiala. ”Integer-making” theorems. Discrete Applied Mathematics, 3(1):1–8,
+1981.
+[11] J´ozsef Beck. Balanced two-colorings of ﬁnite sets in the cube. Discret. Math., 73(1-2):13–25,
+1989.
+[12] T. M. Chan, E. Grant, J. K¨onemann, and M. Sharpe. Weighted Capacitated, Priority, and
+Geometric Set Cover via Improved Quasi-Uniform Sampling. In Proceedings of the 23rd
+ACM-SIAM Symposium on Discrete Algorithms, SODA, pages 1576–1585, 2012.
+[13] Bernard Chazelle. The Discrepancy Method - Randomness and Complexity. Cambridge
+University Press, 2001.
+[14] K. L. Clarkson and K. R. Varadarajan. Improved Approximation Algorithms for Geometric
+Set Cover. Discrete & Computational Geometry, 37(1):43–58, 2007.
+[15] M. Csik´os and N. H. Mustafa. Escaping the Curse of Spatial Partitioning: Matchings with
+Low Crossing Numbers and Their Applications. In Proceedings of the 37th International
+Symposium on Computational Geometry, SoCG, volume 189, pages 28:1–28:17, 2021.
+10
+
+[16] D. Dadush, S. Garg, S. Lovett, and A. Nikolov. Towards a Constructive Version of Ba-
+naszczyk’s Vector Balancing Theorem. In RANDOM, pages 28:1–28:12, 2016.
+[17] K. Dutta, E. Ezra, and A. Ghosh. Two Proofs for Shallow Packings. Discrete & Compu-
+tational Geometry, 56(4):910–939, 2016.
+[18] K. Dutta, A. Ghosh, B. Jartoux, and N. H. Mustafa. Shallow Packings, Semialgebraic
+Set Systems, Macbeath Regions, and Polynomial Partitioning. Discrete & Computational
+Geometry, 61(4):756–777, 2019.
+[19] K. Dutta, A. Ghosh, and S. Moran. Uniform Brackets, Containers, and Combinatorial
+Macbeath Regions. In Proceedings of th13th Innovations in Theoretical Computer Science
+Conference, ITCS, volume 215, pages 59:1–59:10, 2022.
+[20] K. Dutta and G. Ghosh. Size sensitive packing number for Hamming cube and its conse-
+quences. 2014. URL: https://arxiv.org/abs/1412.3922.
+[21] E. Ezra. A Size-Sensitive Discrepancy Bound for Set Systems of Bounded Primal Shatter
+Dimension. SIAM Journal on Computing, 45(1):84–101, 2016.
+[22] E. D. Gluskin. Extremal properties of orthogonal parallelepipeds and their applications to
+the geometry of banach spaces. Sbornik: Mathematics, 64(1):85–96, 1989.
+[23] S. Har-Peled. Approximating Spanning Trees with Low Crossing Number. 2009. URL:
+https://arxiv.org/abs/0907.1131.
+[24] Haim Kaplan, Natan Rubin, Micha Sharir, and Elad Verbin. Counting colors in boxes.
+In Proceedings of the Eighteenth Annual ACM-SIAM Symposium on Discrete Algorithms,
+SODA ’07, page 785–794, USA, 2007. Society for Industrial and Applied Mathematics.
+[25] K. G. Larsen. On Range Searching in the Group Model and Combinatorial Discrepancy.
+SIAM J. Comput., 43(2):673–686, 2014.
+[26] Kasper Green Larsen. Constructive discrepancy minimization with hereditary L2 guar-
+antees.
+In Rolf Niedermeier and Christophe Paul, editors, 36th International Sympo-
+sium on Theoretical Aspects of Computer Science, STACS 2019, March 13-16, 2019,
+Berlin, Germany, volume 126 of LIPIcs, pages 48:1–48:13. Schloss Dagstuhl - Leibniz-
+Zentrum f¨ur Informatik, 2019. URL: https://doi.org/10.4230/LIPIcs.STACS.2019.48,
+doi:10.4230/LIPIcs.STACS.2019.48.
+[27] A. Levy, H. Ramadas, and T. Rothvoss. Deterministic Discrepancy Minimization via the
+Multiplicative Weight Update Method. page to appear, 2017.
+[28] S. Lovett and R. Meka. Constructive Discrepancy Minimization by Walking on the Edges.
+In FOCS, pages 61–67, 2012.
+[29] J. Matouˇsek. Geometric Discrepancy: An Illustrated Guide. Springer, 1999.
+[30] J. Matouˇsek. Geometric discrepancy: An illustrated guide. Springer, 2009.
+[31] J. Matousˇek. On discrepancy bounds via dual shatter function. Mathematika, 44(1):42–49,
+1997.
+[32] J. Matouˇsek, E. Welzl, and L. Wernisch. Discrepancy and approximations for bounded
+VC-dimension. Combinatorica, 13(4):455–466, 1993.
+[33] N. H. Mustafa. A Simple Proof of the Shallow Packing Lemma. Discrete & Computational
+Geometry, 55(3):739–743, 2016.
+11
+
+[34] N. H. Mustafa, K. Dutta, and A. Ghosh. A Simple Proof of Optimal Epsilon-nets. Com-
+binatorica, 2017.
+[35] N. H. Mustafa and K. Varadarajan. Epsilon-approximations and Epsilon-nets. In J. E.
+Goodman, J. O’Rourke, and C. D. T´oth, editors, Handbook of Discrete and Computational
+Geometry. CRC Press LLC, 2017.
+[36] Nabil H. Mustafa. Sampling in Combinatorial and Geometric Systems. American Mathe-
+matical Society, 2022.
+[37] Aleksandar Nikolov. Tighter Bounds for the Discrepancy of Boxes and Polytopes. Mathe-
+matika, 63(3):1091–1113, 2017.
+[38] T. Rothvoss. Better Bin Packing Approximations via Discrepancy Theory. SIAM J. Com-
+put., 45(3):930–946, 2016.
+[39] J. Spencer. Six standard deviations suﬃce. Trans. Amer. Math. Soc., 289(2):679–706,
+1985.
+[40] A. Srinivasan. Improving the Discrepancy Bound for Sparse Matrices: Better Approxima-
+tions for Sparse Lattice Approximation Problems. In SODA, pages 692–701, 1997.
+[41] K. R. Varadarajan. Weighted Geometric Set Cover via Quasi-Uniform Sampling. In Pro-
+ceedings of the 42nd ACM Symposium on Theory of Computing, STOC, pages 641–648,
+2010.
+[42] E. Welzl. Partition trees for triangle counting and other range searching problems. In
+Proceedings of the Fourth Annual Symposium on Computational Geometry, SCG ’88,
+page 23–33, New York, NY, USA, 1988. Association for Computing Machinery.
+URL:
+https://doi.org/10.1145/73393.73397, doi:10.1145/73393.73397.
+[43] Emo Welzl. On spanning trees with low crossing numbers, pages 233–249. Springer Berlin
+Heidelberg, Berlin, Heidelberg, 1992.
+12
+
diff --git a/BNE1T4oBgHgl3EQfpQVQ/content/tmp_files/load_file.txt b/BNE1T4oBgHgl3EQfpQVQ/content/tmp_files/load_file.txt
new file mode 100644
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+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf,len=534
+page_content='arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='03329v1  [cs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='CG]  9 Jan 2023  Sparse Geometric Set Systems and the Beck-Fiala Conjecture  Kunal Dutta ∗ 1 and Arijit Ghosh ∗ 2  1Faculty of Mathematics, Informatics, and Mechanics, University of Warsaw, Poland.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  email: K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='Dutta@mimuw.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='edu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='pl  2Indian Statistical Institute, Kolkata, India email: arijitiitkgpster@gmail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='com  Abstract  We investigate the combinatorial discrepancy of geometric set systems having bounded  shallow cell complexity in the Beck-Fiala setting, where each point belongs to at most t  ranges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' For set systems with shallow cell complexity ψ(m, k) = g(m)kc, where (i) g(m) =  o(mε) for any ε ∈ (0, 1], (ii) ψ is non-decreasing in m, and (iii) c > 0 is independent of m  and k, we get a discrepancy bound of  O  ���  log n + (tcg(n))  1  1+c  �  log n  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  For t = ω(log2 n), in several cases, such as for set systems of points and half-planes / disks  / pseudo-disks in R2, points and orthants in R3 etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=', these bounds are o(  √  t), which veriﬁes  (and improves upon) the conjectured bound of Beck and Fiala (Disc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=', 1981).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  Our bounds are obtained by showing the existence of matchings with low crossing number,  using the multiplicative weights update method of Welzl (SoCG, 1988), together with the  recent bound of Mustafa (Disc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Comp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Geom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=', 2015) on shallow packings of set systems in  terms of their shallow cell complexity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' For set systems of shallow cell complexity ψ(m, k) =  mc1g(m)kc, we obtain matchings with crossing number at most  O  �  (nc1g(n)tc)  1  1+c1+c  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  These are of independent interest.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  1  Introduction  Given a set system (X, R) with ground set X and a collection R ⊂ 2X of subsets of X, the  combinatorial discrepancy of the system is given by  disc(R) :=  min  χ:X→{±1} max  S∈R  �����  �  i∈S  χ(i)  ����� ,  that is, the maximum imbalance over all sets in R, minimized over all possible 2-partitions of X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  Using the incidence matrix A of the system (X, R), an equivalent linear algebraic formulation  – the vector balancing problem can be stated as  disc(A) :=  min  x∈{−1,1}n ∥Ax∥∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  ∗Supported by the Polish NCN-SONATA Grant no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  2019/35/D/ST6/04525 (Probabilistic tools for high-  dimensional geometric inference, topological data analysis and large-scale networks).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  1  For a given class of set systems, the problem of discrepancy minimization seeks to establish  bounds on the discrepancy of systems in the class, as a function of the size of the ground set, or  other parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Besides its inherent interest, discrepancy minimization has many applications  in several areas of mathematics as well as computer science and related subjects [13, 30].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  Beck-Fiala and Komlos Conjectures  In their seminal work which initiated the use of the  term “discrepancy” as well as the study of the discrepancy of set systems, Beck and Fiala [10]  showed that any set system where each element belongs to at most t sets, has discrepancy at  most 2t−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' They conjectured that this bound could be improved to O  �√  t  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' In linear algebraic  terms, the closely related generalization known as the Komlos conjecture, states that for a real  matrix with ℓ2 norm of each column at most 1, the discrepancy is O(1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Despite signiﬁcant  progress in partial results and understanding of discrepancy theory in the last 4 decades, these  tantalizing conjectures have remained open.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  Early and Recent Progress  Since the seminal results of Beck and Fiala, much progress has  been made toward resolving the Beck-Fiala and Komlos conjectures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Early breakthroughs in  the area include those of Spencer [39] and Gluskin [22] who showed that the Komlos conjecture  holds for t = Θ(n).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Later Srinivasan [40] and Banaszczyk [3] proved bounds for general t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' The  latter’s bound of 5√t log n remains the best current result on the Komlos conjecture.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  The above bounds were non-constructive and it was even conjectured that eﬃcient algo-  rithms to construct colorings with the promised discrepancy bounds, did not exist.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' However in  a major breakthrough, Bansal [4] gave an eﬃcient algorithm to construct a coloring matching  Spencer’s discrepancy bounds for |R| = Θ(n).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' This has been followed by a large number of  recent results, both algorithmic and non-algorithmic, for upper and lower bounds, as well as  many applications and generalizations, see [28, 5, 6, 16, 27, 37, 7].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  Geometric Set Systems  The discrepancy of set systems with a geometric interpretation,  such as for example of points and half-planes in R2 and R3 or points and disks in R2, has  been of signiﬁcant theoretical and practical importance, as it relates to several areas like com-  putational geometry, statistical and machine learning, algorithmic analysis, database theory,  etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' [30, 25, 26].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Questions such as Tu´snady’s problem have been studied since the early years  of discrepancy theory [9, 11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Other notable results include those of points and projective planes  (Spencer [1]), primal systems of bounded VC dimension (Matouˇsek [29]), systems of bounded  dual VC dimension, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' (Matouˇsek-Welzl-Wernisch [32]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  More recently Ezra [21] proposed the notion of size-sensitive discrepancy, and further asked  about the discrepancy of geometric set systems with bounded degree.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Using the packing and  chaining framework of Dutta, Ezra and Ghosh [17], together with the partial coloring based  algorithm of Lovett-Meka (or a similar algorithm), it is comparatively straightforward to obtain  bounds of O  �  t1/4 · log n  �  for points and half-planes in R2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' To some extent, this setting has  been considered in the unpublished work [20], but the bounds have an extra √log log t log n  factor (as in the above example) which stems from using the partial coloring approach and a  suboptimal assignment of parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' 1 To the best of our knowledge, other than the above-  mentioned unpublished drafts, there are no published or publicly available works which consider  the question of geometric set systems with bounded degree of elements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' However interesting  questions remain to be asked for such systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' For example it seemed interesting to ask if the  O  �  t1/4 log n  �  bound for points and half-planes in the Beck-Fiala setting, can be improved to  O  �  t1/4√log n  �  or better, using (for instance) the algorithmic frameworks of Bansal and others.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  1Moreover these bounds do not appear in the published version.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  2  Union and Shallow Cell Complexity  Set systems with low union complexity or shallow  cell complexity constitute a fairly general class and include several important cases such as  points and half-spaces in R2 and R3, points and (pseudo)disks in R2 and several others (see, for  example [36, Chapter 4]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Moreover, since dual systems of low union complexity also have low  shallow cell complexity of the corresponding primal systems (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' [35]), they have been studied  in a series of works e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' [14, 41, 12, 8, 34, 18, 19] where better bounds have been obtained for  them for several structures of interest, such as unweighted and weighted epsilon nets, epsilon  approximations, relative approximations, ǫ-brackets, combinatorial Macbeath regions, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  Our Contribution  We investigate the discrepancy of geometric set systems with linear or near-linear shallow cell  complexity, and each element belonging to at most t sets, where t is a given parameter inde-  pendent of n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Our discrepancy bounds are stated below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Let (X, R) be a set system with shallow cell complexity ψ(m, k) = g(m)kc, where  g(m) = o(mε) for every ε ∈ (0, 1), is a non-decreasing function of m and c > 0 is a constant  independent of n and k, and each element of X belongs to at most t sets of R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  Then the  discrepancy of (X, R) is at most  O  ���  log n + (tcg(n))  1  1+c  �  log n  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  In particular, for the following families of set systems with degree at most t, the discrepancy is  bounded as below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Points and half-planes in R2: O  ��  (log n + t1/2) log n  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Points and homothets of a convex body in R2: O  ��  (log n + t1/2) log n  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Points and disks in R2: O  ��  (log n + t1/2) log n  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Points and pseudodisks in R2: O  ��  (log n + t1/2) log n  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Points and α-fat triangles in R2: O  ��  (log n + (t · log∗ n)1/2) log n  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Points and objects with linear union complexity: O  ��  (log n + t1/2) log n  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Points and locally γ-fat semi-algebraic objects in R2 with bounded description complexity:  O  ��  (log n + t1/2 · 2O(log∗ n)) log n  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Points and half-spaces in R3: O  ��  (log n + t2/3) log n  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Points and orthants in R2 and R3: O  ��  (log n + t1/2) log n  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  These bounds match or improve the known, as well as the conjectured general bounds for  systems of bounded degree.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' For instance, for set systems of points and half-planes in R2, we  get the bound of  O  ���  log n +  √  t  �  log n  �1/2�  ,  which is O  �√  t  �  for t = Ω(log n).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  For t = ω  �  log2 n  �  , we have √log n = o(t1/4), so the  O  �  t1/4√log n  �  bound improves upon the conjectured O  �√  t  �  bound of Beck and Fiala.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Thus,  3  they give much better bounds even without using the random walk based framework and intri-  cate analysis of many recent discrepancy minimization algorithms e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' [28, 6, 38].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  More generally, we get the following corollary of Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  Corollary 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' The Beck-Fiala conjecture holds for the following set systems having maximum  degree t, with the given constraints on t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Points and half-planes in R2: t = Ω  �  log2 n  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Points and homothets of a convex body in R2: t = Ω  �  log2 n  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Points and disks in R2: t = Ω  �  log2 n  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Points and pseudodisks in R2: t = Ω  �  log2 n  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Points and α-fat triangles in R2: t = Ω  �  log2 n log∗ n  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Points and objects with linear union complexity: t = Ω  �  log2 n  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Points and locally γ-fat semi-algebraic objects in R2 with bounded description complexity:  t = Ω  �  2O(log∗ n)) log2 n  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Points and half-spaces in R3: t = Ω  �  log3 n  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Points and orthants in R2 and R3: t = Ω  �  log2 n  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  Our techniques are based upon showing the existence of matchings with low crossing number  using the well-known multiplicative weights update method of Welzl [42], together with the  shallow packing bound of Mustafa [33] and Dutta, Ezra and Ghosh [17].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' These crossing number  bounds, which are of independent interest, are as below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Let (X, R) be an n-point set system, with |R| ≥ n, generated by intersections of  X with a class of objects having dual shatter dimension at most d and shallow cell complexity  ψ(m, k) = mc1 · g(m)kc, where c1, c ≥ 0 are independent of m and k, and g(m) is a non-  decreasing function of m such that g(m) = o(mε) for every ε ∈ (0, 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Further, let (X, R) have  the property that each point of X belongs to at most t sets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Then there exists a matching of the  points of X, with crossing number at most  O  �  (nc1tcg(n))  1  1+c1+c  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  In particular, if c1 = 0, then the crossing number is at most  O  �  (tcg(n))  1  1+c  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  Corollary 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' For the following set systems (X, R) with each element of X belonging to at most  t members of R, there exist matchings with the following bounds on the crossing number.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Points and half-planes in R2: O  �  log n +  √  t  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Points and homothets of a convex body in R2: O  �  log n +  √  t  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Points and disks in R2: O  �  log n +  √  t  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Points and pseudodisks in R2: O  �  log n +  √  t  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Points and α-fat triangles in R2: O  �  log n +  �  t · log∗ n  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  4  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Points and objects with linear union complexity: O  �  log n +  √  t  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Points and locally γ-fat semi-algebraic objects in R2 with bounded description complexity:  O  �  log n +  √  t · 2O(log∗ n)  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Points and half-spaces in R3: O  �  log n + t2/3�  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Points and orthants in R2 and R3: O  �  log n + t1/2�  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  The proofs of our results are in Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' While our discrepancy and crossing number bounds  are not diﬃcult to obtain, we believe they are important, as they demonstrate cases of non-  random (and non-smoothed) natural set systems which verify or improve upon the Beck-Fiala  conjecture.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Further, these bounds are much stronger than the bounds for general set systems  of bounded VC dimension or shallow cell complexity (without the degree bound), which are  known to be tight [31].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' It should be noted that merely using low shallow complexity cannot  improve the bound on the crossing number, as the tightness results in [31] hold for systems in  2 and 3 dimensions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Matchings (or spanning paths or trees) with low crossing number are of  wide interest, as they are used in a number of applications [30, 15].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  2  Preliminaries  The projection of a set system (X, R) on to a subset Y ⊂ X of the ground set is denoted by  R|Y := {R ∩ Y | R ∈ R}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  A primal set system has a ground set P of points in Rd and subsets given by all possible  intersections with a class G of geometric objects in Rd, that is the set system (P, G|P ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' A dual set  system given a (ﬁnite) collection G of geometric objects is given by (G, G|Rd), that is, equivalence  classes of points of Rd under intersection with objects in G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  The notion of shallow cell complexity has found many applications in Computational Ge-  ometry, including improved bounds on ε-nets and related structures (see e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' [35]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  Deﬁnition 5 (Shallow-cell Complexity).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' A set system (X, R) has shallow-cell complexity ψ(·, ·)  if for any Y ⊆ X, the number of subsets in R|Y of size l is at most |Y | · ψ(|Y |, l).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  In this paper, we shall throughout work with set systems whose shallow cell complexity is  given by  ψ(l, k)  =  lc1g(l)kc,  (1)  where c1, c > 0 are constants independent of l, k, and g(l) = o(lε) for every ε ∈ (0, 1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  Deﬁnition 6 (Union Complexity).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' A set of m geometric objects O has union complexity f(m)  if the number of faces of all dimensions in the union of the members of O, is at most f(m).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  It is known (see e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' [35]) that set systems formed by intersections of points with objects  having union complexity f(.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' ), have shallow cell complexity at most f(m/k) · k2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  A central lemma for set systems of bounded shallow cell complexity, is the Shallow Packing  Lemma of [17, 33].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' To state the lemma, ﬁrst we need to deﬁne shallow packings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  Deﬁnition 7 (Shallow Packing).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Let (X, R) be a set system, and δ and k be positive integers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  A subset of ranges P ⊆ R is a k-shallow δ-packing or (k, δ)-packing, if any pair of ranges in  P have symmetric diﬀerence greater than δ, and for all R ∈ P we have |R ∩ X| ≤ k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  5  Now follows the Shallow Packing Lemma of Mustafa [33], which gives optimal bounds for  shallow packings of set systems, in terms of their shallow cell complexity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  Theorem 8 (Shallow Packing Lemma, Mustafa [33]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Let (X, R) be a set system with |X| = n  and shallow cell complexity ϕR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' If the VC dimension of (X, R) is at most d0, and (X, R) is a  k-shallow δ-packing then  24d0n  δ  ϕR  �4d0n  δ  , 12d0k  δ  �  ≤ Cd0  n  δ ψ  �n  δ , k  δ  �  ,  where Cd0 is a constant independent of n and δ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  Finally, we deﬁne the notions of crossing number and partitions with low crossing number,  which are central to this paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  Deﬁnition 9 (Crossing Number;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Partitions with Low Crossing Number).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' A range S ∈ R is  crossed by a pair of elements of X, {x, y} if |{x, y} ∩ X| = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Given a partition of the universe  X into pairs Π = ({xi, yi})n/2  i=1 with {xi, yi} ∩ {xj, yj} = ∅ for i ̸= j, and �  i≥1{xi, yi} = X, the  crossing number of Π is the maximum number of pairs of Π which cross any given range of R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  3  Well-Behaved Dual Systems  In this section, we prove our theorems and corollaries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' We begin with the proof of Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  The proof follows immediately from the statements of Theorem 3 and Corollary 4, with the  following additional lemma, which gives a bound on the discrepancy of an arbitrary set system,  in terms of the crossing number of a perfect matching of the elements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' The ﬁrst statement in  the lemma is an easy observation, while the second statement is well-known (see e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Chapter  5 [30]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  Lemma 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Let (X, R) be a set system, |X| even, with degree bounded by t and having a  matching with crossing number at most N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Then the discrepancy of (X, R) is at most  O  �  min  �  N,  �  N · log |R|  ��  = O  ��  N · log |R|  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' It is easy to see that the discrepancy is at most N: just take an arbitrary coloring where  each vertex of matched pair of vertices, is given opposite colors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' The discrepancy of a set S ∈ R  is at most the number of pairs that have exactly one vertex in S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' This is at most the crossing  number, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  To see that the discrepancy is at most O  ��  N log |R|  �  , consider a random coloring which  ensure that in every matched pair, opposite colors are assigned to the vertices in the pair.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Now  for any set S ∈ R, the expected discrepancy of S is zero, and the variance of the discrepancy  of S is at most the number of pairs which cross S, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' at most the crossing number N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Now  applying Chernoﬀ bounds, allowing for a maximum deviation of O  ��  N log |R|  �  , and taking a  union bound over all sets of R, we get the statement of the lemma.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  For the proof of Theorem 3, we shall need the following lemma, which guarantees the  existence of a pair of points which cross a small number of ranges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  Lemma 11 (Short Edge Lemma).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Assume the setting of Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Then for any set or  multiset of ranges T ⊆ R, there exist points x, y ∈ X, such that the edge {x, y} is crossed by at  most δ ranges, where δ is the maximum value satisfying  n  ≤  Cd0  |T|  δ · ψ  �|T|  δ , t  δ  �  ,  where Cd0 is a constant that depends only on d0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  6  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' For each point x ∈ X, deﬁne the set of ranges Dx := {S ∈ T  :  x ∈ S}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  Let  D := {Dx : x ∈ X} be the collection of sets of ranges so formed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Then for any pair of points  x, y ∈ X, the symmetric diﬀerence Dx∆Dy is the set of ranges which are crossed by the pair  {x, y}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' The shallow cell complexity of the system D is at most the union complexity of the dual  set system given by T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Let δ denote the minimum symmetric diﬀerence between any pair of  sets in D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' If there exists a pair {x, y} such that Dx = Dy, then we are done, since δ = 0 for this  pair.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Otherwise, observe that by deﬁnition, D is a δ-packing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Since every element of (X, R)  belongs to at most t ranges, the maximum size of any set in D is t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Thus, we can apply the  Shallow Packing Lemma 8 to bound the size of the δ-packing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' We get  n  =  |D|  ≤  Cd0  |T|  δ · ψ  �|T|  δ , t  δ  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  where Cd0 is a constant that depends only on d0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  We will now give the proof of Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  Theorem 12 (Restatement of Theorem 3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Let (X, R) be an n-point set system, with |R| ≥ n,  generated by intersections of X with a class of objects having dual shatter dimension at most d  and shallow cell complexity ψ(m, k) = mc1 · g(m)kc, where c1, c ≥ 0 are independent of m and  k, and g(m) is a non-decreasing function of m such that g(m) = o(mε) for every ε ∈ (0, 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  Further, let (X, R) have the property that each point of X belongs to at most t sets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Then there  exists a matching of the points of X, with crossing number at most  O  �  (nc1tcg(n))  1  1+c1+c  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  In particular, if c1 = 0, then the crossing number is at most  O  �  (tcg(n))  1  1+c  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' We shall construct the matching by picking pairs of points sequentially, in a greedy  manner.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Each time, we shall choose a pair of points that crosses the least number of ranges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  However, instead of looking at the number of ranges crossed by a given pair, we shall do a  weighted counting, in which we shall assign a weight to each range and look to choose the pair  that minimizes the weight of the ranges that it crosses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' The weight of a range S ∈ R will be  a function of the number of pairs already selected, which cross S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' This will force the selection  of edges which do not cross the ranges that have already been crossed several times, thus our  strategy will tend to favour low crossing number with respect to the already selected edges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  Initially, we assign each range a weight of 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' After the i-th pair has been chosen, for a  given range S ∈ R let cS(i) denote the number of already selected pairs, which cross i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Then  the weight of S is given by wi(S) = 2cS(i).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' The weight of any subset of ranges S ⊆ R is the  sum of the weights of the ranges in S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' At each step, we greedily pick a pair that crosses the  least number of weighted ranges of R, where the weights have been updated at the end of the  previous step.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' At the end of the i-th step, let Ti denote the multiset obtained R by replacing  each range S ∈ R with wi(S) copies of S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Note that wi(R) = |Ti|, where the cardinality of Ti  refers to the weighted cardinality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  By the Short Edge Lemma 11, we have  n  ≤  |Ti|1+c1  δ1+c1+c g(|Ti|/δ)tc  ≤  wi(R)1+c1  δ1+c1+c g(wi(R))tc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  7  Therefore, there exists a pair of points in  X \\ {x1, y1, x2, y2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' , xi, yi},  which cross at most δ ranges, where δ is the maximum value satisfying  δ ≤  �|Ti|1+c1  n  g(|T|)tc  �1/(1+c1+c)  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  We choose this pair {xi+1, yi+1} to be the (i + 1)-st edge of the matching.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Let Ri+1 denote the  ranges of R that are crossed by the pair {xi+1, yi+1}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' The weight of the system R after the  (i + 1)-st step, will therefore be  wi+1(R)  =  wi(R) − wi(Ri+1) + wi+1(Ri+1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  Now since the crossing number of the ranges in R increased by 1 after choosing {x, y}, therefore  by the deﬁnition of the weight function, their weights double after the (i + 1)-st step, that is,  wi+1(Ri+1) = 2wi(Ri+1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  Thus we get  wi+1(R)  =  wi(R) − wi(Ri+1) + 2wi(Ri+1)  =  wi(R)  �  1 + wi(Ri+1)  wi(R)  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  (2)  Noting that |Ri+1| ≤ δ by our choice of the pair {xi+1, yi+1}, we get  wi(Ri+1)  ≤  C ·  �  wi(R)1+c1tc ·  �g(wi(R))  n − 2i  ��1/(1+c1+c)  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  Now substituting in the recurrence relation (2) for the weight of R, gives  wi+1(R)  ≤  wi(R)  �  1 + wi(Ri+1)  wi(R)  �  =  wi(R)  �  1 +  �  tc  (n − 2i) · g(wi(R))  wi(R)c  �  1  1+c1+c  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  Since by deﬁnition g(n) = o(nε) for every ε ∈ (0, 1] and we assumed c is constant, therefore the  ratio g(wi(R))  wi(R)c  is maximized when wi(R) is the minimum, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' w0(R), or |R|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Further, by our  assumption that |R| ≥ n, the ratio becomes at most g(n)  nc .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Thus we get  wn/2(R)  ≤  w0(R)  n/2−1  �  i=1  �  1 +  �  tcg(n))  (n − 2i)nc  �  1  1+c1+c  �  ≤  |R|  n/2−1  �  i=1  �  1 +  �  tcg(n)  (n − 2i)nc  �  1  1+c1+c  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  Taking logarithms with respect to both sides, we get  log wn/2(R)  ≤  log |R| + O  \uf8eb  \uf8ed  �� t  n  �c  g(n)  �  1  1+c1+c n/2−1  �  i=1  1  (n − 2i)1/(1+c1+c)  \uf8f6  \uf8f8  ≤  log |R| + O  �  (tcg(n))  1  1+c1+c nc1/(1+c1+c)�  =  log |R| + O  �  (nc1tcg(n))  1  1+c1+c  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  (3)  8  Here in the second inequality above, we have used the fact that  n/2−1  �  i=1  1  (n − 2i)  1  1+c1+c  ≤ n1−  1  1+c1+c .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  Finally, let cmax := maxS∈R cS(n/2) denote the maximum number of crossings over all sets  S ∈ R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' We have  cmax = max  S∈R log wn/2(S) ≤ log wn/2(R).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  By Equation (3), this is at most  log |R| + O  �  (nc1tcg(n))1/(1+c1+c)�  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  Since the VC dimension of the system is bounded (in fact, substituting k = n in the shallow cell  complexity, we see that the VC dimension is at most 2+ c1 + c), we get that log |R| = O(log n),  since the number of ranges is polynomial in the size of the universe X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  This completes the proof of the theorem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  It only remains to prove Corollary 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' The corollary follows immediately from known bounds  on the shallow cell complexity and the union complexity of various geometric set systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' These  bounds are given in the table below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  Proof of Corollary 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' The proof of the corollary follows by applying the shallow cell complexity  functions in the table below, to the result of Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' These bounds can be found in [18]  and [36][see the list in Chapter 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='3] and the references therein.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' We also recommend the survey [2]  for the interested reader.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' The bounds for orthants was proved in [24].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  Objects  mψ(m, k)  Intervals in R  m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  Half-spaces in R2  mk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  Homothets of a convex body in R2  mk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  Disks in R2  mk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  Pseudodisks in R2  mk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  α-fat triangles in R2  mk log∗ m  k + mk log2 α.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  Locally γ-fat semi-algebraic objects  mk2O(log∗ m).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  with bounded description complexity in R2  Objects with union complexity mφ(m)  mφ(m/k)k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  Halfspaces in R3  mk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  Orthants in R2 and R3  mk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  Table 1: Shallow-cell complexity bounds for diﬀerent geometric set systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  4  Conclusion  We have shown improved discrepancy bounds in set systems with near-linear shallow cell com-  plexity, under the condition that each point belongs to a bounded number of sets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Though  algorithmic considerations are not the focus of our paper, these are now brieﬂy discussed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' In  order to obtain a low-discrepancy coloring, we need to compute a matching with low crossing  number.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Such algorithms have been studied by several authors e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' [42, 43, 23, 15].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' For our  9  purposes, it suﬃces to use the original algorithm of Welzl, which uses at most O(n3t) time in  our case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' We note that the faster algorithms of Csikos and Mustafa [15] as well as Har-Peled [23]  give matchings with slightly worse bounds on the crossing number (by a logarithmic factor in  n), which results in a corresponding increase in the discrepancy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  References  [1] Coloring the Projective Plane.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Discrete Mathematics, 73(1):213–220, 1988.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  [2] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Agarwal, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Pach, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Sharir.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' State of the Union (of Geometric Objects): A Re-  view.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' In J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Goodman, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Pach, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Pollack, editors, Computational Geometry: Twenty  Years Later, pages 9–48.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' American Mathematical Society, 2008.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  [3] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Banaszczyk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Balancing vectors and Gaussian measures of n-dimensional convex bodies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  Random Struct.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Algorithms, 12(4):351–360, 1998.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  [4] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Bansal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Constructive Algorithms for Discrepancy Minimization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' In FOCS, pages 3–10,  2010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  [5] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Bansal, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Dadush, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Garg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  An Algorithm for Koml´os Conjecture Matching  Banaszczyk’s Bound.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' In FOCS, pages 788–799, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  [6] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Bansal and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Garg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Algorithmic Discrepancy Beyond Partial Coloring.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' In STOC 2017:  Proceedings of the 49th Annual ACM SIGACT Symposium on Theory of Computing, pages  914–926, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  [7] Nikhil Bansal, Daniel Dadush, Shashwat Garg, and Shachar Lovett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' The Gram-Schmidt  Walk: A Cure for the Banaszczyk Blues.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' In Proceedings of the 50th Annual ACM SIGACT  Symposium on Theory of Computing, STOC, page 587–597, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  [8] Nikhil  Bansal  and  Kirk  Pruhs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  Weighted  geometric  set  multi-cover  via  quasi-uniform  sampling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  Comput.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  Geom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=',  7(1):221–236,  2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  URL:  https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='20382/jocg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='v7i1a11, doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='20382/jocg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='v7i1a11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  [9] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Beck.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Balanced two-colorings of ﬁnite sets in the square I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Combinatorica, 1(4):327–335,  1981.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  [10] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Beck and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Fiala.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' ”Integer-making” theorems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Discrete Applied Mathematics, 3(1):1–8,  1981.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  [11] J´ozsef Beck.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Balanced two-colorings of ﬁnite sets in the cube.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Discret.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=', 73(1-2):13–25,  1989.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  [12] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Chan, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Grant, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' K¨onemann, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Sharpe.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Weighted Capacitated, Priority, and  Geometric Set Cover via Improved Quasi-Uniform Sampling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' In Proceedings of the 23rd  ACM-SIAM Symposium on Discrete Algorithms, SODA, pages 1576–1585, 2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  [13] Bernard Chazelle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' The Discrepancy Method - Randomness and Complexity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Cambridge  University Press, 2001.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  [14] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Clarkson and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Varadarajan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Improved Approximation Algorithms for Geometric  Set Cover.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Discrete & Computational Geometry, 37(1):43–58, 2007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  [15] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Csik´os and N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Mustafa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Escaping the Curse of Spatial Partitioning: Matchings with  Low Crossing Numbers and Their Applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' In Proceedings of the 37th International  Symposium on Computational Geometry, SoCG, volume 189, pages 28:1–28:17, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  10  [16] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Dadush, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Garg, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Lovett, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Nikolov.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Towards a Constructive Version of Ba-  naszczyk’s Vector Balancing Theorem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' In RANDOM, pages 28:1–28:12, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  [17] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Dutta, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Ezra, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Ghosh.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Two Proofs for Shallow Packings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Discrete & Compu-  tational Geometry, 56(4):910–939, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  [18] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Dutta, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Ghosh, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Jartoux, and N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Mustafa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Shallow Packings, Semialgebraic  Set Systems, Macbeath Regions, and Polynomial Partitioning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Discrete & Computational  Geometry, 61(4):756–777, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  [19] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Dutta, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Ghosh, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Moran.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Uniform Brackets, Containers, and Combinatorial  Macbeath Regions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' In Proceedings of th13th Innovations in Theoretical Computer Science  Conference, ITCS, volume 215, pages 59:1–59:10, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  [20] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Dutta and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Ghosh.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Size sensitive packing number for Hamming cube and its conse-  quences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' URL: https://arxiv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='org/abs/1412.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='3922.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  [21] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Ezra.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' A Size-Sensitive Discrepancy Bound for Set Systems of Bounded Primal Shatter  Dimension.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' SIAM Journal on Computing, 45(1):84–101, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  [22] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Gluskin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Extremal properties of orthogonal parallelepipeds and their applications to  the geometry of banach spaces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Sbornik: Mathematics, 64(1):85–96, 1989.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  [23] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Har-Peled.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Approximating Spanning Trees with Low Crossing Number.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' 2009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' URL:  https://arxiv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='org/abs/0907.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='1131.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  [24] Haim Kaplan, Natan Rubin, Micha Sharir, and Elad Verbin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Counting colors in boxes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  In Proceedings of the Eighteenth Annual ACM-SIAM Symposium on Discrete Algorithms,  SODA ’07, page 785–794, USA, 2007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Society for Industrial and Applied Mathematics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  [25] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Larsen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' On Range Searching in the Group Model and Combinatorial Discrepancy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  SIAM J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Comput.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=', 43(2):673–686, 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  [26] Kasper Green Larsen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Constructive discrepancy minimization with hereditary L2 guar-  antees.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  In Rolf Niedermeier and Christophe Paul, editors, 36th International Sympo-  sium on Theoretical Aspects of Computer Science, STACS 2019, March 13-16, 2019,  Berlin, Germany, volume 126 of LIPIcs, pages 48:1–48:13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Schloss Dagstuhl - Leibniz-  Zentrum f¨ur Informatik, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' URL: https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='4230/LIPIcs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
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+page_content='2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='48,  doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
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+page_content='2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='48.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  [27] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Levy, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Ramadas, and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Rothvoss.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Deterministic Discrepancy Minimization via the  Multiplicative Weight Update Method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' page to appear, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  [28] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Lovett and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Meka.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Constructive Discrepancy Minimization by Walking on the Edges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  In FOCS, pages 61–67, 2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  [29] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Matouˇsek.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Geometric Discrepancy: An Illustrated Guide.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Springer, 1999.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  [30] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Matouˇsek.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Geometric discrepancy: An illustrated guide.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Springer, 2009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  [31] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Matousˇek.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' On discrepancy bounds via dual shatter function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Mathematika, 44(1):42–49,  1997.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  [32] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Matouˇsek, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Welzl, and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Wernisch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Discrepancy and approximations for bounded  VC-dimension.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Combinatorica, 13(4):455–466, 1993.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  [33] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Mustafa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' A Simple Proof of the Shallow Packing Lemma.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Discrete & Computational  Geometry, 55(3):739–743, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  11  [34] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Mustafa, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Dutta, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Ghosh.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' A Simple Proof of Optimal Epsilon-nets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Com-  binatorica, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  [35] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Mustafa and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Varadarajan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Epsilon-approximations and Epsilon-nets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' In J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  Goodman, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' O’Rourke, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' T´oth, editors, Handbook of Discrete and Computational  Geometry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' CRC Press LLC, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  [36] Nabil H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Mustafa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Sampling in Combinatorial and Geometric Systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' American Mathe-  matical Society, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  [37] Aleksandar Nikolov.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Tighter Bounds for the Discrepancy of Boxes and Polytopes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Mathe-  matika, 63(3):1091–1113, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  [38] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Rothvoss.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Better Bin Packing Approximations via Discrepancy Theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' SIAM J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Com-  put.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=', 45(3):930–946, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  [39] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Spencer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Six standard deviations suﬃce.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Amer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=', 289(2):679–706,  1985.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  [40] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Srinivasan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Improving the Discrepancy Bound for Sparse Matrices: Better Approxima-  tions for Sparse Lattice Approximation Problems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' In SODA, pages 692–701, 1997.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  [41] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Varadarajan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Weighted Geometric Set Cover via Quasi-Uniform Sampling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' In Pro-  ceedings of the 42nd ACM Symposium on Theory of Computing, STOC, pages 641–648,  2010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  [42] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Welzl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Partition trees for triangle counting and other range searching problems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' In  Proceedings of the Fourth Annual Symposium on Computational Geometry, SCG ’88,  page 23–33, New York, NY, USA, 1988.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Association for Computing Machinery.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  URL:  https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='1145/73393.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='73397, doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='1145/73393.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='73397.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  [43] Emo Welzl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' On spanning trees with low crossing numbers, pages 233–249.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content=' Springer Berlin  Heidelberg, Berlin, Heidelberg, 1992.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
+page_content='  12' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BNE1T4oBgHgl3EQfpQVQ/content/2301.03329v1.pdf'}
diff --git a/BtAzT4oBgHgl3EQfwP4g/content/tmp_files/2301.01718v1.pdf.txt b/BtAzT4oBgHgl3EQfwP4g/content/tmp_files/2301.01718v1.pdf.txt
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@@ -0,0 +1,1557 @@
+An adaptive, training-free reduced-order model for
+convection-dominated problems based on hybrid snapshots
+Victor Zucattia, Matthew J. Zahra
+aUniversity of Notre Dame, Notre Dame, IN 46556, United States of America
+Abstract
+The vast majority of reduced-order models (ROMs) ﬁrst obtain a low dimensional repre-
+sentation of the problem from high-dimensional model (HDM) training data which is after-
+wards used to obtain a system of reduced complexity. Unfortunately, convection-dominated
+problems generally have a slowly decaying Kolmogorov n-width, which makes obtaining an
+accurate ROM built solely from training data very challenging. The accuracy of a ROM can
+be improved through enrichment with HDM solutions; however, due to the large computa-
+tional expense of HDM evaluations for complex problems, they can only be used parsimo-
+niously to obtain relevant computational savings. In this work, we exploit the local spatial
+and temporal coherence often exhibited by these problems to derive an accurate, cost-eﬃcient
+approach that repeatedly combines HDM and ROM evaluations without a separate training
+phase. Our approach obtains solutions at a given time step by either fully solving the HDM
+or by combining partial HDM and ROM solves. A dynamic sampling procedure identiﬁes
+regions that require the HDM solution for global accuracy and the reminder of the ﬂow is
+reconstructed using the ROM. Moreover, solutions combining both HDM and ROM solves
+use spatial ﬁltering to eliminate potential spurious oscillations that may develop. We test
+the proposed method on inviscid compressible ﬂow problems and demonstrate speedups up
+to an order of magnitude.
+Keywords:
+adaptive model reduction, proper orthogonal decomposition, hyperreduction,
+sparse sampling, convection-dominated problems
+1. Introduction
+Today’s computational power enables the numerical solution of complex engineering
+problems; however, these computations can easily require hundreds of millions of degrees
+of freedom to produce accurate results [1] and, thus, high-ﬁdelity many-query analyses are
+still impractical in many scenarios such as design optimization, ﬂow control and uncer-
+tainty quantiﬁcation, to name a few. Fortunately, the large amount of data generated by
+high-dimensional models (HDMs) can be used to build a reduced-order model (ROM). A
+two-step (oﬄine/online) approach is the standard when building ROMs for time-dependent
+problems. In the oﬄine stage, a smaller dimensional representation is obtained from HDM
+training data and used to generate a lower complexity model through physics-based [2, 3, 4]
+or data-driven methods [5, 6, 7]. This is a precomputation step performed only once but can
+be very costly given the high-dimensional data dependency. On the other hand, the online
+Preprint submitted to Elsevier
+January 5, 2023
+arXiv:2301.01718v1  [math.NA]  4 Jan 2023
+
+stage consists of solving the resulting system of equations of reduced dimensionality (e.g.,
+up to four orders of magnitude smaller [7]). Unfortunately, despite the considerable research
+done in the last 20 years, ROMs still suﬀer from a multitude of problems (e.g., instability,
+inaccuracy, failure to generalize beyond training) making them generally unreliable in an
+industrial setting [2, 8, 9, 10]. This is particularly the case when modeling time-dependent
+convection-dominated problems such as those usually found in viscous or high-speed compu-
+tational ﬂuid dynamics (CFD) problems. Multiple correction methods have been proposed
+[11, 12, 13, 14, 15, 16] and have been rather successful in improving ROM stability. However,
+they have done very little to improve ROM predictive capabilities.
+For convection-dominated problems, failure to generalize has been mainly attributed to
+the slowly decaying Kolmogorov n-width of linear subspace approximations [17]. This is
+also sometimes referred to as Kolmogorov barrier because the error slowly decaying with
+the dimension of the reduced space limits the achievable accuracy of ROMs in practice and
+requires a substantial amount of training data, which can be infeasible to collect oﬄine.
+The Kolmogorov barrier can be overcome, for example, by the use of nonlinear model re-
+duction techniques. In [18], a nonlinear manifold is obtained through deep convolutional
+autoencoders and combined with projection-based methods to produce ROMs capable of
+outperforming their linear counterparts.
+Quadratic manifolds have been used with both
+physics-based [19] and data-driven [20] methods for order reduction. Alternatively, nonlin-
+ear manifolds have been constructed by composing a traditional subspace approximation
+with a transformation to the underlying domain, which has proven particularly eﬀective for
+shock-dominated problems [21, 22]. Another solution is to exploit the local low-rank struc-
+ture of this class of problems [23]. In [24, 25], local low-rank subspaces are systematically
+obtained by partitioning of the state space. Results show that local subspaces improves
+ROMs accuracy and speed by reducing the dimensionality of each subspace.
+Adaptive reduced-order models (AROMs) [26, 27, 28, 29, 23, 30] provide a diﬀerent
+approach by continuously combining HDM and ROM operations. Predictive capabilities
+can be improved by alternating between HDM and ROM generated snapshots [26, 27, 28].
+In [26, 27], on-the-ﬂy criteria relying on the reduced basis suﬃciency is used to determine
+when to use the HDM or local ROM. If deemed necessary, fast low-rank singular value
+decomposition (SVD) modiﬁcations [31] are used to update the reduced-order basis. This
+methodology was successfully tested (factor of two speedup with an error inferior to 1%) on
+heat transfer [26] and ﬂuid ﬂow [27] problems. A similar approach relying on a more rigorous
+a posteriori error estimator to switch between the HDM and ROM is introduced in [28]. A
+diﬀerent AROM method developed in [23] uses the adaptive discrete empirical interpolation
+method (ADEIM) [29] and rank-one updates to adapt the reduced basis. A comparison of
+AROMs relying on this approach and traditional ROMs can be found in [30]. In particular,
+the numerical experiments show that AROMs can be used in a predictive setting to model
+chemically reacting ﬂow problems, whereas traditional ROMs completely fail to generate
+meaningful predictions. These methods may not achieve the same speedup factors commonly
+observed when using the two-step ROM approach [7], but numerical experiments show that
+AROMs can accurately accelerate numerical solutions of problems where traditional order
+reduction methods fail completely.
+In this work, we propose a training-free approach that combines local HDM and ROM
+solutions to circumvent costly full HDM solves. A dynamic relative reconstruction error
+2
+
+strategy is developed to identify regions of the domain where the ROM is inaccurate and we
+locally solve the HDM in these regions. For problems containing spatial derivatives, states
+on neighboring cells are required to locally evolve the state using the HDM. We rely on the
+ROM solution when a neighboring cell is outside the sampled region. Our approach allows
+the sampled region to adapt over time to avoid unnecessary HDM evaluations and improve
+robustness. Furthermore, our method relies on explicit spatial ﬁltering to eliminate spurious
+oscillations that may appear after combining the solutions originating from diﬀerent methods
+(e.g., some regions of the domain evolved using the HDM and others using the ROM). We
+refer to the solutions generated by this approach as hybrid snapshots. Lastly, our AROM is
+validated and tested on time-dependent compressible ﬂow problems with shocks.
+The remainder of this paper is organized as follows. In Section 2, we begin by introducing
+a general governing system of conservation laws and the high-dimensional modeling frame-
+work used to discretize it. Next, we introduce our hybrid snapshot approach, which involves:
+1) the reduced basis approximation and partial HDM solutions, 2) a sampling procedure
+based on relative reconstruction error, and 3) low-pass spatial ﬁlters required to robustly
+mix solutions produced by diﬀerent numerical methods. We ﬁnish this section with a com-
+plete description of the algorithm and a discussion of important aspects of the method such
+as computational eﬃciency. Section 3 applies our adaptive framework to two compressible
+inviscid ﬂow problems. The ﬁrst is a compressible one-dimensional problem and is used to
+conduct a parametric study of the proposed method. The second is a considerably more
+complex two-dimensional problem. Finally, Section 4 highlights the main conclusions and
+discuss future research directions.
+2. Adaptive reduced-order models
+In this section, we introduce the general system of conservation laws that we aim to
+accelerate using our adaptive reduced-order model. We begin by introducing the system of
+conservation laws (Section 2.1) and formulate a high-dimensional discretization (Section 2.2).
+Afterwards, we introduce our cost eﬀective hybrid snapshot approach (Section 2.3), which
+consists of the reduced basis approximation (Section 2.3.1), partial HDM solves (Section
+2.3.2), relative reconstruction error (Section 2.3.3), and spatial low-pass ﬁlters (Section 2.3.4).
+2.1. System of conservation laws
+A general system of c conservation laws, deﬁned in a spatial domain Ω Ă Rd over the
+time interval T “ p0, Ts, takes the form
+Q,t ` ∇ ¨ fpQ, ∇Qq “ hpQ, ∇Qq,
+Qp¨, 0q “ ˚
+Qp¨q,
+(1)
+where f : Rc ˆ Rcˆd Ñ Rcˆd is the ﬂux ﬂunction, h : Rc ˆ Rcˆd Ñ Rc is the source term,
+˚
+Q : Ω Ñ Rc is the initial condition, and Qpx, tq is the vector of conservative variables
+implicity deﬁned as the solution of Eq. (1) at px, tq P Ω ˆ T .
+2.2. High-dimensional model
+The previous system of partial diﬀerential equations (PDEs) is discretized using a method
+of lines approach. After spatial discretization, we have the following system of ordinary
+3
+
+diﬀerential equations (ODEs)
+dq
+dt “ Fpq, tq ,
+(2)
+where qptq P RN is our semi-discrete approximation to Qp¨, tq implicitly deﬁned as the solution
+of Eq. (2), N is the number of degrees of freedom of the spatial discretization, and F is the
+nonlinear function deﬁning the spatial discretization of the inviscid and viscous ﬂuxes.
+A time discretization method is required to solve Eq. (2) numerically. In this work, the
+backward diﬀerentiation formulas (BDFs) are used. The s-order BDF scheme is written as
+sÿ
+j“0
+ajqn`j “ ∆tβFpqn`s, tn`sq ,
+(3)
+where qn « qptnq, ∆t denotes the time step size, tn “ t1 ` n∆t, and coeﬃcients ak and β
+are such that the method is order s and are normalized such that as “ 1. As can be noted
+from Eq. (3), BDF schemes are implicit and, thus, may require the solution of a nonlinear
+system of equations.
+The fully discrete HDM is characterized by the following system of algebraic equations
+to be solved at each time instance k P r1, . . . , Nts,
+qk “ Rkpqkq ,
+(4)
+where Rk : RN Ñ RN is the nonlinear residual function, which is deﬁned as
+Rkpqkq “ ∆tβFpqk, tkq ´
+s´1
+ÿ
+j“0
+ajqk´s`j .
+(5)
+2.3. Hybrid snapshot approach
+We are interested in obtaining an approximation vk « qk that eﬃciently leverages local
+HDM information. For this, consider the sampling points ˆspkq
+1 , . . . , ˆspkq
+ns P t1, . . . , Nu and the
+corresponding sampling points matrix ˆSk “ reˆspkq
+1 , . . . , eˆspkq
+ns s P RNˆns. Here, ns is the number
+of indices retained from the original vector of size N and ei denotes the vector with a 1 in
+the i-th coordinate and 0 elsewhere. Let ˘Sk P RNˆpN´nsq be the complementary sampling
+points matrix derived from points t1, . . . , Nuztˆspkq
+1 , . . . , ˆspkq
+ns u that have not been selected as
+sampling points. We additionally consider sampling matrix ˜Sk P RNˆl generated from the
+neighboring points t˜spkq
+1 , . . . , ˜spkq
+l u needed to calculate the HDM ﬂux function that are not
+already in tˆspkq
+1 , . . . , ˆspkq
+ns u. The sampling matrices can are illustrated in Fig. 1 for the case
+of a ﬁrst-order ﬁnite volume discretization.
+With these deﬁnitions in place, we propose an approximation vk to the fully discrete
+HDM state qk where vk restricted to the points in ˘Sk use a traditional aﬃne subspace
+approximation and vk restricted to the points in ˆSk are deﬁned as the solution of the HDM
+residual restricted to the ˆSk indices. That is, vk is deﬁned such that
+˘SJ
+k vk “ ˘SJ
+k pψk ` Φkykq ,
+(6a)
+ˆSJ
+k vk “ ˆRkp ˆSJ
+k vk, ˜SJ
+k vkq ,
+(6b)
+4
+
+Figure 1: An example of mesh sampling corresponding to a ﬁrst-order ﬁnite volume scheme. Cells sampled
+by ˆSk and ˜Sk are highlighted in yellow and green, respectively. Moreover, ˘Sk samples both the blue and
+green cells.
+where ψk P RN is a reference state, Φk P RNˆm is a basis for a reduced subspace used
+to approximate the state qk at the sampling points ˘Sk, yk P Rm contains the corresponding
+reduced coordinates, and m denotes the dimension of the reduced subspace with m ! N. The
+function ˆRk : Rns ˆRl Ñ Rns is the nonlinear partial residual deﬁned as the restriction of the
+HDM residual Rk to the indices sampled by ˆSk. Due to locality of the HDM discretization
+scheme, the partial residual does not depend on the entire state; rather, it only depends on
+the restriction of the state to the indices sampled by ˆSk and ˜Sk. Mathematically, we write
+this as
+ˆRkpˆv, ˜vq :“ ˆSJ
+k Rkp ˆSkˆv ` ˜Sk˜vq .
+(7)
+Evaluating ˆRk is cost eﬀective provided ns ! N because a relatively small number of entries
+of the HDM residual are required.
+Remark 1. Multistage methods such as Runge–Kutta solve ODEs by taking a few interme-
+diate steps. This requires sequentially solving residuals that depend on the solution of the
+previous stage. As a consequence, each stage is going to require diﬀerent sampling matrices
+that take into consideration neighbors of neighbors. This issue can be avoided by the use of
+multistep methods such as BDF. These rely on a linear combination of previous states and
+residuals and, thus, we only need a set of sampling matrices for each time step.
+2.3.1. Reduced basis approximation
+We apply gappy POD [32, 33] to compute the approximate HDM solution at the points
+corresponding to ˘Sk (Eq. 6a). Given a sampling matrix Pk P RNˆnp constructed from points
+tppkq
+1 , . . . , ppkq
+np u Ă tˆspkq
+1 , . . . , ˆspkq
+ns u, the reduced coordinates yk are calculated as
+yk “ pP J
+k Φkq:P J
+k pvpJq
+k
+´ ψkq ,
+(8)
+where vpJq
+k
+comes from the partial HDM solve, which is deﬁned in Section 2.3.2. The reduced
+basis Φk is constructed by compressing the deviations of the last w snapshots from the
+5
+
+reference state ψk, i.e.,
+Φk “ PODm prγk´w ´ ψk´1, γk´w`1 ´ ψk´1, . . . , γk´2 ´ ψk´1, γk´1 ´ ψk´1sq ,
+(9)
+where γk is either a HDM solution or hybrid snapshot (details deferred to Section 2.4) and
+PODm : RNˆw Ñ RNˆm applies the thin SVD to the argument (snapshot matrix of size N ˆw)
+and extracts the m left singular vectors. The sampling matrix Pk is computed as
+Pk “ ODEIMnppΦkq ,
+(10)
+where ODEIMnp : RNˆm Ñ RNˆnp is the oversampling discrete empirical interpolation method
+(ODEIM) [34], which is derived from the empirical interpolation method (EIM) [35] and its
+discrete counterpart, the discrete empirical interpolation method (DEIM) [36]. As pointed
+out in [34], oversampling (m ă np) leads to more accurate linear-regression based approxi-
+mations rather than interpolation (m “ np). Finally, the reference state is computed as
+ψk “ 1
+w
+k´1
+ÿ
+j“k´w
+γj .
+(11)
+The reference state should be carefully chosen as it impacts accuracy and stability of the
+reduced bases approximation. In particular, our choice allows time-invariant Dirichlet bound-
+ary conditions to be automatically satisﬁed.
+Remark 2. Our SVD approach reconstructs the reduced basis from scratch every time the
+basis needs to be updated, which means all entries are updated.
+A diﬀerent approach is
+adopted in [23]. In this case, the reduced-order basis is locally updated using the adaptive
+discrete empirical interpolation method (ADEIM) [29]. However, not providing any sort of
+correction outside the sampling points can lead to a potentially catastrophic loss of accuracy.
+2.3.2. Partial high-dimensional model
+An estimate of ˜vk « ˜SJ
+k vk is necessary in order to solve Eq. 6b and, thus, obtain an
+approximate HDM solution at the points corresponding to ˆSk. A straightforward choice is
+˜vk “ ˜SJ
+k γk´1, i.e., lag the solution to the previous time step; however, this can lead to a lagged
+solution. We attempt to obtain a more accurate evaluation of ˆSJ
+k vk through subiterations.
+In this approach, solving the partial HDM solution at time step k leads to the following
+iterations: for j “ 1, . . . , J, solve
+ˆvpjq
+k
+“ ˆRkpˆvpjq
+k , ˜vpjq
+k q
+(12)
+for ˆvpjq
+k
+and set
+ypjq
+k
+“ pP J
+k Φkq:P J
+k ˆSkpˆvpjq
+k
+´ ψkq ,
+(13a)
+˜vpj`1q
+k
+“ ˜SJ
+k pψk ` Φkypjq
+k q
+(13b)
+where ˜vp1q
+k
+“ ˜SJ
+k γk´1 is the initial guess and J is determined by the satisfaction of a conver-
+gence criterion. Here, the algorithm is terminated when either
+}ypj`1q
+k
+´ ypjq
+k }2 ă ϵy
+(14)
+or J “ jmax, where ϵy P Rą0 and jmax P N are user deﬁned. In this work, we take ϵy “ 10´4
+and jmax “ 10 unless otherwise stated.
+6
+
+Remark 3. For explicit time-marching methods, the right-hand size of Eq. (4) can be di-
+rectly computed because it only depends on the solution at previous time steps and, thus, no
+subiterations are necessary.
+2.3.3. Relative reconstruction error
+The pointwise reconstruction error of approximating the state γk in the reduced subspace
+is
+εpkq
+j
+“ pγk ´ ψk ´ Φkykq2
+j ,
+(15)
+where yk is given by Eq. 8. Let i1, . . . , iN be an ordering such that
+εpkq
+i1 ě ¨ ¨ ¨ ě εpkq
+iN .
+(16)
+At time step k, we pick the ﬁrst ng indices i1 “ gpkq
+1 , . . . , ing “ gpkq
+ng as the sampling points to
+form Gk. The number of sampling points ng is chosen according to the relative reconstruction
+error (RRE),
+RREpngq “
+řng
+j“1 εpkq
+ij
+řN
+j“1 εpkq
+ij
+. ,
+(17)
+In practice, we choose ng to be the smallest natural number such that RREpngq ď δ.
+Finally, the set of points forming sampling matrix ˆSk is deﬁned as
+tˆspkq
+1 , . . . , ˆspkq
+ns u :“ tgpkq
+1 , . . . , gpkq
+ng u Y tppkq
+1 , . . . , ppkq
+ns u .
+(18)
+Once we have ˆSk, the other sampling matrices ˜Sk and ˘Sk are straightforwardly obtained from
+the discrete stencil.
+2.3.4. Spatial low-pass ﬁlters
+Spatial ﬁltering is an operation commonly used to stabilize time-dependent ﬂuid ﬂow
+simulations [37, 38, 39] by eliminating high-wavenumber noise originating from, for example,
+mesh nonuniformity and nonlinear ﬂow features. Implicit ﬁltering methods require the solu-
+tion of a system of linear equations and have been used extensively in the solution of CFD
+problems [37, 38]. We avoid solving a system of linear equations by using the cheaper and
+easier to implement explicit ﬁlters. However, explicit ﬁlters require bigger stencils to obtain
+same order of accuracy which can be particularly problematic at boundaries.
+Similar to standard CFD simulations, there is no guarantee that a hybrid snapshot vk
+combining entries from partial HDM and reduced basis solves is going to be smooth. To
+remove spurious oscillations that may develop, we apply a one-dimensional explicit Shapiro
+ﬁlter [39, 40] to the solution; we consider second-, fourth-, and sixth-order ﬁlters in Section
+3.
+Remark 4. As pointed out in [38], multidimensional ﬁltering can be performed by applying
+the one-dimensional ﬁlter in each coordinate direction.
+Remark 5. Boundary condition treatment is usually not obvious and have been dealt with in
+diﬀerent ways [38]. One approach is to use smaller, lower order stencils near the boundary,
+which decreases the global order of accuracy of the ﬁlter. Alternatively, decentered stencils
+7
+
+maintaining the same order of accuracy as the centered stencil can be used. However, these
+need to be constructed in such a way that no frequency is ampliﬁed. In this work, for simplic-
+ity, the boundary values are obtained by using a zeroth-order extrapolation at the boundaries.
+Remark 6. Filtering is most commonly used on structured grids in combination with ﬁnite-
+diﬀerence methods. However, ﬁltering can also be used on unstructured grids [41].
+2.4. General considerations, algorithm and computational eﬃciency
+The proposed approach exploits the spatial and temporal locality of propagating coherent
+structures to derive eﬃcient reduced-order models. As previously discussed, reduced-order
+modeling of convection-dominated problems is challenging because of the Kolmogorov bar-
+rier. However, as pointed out in [23], these problems have local low-rank structure: local
+trajectories have fast decaying singular values while the singular values of global trajectories
+decay slowly. The concept of local reduced bases for projection-based model reduction which
+has also been exploited in other work [24, 25]. A comparison of the trajectory of a scalar
+quantity advected linearly at two diﬀerent velocities and their corresponding normalized sin-
+gular values is illustrated in Fig. 2. As mentioned in Section 2.3.1, we construct the reduced
+basis by using the previous w snapshots, where w is chosen suﬃciently small to ensure the
+subspace has a small dimension.
+0
+0.2
+0.4
+0.6
+0.8
+1
+0
+0.2
+0.4
+0.6
+0.8
+1
+x
+qpx, tq
+50
+100
+150
+200
+10´17
+10´12
+10´7
+10´2
+index
+normalized singular value
+Figure 2: On the left, solutions of a scalar quantity at time t “ 0 (
+) and advected linearly at two diﬀerent
+velocities µ1 (
+) and µ2 “ 100µ1 (
+) for the same period of time. First and last snapshots of a scalar
+quantity advected linearly at two diﬀerent velocities pµ2 “ 100µ1q for the same period of time. On the right,
+normalized singular values for snapshots with global (
+) and local (
+) temporal structures. It can
+be noted that singular values of problems with local temporal structure decay orders of magnitudes faster
+compared to problems with global structure.
+Another important AROM ingredient is local spatial coherence. This feature leads to
+the RRE being concentrated at only a few components. In other words, the reduced basis
+is capable of providing an accurate approximation at most entries and, thus, more expen-
+sive HDM evaluations are only necessary at a small fraction of the components. Figure 3
+illustrates an example of a problem where the RRE is concentrated in a few components
+only. Entries where the RRE is small but nonzero will likely grow in time and result in an
+8
+
+inaccurate solution. The proposed approach accounts for this by performing a full HDM
+solve every z time steps.
+(a)
+(b)
+Figure 3: Relative reconstruction error (left) and sampling points (right) of a problem with local spatial
+coherence. The entries corresponding to sampling matrices ˆSk and ˜Sk are highlighted in yellow and green,
+respectively. The neighboring sampling matrix ˜Sk matches a ﬁrst-order ﬁnite volume method, for example.
+2.4.1. Algorithm
+Our AROM procedure is summarized in Algorithm 1. The initial condition is set at
+line 1. The loop on line 2 iterates over all time steps k “ 1, . . . , Nt ´ 1. The conditional
+statement on line 3 chooses between a full (line 4) or partial HDM solution (lines 6-11).
+Initially, a full HDM solution is calculated for the ﬁrst w time steps. Afterwards, the second
+criterion ensures that a full HDM solution is going to take place every z time steps. A partial
+HDM computation takes place between lines 6 and 11. All other points are approximated
+via ODEIM (line 12). Line 13 ﬁlters the hybrid snapshot originating from a partial HDM
+solution and RB reconstruction.
+The conditional statement in line 18 determines if the
+reduced basis and sampling points are computed. The ﬁrst condition assures that the total
+number of snapshots is suﬃcient (i.e., at least w). The second condition checks if a full
+HDM evaluation is going to take place in the next time step. In this case, the reduced basis
+and sampling points are not necessary and, thus, do not need to be updated. Finally, the
+reduced basis, sampling points and reference state are computed between lines 18 and 26.
+The conditional on line 15 ensures the oﬀset ψk is available the ﬁrst time the condition on
+line 18 is satisﬁed. The function Neighbors on line 24 returns the sampling matrix ˜Sk`1
+generated from the neighboring points needed to calculate the HDM ﬂux function that are
+not already sampled by ˆSk`1 (Figure 1). In addition, the set operations union and setdiff
+applied to sampling matrices are deﬁned as the sampling matrix that results from the set
+9
+
+operation applied to the index vector. That is, let A, B P RNˆN be sampling matrices deﬁned
+as A “ rea1, . . . , eass and B “ reb1, . . . , ebts from the index vectors a P Ns, b P Nt. Then,
+C “ unionpA, Bq,
+D “ setdiffpA, Bq
+(19)
+are deﬁned as the sampling matrices corresponding to the index vectors c “ unionpa, bq and
+d “ setdiffpa, bq, respectively.
+Algorithm 1 Hybrid snapshot AROM
+1: Set γ0 “ q0
+Ź Initial condition
+2: for k “ 1, . . . , Nt do
+3:
+if k ` 1 ď w or modpk, zq “ 0 then
+Ź Full HDM solve
+4:
+Solve γk “ Rkpγkq for γk
+5:
+else
+Ź Hybrid snapshot
+6:
+˜v “ ˜SJ
+k γk´1
+7:
+for j “ 1, . . . , J do
+8:
+Solve ˆSJ
+k γk “ ˆRkp ˆSJ
+k γk, ˜vq for ˆSJ
+k γk
+9:
+yk “ pP J
+k Φkq:P J
+k pγk ´ ψkq
+10:
+˜v “ ˜SJ
+k pψk ` Φkykq
+11:
+end for
+12:
+˘SJ
+k γk “ ˘SJ
+k pψk ` Φkykq
+13:
+γk “ SpatialFilterpγkq
+14:
+end if
+15:
+if w “ k ` 1 then
+16:
+ψw´1 “ 1
+w
+w´1
+ÿ
+j“0
+γj
+17:
+end if
+18:
+if w ď k ` 1 and modpk ` 1, zq ‰ 0 then
+19:
+Φk`1 “ PODmprγk´w`1 ´ ψk, γk´w`2 ´ ψk, . . . , γk´1 ´ ψk, γk ´ ψksq
+20:
+Pk`1 “ ODEIMnppΦk`1q
+21:
+Gk`1 computed according to Section 2.3.3
+22:
+ˆSk`1 “ unionpGk`1, Pk`1q
+23:
+˘Sk`1 “ setdiffpIN, ˆSk`1q
+24:
+˜Sk`1 “ Neighborsp ˆSk`1, ˘Sk`1q
+25:
+ψk`1 “ 1
+w
+kÿ
+j“k´w`1
+γj
+26:
+end if
+27: end for
+2.4.2. Computational eﬃciency
+Our adaptive hybrid approach relies on N-dependent operations at every time step. A full
+HDM snapshot typically requires the solution of a nonlinear system by Newton’s method,
+an iterative procedure that requires the solution of a linear system of equations at every
+time step. These large, sparse linear systems are usually solved with an iterative solver
+10
+
+such as generalized minimal residual method (GMRES), which approximates the exact solve
+by a sequence of OpN 2q matrix-vector multiplications.
+A hybrid snapshot computation
+(lines 5-23 of Algorithm 1) is going to require operations that at worst are log-linear. For
+example, obtaining a reduced basis through a thin SVD and explicit ﬁltering are algorithms
+that have linear complexity OpNq. A partial HDM iteration (Opn2
+sq), selecting np points
+with ODEIM pOpm2n2
+pqq [34], and computing the reduced coordinates yk through linear
+least squares pOpnpm2qq are examples of operations independent of N. The RRE algorithm
+requires sorting the entries and, thus, is typically OpN log Nq. While this sorting algorithm
+is the dominant term in terms of complexity, in practice it is not a bottleneck.
+Let tH P Rą0 and tR P Rą0 be the average time required to compute a snapshot relying
+only on full HDM solutions and our adaptive approach, respectively. Our AROM speedup
+S is deﬁned in the following formula:
+S :“ tH
+tR
+.
+(20)
+Suppose that the average sampling matrices are suﬃciently small at all time steps such that
+the time required to compute a hybrid snapshot is negligible in comparison to a full HDM
+solution. In this case it is reasonable to assume tR « tH{z, which results in the following
+approximate speedup S « z. This shows the speedup of our approach is going to depend
+mainly on how often the full HDM must be solved.
+Remark 7. The complexity of obtaining a reduced basis through a thin SVD is OpNw2q.
+Therefore the number of snapshots used in the reconstruction w is important to produce a
+small reduced basis but also a cost eﬃcient construction. If necessary, reduced basis con-
+struction complexity can be reduced to OpNw
+1
+2q by using fast SVD updates [31].
+Remark 8. In this work, we introduce a HDM that relies on BDF schemes for time-
+integration. However, if an explicit scheme (e.g., Adams–Bashforth methods) was adopted
+instead, the computational complexity would be linear in N as opposed to quadratic with an
+implicit scheme. For this class of ODE solvers, obtaining a cost eﬃcient AROM can be
+considerably more challenging and problem dependent.
+3. Numerical experiments
+In this section, we apply our adaptive method to solve two inviscid compressible ﬂow
+problems.
+We start by introducing the conservation laws, error functions and sampling
+average (Section 3.1). The ﬁrst test case consists of a canonical one-dimensional problem
+with known solution and is used to conduct a parametric study (Section 3.2) . For example,
+the impact of diﬀerent ﬁlters and full HDM solve frequency are evaluated for this problem
+and serve as guideline for the next test case. The second problem is two-dimensional and
+considerably more challenging (Section 3.3).
+3.1. The Euler equations of gas dynamics
+We consider compressible inviscid ﬂow through a domain Ω Ă Rd with governing equa-
+tions given by
+Bρ
+Bt ` B
+Bxj
+pρujq “ 0
+(21a)
+11
+
+Bρui
+Bt
+` B
+Bxj
+pρuiuj ` Pδijq “ 0
+(21b)
+BpρEq
+Bt
+` B
+Bxj
+ppρE ` Pqujq “ 0 ,
+(21c)
+for i “ 1, . . . , d. The density of the ﬂuid ρp¨, tq : Ω Ñ Rą0, the ﬂuid velocity up¨, tq Ñ Rd,
+and the total energy of the ﬂuid ρEp¨, tq Ñ Rą0 are implicitly deﬁned as the solution of (21).
+We assume the ﬂuid follows the ideal gas law
+P “ pγ ´ 1q
+´
+ρE ´ ρuiui
+2
+¯
+,
+(22)
+where Pp¨, tq Ñ Rą0 is the pressure of the ﬂuid and γ P Rą0 is the ratio of speciﬁc heats.
+We approximate the Euler equations using a ﬁnite volume method on a cartesian mesh.
+We employ a second-order monotonic upstream schemes for conservation laws (MUSCL)
+[42] approach with Roe ﬂux [43] and minmod limiter to spatially semi-discretize Eq. (1).
+Afterwords, we integrate the resulting system of ODEs using a second-order BDF scheme
+deﬁned by the coeﬃcients a0 “ 1{3, a1 “ ´4{3, a2 “ 1 and β “ 2{3.
+In the following numerical experiments, the AROMs accuracy will be measured using the
+relative L2pΩq error, deﬁned as
+ek :“
+dş
+Ω }γkpxq ´ qkpxq}2
+2 dV
+ş
+Ω }qkpxq}2
+2 dV
+.
+(23)
+To access parametric performance, we also use the temporal mean of the relative error,
+deﬁned as
+¯e :“ 1
+Nt
+Nt
+ÿ
+k“1
+ek .
+(24)
+Similarly, we deﬁne the average sampling as
+¯s :“ 1
+Nt
+Nt
+ÿ
+k“1
+nγk ,
+(25)
+where nγk is the number of entry points of snapshot γk with its value directly computed
+by a HDM solve. For a snapshot γk originating from partial and full HDM solves we have
+nγk “ ns and nγk “ N, respectively. We deﬁne the average sampling of a hybrid snapshot as
+¯s˚ :“ 1
+|I|
+ÿ
+kPI
+nγk ,
+(26)
+where I Ă t1, . . . , Ntu is the set of indices with a partial HDM solve. Lastly, we deﬁne the
+average ODEIM sampling as
+¯p :“ 1
+|I|
+ÿ
+kPI
+pnpqk .
+(27)
+12
+
+3.2. Sod’s shock tube
+In this section we apply study our AROM method using the most canonical Riemann
+problem for the Euler equations, Sod’s shock tube. We consider the one-dimensional (d “ 1)
+Euler equations in the domain Ω “ p0, 1q over the time interval T “ p0, 0.2q with ratio of
+speciﬁc heats γ “ 1.4 and initial condition, in terms of primitive variables, as
+ρpx, 0q “
+#
+1
+x P r0, 0.5q
+0.125
+x P r0.5, 1s ,
+upx, 0q “ 0,
+Ppx, 0q “
+#
+1
+x P r0, 0.5q
+0.1
+x P r0.5, 1s .
+(28)
+We use suitable boundary conditions from the initial condition. This is appropriate because
+the waves do not reach the boundary over the time interval of interest.
+We partition the spatial domain into N “ 399 cells of uniform width. We also equally
+partition the time domain into Nt “ 798 time steps. We chose the number of snapshots
+used in the reduced basis reconstruction to be equal to the number of POD modes used
+in the reconstruction, i.e., w “ m “ 4. Moreover, all hybrid solutions rely on the same
+reconstruction error threshold (δ “ 0.90). These parameter values are used at all time steps
+unless otherwise stated.
+The beneﬁts of hybrid solution ﬁltering is demonstrated in Fig. 4. For z “ 1, only
+full HDM solves are performed (γk “ qk). For all z ą 1, the second-order ﬁltering scheme
+is too dissipative and, thus, leads to bigger sampling matrices and higher errors. In fact,
+the over damping of the hybrid solution causes the RRE to be more equality distributed
+among the entries which in turn leads to bigger sampling matrices. For 2 ď z ď 4, all
+other methods present good results with the unﬁltered AROM yielding the best results. In
+this range, all implemented ﬁlters add more dissipation than necessary for almost identical
+sampling size. In fact, ﬁltering is not needed if the spurious oscillation inhibiting HDM ﬂux
+limiting operations are enough to guarantee wiggle-free solutions. Moreover, previous work
+with similar unﬁltered AROMs [23, 30] demonstrate good performance at this frequency
+range. For z ą 4, the higher order ﬁltering schemes outperform the unﬁltered ROM with
+the sixth-order ﬁlter being more accurate in most cases. Also, despite being less dissipative,
+the sixth-order ﬁlter leads to bigger sampling matrices in comparison to the models relying
+on fourth-order ﬁltering. A careful analysis of the results show that the fourth-order ﬁlter
+introduces more pronounced oscillations near the sharp gradients, which in turn leads to
+more unequal RRE distribution and smaller sampling matrices. This and Fig. 5 demonstrate
+that high frequency structures develop and, if not dissipated, build up over time. Also, the
+error grows considerably slower for ﬁltered solutions as a function of z. For 6 ď z ď 20,
+the unﬁltered ROM has smaller sampling matrices resulting from a more unequal RRE
+distribution.
+We further analyze the AROM with parameters z “ 10 and fourth-order ﬁlter. In this
+case, 2 ď J ď 5 with the average number of subiterations being ¯J “ 2.50. Figure 6 compares
+solutions between this AROM and a simulation relying only on full HDM solves. The AROM
+recovers the main features of the ﬂow with small discrepancies in the range of inﬂuence of
+point x “ 0.5.
+Some blurring at the wavefronts can be observed and is expected given
+that Shapiro ﬁlters are not suited for problems with shocks or sharp gradients. Moreover,
+despite the ﬁltering, some high frequency noise develops.
+The initial zero relative error
+(k ď w) is followed by an error overshoot (Fig. 7) which is probably caused by the initial
+13
+
+5
+10
+15
+20
+0
+20
+40
+60
+80
+100
+z
+¯sp%q
+5
+10
+15
+20
+0
+5
+10
+15
+20
+25
+z
+¯s˚p%q
+5
+10
+15
+20
+0
+2
+4
+6
+z
+¯ep%q
+Figure 4: Time averages of relative sampling (top) and relative error (bottom) as a function of full HDM
+frequency parameter z, for unﬁltered (
+), second-order (
+), fourth-order (
+), and sixth-order (
+)
+ﬁltered solutions. A full HDM solve is equivalent to sampling all vector entries (¯s “ 100% and ¯s˚ “ 0%).
+ﬂow triple point. The temporal mean of the relative error is ¯e “ 0.61%. Fig. 7 also shows
+the relative cardinality of the sampling sets tˆspkq
+1 , . . . , ˆspkq
+ns u and tppkq
+1 , . . . , ppkq
+np u with full HDM
+sampling (nγk “ N) omitted for easier understanding.
+The time average samplings are
+¯p “ 3.12%, ¯s “ 21.96% and ¯s˚ “ 11.96%. Additionally, we can observe that as time goes
+on sampling matrices ˆSk get bigger. This can be at least partially attributed to the growth
+of the expansion fan. Fig. 8 shows the points selected by sampling matrix ˆSk. The ﬁrst
+w “ 4 snapshots are obtained using full HDM solves and, thus, are fully highlighted in
+yellow. From this ﬁgure, it can be noticed that the points are mainly concentrated on the
+propagating expansion, contact and shock waves. Sampling also takes place outside the range
+of inﬂuence of point x “ 0.5. We can attribute this to the development of high frequency
+noise than can be easily observed on Fig. 5 for z “ 20. Moreover, it can be noticed that the
+left boundary is consistently sampled. This can be attributed to the RRE algorithm being
+overly conservative and, thus, selecting entries with εpkq
+j
+“ 0. If two elements have equal
+14
+
+0
+0.2
+0.4
+0.6
+0.8
+1
+0
+0.2
+0.4
+0.6
+0.8
+1
+1.2
+x
+ρpx, tq
+z “ 5
+0
+0.2
+0.4
+0.6
+0.8
+1
+0
+0.2
+0.4
+0.6
+0.8
+1
+1.2
+x
+ρpx, tq
+z “ 10
+0
+0.2
+0.4
+0.6
+0.8
+1
+0
+0.2
+0.4
+0.6
+0.8
+1
+1.2
+x
+ρpx, tq
+z “ 15
+0
+0.2
+0.4
+0.6
+0.8
+1
+0
+0.2
+0.4
+0.6
+0.8
+1
+1.2
+x
+ρpx, tq
+z “ 20
+Figure 5: The exact (
+) solution (density) at k “ Nt and the corresponding HDM (
+) and AROM
+(
+) approximations.
+value, the algorithm breaks the tie by selecting the element with the smallest index. For this
+problem, the elements are indexed from left to right starting from the boundary.
+Figure 9 shows time average error and sampling responses to diﬀerent values of window
+size w and number of POD modes m. For w “ 4, the error is the smallest for m “ 3. An
+additional mode probably degrades the solution by adding nonphysical structures that are
+not dissipated by the ﬁlter. A similar trend is observed for all other cases. A bigger basis
+generally leads to a more accurate reconstruction but could potentially add noise if too many
+modes are added. Moreover, larger windows do not signiﬁcantly improve accuracy. In fact,
+these ROMs are considerably less accurate if the number of modes used in the reconstruction
+is too small. From the sampling side, we can generally observe that larger windows and bigger
+basis lead to bigger sampling matrices. This is expected as bigger basis results in additional
+15
+
+(a)
+(b)
+(c)
+(d)
+(e)
+(f)
+Figure 6: Space-time snapshots of density (top), momentum (center) and energy (bottom) for a simulation
+only relying on full HDM solutions (left) and our AROM (right).
+ODEIM points and would probably be less of an issue for multidimensional problems because
+they usually lead to sparser sampling. It is also worth pointing out that for all values of w
+considered, picking m “ w leads to a relevant increase in error and decrease in sampling. This
+16
+
+0
+0.05
+0.1
+0.15
+0.2
+0
+0.2
+0.4
+0.6
+0.8
+1
+time
+ep%q
+0
+0.05
+0.1
+0.15
+0.2
+0
+10
+20
+30
+40
+50
+60
+time
+samplingp%q
+Figure 7: Relative error (top), and sampling (bottom) of ˆSk (
+) and Pk (
+).
+A full HDM would
+represent a sampling of 100% and, thus, is omitted in the sampling ﬁgure for clarity.
+shows that the last mode is an important source of noise that is not completely dissipated
+by the ﬁlter which in turn leads to a more unequal RRE distribution. As discuss in Section
+2.4.2, the cost of performing POD is also a quadratic function of window width OpNw2q.
+Therefore, a narrower window is preferred if the the beneﬁts of a larger window are little to
+none.
+For three diﬀerent values of z and fourth-order ﬁltering, the implication of diﬀerent values
+of RRE tolerance δ can be observed in Fig. 10. For z “ 5, the error variation is negligible
+17
+
+Figure 8: Sampling points selected by matrix ˆS (in yellow).
+for the range of RRE tolerances considered. In regards to the time average sampling, it
+remains almost constant for most values of δ but abruptly increases for tighter tolerances.
+However, the non-negligible sampling increase did not lead the error to visually decrease. In
+this case, a smaller sampling matrix is enough to generate accurate AROMs. For z “ 10 and
+z “ 15, accuracy can be considerably improved by the use of tighter RRE tolerances. This is
+particularly substantial for z “ 15. On the other hand, accuracy comes at a price as bigger
+sampling matrices become necessary. Moreover, increasing the RRE tolerance did not lead
+to the time average error to monotonically decrease. One explanation is that adding just
+a few sampling points could add noise to solution. In general, having more solution points
+originating from a partial HDM solution leads to a more accurate AROM. However, this
+could introduce undesirable higher frequency structures, especially if the points are sparsely
+distributed, as discussed in Section 2.3.4.
+An assessment of partial HDM subiterations is shown in Fig. 11. Results show a fast con-
+vergence rate for reduced coordinates. However, this does not lead to a monotonic decrease
+of the temporal mean of the relative error. The error increasing could be a symptom of an
+ill-conditioned linear least squares problem and, thus, getting the higher frequency temporal
+modes to converge adds noise to the solution. If this is the case, some form of solution
+regularization would be beneﬁcial. Also, for this problem conﬁguration, subiterations do not
+lead to a signiﬁcant increase in accuracy but, given the reduced cost of partial HDMs, are
+still worth consideration.
+18
+
+2
+4
+6
+8
+10
+15
+30
+45
+m
+¯sp%q
+2
+4
+6
+8
+10
+5
+20
+35
+m
+¯s˚p%q
+2
+4
+6
+8
+10
+0.5
+0.7
+0.9
+1.1
+m
+¯ep%q
+Figure 9: Time averages of relative sampling (top) and relative error (bottom) as a function of reduced-order
+dimension m for windows of size w “ 4 (
+), w “ 6 (
+), w “ 8 (
+) and w “ 10 (
+). A full HDM
+solve is equivalent to sampling all vector entries (¯s “ 100% and ¯s˚ “ 0%).
+3.3. Model implosion
+In this problem, we consider the two-dimensional (d “ 2) Euler equations in the domain
+Ω Ă p0, 0.3q2 over the time interval T “ p0, 1q with ratio of speciﬁc heats γ “ 1.4 and initial
+condition (in terms of primitive variables) as
+ρpx, 0q “
+#
+ρin
+x P D
+ρout
+x R D ,
+upx, 0q “ p0, 0q,
+Ppx, 0q “
+#
+Pin
+x P D
+Pout
+x R D .
+(29)
+where ρin “ 0.125 and Pin “ 0.14 are the pressure and density inside the region D “ tx P
+Ω | x1 ` x2 ď 0.15u Ă Ω and ρout “ 1 and Pout “ 1 are the pressure and density outside
+D. All four boundaries are taken to be walls, which causes the waves to reﬂect back into
+the domain when they reach a boundary. This is a model of an implosion that was adapted
+from [44].
+We solve this problem using a 100 ˆ 100 uniform cartesian grid. We partition the time
+domain into Nt “ 3,300 time steps. Hybrid solutions rely on a forth-order explicit Shapiro
+19
+
+1 10 20 30 40 50 60 70 80 90 99
+10
+15
+20
+25
+30
+35
+40
+45
+δp%q
+¯sp%q
+1 10 20 30 40 50 60 70 80 90 99
+0
+10
+20
+30
+40
+δp%q
+¯s˚p%q
+1 10 20 30 40 50 60 70 80 90 99
+0
+2
+4
+6
+δp%q
+¯ep%q
+Figure 10: Time averages of relative sampling (top) and relative error (bottom) as a function of relative
+reconstruction error tolerance (δ) for full HDM frequency parameter z “ 5 (
+), z “ 10 (
+), and z “ 15
+(
+). A full HDM solve is equivalent to sampling all vector entries (¯s “ 100% and ¯s˚ “ 0%).
+ﬁlter. The full HDM frequency parameter is z “ 5 and the reconstruction error threshold
+is set at δ “ 0.50. Again, we chose the number of snapshots used in the reduced basis
+reconstruction to be equal to the number of POD modes used in the reconstruction, i.e.,
+w “ m “ 4. For these parameters, 3 ď J ď 6 with the average number of subiterations
+being ¯J “ 4.17.
+Figure 12 shows snapshots of a simulation relying only on full HDM solves, our AROM,
+and the cells selected by sampling matrix ˆSk. For all four time instances, the AROM is
+capable of solving the main features of the problem with only some minor discrepancies
+mostly concentrated next to sharp gradient regions and boundaries. The reduced accuracy
+at regions containing sharp gradients was also observed in the previous problem and can be
+blamed again on the explicit ﬁlter. In regards to the bigger errors located close to boundaries,
+20
+
+2
+4
+6
+8
+10´17
+10´12
+10´7
+10´2
+j
+}ypj`1q
+k
+´ ypjq
+k }2
+2
+4
+6
+8
+10
+0.62
+0.66
+0.7
+0.74
+iteration
+¯ep%q
+Figure 11: Increment size (left) and temporal mean of the relative error (right) as a function of iteration j.
+Increment size convergence is veriﬁed at the last snapshot pk “ Ntq. The mean relative error is calculated
+at ﬁxed numbers of iterations j.
+undersampling of the boundary cells could be one explanation. In fact, it can be noticed that
+very few boundary cells are sampled. This is not an issue for the previous one-dimensional
+test case.
+For the shock tube problem, the waves do not reach the boundary over the
+time interval of interest and, thus, do not need to be updated. Moreover, one-dimensional
+problems have only two boundary cells for all meshes with more than one cell and, thus, can
+be cheaply sampled if necessary.
+Figure 13 illustrates the temporal evolution of the relative error. In this case, the temporal
+average of the relative error is ¯e “ 3.28%. This ﬁgure also shows the relative cardinality
+of sets of points sampled by matrices ˆSk and Pk. Again, full HDM sampling pnγ “ Nq
+is omitted for clarity. The time average sampling values are ¯p “ 0.26%, ¯s “ 22.89% and
+¯s˚ “ 2.89%, and the hybrid snapshot sampling never exceeds 20%. From these sampling
+sizes and the complexity discussion in Section 2.4.2, we can conclude that the average cost of
+a hybrid snapshot is negligible compared to a full HDM solve. Moreover, results show that
+the size of the sampling matrix ˆSk changes considerably depending on the ﬂow structure at
+a particular time instance and, thus, suggests that dynamical sampling is beneﬁcial.
+21
+
+(a)
+(b)
+(c)
+(d)
+(e)
+(f)
+(g)
+(h)
+(i)
+(j)
+(k)
+(l)
+Figure 12: Density snapshots a simulation only relying on full HDM solutions (top) and our AROM (center),
+and the sampling points corresponding to matrix ˆS (bottom) at time instances t “ T{4, t “ T{2, t “ 3T{4
+and t “ T (left-to-right).
+22
+
+0.3
+0.25
+0.2
+0.15
+0.1
+0.05
+0
+0
+0.05
+0.1
+0.15
+0.2
+0.25
+0.30.3
+0.25
+0.2
+0.15
+0.1
+0.05
+0
+0
+0.05
+0.1
+0.15
+0.2
+0.25
+0.30.3
+0.25
+0.2
+0.15
+0.1
+0.05
+0
+0
+0.05
+0.1
+0.15
+0.2
+0.25
+0.30.3
+0.25
+0.2
+0.15
+0.1
+0.05
+0
+0
+0.05
+0.1
+0.15
+0.2
+0.25
+0.30.3
+0.25
+0.2
+0.15
+0.1
+0.05
+0
+0
+0.05
+0.1
+0.15
+0.2
+0.25
+0.30.3
+0.25
+0.2
+0.15
+0.1
+0.05
+0
+0
+0.05
+0.1
+0.15
+0.2
+0.25
+0.30.3
+0.25
+0.2
+0.15
+0.1
+0.05
+0
+0
+0.05
+0.1
+0.15
+0.2
+0.25
+0.30.3
+0.25
+0.2
+0.15
+0.1
+0.05
+0
+0
+0.05
+0.1
+0.15
+0.2
+0.25
+0.30.3
+0.25
+0.2
+0.15
+0.1
+0.05
+0
+0
+0.05
+0.1
+0.15
+0.2
+0.25
+0.30.3
+0.25
+0.2
+0.15
+0.1
+0.05
+0
+0.05
+0.1
+0.15
+0.2
+0.25
+0.30.3
+0.25
+0.2
+0.15
+0.1
+0.05
+17
+0
+0.05
+0.1
+0.15
+0.2
+0.25
+0.30.3
+0.25
+0.2
+0.15
+0.1
+0.05
+0
+0.05
+0.1
+0.15
+0.2
+0.25
+0.30
+0.1
+0.2
+0.3
+0.4
+0.5
+0.6
+0.7
+0.8
+0.9
+1
+0
+1
+2
+3
+4
+5
+time
+ep%q
+0
+0.1
+0.2
+0.3
+0.4
+0.5
+0.6
+0.7
+0.8
+0.9
+1
+0
+5
+10
+15
+20
+time
+samplingp%q
+Figure 13: Relative error (top), and sampling (bottom) of ˆSk (
+) and Pk (
+). A full HDM solve would
+represent a sampling of 100% and, thus, is omitted in the sampling ﬁgure for clairy.
+23
+
+4. Conclusions and future directions
+In this work, an adaptive reduced-order model is applied to convection-dominated prob-
+lems. This approach relies on local HDM solves to obtain an accurate representation of the
+main ﬂow features. The remainder of the ﬂow is represented using a subspace approxima-
+tion trained using previous snapshots. The performance of the our approach is validated
+on two compressible ﬂow problems with moving sharp gradient features. The ﬁrst is the
+one-dimensional canonical Sod’s shock tube problem and it is used to conduct a parametric
+study. The second is a considerably more challenging two-dimensional problem simulating
+an implosion inside a box.
+Results show that the proposed method is capable of accelerating convection-dominated
+unsteady CFD problems. If the sampling matrices remain suﬃciently small throughout the
+simulation, a brief complexity analysis establishes that the speedup depends mainly on the
+full HDM solution frequency parameter z. Our ﬁrst test case demonstrates that ﬁltering
+allows for higher z and, thus, is a crucial ingredient for cheaper and accurate AROMs.
+One contribution of this work and an important component of the proposed method is the
+dynamic sampling matrix ˆSk. Our time adaptive approach selects the smallest sampling set
+satisfying a predeﬁned error tolerance at each time instance. This allows the sampling matrix
+to shrink or expand in an attempt to avoid undersampling and oversampling. Furthermore,
+the shock tube problem shows that narrower windows and smaller bases are suﬃcient to
+generate cheap and accurate AROMs. Another important contribution is the partial HDM
+sampling used to construct the hybrid snapshots. It requires an approximation to the state
+on cells neighboring sample points, which can be made more accurate through subiterations
+and generally results in some accuracy gain without a signiﬁcant cost increase.
+The method could beneﬁt from further research in multiple ways. First, our current
+dynamic sampling procedure selects entries based only on their relative contribution to the
+total reconstruction error. For example, if the error tolerance is chosen to be too strict, this
+can lead to bigger sampling matrices than necessary if the residual is uniformly distributed
+across the mesh.
+Therefore, a better sampling algorithm could improve robustness and
+decrease cost. Another research direction is boundary sampling. As previously discussed,
+accuracy at the boundaries could possibly be improved with little eﬀort by sampling interior
+and boundary cells separately. Finally, our approach relies on linear order reduction for most
+hybrid snapshots entries. We avoid the Kolmogorov n-width problem by relying on the local
+low-rank structure of convection-dominated problems. Unfortunately, ROMs built on POD
+can struggle in predictive settings for even very simple problems. Nonlinear model reduction
+techniques could potentially overcome this barrier and produce AROMs less dependent on
+full HDM solves.
+Acknowledgments
+This material is based upon work supported by the Air Force Oﬃce of Scientiﬁc Research
+(AFOSR) under award numbers FA9550-20-1-0236 and FA9550-22-1-0004. The content of
+this publication does not necessarily reﬂect the position or policy of any of these supporters,
+and no oﬃcial endorsement should be inferred.
+24
+
+References
+[1] T. R. Ricciardi, W. R. Wolf, N. J. Moﬃtt, J. R. Kreitzman, P. Bent, Numerical noise
+prediction and source identiﬁcation of a realistic landing gear, Journal of Sound and
+Vibration 496 (2021) 115933. doi:https://doi.org/10.1016/j.jsv.2021.115933.
+URL https://www.sciencedirect.com/science/article/pii/S0022460X21000055
+[2] C. W. Rowley, T. Colonius, R. M. Murray, Model reduction for compressible ﬂows using
+POD and Galerkin projection, Physica D: Nonlinear Phenomena 189 (1–2) (2004) 115
+– 129.
+[3] K. Carlberg, C. Farhat, D. Amsallem, The GNAT method for nonlinear model reduction:
+Eﬀective implementation and application to computational ﬂuid dynamics and tubulent
+ﬂows, Journal of Computational Physics 243 (2013) 623–647. doi:10.1016/j.jcp.
+2013.02.028.
+[4] K. Carlberg, M. Barone, H. Antil, Galerkin v. least-squares Petrov-Galerkin projection
+in nonlinear model reduction, Journal of Computational Physics 330 (2017) 693–734.
+doi:10.1016/j.jcp.2016.10.033.
+[5] S. L. Brunton, J. L. Proctor, J. N. Kutz, Discovering governing equations from data
+by sparse identiﬁcation of nonlinear dynamical systems, Proceedings of the National
+Academy of Sciences 113 (15) (2016) 3932–3937. arXiv:https://www.pnas.org/doi/
+pdf/10.1073/pnas.1517384113, doi:10.1073/pnas.1517384113.
+URL https://www.pnas.org/doi/abs/10.1073/pnas.1517384113
+[6] B. Peherstorfer, K. Willcox, Data-driven operator inference for nonintrusive projection-
+based model reduction, Computer Methods in Applied Mechanics and Engineering 306
+(2016) 196–215. doi:https://doi.org/10.1016/j.cma.2016.03.025.
+URL https://www.sciencedirect.com/science/article/pii/S0045782516301104
+[7] H. F. S. Lui, W. R. Wolf, Construction of reduced-order models for ﬂuid ﬂows using
+deep feedforward neural networks, Journal of Fluid Mechanics 872 (2019) 963–994.
+doi:10.1017/jfm.2019.358.
+[8] W. Cazemier, R. W. C. P. Verstappen, A. E. P. Veldman, Proper orthogonal decom-
+position and low-dimensional models for driven cavity ﬂows, Physics of Fluids 10 (7)
+(1998) 1685–1699. doi:10.1063/1.869686.
+[9] B. R. Noack, P. Papas, P. A. Monkewitz, The need for a pressure-term representation
+in empirical Galerkin models of incompressible shear ﬂows, Journal of Fluid Mechanics
+523 (2005) 339–365. doi:10.1017/S0022112004002149.
+[10] M. Bergmann, C.-H. Bruneau, A. Iollo, Enablers for robust pod models, Journal of
+Computational Physics 228 (2) (2009) 516–538. doi:https://doi.org/10.1016/j.
+jcp.2008.09.024.
+URL https://www.sciencedirect.com/science/article/pii/S002199910800510X
+25
+
+[11] M. Bergmann, C. H. Bruneau, A. Iollo, Enablers for robust POD models, Journal of
+Computational Physics 228 (2009) 516–538. doi:10.1016/j.jcp.2008.09.024.
+[12] O. San, T. Iliescu, Proper orthogonal decomposition closure models for ﬂuid ﬂows:
+Burgers equation, International Journal of Numerical Analysis and Modeling, Series B
+5 (2014) 217–237.
+[13] Z. Wang, I. Akhtar, J. Borggaard, T. Iliescu, Proper orthogonal decomposition closure
+models for turbulent ﬂows: A numerical comparison, Comput. Methods Appl. Mech.
+Eng. 237 (2012) 10–26.
+[14] I. Kalashnikova, B. van Bloemen Waanders, S. Arunajatesan, M. Barone, Stabiliza-
+tion of projection-based reduced order models for linear time-invariant systems via
+optimization-based eigenvalue reassignment, Computer Methods in Applied Mechanics
+and Engineering 272 (2014) 251–270. doi:https://doi.org/10.1016/j.cma.2014.
+01.011.
+[15] S. J. Grimberg, C. Farhat, N. Youkilis, On the stability of projection-based model order
+reduction for convection-dominated laminar and turbulent ﬂows, Journal of Computa-
+tional Physics 419 (2020) 1–28. doi:10.1016/j.jcp.2020.109681.
+[16] V. Zucatti, W. Wolf, Data-driven closure of projection-based reduced order models for
+unsteady compressible ﬂows, Computer Methods in Applied Mechanics and Engineering
+386 (2021) 114120. doi:https://doi.org/10.1016/j.cma.2021.114120.
+[17] M. Ohlberger, S. Rave, Reduced Basis Methods:
+Success, Limitations and Future
+Challenges, Proceedings of the Conference Algoritmy (2016) 1–12.
+URL
+http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/algoritmy/article/
+view/389
+[18] K. Lee, K. T. Carlberg, Model reduction of dynamical systems on nonlinear manifolds
+using deep convolutional autoencoders, Journal of Computational Physics 404 (2020)
+108973. doi:https://doi.org/10.1016/j.jcp.2019.108973.
+[19] J. Barnett, C. Farhat, Quadratic approximation manifold for mitigating the Kolmogorov
+barrier in nonlinear projection-based model order reduction, Journal of Computational
+Physics 464 (2022) 111348. doi:https://doi.org/10.1016/j.jcp.2022.111348.
+URL https://www.sciencedirect.com/science/article/pii/S0021999122004107
+[20] R. Geelen, S. Wright, K. Willcox, Operator inference for non-intrusive model reduction
+with quadratic manifolds (2022). doi:10.48550/ARXIV.2205.02304.
+URL https://arxiv.org/abs/2205.02304
+[21] T. Taddei, A registration method for model order reduction: Data compression and
+geometry reduction, SIAM Journal on Scientiﬁc Computing 42 (2) (2020) A997–A1027.
+arXiv:https://doi.org/10.1137/19M1271270, doi:10.1137/19M1271270.
+URL https://doi.org/10.1137/19M1271270
+26
+
+[22] M. A. Mirhoseini, M. J. Zahr, Model reduction of convection-dominated partial dif-
+ferential equations via optimization-based implicit feature tracking (2021).
+doi:
+10.48550/ARXIV.2109.14694.
+URL https://arxiv.org/abs/2109.14694
+[23] B. Peherstorfer, Model Reduction for Transport-Dominated Problems via Online Adap-
+tive Bases and Adaptive Sampling, SIAM Journal on Scientiﬁc Computing 42 (5) (2020)
+A2803–A2836. doi:10.1137/19M1257275.
+[24] D. Amsallem, M. J. Zahr, C. Farhat, Nonlinear model order reduction based on lo-
+cal reduced-order bases, International Journal for Numerical Methods in Engineer-
+ing 92 (10) (2012) 891–916. arXiv:https://onlinelibrary.wiley.com/doi/pdf/10.
+1002/nme.4371, doi:https://doi.org/10.1002/nme.4371.
+URL https://onlinelibrary.wiley.com/doi/abs/10.1002/nme.4371
+[25] D. Amsallem, M. J. Zahr, K. Washabaugh, Fast local reduced basis updates for the eﬃ-
+cient reduction of nonlinear systems with hyper-reduction, Advances in Computational
+Mathematics 41 (5) (2015) 1187–1230. doi:10.1007/s10444-015-9409-0.
+URL https://doi.org/10.1007/s10444-015-9409-0
+[26] F. Bai, Y. Wang, DEIM reduced order model constructed by hybrid snapshot simulation,
+SN Applied Sciences 2 (12) (2020) 2165. doi:10.1007/s42452-020-03958-7.
+[27] F. Bai, Y. Wang, A reduced order modeling method based on GNAT-embedded hybrid
+snapshot simulation, Mathematics and Computers in Simulation 199 (2022) 100–132.
+doi:https://doi.org/10.1016/j.matcom.2022.03.006.
+[28] L. Feng, G. Fu, Z. Wang, A FOM/ROM Hybrid Approach for Accelerating Numer-
+ical Simulations, Journal of Scientiﬁc Computing 89 (3) (2021) 61.
+doi:10.1007/
+s10915-021-01668-9.
+[29] B. Peherstorfer, K. Willcox, Online Adaptive Model Reduction for Nonlinear Systems
+via Low-Rank Updates, SIAM Journal on Scientiﬁc Computing 37 (4) (2015) A2123–
+A2150. doi:10.1137/140989169.
+[30] W. I. T. Uy, C. R. Wentland, C. Huang, B. Peherstorfer, Reduced models with nonlinear
+approximations of latent dynamics for model premixed ﬂame problems (2022). doi:
+10.48550/ARXIV.2209.06957.
+URL https://arxiv.org/abs/2209.06957
+[31] M. Brand, Fast low-rank modiﬁcations of the thin singular value decomposition, Linear
+Algebra and its Applications 415 (1) (2006) 20–30, special Issue on Large Scale Linear
+and Nonlinear Eigenvalue Problems. doi:https://doi.org/10.1016/j.laa.2005.07.
+021.
+URL https://www.sciencedirect.com/science/article/pii/S0024379505003812
+[32] R. Everson, L. Sirovich, Karhunun-Lo`eve procedure for gappy data, Optical Society of
+America 12 (1995) 1657–1664. doi:10.1364/JOSAA.12.001657.
+27
+
+[33] K. Willcox, Unsteady ﬂow sensing and estimation via the gappy proper orthogonal
+decomposition, Computers & Fluids 35 (2006) 208–226. doi:10.1016/j.compfluid.
+2004.11.006.
+[34] B. Peherstorfer, Z. Drmaˇc, S. Gugercin, Stability of Discrete Empirical Interpolation
+and Gappy Proper Orthogonal Decomposition with Randomized and Deterministic
+Sampling Points, SIAM Journal on Scientiﬁc Computing 42 (5) (2020) A2837–A2864.
+doi:10.1137/19M1307391.
+[35] M. Barrault, Y. Maday, N. C. Nguyen, A. T. Patera, An ‘empirical interpolation’
+method:
+application to eﬃcient reduced-basis discretization of partial diﬀerential
+equations, Comptes Rendus Mathematique 339 (9) (2004) 667 – 672.
+doi:https:
+//doi.org/10.1016/j.crma.2004.08.006.
+URL http://www.sciencedirect.com/science/article/pii/S1631073X04004248
+[36] S. Chaturantabut, D. C. Sorensen, Nonlinear model reduction via discrete empirical
+interpolation, SIAM Journal on Scientiﬁc Computing 32 (2010) 2737–3764. doi:10.
+1137/090766498.
+[37] S. K. Lele, Compact ﬁnite diﬀerence schemes with spectral-like resolution, Journal
+of Computational Physics 103 (1) (1992) 16–42. doi:http://dx.doi.org/10.1016/
+0021-9991(92)90324-R.
+URL http://www.sciencedirect.com/science/article/pii/002199919290324R
+[38] M. R. Visbal, D. V. Gaitonde, On the use of higher-order ﬁnite-diﬀerence schemes on
+curvilinear and deforming meshes, Journal of Computational Physics 181 (1) (2002)
+155–185. doi:https://doi.org/10.1006/jcph.2002.7117.
+URL https://www.sciencedirect.com/science/article/pii/S0021999102971172
+[39] F. Falissard, Genuinely multi-dimensional explicit and implicit generalized Shapiro ﬁl-
+ters for weather forecasting, computational ﬂuid dynamics and aeroacoustics, Journal
+of Computational Physics 253 (2013) 344–367. doi:10.1016/j.jcp.2013.07.001.
+[40] R. Shapiro, Smoothing, ﬁltering, and boundary eﬀects, Reviews of Geophysics 8 (2)
+(1970) 359–387.
+arXiv:https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.
+1029/RG008i002p00359, doi:https://doi.org/10.1029/RG008i002p00359.
+URL
+https://agupubs.onlinelibrary.wiley.com/doi/abs/10.1029/
+RG008i002p00359
+[41] P. J. Wolfram, O. B. Fringer, Mitigating horizontal divergence “checker-board” oscil-
+lations on unstructured triangular c-grids for nonlinear hydrostatic and nonhydrostatic
+ﬂows, Ocean Modelling 69 (2013) 64–78. doi:https://doi.org/10.1016/j.ocemod.
+2013.05.007.
+URL https://www.sciencedirect.com/science/article/pii/S1463500313000929
+[42] B. van Leer, Towards the ultimate conservative diﬀerence scheme. v. a second-order
+sequel to godunov’s method, Journal of Computational Physics 32 (1) (1979) 101–136.
+28
+
+doi:https://doi.org/10.1016/0021-9991(79)90145-1.
+URL https://www.sciencedirect.com/science/article/pii/0021999179901451
+[43] P. Roe, Approximate riemann solvers, parameter vectors, and diﬀerence schemes, Jour-
+nal of Computational Physics 43 (2) (1981) 357–372. doi:https://doi.org/10.1016/
+0021-9991(81)90128-5.
+URL https://www.sciencedirect.com/science/article/pii/0021999181901285
+[44] D. Ghosh, J. D. Baeder, Compact Reconstruction Schemes with Weighted ENO Lim-
+iting for Hyperbolic Conservation Laws, SIAM Journal on Scientiﬁc Computing 34 (3)
+(2012) A1678–A1706.
+arXiv:https://doi.org/10.1137/110857659, doi:10.1137/
+110857659.
+URL https://doi.org/10.1137/110857659
+29
+
diff --git a/BtAzT4oBgHgl3EQfwP4g/content/tmp_files/load_file.txt b/BtAzT4oBgHgl3EQfwP4g/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..219642422a482a65506d6706ac52a91a8bf22c60
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@@ -0,0 +1,1233 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf,len=1232
+page_content='An adaptive, training-free reduced-order model for  convection-dominated problems based on hybrid snapshots  Victor Zucattia, Matthew J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Zahra  aUniversity of Notre Dame, Notre Dame, IN 46556, United States of America  Abstract  The vast majority of reduced-order models (ROMs) ﬁrst obtain a low dimensional repre-  sentation of the problem from high-dimensional model (HDM) training data which is after-  wards used to obtain a system of reduced complexity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Unfortunately, convection-dominated  problems generally have a slowly decaying Kolmogorov n-width, which makes obtaining an  accurate ROM built solely from training data very challenging.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' The accuracy of a ROM can  be improved through enrichment with HDM solutions;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' however, due to the large computa-  tional expense of HDM evaluations for complex problems, they can only be used parsimo-  niously to obtain relevant computational savings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' In this work, we exploit the local spatial  and temporal coherence often exhibited by these problems to derive an accurate, cost-eﬃcient  approach that repeatedly combines HDM and ROM evaluations without a separate training  phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Our approach obtains solutions at a given time step by either fully solving the HDM  or by combining partial HDM and ROM solves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' A dynamic sampling procedure identiﬁes  regions that require the HDM solution for global accuracy and the reminder of the ﬂow is  reconstructed using the ROM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Moreover, solutions combining both HDM and ROM solves  use spatial ﬁltering to eliminate potential spurious oscillations that may develop.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' We test  the proposed method on inviscid compressible ﬂow problems and demonstrate speedups up  to an order of magnitude.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='  Keywords:  adaptive model reduction, proper orthogonal decomposition, hyperreduction,  sparse sampling, convection-dominated problems  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Introduction  Today’s computational power enables the numerical solution of complex engineering  problems;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' however, these computations can easily require hundreds of millions of degrees  of freedom to produce accurate results [1] and, thus, high-ﬁdelity many-query analyses are  still impractical in many scenarios such as design optimization, ﬂow control and uncer-  tainty quantiﬁcation, to name a few.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Fortunately, the large amount of data generated by  high-dimensional models (HDMs) can be used to build a reduced-order model (ROM).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' A  two-step (oﬄine/online) approach is the standard when building ROMs for time-dependent  problems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' In the oﬄine stage, a smaller dimensional representation is obtained from HDM  training data and used to generate a lower complexity model through physics-based [2, 3, 4]  or data-driven methods [5, 6, 7].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' This is a precomputation step performed only once but can  be very costly given the high-dimensional data dependency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' On the other hand, the online  Preprint submitted to Elsevier  January 5, 2023  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='01718v1  [math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='NA]  4 Jan 2023  stage consists of solving the resulting system of equations of reduced dimensionality (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=',  up to four orders of magnitude smaller [7]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Unfortunately, despite the considerable research  done in the last 20 years, ROMs still suﬀer from a multitude of problems (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=', instability,  inaccuracy, failure to generalize beyond training) making them generally unreliable in an  industrial setting [2, 8, 9, 10].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' This is particularly the case when modeling time-dependent  convection-dominated problems such as those usually found in viscous or high-speed compu-  tational ﬂuid dynamics (CFD) problems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Multiple correction methods have been proposed  [11, 12, 13, 14, 15, 16] and have been rather successful in improving ROM stability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' However,  they have done very little to improve ROM predictive capabilities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='  For convection-dominated problems, failure to generalize has been mainly attributed to  the slowly decaying Kolmogorov n-width of linear subspace approximations [17].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' This is  also sometimes referred to as Kolmogorov barrier because the error slowly decaying with  the dimension of the reduced space limits the achievable accuracy of ROMs in practice and  requires a substantial amount of training data, which can be infeasible to collect oﬄine.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='  The Kolmogorov barrier can be overcome, for example, by the use of nonlinear model re-  duction techniques.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' In [18], a nonlinear manifold is obtained through deep convolutional  autoencoders and combined with projection-based methods to produce ROMs capable of  outperforming their linear counterparts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='  Quadratic manifolds have been used with both  physics-based [19] and data-driven [20] methods for order reduction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Alternatively, nonlin-  ear manifolds have been constructed by composing a traditional subspace approximation  with a transformation to the underlying domain, which has proven particularly eﬀective for  shock-dominated problems [21, 22].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Another solution is to exploit the local low-rank struc-  ture of this class of problems [23].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' In [24, 25], local low-rank subspaces are systematically  obtained by partitioning of the state space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Results show that local subspaces improves  ROMs accuracy and speed by reducing the dimensionality of each subspace.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='  Adaptive reduced-order models (AROMs) [26, 27, 28, 29, 23, 30] provide a diﬀerent  approach by continuously combining HDM and ROM operations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Predictive capabilities  can be improved by alternating between HDM and ROM generated snapshots [26, 27, 28].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='  In [26, 27], on-the-ﬂy criteria relying on the reduced basis suﬃciency is used to determine  when to use the HDM or local ROM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' If deemed necessary, fast low-rank singular value  decomposition (SVD) modiﬁcations [31] are used to update the reduced-order basis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' This  methodology was successfully tested (factor of two speedup with an error inferior to 1%) on  heat transfer [26] and ﬂuid ﬂow [27] problems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' A similar approach relying on a more rigorous  a posteriori error estimator to switch between the HDM and ROM is introduced in [28].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' A  diﬀerent AROM method developed in [23] uses the adaptive discrete empirical interpolation  method (ADEIM) [29] and rank-one updates to adapt the reduced basis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' A comparison of  AROMs relying on this approach and traditional ROMs can be found in [30].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' In particular,  the numerical experiments show that AROMs can be used in a predictive setting to model  chemically reacting ﬂow problems, whereas traditional ROMs completely fail to generate  meaningful predictions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' These methods may not achieve the same speedup factors commonly  observed when using the two-step ROM approach [7], but numerical experiments show that  AROMs can accurately accelerate numerical solutions of problems where traditional order  reduction methods fail completely.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='  In this work, we propose a training-free approach that combines local HDM and ROM  solutions to circumvent costly full HDM solves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' A dynamic relative reconstruction error  2  strategy is developed to identify regions of the domain where the ROM is inaccurate and we  locally solve the HDM in these regions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' For problems containing spatial derivatives, states  on neighboring cells are required to locally evolve the state using the HDM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' We rely on the  ROM solution when a neighboring cell is outside the sampled region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Our approach allows  the sampled region to adapt over time to avoid unnecessary HDM evaluations and improve  robustness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Furthermore, our method relies on explicit spatial ﬁltering to eliminate spurious  oscillations that may appear after combining the solutions originating from diﬀerent methods  (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=', some regions of the domain evolved using the HDM and others using the ROM).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' We  refer to the solutions generated by this approach as hybrid snapshots.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Lastly, our AROM is  validated and tested on time-dependent compressible ﬂow problems with shocks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='  The remainder of this paper is organized as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' In Section 2, we begin by introducing  a general governing system of conservation laws and the high-dimensional modeling frame-  work used to discretize it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Next, we introduce our hybrid snapshot approach, which involves:  1) the reduced basis approximation and partial HDM solutions, 2) a sampling procedure  based on relative reconstruction error, and 3) low-pass spatial ﬁlters required to robustly  mix solutions produced by diﬀerent numerical methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' We ﬁnish this section with a com-  plete description of the algorithm and a discussion of important aspects of the method such  as computational eﬃciency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Section 3 applies our adaptive framework to two compressible  inviscid ﬂow problems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' The ﬁrst is a compressible one-dimensional problem and is used to  conduct a parametric study of the proposed method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' The second is a considerably more  complex two-dimensional problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Finally, Section 4 highlights the main conclusions and  discuss future research directions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Adaptive reduced-order models  In this section, we introduce the general system of conservation laws that we aim to  accelerate using our adaptive reduced-order model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' We begin by introducing the system of  conservation laws (Section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='1) and formulate a high-dimensional discretization (Section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='  Afterwards, we introduce our cost eﬀective hybrid snapshot approach (Section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='3), which  consists of the reduced basis approximation (Section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='1), partial HDM solves (Section  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='2), relative reconstruction error (Section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='3), and spatial low-pass ﬁlters (Section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' System of conservation laws  A general system of c conservation laws, deﬁned in a spatial domain Ω Ă Rd over the  time interval T “ p0, Ts, takes the form  Q,t ` ∇ ¨ fpQ, ∇Qq “ hpQ, ∇Qq,  Qp¨, 0q “ ˚  Qp¨q,  (1)  where f : Rc ˆ Rcˆd Ñ Rcˆd is the ﬂux ﬂunction, h : Rc ˆ Rcˆd Ñ Rc is the source term,  ˚  Q : Ω Ñ Rc is the initial condition, and Qpx, tq is the vector of conservative variables  implicity deﬁned as the solution of Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' (1) at px, tq P Ω ˆ T .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' High-dimensional model  The previous system of partial diﬀerential equations (PDEs) is discretized using a method  of lines approach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' After spatial discretization, we have the following system of ordinary  3  diﬀerential equations (ODEs)  dq  dt “ Fpq, tq ,  (2)  where qptq P RN is our semi-discrete approximation to Qp¨, tq implicitly deﬁned as the solution  of Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' (2), N is the number of degrees of freedom of the spatial discretization, and F is the  nonlinear function deﬁning the spatial discretization of the inviscid and viscous ﬂuxes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='  A time discretization method is required to solve Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' (2) numerically.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' In this work, the  backward diﬀerentiation formulas (BDFs) are used.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' The s-order BDF scheme is written as  sÿ  j“0  ajqn`j “ ∆tβFpqn`s, tn`sq ,  (3)  where qn « qptnq, ∆t denotes the time step size, tn “ t1 ` n∆t, and coeﬃcients ak and β  are such that the method is order s and are normalized such that as “ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' As can be noted  from Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' (3), BDF schemes are implicit and, thus, may require the solution of a nonlinear  system of equations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='  The fully discrete HDM is characterized by the following system of algebraic equations  to be solved at each time instance k P r1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' , Nts,  qk “ Rkpqkq ,  (4)  where Rk : RN Ñ RN is the nonlinear residual function, which is deﬁned as  Rkpqkq “ ∆tβFpqk, tkq ´  s´1  ÿ  j“0  ajqk´s`j .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='  (5)  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Hybrid snapshot approach  We are interested in obtaining an approximation vk « qk that eﬃciently leverages local  HDM information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' For this, consider the sampling points ˆspkq  1 , .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' , ˆspkq  ns P t1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' , Nu and the  corresponding sampling points matrix ˆSk “ reˆspkq  1 , .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' , eˆspkq  ns s P RNˆns.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Here, ns is the number  of indices retained from the original vector of size N and ei denotes the vector with a 1 in  the i-th coordinate and 0 elsewhere.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Let ˘Sk P RNˆpN´nsq be the complementary sampling  points matrix derived from points t1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' , Nuztˆspkq  1 , .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' , ˆspkq  ns u that have not been selected as  sampling points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' We additionally consider sampling matrix ˜Sk P RNˆl generated from the  neighboring points t˜spkq  1 , .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' , ˜spkq  l u needed to calculate the HDM ﬂux function that are not  already in tˆspkq  1 , .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' , ˆspkq  ns u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' The sampling matrices can are illustrated in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' 1 for the case  of a ﬁrst-order ﬁnite volume discretization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='  With these deﬁnitions in place, we propose an approximation vk to the fully discrete  HDM state qk where vk restricted to the points in ˘Sk use a traditional aﬃne subspace  approximation and vk restricted to the points in ˆSk are deﬁned as the solution of the HDM  residual restricted to the ˆSk indices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' That is, vk is deﬁned such that  ˘SJ  k vk “ ˘SJ  k pψk ` Φkykq ,  (6a)  ˆSJ  k vk “ ˆRkp ˆSJ  k vk, ˜SJ  k vkq ,  (6b)  4  Figure 1: An example of mesh sampling corresponding to a ﬁrst-order ﬁnite volume scheme.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Cells sampled  by ˆSk and ˜Sk are highlighted in yellow and green, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Moreover, ˘Sk samples both the blue and  green cells.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='  where ψk P RN is a reference state, Φk P RNˆm is a basis for a reduced subspace used  to approximate the state qk at the sampling points ˘Sk, yk P Rm contains the corresponding  reduced coordinates, and m denotes the dimension of the reduced subspace with m !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' The  function ˆRk : Rns ˆRl Ñ Rns is the nonlinear partial residual deﬁned as the restriction of the  HDM residual Rk to the indices sampled by ˆSk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Due to locality of the HDM discretization  scheme, the partial residual does not depend on the entire state;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' rather, it only depends on  the restriction of the state to the indices sampled by ˆSk and ˜Sk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Mathematically, we write  this as  ˆRkpˆv, ˜vq :“ ˆSJ  k Rkp ˆSkˆv ` ˜Sk˜vq .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='  (7)  Evaluating ˆRk is cost eﬀective provided ns !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' N because a relatively small number of entries  of the HDM residual are required.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='  Remark 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Multistage methods such as Runge–Kutta solve ODEs by taking a few interme-  diate steps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' This requires sequentially solving residuals that depend on the solution of the  previous stage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' As a consequence, each stage is going to require diﬀerent sampling matrices  that take into consideration neighbors of neighbors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' This issue can be avoided by the use of  multistep methods such as BDF.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' These rely on a linear combination of previous states and  residuals and, thus, we only need a set of sampling matrices for each time step.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Reduced basis approximation  We apply gappy POD [32, 33] to compute the approximate HDM solution at the points  corresponding to ˘Sk (Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' 6a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Given a sampling matrix Pk P RNˆnp constructed from points  tppkq  1 , .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' , ppkq  np u Ă tˆspkq  1 , .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' , ˆspkq  ns u, the reduced coordinates yk are calculated as  yk “ pP J  k Φkq:P J  k pvpJq  k  ´ ψkq ,  (8)  where vpJq  k  comes from the partial HDM solve, which is deﬁned in Section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' The reduced  basis Φk is constructed by compressing the deviations of the last w snapshots from the  5  reference state ψk, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=',  Φk “ PODm prγk´w ´ ψk´1, γk´w`1 ´ ψk´1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' , γk´2 ´ ψk´1, γk´1 ´ ψk´1sq ,  (9)  where γk is either a HDM solution or hybrid snapshot (details deferred to Section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='4) and  PODm : RNˆw Ñ RNˆm applies the thin SVD to the argument (snapshot matrix of size N ˆw)  and extracts the m left singular vectors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' The sampling matrix Pk is computed as  Pk “ ODEIMnppΦkq ,  (10)  where ODEIMnp : RNˆm Ñ RNˆnp is the oversampling discrete empirical interpolation method  (ODEIM) [34], which is derived from the empirical interpolation method (EIM) [35] and its  discrete counterpart, the discrete empirical interpolation method (DEIM) [36].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' As pointed  out in [34], oversampling (m ă np) leads to more accurate linear-regression based approxi-  mations rather than interpolation (m “ np).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Finally, the reference state is computed as  ψk “ 1  w  k´1  ÿ  j“k´w  γj .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='  (11)  The reference state should be carefully chosen as it impacts accuracy and stability of the  reduced bases approximation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' In particular, our choice allows time-invariant Dirichlet bound-  ary conditions to be automatically satisﬁed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='  Remark 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Our SVD approach reconstructs the reduced basis from scratch every time the  basis needs to be updated, which means all entries are updated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='  A diﬀerent approach is  adopted in [23].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' In this case, the reduced-order basis is locally updated using the adaptive  discrete empirical interpolation method (ADEIM) [29].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' However, not providing any sort of  correction outside the sampling points can lead to a potentially catastrophic loss of accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Partial high-dimensional model  An estimate of ˜vk « ˜SJ  k vk is necessary in order to solve Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' 6b and, thus, obtain an  approximate HDM solution at the points corresponding to ˆSk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' A straightforward choice is  ˜vk “ ˜SJ  k γk´1, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=', lag the solution to the previous time step;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' however, this can lead to a lagged  solution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' We attempt to obtain a more accurate evaluation of ˆSJ  k vk through subiterations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='  In this approach, solving the partial HDM solution at time step k leads to the following  iterations: for j “ 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' , J, solve  ˆvpjq  k  “ ˆRkpˆvpjq  k , ˜vpjq  k q  (12)  for ˆvpjq  k  and set  ypjq  k  “ pP J  k Φkq:P J  k ˆSkpˆvpjq  k  ´ ψkq ,  (13a)  ˜vpj`1q  k  “ ˜SJ  k pψk ` Φkypjq  k q  (13b)  where ˜vp1q  k  “ ˜SJ  k γk´1 is the initial guess and J is determined by the satisfaction of a conver-  gence criterion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Here, the algorithm is terminated when either  }ypj`1q  k  ´ ypjq  k }2 ă ϵy  (14)  or J “ jmax, where ϵy P Rą0 and jmax P N are user deﬁned.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' In this work, we take ϵy “ 10´4  and jmax “ 10 unless otherwise stated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='  6  Remark 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' For explicit time-marching methods, the right-hand size of Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' (4) can be di-  rectly computed because it only depends on the solution at previous time steps and, thus, no  subiterations are necessary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Relative reconstruction error  The pointwise reconstruction error of approximating the state γk in the reduced subspace  is  εpkq  j  “ pγk ´ ψk ´ Φkykq2  j ,  (15)  where yk is given by Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Let i1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' , iN be an ordering such that  εpkq  i1 ě ¨ ¨ ¨ ě εpkq  iN .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='  (16)  At time step k, we pick the ﬁrst ng indices i1 “ gpkq  1 , .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' , ing “ gpkq  ng as the sampling points to  form Gk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' The number of sampling points ng is chosen according to the relative reconstruction  error (RRE),  RREpngq “  řng  j“1 εpkq  ij  řN  j“1 εpkq  ij  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' ,  (17)  In practice, we choose ng to be the smallest natural number such that RREpngq ď δ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='  Finally, the set of points forming sampling matrix ˆSk is deﬁned as  tˆspkq  1 , .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' , ˆspkq  ns u :“ tgpkq  1 , .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' , gpkq  ng u Y tppkq  1 , .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' , ppkq  ns u .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='  (18)  Once we have ˆSk, the other sampling matrices ˜Sk and ˘Sk are straightforwardly obtained from  the discrete stencil.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Spatial low-pass ﬁlters  Spatial ﬁltering is an operation commonly used to stabilize time-dependent ﬂuid ﬂow  simulations [37, 38, 39] by eliminating high-wavenumber noise originating from, for example,  mesh nonuniformity and nonlinear ﬂow features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Implicit ﬁltering methods require the solu-  tion of a system of linear equations and have been used extensively in the solution of CFD  problems [37, 38].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' We avoid solving a system of linear equations by using the cheaper and  easier to implement explicit ﬁlters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' However, explicit ﬁlters require bigger stencils to obtain  same order of accuracy which can be particularly problematic at boundaries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='  Similar to standard CFD simulations, there is no guarantee that a hybrid snapshot vk  combining entries from partial HDM and reduced basis solves is going to be smooth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' To  remove spurious oscillations that may develop, we apply a one-dimensional explicit Shapiro  ﬁlter [39, 40] to the solution;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' we consider second-, fourth-, and sixth-order ﬁlters in Section  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='  Remark 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' As pointed out in [38], multidimensional ﬁltering can be performed by applying  the one-dimensional ﬁlter in each coordinate direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='  Remark 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Boundary condition treatment is usually not obvious and have been dealt with in  diﬀerent ways [38].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' One approach is to use smaller, lower order stencils near the boundary,  which decreases the global order of accuracy of the ﬁlter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Alternatively, decentered stencils  7  maintaining the same order of accuracy as the centered stencil can be used.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' However, these  need to be constructed in such a way that no frequency is ampliﬁed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' In this work, for simplic-  ity, the boundary values are obtained by using a zeroth-order extrapolation at the boundaries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='  Remark 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Filtering is most commonly used on structured grids in combination with ﬁnite-  diﬀerence methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' However, ﬁltering can also be used on unstructured grids [41].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' General considerations, algorithm and computational eﬃciency  The proposed approach exploits the spatial and temporal locality of propagating coherent  structures to derive eﬃcient reduced-order models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' As previously discussed, reduced-order  modeling of convection-dominated problems is challenging because of the Kolmogorov bar-  rier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' However, as pointed out in [23], these problems have local low-rank structure: local  trajectories have fast decaying singular values while the singular values of global trajectories  decay slowly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' The concept of local reduced bases for projection-based model reduction which  has also been exploited in other work [24, 25].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' A comparison of the trajectory of a scalar  quantity advected linearly at two diﬀerent velocities and their corresponding normalized sin-  gular values is illustrated in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' As mentioned in Section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='1, we construct the reduced  basis by using the previous w snapshots, where w is chosen suﬃciently small to ensure the  subspace has a small dimension.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='8  1  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='8  1  x  qpx, tq  50  100  150  200  10´17  10´12  10´7  10´2  index  normalized singular value  Figure 2: On the left, solutions of a scalar quantity at time t “ 0 (  ) and advected linearly at two diﬀerent  velocities µ1 (  ) and µ2 “ 100µ1 (  ) for the same period of time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' First and last snapshots of a scalar  quantity advected linearly at two diﬀerent velocities pµ2 “ 100µ1q for the same period of time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' On the right,  normalized singular values for snapshots with global (  ) and local (  ) temporal structures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' It can  be noted that singular values of problems with local temporal structure decay orders of magnitudes faster  compared to problems with global structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='  Another important AROM ingredient is local spatial coherence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' This feature leads to  the RRE being concentrated at only a few components.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' In other words, the reduced basis  is capable of providing an accurate approximation at most entries and, thus, more expen-  sive HDM evaluations are only necessary at a small fraction of the components.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Figure 3  illustrates an example of a problem where the RRE is concentrated in a few components  only.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Entries where the RRE is small but nonzero will likely grow in time and result in an  8  inaccurate solution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' The proposed approach accounts for this by performing a full HDM  solve every z time steps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='  (a)  (b)  Figure 3: Relative reconstruction error (left) and sampling points (right) of a problem with local spatial  coherence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' The entries corresponding to sampling matrices ˆSk and ˜Sk are highlighted in yellow and green,  respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' The neighboring sampling matrix ˜Sk matches a ﬁrst-order ﬁnite volume method, for example.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Algorithm  Our AROM procedure is summarized in Algorithm 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' The initial condition is set at  line 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' The loop on line 2 iterates over all time steps k “ 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' , Nt ´ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' The conditional  statement on line 3 chooses between a full (line 4) or partial HDM solution (lines 6-11).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='  Initially, a full HDM solution is calculated for the ﬁrst w time steps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Afterwards, the second  criterion ensures that a full HDM solution is going to take place every z time steps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' A partial  HDM computation takes place between lines 6 and 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' All other points are approximated  via ODEIM (line 12).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Line 13 ﬁlters the hybrid snapshot originating from a partial HDM  solution and RB reconstruction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='  The conditional statement in line 18 determines if the  reduced basis and sampling points are computed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' The ﬁrst condition assures that the total  number of snapshots is suﬃcient (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=', at least w).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' The second condition checks if a full  HDM evaluation is going to take place in the next time step.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' In this case, the reduced basis  and sampling points are not necessary and, thus, do not need to be updated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Finally, the  reduced basis, sampling points and reference state are computed between lines 18 and 26.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='  The conditional on line 15 ensures the oﬀset ψk is available the ﬁrst time the condition on  line 18 is satisﬁed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' The function Neighbors on line 24 returns the sampling matrix ˜Sk`1  generated from the neighboring points needed to calculate the HDM ﬂux function that are  not already sampled by ˆSk`1 (Figure 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' In addition, the set operations union and setdiff  applied to sampling matrices are deﬁned as the sampling matrix that results from the set  9  operation applied to the index vector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' That is, let A, B P RNˆN be sampling matrices deﬁned  as A “ rea1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' , eass and B “ reb1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' , ebts from the index vectors a P Ns, b P Nt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Then,  C “ unionpA, Bq,  D “ setdiffpA, Bq  (19)  are deﬁned as the sampling matrices corresponding to the index vectors c “ unionpa, bq and  d “ setdiffpa, bq, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='  Algorithm 1 Hybrid snapshot AROM  1: Set γ0 “ q0  Ź Initial condition  2: for k “ 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' , Nt do  3:  if k ` 1 ď w or modpk, zq “ 0 then  Ź Full HDM solve  4:  Solve γk “ Rkpγkq for γk  5:  else  Ź Hybrid snapshot  6:  ˜v “ ˜SJ  k γk´1  7:  for j “ 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' , J do  8:  Solve ˆSJ  k γk “ ˆRkp ˆSJ  k γk, ˜vq for ˆSJ  k γk  9:  yk “ pP J  k Φkq:P J  k pγk ´ ψkq  10:  ˜v “ ˜SJ  k pψk ` Φkykq  11:  end for  12:  ˘SJ  k γk “ ˘SJ  k pψk ` Φkykq  13:  γk “ SpatialFilterpγkq  14:  end if  15:  if w “ k ` 1 then  16:  ψw´1 “ 1  w  w´1  ÿ  j“0  γj  17:  end if  18:  if w ď k ` 1 and modpk ` 1, zq ‰ 0 then  19:  Φk`1 “ PODmprγk´w`1 ´ ψk, γk´w`2 ´ ψk, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' , γk´1 ´ ψk, γk ´ ψksq  20:  Pk`1 “ ODEIMnppΦk`1q  21:  Gk`1 computed according to Section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='3  22:  ˆSk`1 “ unionpGk`1, Pk`1q  23:  ˘Sk`1 “ setdiffpIN, ˆSk`1q  24:  ˜Sk`1 “ Neighborsp ˆSk`1, ˘Sk`1q  25:  ψk`1 “ 1  w  kÿ  j“k´w`1  γj  26:  end if  27: end for  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Computational eﬃciency  Our adaptive hybrid approach relies on N-dependent operations at every time step.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' A full  HDM snapshot typically requires the solution of a nonlinear system by Newton’s method,  an iterative procedure that requires the solution of a linear system of equations at every  time step.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' These large, sparse linear systems are usually solved with an iterative solver  10  such as generalized minimal residual method (GMRES), which approximates the exact solve  by a sequence of OpN 2q matrix-vector multiplications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='  A hybrid snapshot computation  (lines 5-23 of Algorithm 1) is going to require operations that at worst are log-linear.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' For  example, obtaining a reduced basis through a thin SVD and explicit ﬁltering are algorithms  that have linear complexity OpNq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' A partial HDM iteration (Opn2  sq), selecting np points  with ODEIM pOpm2n2  pqq [34], and computing the reduced coordinates yk through linear  least squares pOpnpm2qq are examples of operations independent of N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' The RRE algorithm  requires sorting the entries and, thus, is typically OpN log Nq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' While this sorting algorithm  is the dominant term in terms of complexity, in practice it is not a bottleneck.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='  Let tH P Rą0 and tR P Rą0 be the average time required to compute a snapshot relying  only on full HDM solutions and our adaptive approach, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Our AROM speedup  S is deﬁned in the following formula:  S :“ tH  tR  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='  (20)  Suppose that the average sampling matrices are suﬃciently small at all time steps such that  the time required to compute a hybrid snapshot is negligible in comparison to a full HDM  solution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' In this case it is reasonable to assume tR « tH{z, which results in the following  approximate speedup S « z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' This shows the speedup of our approach is going to depend  mainly on how often the full HDM must be solved.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='  Remark 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' The complexity of obtaining a reduced basis through a thin SVD is OpNw2q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='  Therefore the number of snapshots used in the reconstruction w is important to produce a  small reduced basis but also a cost eﬃcient construction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' If necessary, reduced basis con-  struction complexity can be reduced to OpNw  1  2q by using fast SVD updates [31].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='  Remark 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' In this work, we introduce a HDM that relies on BDF schemes for time-  integration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' However, if an explicit scheme (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=', Adams–Bashforth methods) was adopted  instead, the computational complexity would be linear in N as opposed to quadratic with an  implicit scheme.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' For this class of ODE solvers, obtaining a cost eﬃcient AROM can be  considerably more challenging and problem dependent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Numerical experiments  In this section, we apply our adaptive method to solve two inviscid compressible ﬂow  problems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='  We start by introducing the conservation laws, error functions and sampling  average (Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' The ﬁrst test case consists of a canonical one-dimensional problem  with known solution and is used to conduct a parametric study (Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='2) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' For example,  the impact of diﬀerent ﬁlters and full HDM solve frequency are evaluated for this problem  and serve as guideline for the next test case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' The second problem is two-dimensional and  considerably more challenging (Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' The Euler equations of gas dynamics  We consider compressible inviscid ﬂow through a domain Ω Ă Rd with governing equa-  tions given by  Bρ  Bt ` B  Bxj  pρujq “ 0  (21a)  11  Bρui  Bt  ` B  Bxj  pρuiuj ` Pδijq “ 0  (21b)  BpρEq  Bt  ` B  Bxj  ppρE ` Pqujq “ 0 ,  (21c)  for i “ 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' , d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' The density of the ﬂuid ρp¨, tq : Ω Ñ Rą0, the ﬂuid velocity up¨, tq Ñ Rd,  and the total energy of the ﬂuid ρEp¨, tq Ñ Rą0 are implicitly deﬁned as the solution of (21).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='  We assume the ﬂuid follows the ideal gas law  P “ pγ ´ 1q  ´  ρE ´ ρuiui  2  ¯  ,  (22)  where Pp¨, tq Ñ Rą0 is the pressure of the ﬂuid and γ P Rą0 is the ratio of speciﬁc heats.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='  We approximate the Euler equations using a ﬁnite volume method on a cartesian mesh.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='  We employ a second-order monotonic upstream schemes for conservation laws (MUSCL)  [42] approach with Roe ﬂux [43] and minmod limiter to spatially semi-discretize Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' (1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='  Afterwords, we integrate the resulting system of ODEs using a second-order BDF scheme  deﬁned by the coeﬃcients a0 “ 1{3, a1 “ ´4{3, a2 “ 1 and β “ 2{3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='  In the following numerical experiments, the AROMs accuracy will be measured using the  relative L2pΩq error, deﬁned as  ek :“  dş  Ω }γkpxq ´ qkpxq}2  2 dV  ş  Ω }qkpxq}2  2 dV  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='  (23)  To access parametric performance, we also use the temporal mean of the relative error,  deﬁned as  ¯e :“ 1  Nt  Nt  ÿ  k“1  ek .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='  (24)  Similarly, we deﬁne the average sampling as  ¯s :“ 1  Nt  Nt  ÿ  k“1  nγk ,  (25)  where nγk is the number of entry points of snapshot γk with its value directly computed  by a HDM solve.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' For a snapshot γk originating from partial and full HDM solves we have  nγk “ ns and nγk “ N, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' We deﬁne the average sampling of a hybrid snapshot as  ¯s˚ :“ 1  |I|  ÿ  kPI  nγk ,  (26)  where I Ă t1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' , Ntu is the set of indices with a partial HDM solve.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Lastly, we deﬁne the  average ODEIM sampling as  ¯p :“ 1  |I|  ÿ  kPI  pnpqk .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='  (27)  12  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Sod’s shock tube  In this section we apply study our AROM method using the most canonical Riemann  problem for the Euler equations, Sod’s shock tube.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' We consider the one-dimensional (d “ 1)  Euler equations in the domain Ω “ p0, 1q over the time interval T “ p0, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='2q with ratio of  speciﬁc heats γ “ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='4 and initial condition, in terms of primitive variables, as  ρpx, 0q “  #  1  x P r0, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='5q  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='125  x P r0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='5, 1s ,  upx, 0q “ 0,  Ppx, 0q “  #  1  x P r0, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='5q  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='1  x P r0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='5, 1s .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='  (28)  We use suitable boundary conditions from the initial condition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' This is appropriate because  the waves do not reach the boundary over the time interval of interest.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='  We partition the spatial domain into N “ 399 cells of uniform width.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' We also equally  partition the time domain into Nt “ 798 time steps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' We chose the number of snapshots  used in the reduced basis reconstruction to be equal to the number of POD modes used  in the reconstruction, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=', w “ m “ 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Moreover, all hybrid solutions rely on the same  reconstruction error threshold (δ “ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='90).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' These parameter values are used at all time steps  unless otherwise stated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='  The beneﬁts of hybrid solution ﬁltering is demonstrated in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' For z “ 1, only  full HDM solves are performed (γk “ qk).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' For all z ą 1, the second-order ﬁltering scheme  is too dissipative and, thus, leads to bigger sampling matrices and higher errors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' In fact,  the over damping of the hybrid solution causes the RRE to be more equality distributed  among the entries which in turn leads to bigger sampling matrices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' For 2 ď z ď 4, all  other methods present good results with the unﬁltered AROM yielding the best results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' In  this range, all implemented ﬁlters add more dissipation than necessary for almost identical  sampling size.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' In fact, ﬁltering is not needed if the spurious oscillation inhibiting HDM ﬂux  limiting operations are enough to guarantee wiggle-free solutions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Moreover, previous work  with similar unﬁltered AROMs [23, 30] demonstrate good performance at this frequency  range.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' For z ą 4, the higher order ﬁltering schemes outperform the unﬁltered ROM with  the sixth-order ﬁlter being more accurate in most cases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Also, despite being less dissipative,  the sixth-order ﬁlter leads to bigger sampling matrices in comparison to the models relying  on fourth-order ﬁltering.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' A careful analysis of the results show that the fourth-order ﬁlter  introduces more pronounced oscillations near the sharp gradients, which in turn leads to  more unequal RRE distribution and smaller sampling matrices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' This and Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' 5 demonstrate  that high frequency structures develop and, if not dissipated, build up over time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Also, the  error grows considerably slower for ﬁltered solutions as a function of z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' For 6 ď z ď 20,  the unﬁltered ROM has smaller sampling matrices resulting from a more unequal RRE  distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='  We further analyze the AROM with parameters z “ 10 and fourth-order ﬁlter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' In this  case, 2 ď J ď 5 with the average number of subiterations being ¯J “ 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Figure 6 compares  solutions between this AROM and a simulation relying only on full HDM solves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' The AROM  recovers the main features of the ﬂow with small discrepancies in the range of inﬂuence of  point x “ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='  Some blurring at the wavefronts can be observed and is expected given  that Shapiro ﬁlters are not suited for problems with shocks or sharp gradients.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Moreover,  despite the ﬁltering, some high frequency noise develops.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='  The initial zero relative error  (k ď w) is followed by an error overshoot (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' 7) which is probably caused by the initial  13  5  10  15  20  0  20  40  60  80  100  z  ¯sp%q  5  10  15  20  0  5  10  15  20  25  z  ¯s˚p%q  5  10  15  20  0  2  4  6  z  ¯ep%q  Figure 4: Time averages of relative sampling (top) and relative error (bottom) as a function of full HDM  frequency parameter z, for unﬁltered (  ), second-order (  ), fourth-order (  ), and sixth-order (  )  ﬁltered solutions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' A full HDM solve is equivalent to sampling all vector entries (¯s “ 100% and ¯s˚ “ 0%).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='  ﬂow triple point.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' The temporal mean of the relative error is ¯e “ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='61%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' 7 also shows  the relative cardinality of the sampling sets tˆspkq  1 , .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' , ˆspkq  ns u and tppkq  1 , .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' , ppkq  np u with full HDM  sampling (nγk “ N) omitted for easier understanding.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='  The time average samplings are  ¯p “ 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='12%, ¯s “ 21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='96% and ¯s˚ “ 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='96%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Additionally, we can observe that as time goes  on sampling matrices ˆSk get bigger.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' This can be at least partially attributed to the growth  of the expansion fan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' 8 shows the points selected by sampling matrix ˆSk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' The ﬁrst  w “ 4 snapshots are obtained using full HDM solves and, thus, are fully highlighted in  yellow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' From this ﬁgure, it can be noticed that the points are mainly concentrated on the  propagating expansion, contact and shock waves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Sampling also takes place outside the range  of inﬂuence of point x “ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' We can attribute this to the development of high frequency  noise than can be easily observed on Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' 5 for z “ 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Moreover, it can be noticed that the  left boundary is consistently sampled.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' This can be attributed to the RRE algorithm being  overly conservative and, thus, selecting entries with εpkq  j  “ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' If two elements have equal  14  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
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+page_content='2  x  ρpx, tq  z “ 5  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
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+page_content='2  x  ρpx, tq  z “ 10  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
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+page_content='8  1  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
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+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
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+page_content='2  x  ρpx, tq  z “ 15  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
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+page_content='8  1  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='8  1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='2  x  ρpx, tq  z “ 20  Figure 5: The exact (  ) solution (density) at k “ Nt and the corresponding HDM (  ) and AROM  (  ) approximations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='  value, the algorithm breaks the tie by selecting the element with the smallest index.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' For this  problem, the elements are indexed from left to right starting from the boundary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='  Figure 9 shows time average error and sampling responses to diﬀerent values of window  size w and number of POD modes m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' For w “ 4, the error is the smallest for m “ 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' An  additional mode probably degrades the solution by adding nonphysical structures that are  not dissipated by the ﬁlter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' A similar trend is observed for all other cases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' A bigger basis  generally leads to a more accurate reconstruction but could potentially add noise if too many  modes are added.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Moreover, larger windows do not signiﬁcantly improve accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' In fact,  these ROMs are considerably less accurate if the number of modes used in the reconstruction  is too small.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' From the sampling side, we can generally observe that larger windows and bigger  basis lead to bigger sampling matrices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' This is expected as bigger basis results in additional  15  (a)  (b)  (c)  (d)  (e)  (f)  Figure 6: Space-time snapshots of density (top), momentum (center) and energy (bottom) for a simulation  only relying on full HDM solutions (left) and our AROM (right).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='  ODEIM points and would probably be less of an issue for multidimensional problems because  they usually lead to sparser sampling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' It is also worth pointing out that for all values of w  considered, picking m “ w leads to a relevant increase in error and decrease in sampling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' This  16  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='15  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='2  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='8  1  time  ep%q  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='15  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='2  0  10  20  30  40  50  60  time  samplingp%q  Figure 7: Relative error (top), and sampling (bottom) of ˆSk (  ) and Pk (  ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='  A full HDM would  represent a sampling of 100% and, thus, is omitted in the sampling ﬁgure for clarity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='  shows that the last mode is an important source of noise that is not completely dissipated  by the ﬁlter which in turn leads to a more unequal RRE distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' As discuss in Section  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='2, the cost of performing POD is also a quadratic function of window width OpNw2q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='  Therefore, a narrower window is preferred if the the beneﬁts of a larger window are little to  none.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='  For three diﬀerent values of z and fourth-order ﬁltering, the implication of diﬀerent values  of RRE tolerance δ can be observed in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' For z “ 5, the error variation is negligible  17  Figure 8: Sampling points selected by matrix ˆS (in yellow).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='  for the range of RRE tolerances considered.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' In regards to the time average sampling, it  remains almost constant for most values of δ but abruptly increases for tighter tolerances.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='  However, the non-negligible sampling increase did not lead the error to visually decrease.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' In  this case, a smaller sampling matrix is enough to generate accurate AROMs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' For z “ 10 and  z “ 15, accuracy can be considerably improved by the use of tighter RRE tolerances.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' This is  particularly substantial for z “ 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' On the other hand, accuracy comes at a price as bigger  sampling matrices become necessary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Moreover, increasing the RRE tolerance did not lead  to the time average error to monotonically decrease.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' One explanation is that adding just  a few sampling points could add noise to solution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' In general, having more solution points  originating from a partial HDM solution leads to a more accurate AROM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' However, this  could introduce undesirable higher frequency structures, especially if the points are sparsely  distributed, as discussed in Section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='  An assessment of partial HDM subiterations is shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Results show a fast con-  vergence rate for reduced coordinates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' However, this does not lead to a monotonic decrease  of the temporal mean of the relative error.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' The error increasing could be a symptom of an  ill-conditioned linear least squares problem and, thus, getting the higher frequency temporal  modes to converge adds noise to the solution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' If this is the case, some form of solution  regularization would be beneﬁcial.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Also, for this problem conﬁguration, subiterations do not  lead to a signiﬁcant increase in accuracy but, given the reduced cost of partial HDMs, are  still worth consideration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='  18  2  4  6  8  10  15  30  45  m  ¯sp%q  2  4  6  8  10  5  20  35  m  ¯s˚p%q  2  4  6  8  10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='7  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='9  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='1  m  ¯ep%q  Figure 9: Time averages of relative sampling (top) and relative error (bottom) as a function of reduced-order  dimension m for windows of size w “ 4 (  ), w “ 6 (  ), w “ 8 (  ) and w “ 10 (  ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' A full HDM  solve is equivalent to sampling all vector entries (¯s “ 100% and ¯s˚ “ 0%).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Model implosion  In this problem, we consider the two-dimensional (d “ 2) Euler equations in the domain  Ω Ă p0, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='3q2 over the time interval T “ p0, 1q with ratio of speciﬁc heats γ “ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='4 and initial  condition (in terms of primitive variables) as  ρpx, 0q “  #  ρin  x P D  ρout  x R D ,  upx, 0q “ p0, 0q,  Ppx, 0q “  #  Pin  x P D  Pout  x R D .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='  (29)  where ρin “ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='125 and Pin “ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='14 are the pressure and density inside the region D “ tx P  Ω | x1 ` x2 ď 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='15u Ă Ω and ρout “ 1 and Pout “ 1 are the pressure and density outside  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' All four boundaries are taken to be walls, which causes the waves to reﬂect back into  the domain when they reach a boundary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' This is a model of an implosion that was adapted  from [44].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='  We solve this problem using a 100 ˆ 100 uniform cartesian grid.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' We partition the time  domain into Nt “ 3,300 time steps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Hybrid solutions rely on a forth-order explicit Shapiro  19  1 10 20 30 40 50 60 70 80 90 99  10  15  20  25  30  35  40  45  δp%q  ¯sp%q  1 10 20 30 40 50 60 70 80 90 99  0  10  20  30  40  δp%q  ¯s˚p%q  1 10 20 30 40 50 60 70 80 90 99  0  2  4  6  δp%q  ¯ep%q  Figure 10: Time averages of relative sampling (top) and relative error (bottom) as a function of relative  reconstruction error tolerance (δ) for full HDM frequency parameter z “ 5 (  ), z “ 10 (  ), and z “ 15  (  ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' A full HDM solve is equivalent to sampling all vector entries (¯s “ 100% and ¯s˚ “ 0%).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='  ﬁlter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' The full HDM frequency parameter is z “ 5 and the reconstruction error threshold  is set at δ “ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Again, we chose the number of snapshots used in the reduced basis  reconstruction to be equal to the number of POD modes used in the reconstruction, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=',  w “ m “ 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' For these parameters, 3 ď J ď 6 with the average number of subiterations  being ¯J “ 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='  Figure 12 shows snapshots of a simulation relying only on full HDM solves, our AROM,  and the cells selected by sampling matrix ˆSk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' For all four time instances, the AROM is  capable of solving the main features of the problem with only some minor discrepancies  mostly concentrated next to sharp gradient regions and boundaries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' The reduced accuracy  at regions containing sharp gradients was also observed in the previous problem and can be  blamed again on the explicit ﬁlter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' In regards to the bigger errors located close to boundaries,  20  2  4  6  8  10´17  10´12  10´7  10´2  j  }ypj`1q  k  ´ ypjq  k }2  2  4  6  8  10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='62  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='66  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='7  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='74  iteration  ¯ep%q  Figure 11: Increment size (left) and temporal mean of the relative error (right) as a function of iteration j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='  Increment size convergence is veriﬁed at the last snapshot pk “ Ntq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' The mean relative error is calculated  at ﬁxed numbers of iterations j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='  undersampling of the boundary cells could be one explanation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' In fact, it can be noticed that  very few boundary cells are sampled.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' This is not an issue for the previous one-dimensional  test case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='  For the shock tube problem, the waves do not reach the boundary over the  time interval of interest and, thus, do not need to be updated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Moreover, one-dimensional  problems have only two boundary cells for all meshes with more than one cell and, thus, can  be cheaply sampled if necessary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='  Figure 13 illustrates the temporal evolution of the relative error.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' In this case, the temporal  average of the relative error is ¯e “ 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='28%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' This ﬁgure also shows the relative cardinality  of sets of points sampled by matrices ˆSk and Pk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Again, full HDM sampling pnγ “ Nq  is omitted for clarity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' The time average sampling values are ¯p “ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='26%, ¯s “ 22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='89% and  ¯s˚ “ 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='89%, and the hybrid snapshot sampling never exceeds 20%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' From these sampling  sizes and the complexity discussion in Section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='2, we can conclude that the average cost of  a hybrid snapshot is negligible compared to a full HDM solve.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Moreover, results show that  the size of the sampling matrix ˆSk changes considerably depending on the ﬂow structure at  a particular time instance and, thus, suggests that dynamical sampling is beneﬁcial.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='  21  (a)  (b)  (c)  (d)  (e)  (f)  (g)  (h)  (i)  (j)  (k)  (l)  Figure 12: Density snapshots a simulation only relying on full HDM solutions (top) and our AROM (center),  and the sampling points corresponding to matrix ˆS (bottom) at time instances t “ T{4, t “ T{2, t “ 3T{4  and t “ T (left-to-right).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
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+page_content='9  1  0  5  10  15  20  time  samplingp%q  Figure 13: Relative error (top), and sampling (bottom) of ˆSk (  ) and Pk (  ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
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+page_content=' Conclusions and future directions  In this work, an adaptive reduced-order model is applied to convection-dominated prob-  lems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' This approach relies on local HDM solves to obtain an accurate representation of the  main ﬂow features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' The remainder of the ﬂow is represented using a subspace approxima-  tion trained using previous snapshots.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' The performance of the our approach is validated  on two compressible ﬂow problems with moving sharp gradient features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' The ﬁrst is the  one-dimensional canonical Sod’s shock tube problem and it is used to conduct a parametric  study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' The second is a considerably more challenging two-dimensional problem simulating  an implosion inside a box.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='  Results show that the proposed method is capable of accelerating convection-dominated  unsteady CFD problems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' If the sampling matrices remain suﬃciently small throughout the  simulation, a brief complexity analysis establishes that the speedup depends mainly on the  full HDM solution frequency parameter z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Our ﬁrst test case demonstrates that ﬁltering  allows for higher z and, thus, is a crucial ingredient for cheaper and accurate AROMs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='  One contribution of this work and an important component of the proposed method is the  dynamic sampling matrix ˆSk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Our time adaptive approach selects the smallest sampling set  satisfying a predeﬁned error tolerance at each time instance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' This allows the sampling matrix  to shrink or expand in an attempt to avoid undersampling and oversampling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Furthermore,  the shock tube problem shows that narrower windows and smaller bases are suﬃcient to  generate cheap and accurate AROMs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Another important contribution is the partial HDM  sampling used to construct the hybrid snapshots.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' It requires an approximation to the state  on cells neighboring sample points, which can be made more accurate through subiterations  and generally results in some accuracy gain without a signiﬁcant cost increase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='  The method could beneﬁt from further research in multiple ways.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' First, our current  dynamic sampling procedure selects entries based only on their relative contribution to the  total reconstruction error.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' For example, if the error tolerance is chosen to be too strict, this  can lead to bigger sampling matrices than necessary if the residual is uniformly distributed  across the mesh.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='  Therefore, a better sampling algorithm could improve robustness and  decrease cost.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Another research direction is boundary sampling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' As previously discussed,  accuracy at the boundaries could possibly be improved with little eﬀort by sampling interior  and boundary cells separately.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Finally, our approach relies on linear order reduction for most  hybrid snapshots entries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' We avoid the Kolmogorov n-width problem by relying on the local  low-rank structure of convection-dominated problems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Unfortunately, ROMs built on POD  can struggle in predictive settings for even very simple problems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Nonlinear model reduction  techniques could potentially overcome this barrier and produce AROMs less dependent on  full HDM solves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='  Acknowledgments  This material is based upon work supported by the Air Force Oﬃce of Scientiﬁc Research  (AFOSR) under award numbers FA9550-20-1-0236 and FA9550-22-1-0004.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' The content of  this publication does not necessarily reﬂect the position or policy of any of these supporters,  and no oﬃcial endorsement should be inferred.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='  24  References  [1] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Ricciardi, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Wolf, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Moﬃtt, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Kreitzman, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Bent, Numerical noise  prediction and source identiﬁcation of a realistic landing gear, Journal of Sound and  Vibration 496 (2021) 115933.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' doi:https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='jsv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='115933.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='  URL https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='sciencedirect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='com/science/article/pii/S0022460X21000055  [2] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Rowley, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Colonius, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Murray, Model reduction for compressible ﬂows using  POD and Galerkin projection, Physica D: Nonlinear Phenomena 189 (1–2) (2004) 115  – 129.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='  [3] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Carlberg, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Farhat, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Amsallem, The GNAT method for nonlinear model reduction:  Eﬀective implementation and application to computational ﬂuid dynamics and tubulent  ﬂows, Journal of Computational Physics 243 (2013) 623–647.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='jcp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='  2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='02.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='028.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='  [4] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Carlberg, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Barone, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Antil, Galerkin v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' least-squares Petrov-Galerkin projection  in nonlinear model reduction, Journal of Computational Physics 330 (2017) 693–734.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='  doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='jcp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='033.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='  [5] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Brunton, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Proctor, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Kutz, Discovering governing equations from data  by sparse identiﬁcation of nonlinear dynamical systems, Proceedings of the National  Academy of Sciences 113 (15) (2016) 3932–3937.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' arXiv:https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='pnas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='org/doi/  pdf/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='1073/pnas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='1517384113, doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='1073/pnas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='1517384113.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='  URL https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='pnas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='org/doi/abs/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='1073/pnas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='1517384113  [6] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Peherstorfer, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Willcox, Data-driven operator inference for nonintrusive projection-  based model reduction, Computer Methods in Applied Mechanics and Engineering 306  (2016) 196–215.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' doi:https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='cma.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='03.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='025.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='  URL https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='sciencedirect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='com/science/article/pii/S0045782516301104  [7] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Lui, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Wolf, Construction of reduced-order models for ﬂuid ﬂows using  deep feedforward neural networks, Journal of Fluid Mechanics 872 (2019) 963–994.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='  doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='1017/jfm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='358.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='  [8] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Cazemier, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
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+page_content=' Verstappen, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
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+page_content=' Veldman, Proper orthogonal decom-  position and low-dimensional models for driven cavity ﬂows, Physics of Fluids 10 (7)  (1998) 1685–1699.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
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+page_content='  [9] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Noack, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Papas, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Monkewitz, The need for a pressure-term representation  in empirical Galerkin models of incompressible shear ﬂows, Journal of Fluid Mechanics  523 (2005) 339–365.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
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+page_content='  [10] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Bergmann, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
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+page_content=' Iollo, Enablers for robust pod models, Journal of  Computational Physics 228 (2) (2009) 516–538.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
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+page_content='com/science/article/pii/S002199910800510X  25  [11] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Bergmann, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
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+page_content=' Bruneau, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Iollo, Enablers for robust POD models, Journal of  Computational Physics 228 (2009) 516–538.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
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+page_content=' San, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Iliescu, Proper orthogonal decomposition closure models for ﬂuid ﬂows:  Burgers equation, International Journal of Numerical Analysis and Modeling, Series B  5 (2014) 217–237.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='  [13] Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Wang, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Akhtar, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Borggaard, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Iliescu, Proper orthogonal decomposition closure  models for turbulent ﬂows: A numerical comparison, Comput.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Methods Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Mech.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='  Eng.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' 237 (2012) 10–26.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='  [14] I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Kalashnikova, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' van Bloemen Waanders, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Arunajatesan, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Barone, Stabiliza-  tion of projection-based reduced order models for linear time-invariant systems via  optimization-based eigenvalue reassignment, Computer Methods in Applied Mechanics  and Engineering 272 (2014) 251–270.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' doi:https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='cma.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
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+page_content='011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='  [15] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Grimberg, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Farhat, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Youkilis, On the stability of projection-based model order  reduction for convection-dominated laminar and turbulent ﬂows, Journal of Computa-  tional Physics 419 (2020) 1–28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
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+page_content='  [16] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Zucatti, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Wolf, Data-driven closure of projection-based reduced order models for  unsteady compressible ﬂows, Computer Methods in Applied Mechanics and Engineering  386 (2021) 114120.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' doi:https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
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+page_content='  [17] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Ohlberger, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Rave, Reduced Basis Methods:  Success, Limitations and Future  Challenges, Proceedings of the Conference Algoritmy (2016) 1–12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
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+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Carlberg, Model reduction of dynamical systems on nonlinear manifolds  using deep convolutional autoencoders, Journal of Computational Physics 404 (2020)  108973.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
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+page_content=' Farhat, Quadratic approximation manifold for mitigating the Kolmogorov  barrier in nonlinear projection-based model order reduction, Journal of Computational  Physics 464 (2022) 111348.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
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+page_content=' Geelen, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Wright, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Willcox, Operator inference for non-intrusive model reduction  with quadratic manifolds (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
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+page_content='02304  [21] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Taddei, A registration method for model order reduction: Data compression and  geometry reduction, SIAM Journal on Scientiﬁc Computing 42 (2) (2020) A997–A1027.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
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+page_content='1137/19M1271270  26  [22] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Mirhoseini, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Zahr, Model reduction of convection-dominated partial dif-  ferential equations via optimization-based implicit feature tracking (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='  doi:  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
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+page_content=' Peherstorfer, Model Reduction for Transport-Dominated Problems via Online Adap-  tive Bases and Adaptive Sampling, SIAM Journal on Scientiﬁc Computing 42 (5) (2020)  A2803–A2836.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
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+page_content='  [24] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Amsallem, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Zahr, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Farhat, Nonlinear model order reduction based on lo-  cal reduced-order bases, International Journal for Numerical Methods in Engineer-  ing 92 (10) (2012) 891–916.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' arXiv:https://onlinelibrary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
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+page_content='4371  [25] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Amsallem, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Zahr, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Washabaugh, Fast local reduced basis updates for the eﬃ-  cient reduction of nonlinear systems with hyper-reduction, Advances in Computational  Mathematics 41 (5) (2015) 1187–1230.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
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+page_content='1007/s10444-015-9409-0  [26] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Bai, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Wang, DEIM reduced order model constructed by hybrid snapshot simulation,  SN Applied Sciences 2 (12) (2020) 2165.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='1007/s42452-020-03958-7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='  [27] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Bai, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Wang, A reduced order modeling method based on GNAT-embedded hybrid  snapshot simulation, Mathematics and Computers in Simulation 199 (2022) 100–132.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='  doi:https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
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+page_content='matcom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='03.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='006.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='  [28] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Feng, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Fu, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Wang, A FOM/ROM Hybrid Approach for Accelerating Numer-  ical Simulations, Journal of Scientiﬁc Computing 89 (3) (2021) 61.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='  doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='1007/  s10915-021-01668-9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='  [29] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Peherstorfer, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Willcox, Online Adaptive Model Reduction for Nonlinear Systems  via Low-Rank Updates, SIAM Journal on Scientiﬁc Computing 37 (4) (2015) A2123–  A2150.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='1137/140989169.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='  [30] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Uy, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Wentland, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Huang, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Peherstorfer, Reduced models with nonlinear  approximations of latent dynamics for model premixed ﬂame problems (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' doi:  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='48550/ARXIV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
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+page_content='06957.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='  URL https://arxiv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='org/abs/2209.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='06957  [31] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Brand, Fast low-rank modiﬁcations of the thin singular value decomposition, Linear  Algebra and its Applications 415 (1) (2006) 20–30, special Issue on Large Scale Linear  and Nonlinear Eigenvalue Problems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' doi:https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
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+page_content='2005.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='07.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='  021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='  URL https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
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+page_content='com/science/article/pii/S0024379505003812  [32] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Everson, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Sirovich, Karhunun-Lo`eve procedure for gappy data, Optical Society of  America 12 (1995) 1657–1664.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
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+page_content='12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='001657.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='  27  [33] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Willcox, Unsteady ﬂow sensing and estimation via the gappy proper orthogonal  decomposition, Computers & Fluids 35 (2006) 208–226.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='compfluid.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='  2004.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='006.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='  [34] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Peherstorfer, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Drmaˇc, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Gugercin, Stability of Discrete Empirical Interpolation  and Gappy Proper Orthogonal Decomposition with Randomized and Deterministic  Sampling Points, SIAM Journal on Scientiﬁc Computing 42 (5) (2020) A2837–A2864.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='  doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='1137/19M1307391.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='  [35] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Barrault, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Maday, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Nguyen, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Patera, An ‘empirical interpolation’  method:  application to eﬃcient reduced-basis discretization of partial diﬀerential  equations, Comptes Rendus Mathematique 339 (9) (2004) 667 – 672.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='  doi:https:  //doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='crma.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='2004.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='08.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='006.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='  URL http://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='sciencedirect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='com/science/article/pii/S1631073X04004248  [36] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Chaturantabut, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Sorensen, Nonlinear model reduction via discrete empirical  interpolation, SIAM Journal on Scientiﬁc Computing 32 (2010) 2737–3764.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='  1137/090766498.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='  [37] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Lele, Compact ﬁnite diﬀerence schemes with spectral-like resolution, Journal  of Computational Physics 103 (1) (1992) 16–42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' doi:http://dx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
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+page_content='1016/  0021-9991(92)90324-R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='  URL http://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='sciencedirect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='com/science/article/pii/002199919290324R  [38] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Visbal, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Gaitonde, On the use of higher-order ﬁnite-diﬀerence schemes on  curvilinear and deforming meshes, Journal of Computational Physics 181 (1) (2002)  155–185.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' doi:https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='1006/jcph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='2002.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='7117.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='  URL https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='sciencedirect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='com/science/article/pii/S0021999102971172  [39] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Falissard, Genuinely multi-dimensional explicit and implicit generalized Shapiro ﬁl-  ters for weather forecasting, computational ﬂuid dynamics and aeroacoustics, Journal  of Computational Physics 253 (2013) 344–367.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='jcp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='07.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='001.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='  [40] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Shapiro, Smoothing, ﬁltering, and boundary eﬀects, Reviews of Geophysics 8 (2)  (1970) 359–387.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='  arXiv:https://agupubs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='onlinelibrary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='wiley.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='com/doi/pdf/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='  1029/RG008i002p00359, doi:https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
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+page_content='  URL  https://agupubs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='onlinelibrary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='wiley.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='com/doi/abs/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='1029/  RG008i002p00359  [41] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Wolfram, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Fringer, Mitigating horizontal divergence “checker-board” oscil-  lations on unstructured triangular c-grids for nonlinear hydrostatic and nonhydrostatic  ﬂows, Ocean Modelling 69 (2013) 64–78.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' doi:https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='ocemod.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='  2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='05.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='  URL https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='sciencedirect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='com/science/article/pii/S1463500313000929  [42] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' van Leer, Towards the ultimate conservative diﬀerence scheme.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' a second-order  sequel to godunov’s method, Journal of Computational Physics 32 (1) (1979) 101–136.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='  28  doi:https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='1016/0021-9991(79)90145-1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='  URL https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='sciencedirect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='com/science/article/pii/0021999179901451  [43] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Roe, Approximate riemann solvers, parameter vectors, and diﬀerence schemes, Jour-  nal of Computational Physics 43 (2) (1981) 357–372.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' doi:https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='1016/  0021-9991(81)90128-5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='  URL https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='sciencedirect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content='com/science/article/pii/0021999181901285  [44] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Ghosh, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
+page_content=' Baeder, Compact Reconstruction Schemes with Weighted ENO Lim-  iting for Hyperbolic Conservation Laws, SIAM Journal on Scientiﬁc Computing 34 (3)  (2012) A1678–A1706.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAzT4oBgHgl3EQfwP4g/content/2301.01718v1.pdf'}
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+Analytic RFR Option Pricing with Smile and Skew
+Colin Turfus* and Aurelio Romero-Bermudez*,†
+*Deutsche Bank
+†ABN Amro
+Initial Version: December 22, 2022
+Current Version: January 4, 2023
+Abstract
+We extend the short rate model of Turfus and Romero-Bermúdez [2021] to facilitate accurate arbitrage-free
+analytic pricing of SOFR, SONIA or ESTR caplets, i.e. options on backward-looking compounded rates payments,
+in a manner consistent with the smile and skew levels observed in the market. These caplet pricing formulae and
+corresponding LIBOR or term-rate caplet results are translated into effective variance (implied vol) formulae, which
+are seen to be of a particularly simple form. They show that the model is essentially equivalent to imposing on a Hull-
+White model an effective variance which is a quadratic function of the moneyness parameter (rather than a constant)
+for any given maturity. Results are also illustrated graphically.
+1
+Introduction
+The short rate model of Turfus and Romero-Bermúdez [2021] allows analytic pricing of caplets based on term rates
+such as LIBOR with smile and skew. We extend this model here to support analytic pricing of options on compounding
+risk-free rates (RFR) such as SOFR, SONIA or ESTR, in a manner consistent with the smile and skew levels observed
+in the market. Our approach is based on the observation that for small perturbations from equilibrium under this model
+the short rate is essentially a linear function of a (mean-reverting) Gaussian variable y. This makes the situation similar
+to that captured by the model of Hull and White [1990]. An exact analytic pricing kernel for this model was derived
+by Van Steenkiste and Foresi [1999], Turfus [2019] and the extension of this kernel to address compounding rates by
+Turfus [2021a, 2022].
+For a review of related work on options on compounded rates, the reader is referred to Turfus [2022], which
+follows the approach of Van Steenkiste and Foresi [1999] in introducing the integrated short rate as an additional state
+variable. Option prices are in this way derived analogous to the formulae of Henrard [2004], including taking account
+of delayed payment of the option premium. This work was extended to incorporate counterparty credit risk by Turfus
+[2021b] through a highly accurate asymptotic approximation.
+In relation to analytic option pricing with smile and skew, the reader is referred to Turfus and Romero-Bermúdez
+[2021, 2022]. Their approach, which we extend below, is based on modelling the short rate as a sinh function of a
+Gaussian Ornstein-Uhlenbeck process, which they argue is equivalent to assuming a quadratic dependence of the local
+volatility on the short rate. They make the point that little work has been done in this space, albeit that the Beta Blend
+model proposed by Horvath et al. [2017] interpolating between the model of Hull and White [1990] and that of Black
+and Karasinski [1991] can be viewed as allowing a term structure of skew to be speciﬁed. Also analytic LIBOR option
+and swaption prices incorporating smile and skew are available under the SABR model, as discussed by Antonov et al.
+[2019]. But this approach allows only one rate to be modelled at a time and does not constitute a short rate model
+capable of capturing multiple rates within a uniﬁed framework.
+We single out for special mention here the work of Antonov and Spector [2011]. Like us they started out by
+considering Gaussian variables driven by Ornstein-Uhlenbeck dynamics and took the short rate to be a function
+1
+arXiv:2301.01260v1  [q-fin.MF]  3 Jan 2023
+
+thereof. One of the two cases they considered1 was a quotient of afﬁne functions of exponentials of the Gaussian,
+under which assumption the short rate was constrained to lie between an upper and a lower limit. They did not like
+us attempt to capture volatility smile and skew explicitly. Nor did they consider a more general formulation involving
+an afﬁne function of two exponentials with different exponents as we do here. Also, the (ﬁrst-order) perturbation
+expansion they used to obtain analytic option prices was based on a small lognormal-volatility assumption, which
+limits the accuracy which can be obtained, particularly under low rates where lognormal volatilities can be quite high
+(in excess of 50%). We expect our expansion based on the smallness of the rates themselves to be more accurate,
+especially in circumstances of low rates.
+We look to obtain analytic expressions for prices of SOFR options which take account of smile and skew by
+a method similar to that employed by Turfus and Romero-Bermúdez [2021] to price LIBOR caplets based on an
+extension of the Bachelier pricing kernel (for a Gaussian underlying). We do this by extending instead the Hull-White
+compounded rates kernel of Turfus [2022]. The challenge is that, as well as observing that the representations of
+the interest rate are similar (linear functions of a Gaussian variable) with and without smile or skew, we need to ﬁnd
+a means of taking advantage of that observation systematically to obtain an explicit mathematical representation of
+the perturbation which must be applied to the known (Hull-White) analytic kernel. We do this using the operator
+expansion method expounded by Turfus [2021a].
+We start off in §2 by setting out the pricing equation for our model. The associated pricing kernel is presented in
+§3 as a perturbation expansion based on a low-rates assumption, with a summary proof provided in Appendix A. The
+calibration of the model to the term structure of forward rates and volatility (with skew and smile) is considered in §4,
+where bond price formulae are also set out. The further application of the kernel to the pricing of forward rates and
+SOFR/ESTR caplets is considered in §5, with a proof of the latter in Appendix B. A LIBOR caplet pricing formula
+is also deduced providing more accuracy than that of Turfus and Romero-Bermúdez [2021]. The caplet prices are
+also give a convenient expression as implied volatilities, which simpliﬁes calculation and helps ensure consistency of
+behaviour far from the money. Numerical calculations of caplet prices and implied volatility surfaces based on the
+formulae deduced are illustrated in §6. Conclusions are set out in §7.
+2
+Model Description
+We consider the short rate model of Turfus and Romero-Bermúdez [2021] which incorporates smile and skew into the
+Hull-White model through a variable transformation. We shall ﬁnd it convenient to work with the reduced variable yt
+deﬁned through the following Ornstein-Uhlenbeck process:
+dyt = −α(t)ytdt + σ(t) dWt,
+(2.1)
+with Wt a Wiener process for t ≥ 0. This auxiliary variable is related to the short rate by rt = r(yt, t) where
+r(y, t) := r(t) + R∗(t) + sinh γ(t)(y + y∗(t))
+γ(t)
+.
+(2.2)
+Here r, y∗ : R+ → R are the instantaneous forward rate and a skewness function, respectively, and σ, α, γ, R∗ :
+R+ → R+ are functions representing volatility, mean reversion rate, a smile factor and a convexity adjustment factor,
+respectively, all assumed to be piecewise continuous and bounded. We further assume that y0 = 0, with t = 0 the “as
+of” date for which the model is calibrated. The function R∗(t) is determined by calibration to the forward curve but
+will tend in the zero volatility limit to zero.2 The formal no-arbitrage constraint which determines this function is as
+follows
+E
+�
+e−
+� t
+0 rs ds�
+= D(0, t)
+(2.3)
+1The other case addressed was the well-known lognormal rates model of Black and Karasinski [1991] (see further §2 below).
+2Strictly speaking, the function y∗(·) is the drift adjustment parameter which must be chosen to satisfy the no-arbitrage condition for a given
+choice of R∗(t), so the latter should really be thought of as controlling the skew. However, the calculation of R∗(t) as a power series of nested
+integrals involving y∗(·) is much more convenient than attempting to perform the equivalent process in reverse, so in practice we consider y∗(t) to
+be inferred directly from the no-arbitrage condition, constructing the implied R∗(t) using the mathematical techniques expounded below.
+2
+
+under the martingale measure for 0 < t ≤ Tm, where Tm is the longest maturity date for which the model is calibrated,
+and
+D(t1, t2) := e−
+� t2
+t1 r(s) ds
+(2.4)
+is the t1-forward price of the t2-maturity zero coupon bond. This is to be contrasted with the Hull and White [1990]
+(H-W) model which is obtained by taking the limit as γ(t) → 0 in (2.2):
+r(y, t) = R∗
+H-W(t) + y
+and the Black and Karasinski [1991] (B-K) model which is obtained by choosing
+r(y, t) = R∗
+B-K(t)ey.
+Notably our model reverts to the ﬁrst of these in the limit as γ(t) → 0.
+Since we are interested in pricing options on daily-compounded rates payments, we introduce a new variable
+zt representing the integral of the short rate, making use of the fact that daily compounding can be to a good
+approximation captured by assuming continuous compounding. We shall make the choice
+zt :=
+� t
+0
+(rs − r(s))ds.
+(2.5)
+We consider the (stochastic) time-t price of a European-style security which pays a cash amount P(yT , zT ) at
+maturity T, denoting this by f(yt, zt, t). We note in particular that the price of a T-maturity zero coupon bond is
+obtained by taking P(y, z) = 1. We will look to derive the functional form of f(·, ·, ·) implied by our model in this
+case and in the process to determine the conditions on R∗(t) necessary to satisfy (2.3).
+From the Feynman-Kac theorem we infer that f(y, z, t) emerges as the solution to the following backward
+Kolmogorov diffusion equation:
+∂f
+∂t − α(t)y ∂f
+∂y + (r(y, t) − r(t))
+� ∂
+∂z − 1
+�
+f + 1
+2σ2(t)∂2f
+∂y2 − r(t)f = 0,
+(2.6)
+with r(y, t) given by (2.2), subject to the termiinal condition f(y, z, T) = P(y, z).
+3
+Pricing Kernel
+We deﬁne at this point the following notation for future reference:
+φr(t, v) := e−
+� v
+t α(u)du,
+(3.1)
+Σrr(t, v) :=
+� v
+t
+φ2
+r(u, v)σ2(u)du,
+(3.2)
+ψr(t, v) := e
+1
+2 γ2(v)Σrr(t,v),
+(3.3)
+Σrz(t, v) :=
+� v
+t
+ψr(t, u)φr(u, v)Σrr(t, u)du,
+(3.4)
+Σzz(t, v) := 2
+� v
+t
+ψr(t, u)Σrz(t, u)du,
+(3.5)
+Σ(t, v) :=
+�
+Σrr(t, v)
+Σrz(t, v)
+Σrz(t, v)
+Σzz(t, v)
+�
+,
+(3.6)
+B∗(t, v) :=
+� v
+t
+ψr(t, u)φr(t, u)du,
+(3.7)
+B+(t, t1, v) := B∗(t, v) − B∗(t, t1)
+φr(t, t1)
+=
+� v
+t1
+ψr(t, u)φr(t1, u)du,
+(3.8)
+µ∗(y, t, v) := B∗(t, v)(y + Σrz(0, t)) + 1
+2B∗2(t, v)Σrr(0, t).
+(3.9)
+3
+
+We observe here that φr(t, v) represents the impact of mean reversion and ψr(t, v) that of the counteracting dispersion
+from the mean induced by smile.
+We look to obtain the pricing kernel or Green’s function for (2.6), deﬁned as a (generalised) function
+G(y, z, t; η, ζ, T) such that the solution subject to the speciﬁed terminal condition can be obtained from the following
+convolution expression:
+f(y, z, t) =
+��
+R2 G(y, z, t; η, ζ, T)P(η, ζ) dη dζ.
+(3.10)
+In the absence of exact analytic solutions, we seek the pricing kernel as a perturbation expansion in the limit that the
+deviations of the short rate from the forward rate curve are small under some suitable norm. To that end let us deﬁne
+the small parameter
+ϵ :=
+��γ2(·)Σrr(·, ·)
+��
+(3.11)
+and seek an asymptotic expansion of the pricing kernel in powers of ϵ. To allow of a skew adjustment that contributes
+at the same order of approximation as the smile adjustment we shall make the assumption that ∥γ(·)y∗(·)∥= O(√ϵ).3
+Let us further express R∗(·) asymptotically as
+R∗(t) =
+∞
+�
+n=1
+R∗
+n(t),
+(3.12)
+with R∗
+n(·) = O(ϵn).
+To express our result conveniently, we introduce the functions
+R±
+1 (y, t, t1, v) := ψr(t, t1)e±γ(t1)(φr(t,t1)y+y∗(t1)−B+(t,t1,v)Σrr(t,t1)−Σrz(t,t1))
+2γ(t1)
+,
+(3.13)
+and shift operators M±(t, t1) deﬁned for t ≤ t1 by
+M±(t, t1)f(y, z, . . .) := f (y ± γ(t1)∆y(t, t1), z ± γ(t1)∆z(t, t1), . . .)
+(3.14)
+∆y(t, t1) := Σrr(t, t1)
+φr(t, t1) ,
+(3.15)
+∆z(t, t1) := Σrz(t, t1) − B∗(t, t1)Σrr(t, t1)
+φr(t, t1) .
+(3.16)
+Using this notation we deﬁne also the following operators:
+R1(t, t1, v) := R+
+1 (y, t, t1, v) M+(t, t1) − R−
+1 (y, t, t1, v) M−(t, t1),
+(3.17)
+R1(t, t1, v) := R+
+1 (y, t, t1, v) M+(t, t1) + R−
+1 (y, t, t1, v) M−(t, t1),
+(3.18)
+G1(t, t1, v) := R1(t, t1, v) + R∗
+1(t1) − e
+1
+2 γ2(t1)Σrr(t,t1)
+�
+φr(t, t1)(y + Σrz(0, t) + B∗(t, t1)Σrr(0, t))
+− B+(t, t1, v)Σrr(t, t1)
+�
+.
+(3.19)
+Using the operator expansion method of Turfus [2021a] in the same manner as Turfus and Romero-Bermúdez [2021]
+we obtain the following result.
+Theorem 3.1 (Pricing Kernel). Making use of the above-deﬁned notation, the pricing kernel for (2.6) can be written
+asymptotically in the limit as ϵ → 0 as
+G(y, z, t; η, ζ, v) = D(t, v)e−µ∗(y,t,v)
+∞
+�
+n=0
+Gn(y, z, t; η, ζ, v)
+(3.20)
+3We have avoided being explicit about the range of t over which the norms are assessed. A typical choice would be a weighted integral over
+[0, T] for some ﬁnite T.
+4
+
+with the Gn(·) = O(ϵn) and in particular
+G0(y, z, t; η, ζ, v) = N2
+�
+η + Σrz(t, v) − φr(t, v)y, ζ − µ∗(y, t, v) + 1
+2Σzz(t, v) − z; Σ(t, v)
+�
+,
+(3.21)
+G1(y, z, t; η, ζ, v) =
+�� v
+t
+G1(t, t1, v)dt1 − Q(t, v)
+� � ∂
+∂z − 1
+�
+G0(y, z, t; η, ζ, v),
+(3.22)
+G2(y, z, t; η, ζ, v) =
+� � v
+t
+� t2
+t
+G1(t, t1, v) G1(t, t2, v)dt1dt2
+� ∂
+∂z − 1
+�2
+−
+� v
+t
+G1(t, t1, v)dt1 Q(t, v)
+� ∂
+∂z − 1
+�2
++ 1
+2
+�
+Q2(t, v) −
+� v
+t
+Σrz(t, t1)(γ(t1)R1(t, t1, v) − 1)dt1
+� � ∂
+∂z − 1
+�2
++
+� v
+t
+R∗
+2(t1)dt1
+� ∂
+∂z − 1
+��
+G0(y, z, t; η, ζ, v),
+(3.23)
+with
+Q(t, v) := Σrz(t, v)
+φr(t, v)
+� ∂
+∂y − B∗(t, v) ∂
+∂z
+�
++ Σzz(t, v) ∂
+∂z
+(3.24)
+and N2(·, ·; Σ) a bivariate Gaussian probability density function with covariance Σ.
+Proof. A proof of this result is given in Appendix A below. Note in (3.23) that the shift operator in G1(t, t1, v) acts
+on the y-variables in G1(t, t2, v).
+What has effectively been achieved here is that representations of the O(1) drift and diffusion associated with z
+and the O(ϵ1/2) Hull-White stochastic discounting, as captured by µ∗(y, t, v)+Q(t, v), are subtracted out of the time-
+ordered exponential operator W(t, u) in (A.7) and incorporated directly into the modiﬁed Gaussian kernel G0(·; ·) on
+which it acts. In this way a zeroth order operator is replaced by the ﬁrst order operator W1(t, u) in (A.12). Only by
+use of this device does the asymptotic expansion of the (modiﬁed) operator become possible.
+It will be observed that the leading-order contribution (n = 0) is in its functional form identical to the Hull-White
+kernel of Turfus [2022], with the caveat that the mean reversion function φr(t, u) is adjusted up (reducing its impact)
+by inclusion of the smile factor ψr(t, t1) in (3.7), with no impact from skew. This means that solutions based on our
+expansion are likely to retain better accuracy even at longer maturities than those of Turfus and Romero-Bermúdez
+[2021]. Note that we could have expressed our results as a perturbation operator acting on the Hull-White kernel but
+choose, for reasons of convenience of use, to multiply by the stochastic discounting operator in the ansatz (3.20) after
+applying the perturbation operators term-by-term.
+4
+Fitting to the Forward Curve
+Let us further deﬁne for future notational convenience
+F1(t, T) :=
+� T
+t
+G1(t, t1, T)dt1
+=
+� T
+t
+(R1(t, t1, T) + R∗
+1(t1))dt1 − µ∗(y, t, T) + 1
+2Σzz(t, T)
+(4.1)
+F2(t, T) :=
+� T
+t
+�� t2
+t
+G1(t, t1, T) G1(t, t2, T)dt1 − R∗
+2(t2)
+�
+dt2.
+(4.2)
+Note that y-shifts apply in the integral term in (4.2), but can in practice be ignored, since they give rise to terms
+impacting at higher than second order; also that, in deriving (4.1), we have made use of the identity (A.18).
+5
+
+The calibration of our model to the forward interest rate market is achieved by considering zero coupon bond
+prices.
+Theorem 4.1 (Calibration). Applying (3.20) to a unit payoff at T, the T-maturity zero coupon bond price associated
+with the pricing kernel (3.20) is seen to be given asymptotically by
+F T (y, t) ∼ D(t, T)e−µ∗(y,t,T ) (1 − F1(t, T) + F2(t, T)) .
+(4.3)
+Differentiating the calibration condition F T (0, 0) = D(0, T) w.r.t. T, applying this to second order accuracy and
+setting T = t gives rise to the requirement that the ﬁrst two terms of (3.12) are given by
+R∗
+1(t) = −R+
+1 (0, 0, t, t) + R−
+1 (0, 0, t, t)
+− ψr(0, t)
+� t
+0
+φr(t1, t)Σrr(0, t1)(γ(t1)(R+
+1 (0, 0, t1, t) + R−
+1 (0, 0, t1, t)) − ψr(0, t1))dt1
+= −ψr(0, t)
+�sinh Y ∗(t, t)
+γ(t)
++
+� t
+0
+ψr(0, t1)φr(t1, t)Σrr(0, t1) (cosh Y ∗(t1, t) − 1) dt1
+�
+,
+(4.4)
+R∗
+2(t) ∼ R∗
+1(t)
+� t
+0
+R∗
+1(t1)dt1,
+(4.5)
+where for t1 ∈ [0, t],
+Y ∗(t1, t) := γ(t1)
+�
+y∗(t1) − B+(0, t1, t)Σrr(0, t1) − Σrz(0, t1)
+�
+.
+(4.6)
+We observe that, excluding the bracketed expression which provides the main skew-smile adjustment, (4.3) is
+essentially a Hull-White representation of the bond price making use of a modiﬁed mean reversion factor in place of
+the usual φr(t, u) as the integrand in (3.7). A ﬁrst-order representation which should sufﬁce for many purposes, is
+obtained by neglecting F2(t, T) in (4.3). Provided the leading-order skew-smile correction terms remain small, the
+approximation should be a good one: the variable y would have to take on improbably large values for this not to be
+the case. Note that these results are, up to second order, equivalent to those presented in Turfus and Romero-Bermúdez
+[2021], as might be expected since the model is unchanged here, only the method of building the expansion slightly
+different.
+5
+Applications
+5.1
+Forward Rates
+An expression for forward rates is easily deduced from our zero coupon bond formula.
+Corollary 5.1 (Instantaneous Forward Rate). The instantaneous forward rate is given by
+f T (y, t) = r(T) + ψr(t, T)φr(t, T)(y + Σrz(0, t) + B∗(t, T)Σrr(0, t))
++ D(t, T)e−µ∗(y,t,T )
+F T (y, t)
+�
+G1(t, T, T) −
+� T
+t
+G1(t, t1, T) G1(t, T, T)dt1 + R∗
+2(T)
+�
++ O(ϵ3),
+(5.1)
+with F T (y, t) as given by Theorem 4.1. The corresponding ﬁrst order version of this result is obtained by ignoring the
+second two terms in parentheses and taking a ﬁrst order representation of F T (y, t).
+Proof. This result is obtained by noting that the instantaneous forward rate is given by f T (yt, t) where
+f T (y, t) = − ∂
+∂T ln F T (y, t)
+and making use of (4.3).
+6
+
+5.2
+Option Pricing
+We assume below that, in option pricing, the interest rate that is used as the underlying is the same one that is used in the
+discounting of cash ﬂows. If, particularly in the case of LIBOR, there is a spread over the risk-free rate, this situation
+can effectively be managed by calibrating the model to the risk-free rate and subtracting the (assumed deterministic)
+spread off of the strike (or coupon rate).
+Compounded Rate Caplet Pricing
+RFR cap and caplet prices are obtained to leading order from the following
+theorem.
+Theorem 5.1 (RFR Caplet Price). Consider a caplet based on the compounded risk-free rate over a payment period
+[T1, T2] and a payoff with strike K at time T2 of
+�
+e
+� T2
+T1 r(yt,t)dt − 1 − Kδ(T1, T2)
+�+
+=
+�
+D(T1, T2)−1ez2−z1 − κ−1�+
+=: Pcaplet(z1, z2)
+(5.2)
+where zT1 = z1, zT2 = z2 and κ = (1 + Kδ(T1, T2))−1, with δ(·, ·) providing the relevant year fraction. Using the
+above-deﬁned notation and deﬁning the critical value of z2 − z1 at which the option comes into the money as
+∆z∗ = ln
+�
+κ−1D(T1, T2)
+�
+,
+(5.3)
+the caplet PV will be given asymptotically with relative errors = O(ϵ2) by
+PVCaplet ∼ D(0, T1)
+�
+1 −
+� T1
+0
+˜G1(0, t1, T1)dt1
+�
+Φ(d1(y, z − z1, 0))
+�����
+y=0,z=z1
+− κ−1D(0, T2)
+�
+1 −
+� T2
+0
+˜G1(0, t1, T2)e−θ(y,0)H(T1−t1)dt1 − B∗(T1, T2)Σrz(0, T1)
+�
+Φ(d2(y, z − z1, 0))
+�����
+y=0,z=z1
+− κ−1D(0, T2)
+�
+B∗2(T1, T2)Σrr(0, T1) + Σzz(T1, T2)N(d2(0, 0, 0)),
+(5.4)
+with Φ(·) a cumulative normal distribution function, N(·) the corresponding density and H(·) the Heaviside step
+function, where we deﬁne
+d1(y, w, t) := θ(y, t) + w − ∆z∗ + 1
+2(B∗2(T1, T2)Σrr(t, T1) + Σzz(T1, T2))
+�
+B∗2(T1, T2)Σrr(t, T1) + Σzz(T1, T2)
+(5.5)
+d2(y, w, t) := d1(y, w, t) −
+�
+B∗2(T1, T2)Σrr(t, T1) + Σzz(T1, T2),
+(5.6)
+θ(y, t) := B∗(T1, T2)(φr(t, T1)y − Σrz(t, T1) + Σrz(0, T1)) + 1
+2B∗2(T1, T2)φ2
+r(t, T1)Σrr(0, t),
+(5.7)
+and ˜G1(t, t1, T2) is deﬁned analogously to G1(t, t1, T2) above except in that we re-deﬁne
+∆y(t, t1) = φr(T1 ∧ t1, T1 ∨ t1)Σrr(t, T1 ∧ t1)
+φr(t, T1)
+,
+(5.8)
+∆z(t, t1) =
+�
+Σrz(T1, t1) + B+(T1, t1, T2)Σrr(T1, t1)
+�
+1t1>T1.
+(5.9)
+Proof. The proof of this result is set out in Appendix B. Cap prices are of course obtained as an algebraic sum of
+caplet prices.
+7
+
+LIBOR Caplet Pricing
+LIBOR or term-rate cap and caplet prices are obtained similarly.
+Theorem 5.2 (LIBOR Caplet Price). Consider a caplet based on the term rate over a payment period [T1, T2] and a
+payoff with strike K at time T2 of
+PLIBOR caplet(y1) :=
+�
+1/F T2(y1, T1) − κ−1�+
+(5.10)
+where yT1 = y1. This gives rise to a T1-value of
+VLIBOR caplet(y, T1) =
+�
+1 − κ−1F T2(y, T1)
+�+
+.
+Using the above-deﬁned notation, the caplet PV will be given asymptotically with relative errors = O(ϵ2) by
+PVLIBOR Caplet ∼ D(0, T1)
+�
+1 −
+� T1
+0
+˜G1(0, t1, T1)dt1
+�
+Φ(d1(y, 0))
+�����
+y=0
+− κ−1D(0, T2)
+�
+1 −
+� T2
+0
+˜G1(0, t1, T2)e−θ(y,0)H(T1−t1)dt1 − B∗(T1, T2)Σrz(0, T1)
+�
+Φ(d2(y, 0))
+�����
+y=0
+− κ−1D(0, T2)
+�
+B∗2(T1, T2)Σrr(0, T1)N(d2(0, 0)),
+(5.11)
+where we deﬁne additionally
+d1(y, t) := θ(y, t) − ∆z∗ + 1
+2B∗2(T1, T2)Σrr(t, T1)
+�
+B∗2(T1, T2)Σrr(t, T1)
+(5.12)
+d2(y, t) := d1(y, t) −
+�
+B∗2(T1, T2)Σrr(t, T1).
+(5.13)
+Proof. This result can be understood as a special case of Theorem 5.1 when a zero value is assigned to the volatility
+σ(t) for t ∈ [T1, T2].
+Swaption Pricing
+Swaption prices are obtained similarly.
+Theorem 5.3 (Swaption Price). Consider a payer swaption based on a LIBOR or compounded-rate swap with payment
+periods [Ti−1, Ti] for i = 1, 2, . . . , n and a ﬁxed coupon K with payoff at time T0 given by the swap value at time T0
+if this is in the money.
+8
+
+Using the above-deﬁned notation, the swaption PV will be given asymptotically with relative errors = O(ϵ2) by
+PVSwaption ∼ D(0, T0)
+�
+1 −
+� T0
+0
+˜G1(0, t1, T0)dt1
+�
+Φ(d(0)(y))
+�����
+y=0
+− D(0, Tn)
+�
+1 −
+� Tn
+0
+˜G1(0, t1, Tn)e−B∗(T0,Tn)φr(0,T0)yH(T0−t1)dt1 − B∗(T0, Tn)Σrz(0, T0)
+�
+Φ(d(n)(y))
+�����
+y=0
++
+�
+B∗2(T0, Tn)Σrr(0, T0)N(d(n)(0))
+− K
+n
+�
+i=1
+δ(Ti−1, Ti)D(0, Ti)
+� �
+1 −
+� Ti
+0
+˜G1(0, t1, Ti)e−B∗(T0,Ti)φr(0,T0)yH(T0−t1)dt1 − B∗(T0, Ti)Σrz(0, T0)
+�
+Φ(d(i)(y))
+�����
+y=0
++
+�
+B∗2(T0, Ti)Σrr(0, T0)N(d(i)(0))
+�
+,
+(5.14)
+where we deﬁne additionally for i = 0, 1, . . . , n
+d(i)(y) := φr(0, T0)y − yc − Σrz(0, T0)
+�
+Σrr(0, T0)
+−
+�
+B∗2(T0, Ti)Σrr(0, T0),
+(5.15)
+where yc is the value of yT0 at which the swap comes into the money.
+Proof. The proof of this result is analogous to that provided in Appendix B. This follows from the similarity of the
+swaption payoff:
+PSwaption(y, T0) = 1 − F Tn(y, T0) − K
+n
+�
+i=1
+δ(Ti−1, Ti)F Ti(y, T0)
+with Eq. (5.10). A key observation is that the value of a risk-free interest rate payment stream, starting at T0 with
+ﬁnal payment at Tn and discounted at the risk-free interest rate is PV = F T0(y, t) − F Tn(y, t), i.e. the difference
+between the value of a unit payment at time T0 and one at time Tn. We note further that this observation is equally
+true of compounded-rate and term-rate swaptions, since the term-rate payment is by deﬁnition the expected value of a
+compounded-rate payment, observed on its initial ﬁxing date.
+5.3
+Implied Volatility Formulae
+We look to translate the formulae set out in (5.4) and (5.11) above into expressions for effective/implied Hull-White
+term variances. This has the advantage of making it more intuitively obvious how the smile and skew impact on the
+caplet pricing as a function of moneyness. Indeed, one of the ﬁrst things practitioners typically want to do with option
+prices is to translate them into effective/implied volatility equivalents. A second advantage is that if, rather than using
+our asymptotic formulae directly, we use the Hull-White formulae with our best estimate of the effective variance
+substituted for the Hull-White variance, we naturally obtain better extrapolated behaviour far from the money, with
+arbitrage avoided.4
+4The quadratic expressions (5.26) and (5.32) obtained below may arguably give rise for values of ϵ of order unity to effective variance
+speciﬁcations which are negative. But such circumstances are of no practical relevance and would in any event compromise the asymptotic approach
+entirely, not just the implied volatility speciﬁcation.
+9
+
+We note in passing that one of the main reasons for the popularity of the SABR model of Hagan et al. [2002] was
+precisely that the asymptotic representation of option prices was explicitly as a formula for the implied Black-Scholes
+volatility. The approach we take is along the lines of that made use of by Alòs et al. [2015].
+Effective Compounded Rates Variance
+Starting with the expression (5.4) for the compounded caplet price, we
+look to re-express this as
+PVCaplet ∼ D(0, T1)Φ(d(1)(K, T1, T2)) − κ−1D(0, T2)Φ(d(2)(K, T1, T2))
+(5.16)
+with relative errors = O(ϵ2), where
+d(1)(K, T1, T2)) := −∆z∗ + 1
+2 (VC + v(K, T1, T2))
+�
+VC + v(K, T1, T2)
+(5.17)
+d(2)(K, T1, T2)) := d(1)(K, T1, T2) −
+�
+VC + v(K, T1, T2),
+(5.18)
+for some variance adjustment function v(K, T1, T2) deﬁned against a baseline compounded-rate term variance
+VC = B∗2(T1, T2)Σrr(0, T1) + Σzz(T1, T2),
+(5.19)
+so that the effective variance is
+Veffective = VC + v(K, T1, T2).
+(5.20)
+To determine the appropriate functional form for v(K, T1, T2), we expand (5.4) and (5.16) as Taylor expansions
+and equate terms. To that end we note expanding (5.16) to ﬁrst order in terms of the small parameter v(K, T1, T2) that
+PVCaplet ∼ D(0, T1)Φ(d(1)) − κ−1D(0, T2)
+�
+Φ(d(2)) − v(K, T1, T2)
+2√VC
+N(d(2))
+�
+,
+(5.21)
+with d(j) given by dj(0, 0, 0), while the expansion of (5.4) gives rise with O(ϵ2) relative error to
+D(0, T1)Φ(d(1)) − κ−1D(0, T2)Φ(d(2))
++
+�
+C1(T1, T2) − C2(T1, T2) d(2) + C3(T1, T2)
+�
+d(2)
+2 − 1
+��
+κ−1D(0, T2)N(d(2))
+where
+C1(T1, T2) :=
+� T2
+T1
+(ψr(0, t1) cosh Y ∗(t1, T2) − ψr(T1, t1)) ΨC(T1, t1, T2) dt1
+(5.22)
+C2(T1, T2) := 1
+2
+� T2
+T1
+ψr(0, t1) sinh Y ∗(t1, T2)γ(t1)Ψ2
+C(T1, t1, T2) dt1
+(5.23)
+C3(T1, T2) := 1
+3!
+� T2
+T1
+ψr(0, t1) cosh Y ∗(t1, T2)γ2(t1)Ψ3
+C(T1, t1, T2) dt1,
+(5.24)
+with
+ΨC(T1, t1, T2) := V
+− 1
+2
+C
+�
+B∗(T1, T2)φr(T1, t1)Σrr(0, T1) + Σrz(T1, t1) + B+(T1, t1, T2)Σrr(T1, t1)
+�
+(5.25)
+and Y ∗(·, ·) deﬁned by (4.6) above.
+Equating terms in the two expansions, we conclude that we must have
+v(K, T1, T2) ∼ 2V
+1
+2
+C
+�
+C1(T1, T2) − C2(T1, T2) d(2) + C3(T1, T2)
+�
+d(2)
+2 − 1
+��
+,
+(5.26)
+from which we deduce an effective compounding rate caplet term variance given by (5.20) with O(ϵ2) relative
+error. It is at this point evident how the linear term involving C2(T1, T2) gives rise to the skew and the quadratic
+term involving C3(T1, T2) to the smile. We suggest on this basis that taking the parameter ϵ to be given here by
+max{|C2(T1, T2)|, C3(T1, T2)}/V
+1
+2
+C would furnish a good guide as to the level of accuracy of the ﬁrst order effective
+variance expansion, with relative errors being expected to be of magnitude ϵ2.
+10
+
+Effective LIBOR Variance
+Starting instead with the expression (5.11) for the LIBOR or term-rate caplet price, we
+look to re-express this as
+PVLIBOR Caplet ∼ D(0, T1)Φ(d(1)(K, T1, T2)) − κ−1D(0, T2)Φ(d(2)(K, T1, T2))
+(5.27)
+with relative errors = O(ϵ2), where
+d(1)(K, T1, T2)) := −∆z∗ + 1
+2 (VL + v(K, T1, T2))
+�
+VL + v(K, T1, T2)
+(5.28)
+d(2)(K, T1, T2)) := d(1)(K, T1, T2) −
+�
+VL + v(K, T1, T2),
+(5.29)
+for some variance adjustment function v(K, T1, T2) deﬁned against a baseline LIBOR term variance
+VL := B∗2(T1, T2)Σrr(0, T1),
+(5.30)
+so that the effective variance is
+Veffective = VL + v(K, T1, T2)
+(5.31)
+By a calculation analogous to the above, we conclude that we must have
+v(K, T1, T2) ∼ 2V
+1
+2
+L
+�
+C1(T1, T2) − C2(T1, T2) d(2) + C3(T1, T2)
+�
+d(2)
+2 − 1
+��
+,
+(5.32)
+with d(j) given by dj(0, 0) and
+C1(T1, T2) :=
+� T2
+T1
+(ψr(0, t1) cosh Y ∗(t1, T2) − ψr(T1, t1)) ΨL(T1, t1) dt1,
+(5.33)
+C2(T1, T2) := 1
+2
+� T2
+T1
+ψr(0, t1) sinh Y ∗(t1, T2)γ(t1)Ψ2
+L(T1, t1) dt1,
+(5.34)
+C3(T1, T2) := 1
+3!
+� T2
+T1
+ψr(0, t1) cosh Y ∗(t1, T2)γ2(t1)Ψ3
+L(T1, t1) dt1,
+(5.35)
+with
+ΨL(T1, t1) := φr(T1, t1)
+�
+Σrr(0, T1).
+(5.36)
+Effective Swaption Variance
+Starting instead with the expression (5.14) for the swaption price, we look to re-
+express this as
+PVSwaption ∼ D(0, T0)Φ( ˜d(0)(K, T)) − D(0, Tn)Φ( ˜d(n)(K, T)) − K
+n
+�
+i=1
+δ(Ti−1, Ti)D(0, Ti)Φ( ˜d(i)(K, T)),
+(5.37)
+with relative errors = O(ϵ2), where
+˜d(i)(K, T)) :=
+−yc − Σrz(0, T0)
+�
+Σrr(0, T0) + ˜v(K, T)
+− B∗(T0, Ti)
+�
+Σrr(0, T0) + ˜v(K, T)
+(5.38)
+for some variance adjustment function ˜v(K, T) with T := (T0, T1, . . . , Tn), with the effective short rate term variance
+taken to be
+Veffective = Σrr(0, T0) + ˜v(K, T).
+(5.39)
+11
+
+Deﬁning ˜d(i) to be the result obtained by setting ˜v(K, T) = 0 in (5.38), we can expand (5.37) as
+PVSwaption ∼ D(0, T0)Φ
+�
+˜d(0)
+�
+− D(0, Tn)Φ
+�
+˜d(n)
+�
+− K
+n
+�
+i=1
+δ(Ti−1, Ti)D(0, Ti)Φ
+�
+˜d(i)
+�
++
+˜v(K, T)
+2
+�
+Σrr(0, T0)
+n
+�
+i=1
+(δin + Kδ(Ti−1, Ti))
+�
+1 + ∆ ˜d(i) ˜d(n)
+�
+B∗(T0, Ti)D(0, Ti)N
+�
+˜d(n)
+�
+,
+(5.40)
+where we have made use of the fact that
+N
+�
+˜d(i)
+�
+∼
+�
+1 + ∆ ˜d(i) ˜d(n)
+�
+N
+�
+˜d(n)
+�
+(5.41)
+with
+∆ ˜d(i) := ˜d(n) − ˜d(i)
+(5.42)
+and δin the Kronecker delta. We observe that the sum in the second line of (5.40) can be written more compactly as
+�
+An + Bn ˜d(n)
+�
+N
+�
+˜d(n)
+�
+Expanding (5.14) as in the previous cases leads to the conclusion that the second line in (5.40) must be equated with
+n
+�
+i=1
+�
+C1(T0, Ti) − C2(T0, Ti) ˜d(i) + C3(T0, Ti)
+�
+˜d2
+(i) − 1
+��
+(δin + Kδ(Ti−1, Ti)) D(0, Ti)N
+�
+˜d(i)
+�
+.
+This can be written asymptotically, making use of (5.41), as
+n
+�
+i=1
+�
+C1(T0, Ti) − C2(T0, Ti)
+�
+˜d(n) − ∆ ˜d(i)
+�
++ C3(T0, Ti)
+��
+˜d(n) − ∆ ˜d(i)
+�2
+− 1
+��
+(δin + Kδ(Ti−1, Ti))
+�
+1 + ∆ ˜d(i) ˜d(n)
+�
+D(0, Ti)N
+�
+˜d(n)
+�
+,
+which we write more compactly as
+�
+Dn + En ˜d(n) + Fn
+�
+˜d2
+(n) − 1
+��
+N
+�
+˜d(n)
+�
+.
+Asymptotic matching then requires that ˜v(K, T) be chosen to satisfy
+˜v(K, T) ∼
+2
+�
+Dn + En ˜d(n) + Fn
+�
+˜d2
+(n) − 1
+��
+�
+An + Bn ˜d(n)
+� �
+Σrr(0, T0)
+.
+(5.43)
+As can be seen, the effective term variance is on this occasion not quite quadratic in its dependence on log-moneyness.
+Further, the form of the denominator will cause it to give rise to singular behaviour for values of ˜d(n) sufﬁciently far
+from the ATM level. However, since the model would not in any event be calibrated to give credible results in such
+extreme cases, this ought not to be a signiﬁcant limitation in practice.
+6
+Numerical Calculations
+Caplets
+The above model has been calibrated to caplet market data capturing the skew and smile for SAR 6M
+LIBOR rates in May 2021. For the mean reversion, we choose a representative ﬁxed value of α(t) = 0.15. Choosing
+other values made little difference to the results obtained. Since the model has three other disposable parameters
+(σ(t), y∗(t) and γ(t)) it should be possible making use of (5.26) to match the ATM level, smile and skew of the
+12
+
+implied volatility surface at each maturity for which market data are provided. Indeed this is found to be the case.5
+The resulting ﬁt is illustrated in Fig. 1 and is seen to be excellent. Results are expressed as σIV (K, T2), the constant
+value of σ(t) which would have to be inserted in the Hull-White formula to replicate the price of a (6M tenor) caplet
+with strike K and maturity T2. For the smile, calibrated values of γ(t) ranged from around 300 at the short end to 40
+for t = 10y while, for the skew, the corresponding values of γ(t)y∗(t) were 0.5 and 0.08. The corresponding implied
+volatility surface is illustrated in Fig. 2.
+0.1
+0.5
+1.0
+1.5
+2.0
+2.5
+3.0
+3.5
+4.0
+4.5
+K
+1e
+2
+2
+3
+4
+5
+6
+7
+IV(K, T2)
+1e
+3
+T2 = 0.5
+T2 = 1
+T2 = 2
+T2 = 5
+T2 = 10
+Figure 1: Implied volatilities for various caplet maturities T2
+5In fact the ﬁtting was done to LIBOR caplet data treated as compounded-rate caplets, since the latter were not available and this approach
+satisﬁed the exigency of convenient presentation of numerical results for compounded-rate formulae. In any event, it was found to be no more
+difﬁcult to calibrate the model interpreting the data as being for LIBOR caplets.
+13
+
+K
+0.002
+0.010
+0.018
+0.026
+T2
+0.5
+1.0
+2.0
+3.0
+2.00
+3.00
+4.00
+5.00
+6.00
+7.00
+IV(K, T2) × 10
+3
+Figure 2: Caplet implied volatility surface
+Values of σIV (K, T2) were also explicitly backed out from the compounded-rate caplet price formula (5.4). These
+are shown for comparison in Fig. 3. As can be seen, the ﬁt is similarly good close to the money but the asymptotic
+caplet price formula clearly becomes unreliable for more extreme strikes so caution should be exercised in its direct
+use to calculate prices. Rather, the use of an asymptotic representation of the implied volatility surface, embedding as
+it does the avoidance of arbitrage (negative option prices) for any reasonable strikes, is to be preferred.6
+6For the same reason analytic option prices under the SABR model are always constructed indirectly from asymptotic representation of implied
+volatilities.
+14
+
+0.005
+0.010
+0.015
+0.020
+0.025
+0.030
+0.035
+0.040
+0.045
+K
+2
+3
+4
+5
+6
+7
+IV(K, T2)
+1e
+3
+Solid: analytic using Eq. (5.26). 
+ Dashed: numerical using Eq. (5.4). Dots: Mkt data
+T2 = 0.5
+T2 = 1
+T2 = 2
+T2 = 5
+T2 = 10
+Figure 3: Implied volatilities for various maturities
+It is of interest to consider how much impact results from use of a compounded rate rather than a term rate as the
+caplet underlying. This is illustrated in Figs. 4 and 5 where PVs based on formulae (5.16) and (5.27) are compared.
+As is evident, the impact is much greater for shorter maturities where T2 − T1 is comparable with T1, and becomes
+rather insigniﬁcant when T2 − T1 ≪ T1
+0.004 0.006 0.008 0.010 0.012 0.014 0.016 0.018
+K
+0.0
+0.5
+1.0
+1.5
+2.0
+2.5
+3.0
+PVCaplet × 103
+O(
+1) CMP T2 = 1
+O(
+1) LIBOR T2 = 1
+O(
+1) CMP T2 = 2
+O(
+1) LIBOR T2 = 2
+Figure 4: Comparison of term-rate and compounded-rate caplet prices for short maturities
+15
+
+0.030
+0.035
+0.040
+0.045
+0.050
+K
+0.0
+0.5
+1.0
+1.5
+2.0
+2.5
+3.0
+PVCaplet × 103
+O(
+1) CMP T2 = 5
+O(
+1) LIBOR T2 = 5
+O(
+1) CMP T2 = 10
+O(
+1) LIBOR T2 = 5
+Figure 5: Comparison of term-rate and compounded-rate caplet prices for longer maturities
+For completeness we also looked at instantaneous forward rates calculated in accordance with (5.1), with ﬁxing
+date T = t + 0.5. Results are shown in Fig. 6. Since these results incorporate second order terms, unlike the
+caplet results shown above, they are expected to be highly accurate. The impact of the skew/smile can be inferred by
+comparing with the dashed lines (Hull-White). As expected, the model is seen to behave just like Hull-White with
+forward rates linear in the underlying Gaussian variable y when this is small in magnitude.
+4
+2
+0
+2
+4
+y
+(0, t)
+0.02
+0.00
+0.02
+0.04
+0.06
+fT(y, t)
+t = 0.1 ,
+(
+2)
+t = 0.1, = y * = 0
+t = 1 ,
+(
+2)
+t = 1, = y * = 0
+t = 2 ,
+(
+2)
+t = 2, = y * = 0
+t = 5 ,
+(
+2)
+t = 5, = y * = 0
+Figure 6: Forward rates for various observation dates t with payment date T = t + 0.5.
+Swaptions
+The implied volatility surface of swaptions with two payment periods of 3 months is shown in Fig. 7.
+16
+
+K
+0.002 0.005 0.008 0.011 0.014 0.017
+T2
+1
+2
+3
+4
+5
+4.00
+6.00
+8.00
+IV(K, T2) × 10
+3
+0.005
+0.010
+0.015
+0.020
+0.025
+0.030
+0.035
+0.040
+0.045
+K
+0.2
+0.3
+0.4
+0.5
+0.6
+0.7
+0.8
+0.9
+1.0
+IV(K, T2)
+1e
+2
+Swaption 2 period, 3M
+T2 = 1
+T2 = 1.5
+T2 = 2
+T2 = 3
+T2 = 5
+T2 = 7
+T2 = 10
+Figure 7: Swaption implied volatilities for various maturities
+7
+Conclusions
+We have successfully extended the short rate model of Turfus and Romero-Bermúdez [2021] to address the pricing of
+SOFR/SONIA/ESTR caplets based on compounded rates. This we achieved by expressing the result as a perturbation
+of the analytic kernel of Turfus [2022]. The model is seen to have the following properties:
+1. Convenient analytic representations are available for bond and option prices.
+2. A single calibration addresses options of any maturity and tenor.
+3. Option pricing takes account of volatility skew and smile.
+4. Prices can be calculated for LIBOR or term-rate options as well as for options on backward-looking compounded
+rates.
+We believe our model to be unique in satisfying all of the above criteria.
+The asymptotic expansion developed here provides the further beneﬁt of pricing forward rates and LIBOR caplets
+more accurately than that of Turfus and Romero-Bermúdez [2021]. The expression for forward rates is (5.1). Caplet
+prices are best calculated noting that the effective Hull-White term variance is given by (5.20) and (5.26) for a
+compounded-rate caplet and by (5.31) and (5.32) for a LIBOR or term-rate caplet.
+A
+Proof of Pricing Kernel Result
+We offer a sketch of the proof that (3.20) represents the pricing kernel for (2.6). We follow Turfus [2019, 2021a] in
+introducing the following deﬁnitions and notation.
+17
+
+Deﬁnition A.1. The time-ordered exponential or Dyson series deﬁned for a linear operator L(t) by
+ET
+t (L(·)) = I +
+∞
+�
+n=1
+�
+t≤t1≤...≤tn≤T
+L(t1) . . . L(tn)dt1 . . . dtn
+= I +
+∞
+�
+n=1
+� T
+t
+� T
+t1
+· · ·
+� T
+tn−1
+L(u) L(t2) . . . L(tn)dtn . . . dt2dt1
+= I +
+∞
+�
+n=1
+� T
+t
+� tn
+t
+· · ·
+� t2
+t
+L(t1) L(t2) . . . L(tn)dt1dt2 . . . dtn
+(A.1)
+generalises the exponentiation of the integral of a function f(t) to the case of a time-dependent linear operator L(t).
+Deﬁnition A.2. We deﬁne the commutator of an operator L(t) with an operator V(t) where both operators act on the
+same function space by the following operator:
+adL(t1)(V(t2)) := L(t1) V(t2) − V(t2) L(t1).
+(A.2)
+We will have need to combine these two ideas in computing the time-ordered exponential of a commutator operator,
+interpreted as follows:
+Eu
+t
+�
+adL(·)
+�
+(V(u)) = V(u) +
+� u
+t
+adL(t1)(V(u))dt1 +
+� u
+t
+� u
+t2
+adL(t2)
+�
+adL(t1)(V(u))
+�
+dt1dt2 + . . . .
+(A.3)
+Proof of Theorem 3.1. We start by observing that, although r(y, t) − r(t) = O(ϵ
+1
+2 ), the term (r(y, t) − r(t))∂/∂z is
+O(1) so prevents direct use of a naïve perturbation expansion. Noting however that r(y, t) − r(t) ∼ y for small y
+we can subtract out the asymptotic representation and look to handle it separately. To that end we write the evolution
+operator associated with (2.6) as Ev
+t (L0(·) + V0(·)) where
+L0(t) = −α(t)y ∂
+∂y + 1
+2σ2(t) ∂2
+∂y2 − r(t),
+(A.4)
+V0(t) = (r(y, t) − r(t))
+� ∂
+∂z − 1
+�
+.
+(A.5)
+Following Turfus and Romero-Bermúdez [2021] who apply the exponential expansion formula of Turfus [2021a] to a
+closely analogous evolution operator, we can write the Green’s function solution of (2.6) as
+G(y, z, t; η, ζ, v) = D(t, v) Ev
+t (W(t, ·))N
+�
+η − φr(t, v)y
+�
+Σrr(t, v)
+�
+,
+(A.6)
+where7
+W(t, u) :=
+�
+R+(y, t, u)eγ(u)∆y(t,u) ∂
+∂y − R−(y, t, u)e−γ(u)∆y(t,u) ∂
+∂y + R∗(u)
+� � ∂
+∂z − 1
+�
+,
+(A.7)
+with
+R±(y, t, u) := e
+1
+2 γ2(u)Σrr(t,u)±γ(u)(φr(t,u)y+y∗(u))
+2γ(u)
+,
+(A.8)
+7Observe that the only difference at this stage compared to their result is in the inclusion of the derivative w.r.t. z in (A.7). However there is
+an important difference in the solution strategy. By subtracting out of (A.14) below a Hull-White (linear) representation of the discounting rate in
+addition to the z-drift, we are able to incorporate both directly into the analytic kernel. So, rather than the stochastic discounting being represented
+by a perturbation as in Turfus and Romero-Bermúdez [2021], it is only the difference between that and the Hull-White representation thereof which
+is so represented.
+18
+
+Let us deﬁne
+L1(t, u) := ψr(t, u)
+�Σrr(t, u)
+φr(t, u)
+∂
+∂y + Σrz(t, u) ∂
+∂z
+� � ∂
+∂z − 1
+�
+.
+(A.9)
+V1(t, u) := W(t, u) − L1(t, u).
+(A.10)
+We deduce
+Ev
+t (W(t, ·)) = Ev
+t (W1(t, ·)) Ev
+t (L1(t, ·)),
+(A.11)
+W1(t, u) = Eu
+t
+�
+adL1(t,·)
+�
+(V1(t, u))
+=
+�
+R+(y, t, u)eγ(u)(∆y(t,u) ∂
+∂y +Σrz(t,u)( ∂
+∂z −1))
+− R−(y, t, u)e−γ(u)(∆y(t,u) ∂
+∂y +Σrz(t,u)( ∂
+∂z −1)) + R∗(u)
+� � ∂
+∂z − 1
+�
+− L1(t, u). (A.12)
+Next deﬁning
+L2(t, u) := ∂
+∂uµ∗(y, t, u)
+� ∂
+∂z − 1
+�
+= ψr(t, u) (φr(t, u)(y + Σrz(0, t) + B∗(t, u)Σrr(0, t)))
+� ∂
+∂z − 1
+�
+,
+(A.13)
+V2(t, u) := W1(t, u) − L2(t, u).
+(A.14)
+we deduce
+Ev
+t (W1(t, ·)) = Ev
+t (W2(t, ·)) Ev
+t (L2(t, ·)),
+(A.15)
+W2(t, u) = Eu
+t
+�
+adL2(t,·)
+�
+(V2(t, u))
+=
+�
+R+(y, t, u)eγ(u)(∆y(t,u) ∂
+∂y +∆z(t,u)( ∂
+∂z −1))
+− R−(y, t, u)e−γ(u)(∆y(t,u) ∂
+∂y +∆z(t,u)( ∂
+∂z −1)) + R∗(u)
+� � ∂
+∂z − 1
+�
+− L3(t, u).
+(A.16)
+where
+L3(t, u) := Eu
+t
+�
+adL2(t,·)
+�
+(L1(t, u) + L2(t, u))
+= L1(t, u) + L2(t, u) − B∗(t, u)ψr(t, u)Σrr(t, u)
+φr(t, u)
+� ∂
+∂z − 1
+�2
+.
+(A.17)
+We observe, making use of the identity8
+� v
+t
+B+(t, u, v)ψr(t, u)Σrr(t, u)du = 1
+2Σzz(t, v),
+(A.18)
+that
+� v
+t
+B∗(t, u)ψr(t, u)Σrr(t, u)
+φr(t, u) du = B∗(t, v)Σrz(t, v)
+φr(t, v) − 1
+2Σzz(t, v),
+(A.19)
+whence we deduce
+� v
+t
+L3(t, u)du =
+�
+µ∗(y, t, v) + Σrz(t, v)
+φr(t, v)
+∂
+∂y + 1
+2Σzz(t, v) ∂
+∂z
++
+�1
+2Σzz(t, v) − B∗(t, v)Σrz(t, v)
+φr(t, v)
+� � ∂
+∂z − 1
+�� � ∂
+∂z − 1
+�
+.
+8This is readily proved by differentiating both sides w.r.t. v.
+19
+
+Applying Ev
+t (L2(t, ·)) Ev
+t (L1(t, ·)) to the Gaussian kernel, so increasing its dimension from 1 to 2, gives rise to
+G(y, z, t; η, ζ, v) = D(t, v) Ev
+t (W2(t, ·))e−µ∗(y,t,v)G0(y, z, t; η, ζ, v),
+(A.20)
+with G0(·; ·) deﬁned by (3.21) above. It is convenient to move the exponential function to the left of this expression.
+To this end we note that the exponential of a derivative acts as a shift operator, whence
+e±γ(u)∆y(t,u) ∂
+∂y e−µ∗(y,t,v) = e−µ∗(y,t,v)e±γ(u)( ∂
+∂y −B∗(t,v))∆y(t,u),
+L3(t, u) e−µ∗(y,t,v) = e−µ∗(y,t,v)
+�
+L3(t, u) − B∗(t, v)Σrr(t, u)
+φr(t, u)
+� ∂
+∂z − 1
+��
+.
+We obtain
+G(y, z, t; η, ζ, v) = D(t, v)e−µ∗(y,t,v) Ev
+t (W3(t, ·, v))G0(y, z, t; η, ζ, v),
+(A.21)
+W3(t, u, v) =
+�
+R+
+1 (y, t, u, v) M+(t, u) − R−
+1 (y, t, u, v) M−(t, u) + R∗(u)
+� � ∂
+∂z − 1
+�
+− L3(t, u) + B∗(t, v)ψr(t, u)Σrr(t, u)
+φr(t, u)
+� ∂
+∂z − 1
+�
+,
+(A.22)
+with R±
+1 (y, t, u, v) deﬁned by (3.13), where we have made use of the fact that
+e±γ(u)(∆y(t,u) ∂
+∂y +∆z(t,u) ∂
+∂z) ≡ M±(t, u).
+Expanding Ev
+t (W3(t, ·, v)) as a power series in (A.21) and making use of the above identities, we obtain (3.20), with
+(3.21)–(3.23) as the ﬁrst three terms, as claimed. This completes the proof.
+B
+Proof of RFR Caplet Pricing Result
+Proof of Theorem 5.1. Making use of (3.20), the ﬁrst order caplet value as of time T1 with yT1 = y and zT1 = z1 will
+be
+Vcaplet(y, T1) = lim
+z→z1
+��
+R2 G(y, z, T1; η, ζ, T2)Pcaplet(z1, ζ)dηdζ
+∼ e−µ∗(y,T1,T2)
+�
+Σzz(T1, T2)
+�
+1 +
+�� T2
+T1
+G1(T1, t1, T2)dt1 − Q(T1, T2)
+� � ∂
+∂z − 1
+��
+� ∞
+z1+∆z∗
+�
+eζ−z1 − κ−1D(T1, T2)
+�
+N
+�
+ζ − µ∗(y, T1, T2) + 1
+2Σzz(T1, T2) − z
+�
+Σzz(T1, T2)
+�
+dζ
+�����
+z=z1
+.
+(B.1)
+We see the z-dependence drops out at this stage. Letting V (i,j) denote the result of applying Gi(·; ·) to the jth order
+contribution to Vcaplet, we ﬁnd
+V (0,0)(y, T1) = Φ(d1(y, 0, T1)) − κ−1D(T1, T2)e−µ∗(y,T1,T2)Φ(d2(y, 0, T1)),
+with d1(·) and d2(·) deﬁned by (5.5) and (5.6), respectively. Applying the ﬁrst-order operator and making use of the
+identity
+N(d1(y, 0, t)) − κ−1D(T1, T2)e−θ(y,t)N(d2(y, 0, t) = 0
+(B.2)
+20
+
+yields at ﬁrst order9
+V (1,0)(y, T1) = κ−1D(T1, T2)e−µ∗(y,T1,T2)
+�� T2
+T1
+G1(T1, t1, T2)dt1 − Σzz(T1, T2) ∂
+∂z
+�
+Φ(d2(y, z − z1, T1))
+����
+z=z1
+.
+Here the effect of the shift operators is to transform
+Φ(d2(y, 0, T1) → Φ(d2(y, ±γ(t1)∆z1(t1), T1),
+where
+∆z1(t1) := Σrz(T1, t1) + B+(T1, t1, T2)Σrr(T1, t1).
+(B.3)
+Combining this with the leading-order term (and noting that there is no ﬁrst-order payoff contribution), we obtain
+Vcaplet(y, T1) ∼ V (0,0)(y, T1) + V (1,0)(y, T1). Taking this in turn as the payoff at T1 and valuing as of time t ∈ [0, T1)
+gives rise to
+Vcaplet(y, t) =
+��
+R2 G(y, z, t; η, ζ, T1)Vcaplet(η, T1)dηdζ
+∼ V (0,0)(y, t) + V (0,1)(y, t) + V (1,0)(y, t),
+(B.4)
+The ζ-integration is in this case trivial. In particular we have the quasi-Hull-White result
+V (0,0)(y, t) = e−µ∗(y,t,T1) �
+D(t, T1)Φ(d1(y, 0, t)) − κ−1D(t, T2)e−θ(y,t)Φ(d2(y, 0, t))
+�
+,
+(B.5)
+whence
+V (0,0)(0, 0) = D(0, T1)Φ(d1(0, 0, 0)) − κ−1D(0, T2)Φ(d2(0, 0, 0)),
+(B.6)
+Considering next the action of the ﬁrst-order Green’s function term on the leading-order term, we obtain
+V (1,0)(y, t) = −e−µ∗(y,t,T1)
+�� T1
+t
+G1(t, t1, T1)dt1 − Σrz(t, T1)
+φr(t, T1)
+∂
+∂y
+�
+�
+D(t, T1)Φ(d1(y, 0, t)) − κ−1D(t, T2)e−θ(y,t)Φ(d2(y, 0, t))
+�
+.
+(B.7)
+Setting y = t = 0, we ﬁnd
+V (1,0)(0, 0) ∼ −D(0, T1)
+� T1
+0
+G1(0, t1, T1)dt1 Φ(d1(y, 0, 0))
+�����
+y=0
++ κ−1D(0, T2)
+� � T1
+0
+G1(0, t1, T2)dt1 e−θ(y,0) + B∗(T1, T2)Σrz(0, T1)
+�
+Φ(d2(y, 0, 0))
+�����
+y=0
+.(B.8)
+9We use the convention here that the integration in the operator expression is applied after the operator has been applied to the operand; likewise
+for the assignment of the z-value.
+21
+
+Considering next the action of the leading-order Green’s function term on the ﬁrst-order term V (1,0)(y, T1), we obtain
+V (0,1)(y, t) ∼ κ−1D(t, T2)e−µ∗(y,t,T1)−θ(y,t)
+� � T2
+T1
+R+(y − ∆y1(t), t, t1)e−γ(t1)(B+(T1,t1,T2)Σrr(T1,t1)+Σrz(T1,t1))
+Φ(d2(y + γ(t1)φr(T1, t1)∆y(t, T1), γ(t1)∆z1(t1), t))dt1
+−
+� T2
+T1
+R−(y + ∆y1(t), t, t1)eγ(t1)(B+(T1,t1,T2)Σrr(T1,t1)+Σrz(T1,t1))
+Φ(d2(y − γ(t1)φr(T1, t1)∆y(t, T1), −γ(t1)∆z1(t1), t))dt1
++
+� � T2
+T1
+�
+R∗
+1(t1) + e
+1
+2 γ2(t1)Σrr(0,t1)B+(T1, t1, T2)Σrr(t, t1)
+�
+dt1 − θ(y, t)
+�
+Φ(d2(y, 0, t))
+−
+�
+B∗2(T1, T2)Σrr(t, T1) + Σzz(T1, T2)N(d2(y, 0, t))
+�
+,
+(B.9)
+with O(ϵ) relative errors, where
+∆y1(t) := Σrz(t, T1)
+φr(t, T1) + B∗(T1, T2)Σrr(t, T1)
+φr(t, T1) .
+(B.10)
+We conclude, making use of the fact that µ∗(0, 0, T1) = θ(0, 0) = 0, that
+V (0,1)(0, 0) ∼ κ−1D(0, T2)
+� � T2
+T1
+R+
+1 (0, 0, t1, T2)Φ(d2(γ(t1)φr(T1, t1)∆y(0, T1), γ(t1)∆z1(t1), 0))dt1
+−
+� T2
+T1
+R−
+1 (0, 0, t1, T2)Φ(d2(−γ(t1)φr(T1, t1)∆y(0, T1), −γ(t1)∆z1(t1), 0))dt1
++
+� T2
+T1
+R∗
+1(t1)dt1Φ(d2(0, 0, 0))
+−
+�
+B∗2(T1, T2)Σrr(0, T1) + Σzz(T1, T2)N(d2(0, 0, 0))
+�
+.
+(B.11)
+We make use here of the identity that, for t ≤ T1 ≤ t1 ≤ T2,
+Σrz(T1, t1) + B+(T1, t1, T2)Σrr(T1, t1) + φr(t, t1)∆y1(t, T1)
+= Σrz(T1, t1) + B+(T1, t1, T2)Σrr(t, t1) + φr(T1, t1)(Σrz(t, T1) + B∗(T1, t1)Σrr(t, T1))
+= Σrz(t, t1) + B+(t, t1, T2)Σrr(t, t1) − φr(t, t1)∆y2(t, t1)
+where
+∆y2(t, t1) =
+1
+φr(t, t1)
+� T2
+T1
+(ψr(t, u) − ψr(T1, t1))
+(φr(u, t1)Σrr(T1, u)1u≤t1 + φr(T1, u)Σrr(t, T1)1u>t1) du.
+(B.12)
+We neglect this subdominant adjustment factor in our asymptotic estimate, arguing that the result would otherwise not
+be consistent with the price of deep in-the-money forward contracts. Combining all V (i,j)(0, 0) terms and simplifying
+gives rise to (5.4). This completes the proof.
+22
+
+C
+Calibration to Caplet market data
+The calibration of the forward curve has already been explained in Sec. 4. As mentioned before, for the mean reversion,
+we choose a representative ﬁxed value of α(t) = 0.15. The calibration of σ(t), y∗(t) and γ(t) follows from matching
+the analytical implied volatility formula to the implied volatilities quoted in the market for 6-month caps. We take
+piece-wise parametrisations for these parameters and calibrate on the available maturities. The result of the calibration
+is given in Fig. 9.
+0
+2
+4
+6
+8
+10
+t (y)
+0.000
+0.001
+0.002
+0.003
+0.004
+0.005
+0
+2
+4
+6
+8
+10
+t (y)
+0
+50
+100
+150
+200
+250
+300
+0
+2
+4
+6
+8
+10
+t (y)
+0.0000
+0.0005
+0.0010
+0.0015
+0.0020
+0.0025
+0.0030
+y *
+Figure 9: Piece-wise functions for σ(t), y∗(t) and γ(t) after calibration to market data. The black dots indicate the
+cap maturities used for calibration.
+References
+E. Alòs, R. De Santiago, and J. Vives. Calibration of stochastic volatility models via second-order approximation: the
+Heston case. International Journal of Theoretical and Applied Finance, 18(6):1550036, 2015.
+A. Antonov and M. Spector. General Short-Rate Analytics. Risk, April:66–71, 2011.
+A. Antonov, M. Konikov, and M. Spector. Modern SABR Analytics: Formulas and Insights for Quants, Former
+Physicists and Mathematicians. Springer, 2019. ISBN 978-3030106553.
+F. Black and P. Karasinski. Bond and Option Pricing when Short Rates are Lognormal. Financial Analysts Journal,
+47(4):52–59, 1991.
+P. S. Hagan, D. Kumar, A. S. Lesniewski, and D. E. Woodward. Managing Smile Risk. Wilmott Magazine, July:
+84–108, 2002.
+M. P. A. Henrard.
+Overnight Indexed Swaps and Floored Compounded Instrument in HJM One-Factor Model.
+Research paper, University Library of Munich, 2004. URL https://ideas.repec.org/p/wpa/wuwpfi/
+0402008.html.
+B. Horvath, A. Jacquier, and C. Turfus. Analytic Option Prices for the Black-Karasinski Short Rate Model. Research
+Paper, SSRN, 2017. URL https://ssrn.com/abstract=3253833.
+J. Hull and A. White. Pricing Interest Rate Derivative Securities. The Review of Financial Studies, 3:573–592, 1990.
+C. Turfus. Closed-Form Arrow-Debreu Pricing for the Hull-White Short Rate Model. Quantitative Finance, 19(12):
+2087–2094, 2019.
+C. Turfus. Perturbation Methods in Credit Derivatives: Strategies for efﬁcient risk management. Wiley Finance,
+2021a. ISBN 978-1-119-60961-2.
+C. Turfus. Risky Caplet Pricing with Backward-Looking Rates. Risk, August, 2021b.
+C. Turfus. Caplet Pricing with Backward-Looking Rates. Wilmott Magazine, September:106–109, 2022.
+23
+
+C. Turfus and A. Romero-Bermúdez. Analytic Short Rate Model with Smile and Skew. Research paper, SSRN, 2021.
+URL https://ssrn.com/abstract=3840044.
+C. Turfus and A. Romero-Bermúdez. What Short Rate Model Should I Use? Wilmott Magazine, March:28–38, 2022.
+R. J. Van Steenkiste and S. Foresi. Arrow-Debreu prices for afﬁne models. Research Paper, SSRN, 1999. URL
+http://dx.doi.org/10.2139/ssrn.158630.
+24
+
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+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf,len=803
+page_content='Analytic RFR Option Pricing with Smile and Skew  Colin Turfus* and Aurelio Romero-Bermudez*,†  Deutsche Bank  †ABN Amro  Initial Version: December 22, 2022  Current Version: January 4, 2023  Abstract  We extend the short rate model of Turfus and Romero-Bermúdez [2021] to facilitate accurate arbitrage-free  analytic pricing of SOFR, SONIA or ESTR caplets, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' options on backward-looking compounded rates payments,  in a manner consistent with the smile and skew levels observed in the market.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' These caplet pricing formulae and  corresponding LIBOR or term-rate caplet results are translated into effective variance (implied vol) formulae, which  are seen to be of a particularly simple form.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' They show that the model is essentially equivalent to imposing on a Hull-  White model an effective variance which is a quadratic function of the moneyness parameter (rather than a constant)  for any given maturity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' Results are also illustrated graphically.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='  1  Introduction  The short rate model of Turfus and Romero-Bermúdez [2021] allows analytic pricing of caplets based on term rates  such as LIBOR with smile and skew.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' We extend this model here to support analytic pricing of options on compounding  risk-free rates (RFR) such as SOFR, SONIA or ESTR, in a manner consistent with the smile and skew levels observed  in the market.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' Our approach is based on the observation that for small perturbations from equilibrium under this model  the short rate is essentially a linear function of a (mean-reverting) Gaussian variable y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' This makes the situation similar  to that captured by the model of Hull and White [1990].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' An exact analytic pricing kernel for this model was derived  by Van Steenkiste and Foresi [1999], Turfus [2019] and the extension of this kernel to address compounding rates by  Turfus [2021a, 2022].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='  For a review of related work on options on compounded rates, the reader is referred to Turfus [2022], which  follows the approach of Van Steenkiste and Foresi [1999] in introducing the integrated short rate as an additional state  variable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' Option prices are in this way derived analogous to the formulae of Henrard [2004], including taking account  of delayed payment of the option premium.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' This work was extended to incorporate counterparty credit risk by Turfus  [2021b] through a highly accurate asymptotic approximation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='  In relation to analytic option pricing with smile and skew, the reader is referred to Turfus and Romero-Bermúdez  [2021, 2022].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' Their approach, which we extend below, is based on modelling the short rate as a sinh function of a  Gaussian Ornstein-Uhlenbeck process, which they argue is equivalent to assuming a quadratic dependence of the local  volatility on the short rate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' They make the point that little work has been done in this space, albeit that the Beta Blend  model proposed by Horvath et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' [2017] interpolating between the model of Hull and White [1990] and that of Black  and Karasinski [1991] can be viewed as allowing a term structure of skew to be speciﬁed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' Also analytic LIBOR option  and swaption prices incorporating smile and skew are available under the SABR model, as discussed by Antonov et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='  [2019].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' But this approach allows only one rate to be modelled at a time and does not constitute a short rate model  capable of capturing multiple rates within a uniﬁed framework.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='  We single out for special mention here the work of Antonov and Spector [2011].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' Like us they started out by  considering Gaussian variables driven by Ornstein-Uhlenbeck dynamics and took the short rate to be a function  1  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='01260v1  [q-fin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='MF]  3 Jan 2023  thereof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' One of the two cases they considered1 was a quotient of afﬁne functions of exponentials of the Gaussian,  under which assumption the short rate was constrained to lie between an upper and a lower limit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' They did not like  us attempt to capture volatility smile and skew explicitly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' Nor did they consider a more general formulation involving  an afﬁne function of two exponentials with different exponents as we do here.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' Also, the (ﬁrst-order) perturbation  expansion they used to obtain analytic option prices was based on a small lognormal-volatility assumption, which  limits the accuracy which can be obtained, particularly under low rates where lognormal volatilities can be quite high  (in excess of 50%).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' We expect our expansion based on the smallness of the rates themselves to be more accurate,  especially in circumstances of low rates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='  We look to obtain analytic expressions for prices of SOFR options which take account of smile and skew by  a method similar to that employed by Turfus and Romero-Bermúdez [2021] to price LIBOR caplets based on an  extension of the Bachelier pricing kernel (for a Gaussian underlying).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' We do this by extending instead the Hull-White  compounded rates kernel of Turfus [2022].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' The challenge is that, as well as observing that the representations of  the interest rate are similar (linear functions of a Gaussian variable) with and without smile or skew, we need to ﬁnd  a means of taking advantage of that observation systematically to obtain an explicit mathematical representation of  the perturbation which must be applied to the known (Hull-White) analytic kernel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' We do this using the operator  expansion method expounded by Turfus [2021a].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='  We start off in §2 by setting out the pricing equation for our model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' The associated pricing kernel is presented in  §3 as a perturbation expansion based on a low-rates assumption, with a summary proof provided in Appendix A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' The  calibration of the model to the term structure of forward rates and volatility (with skew and smile) is considered in §4,  where bond price formulae are also set out.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' The further application of the kernel to the pricing of forward rates and  SOFR/ESTR caplets is considered in §5, with a proof of the latter in Appendix B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' A LIBOR caplet pricing formula  is also deduced providing more accuracy than that of Turfus and Romero-Bermúdez [2021].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' The caplet prices are  also give a convenient expression as implied volatilities, which simpliﬁes calculation and helps ensure consistency of  behaviour far from the money.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' Numerical calculations of caplet prices and implied volatility surfaces based on the  formulae deduced are illustrated in §6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' Conclusions are set out in §7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='  2  Model Description  We consider the short rate model of Turfus and Romero-Bermúdez [2021] which incorporates smile and skew into the  Hull-White model through a variable transformation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' We shall ﬁnd it convenient to work with the reduced variable yt  deﬁned through the following Ornstein-Uhlenbeck process:  dyt = −α(t)ytdt + σ(t) dWt,  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='1)  with Wt a Wiener process for t ≥ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' This auxiliary variable is related to the short rate by rt = r(yt, t) where  r(y, t) := r(t) + R∗(t) + sinh γ(t)(y + y∗(t))  γ(t)  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='2)  Here r, y∗ : R+ → R are the instantaneous forward rate and a skewness function, respectively, and σ, α, γ, R∗ :  R+ → R+ are functions representing volatility, mean reversion rate, a smile factor and a convexity adjustment factor,  respectively, all assumed to be piecewise continuous and bounded.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' We further assume that y0 = 0, with t = 0 the “as  of” date for which the model is calibrated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' The function R∗(t) is determined by calibration to the forward curve but  will tend in the zero volatility limit to zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='2 The formal no-arbitrage constraint which determines this function is as  follows  E  �  e−  � t  0 rs ds�  = D(0, t)  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='3)  1The other case addressed was the well-known lognormal rates model of Black and Karasinski [1991] (see further §2 below).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='  2Strictly speaking, the function y∗(·) is the drift adjustment parameter which must be chosen to satisfy the no-arbitrage condition for a given  choice of R∗(t), so the latter should really be thought of as controlling the skew.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' However, the calculation of R∗(t) as a power series of nested  integrals involving y∗(·) is much more convenient than attempting to perform the equivalent process in reverse, so in practice we consider y∗(t) to  be inferred directly from the no-arbitrage condition, constructing the implied R∗(t) using the mathematical techniques expounded below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='  2  under the martingale measure for 0 < t ≤ Tm, where Tm is the longest maturity date for which the model is calibrated,  and  D(t1, t2) := e−  � t2  t1 r(s) ds  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='4)  is the t1-forward price of the t2-maturity zero coupon bond.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' This is to be contrasted with the Hull and White [1990]  (H-W) model which is obtained by taking the limit as γ(t) → 0 in (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='2):  r(y, t) = R∗  H-W(t) + y  and the Black and Karasinski [1991] (B-K) model which is obtained by choosing  r(y, t) = R∗  B-K(t)ey.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='  Notably our model reverts to the ﬁrst of these in the limit as γ(t) → 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='  Since we are interested in pricing options on daily-compounded rates payments, we introduce a new variable  zt representing the integral of the short rate, making use of the fact that daily compounding can be to a good  approximation captured by assuming continuous compounding.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' We shall make the choice  zt :=  � t  0  (rs − r(s))ds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='5)  We consider the (stochastic) time-t price of a European-style security which pays a cash amount P(yT , zT ) at  maturity T, denoting this by f(yt, zt, t).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' We note in particular that the price of a T-maturity zero coupon bond is  obtained by taking P(y, z) = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' We will look to derive the functional form of f(·, ·, ·) implied by our model in this  case and in the process to determine the conditions on R∗(t) necessary to satisfy (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='  From the Feynman-Kac theorem we infer that f(y, z, t) emerges as the solution to the following backward  Kolmogorov diffusion equation:  ∂f  ∂t − α(t)y ∂f  ∂y + (r(y, t) − r(t))  � ∂  ∂z − 1  �  f + 1  2σ2(t)∂2f  ∂y2 − r(t)f = 0,  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='6)  with r(y, t) given by (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='2), subject to the termiinal condition f(y, z, T) = P(y, z).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='  3  Pricing Kernel  We deﬁne at this point the following notation for future reference:  φr(t, v) := e−  � v  t α(u)du,  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='1)  Σrr(t, v) :=  � v  t  φ2  r(u, v)σ2(u)du,  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='2)  ψr(t, v) := e  1  2 γ2(v)Σrr(t,v),  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='3)  Σrz(t, v) :=  � v  t  ψr(t, u)φr(u, v)Σrr(t, u)du,  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='4)  Σzz(t, v) := 2  � v  t  ψr(t, u)Σrz(t, u)du,  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='5)  Σ(t, v) :=  �  Σrr(t, v)  Σrz(t, v)  Σrz(t, v)  Σzz(t, v)  �  ,  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='6)  B∗(t, v) :=  � v  t  ψr(t, u)φr(t, u)du,  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='7)  B+(t, t1, v) := B∗(t, v) − B∗(t, t1)  φr(t, t1)  =  � v  t1  ψr(t, u)φr(t1, u)du,  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='8)  µ∗(y, t, v) := B∗(t, v)(y + Σrz(0, t)) + 1  2B∗2(t, v)Σrr(0, t).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='9)  3  We observe here that φr(t, v) represents the impact of mean reversion and ψr(t, v) that of the counteracting dispersion  from the mean induced by smile.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='  We look to obtain the pricing kernel or Green’s function for (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='6), deﬁned as a (generalised) function  G(y, z, t;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' η, ζ, T) such that the solution subject to the speciﬁed terminal condition can be obtained from the following  convolution expression:  f(y, z, t) =  ��  R2 G(y, z, t;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' η, ζ, T)P(η, ζ) dη dζ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='10)  In the absence of exact analytic solutions, we seek the pricing kernel as a perturbation expansion in the limit that the  deviations of the short rate from the forward rate curve are small under some suitable norm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' To that end let us deﬁne  the small parameter  ϵ :=  ��γ2(·)Σrr(·, ·)  ��  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='11)  and seek an asymptotic expansion of the pricing kernel in powers of ϵ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' To allow of a skew adjustment that contributes  at the same order of approximation as the smile adjustment we shall make the assumption that ∥γ(·)y∗(·)∥= O(√ϵ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='3  Let us further express R∗(·) asymptotically as  R∗(t) =  ∞  �  n=1  R∗  n(t),  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='12)  with R∗  n(·) = O(ϵn).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='  To express our result conveniently, we introduce the functions  R±  1 (y, t, t1, v) := ψr(t, t1)e±γ(t1)(φr(t,t1)y+y∗(t1)−B+(t,t1,v)Σrr(t,t1)−Σrz(t,t1))  2γ(t1)  ,  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='13)  and shift operators M±(t, t1) deﬁned for t ≤ t1 by  M±(t, t1)f(y, z, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=') := f (y ± γ(t1)∆y(t, t1), z ± γ(t1)∆z(t, t1), .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=')  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='14)  ∆y(t, t1) := Σrr(t, t1)  φr(t, t1) ,  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='15)  ∆z(t, t1) := Σrz(t, t1) − B∗(t, t1)Σrr(t, t1)  φr(t, t1) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='16)  Using this notation we deﬁne also the following operators:  R1(t, t1, v) := R+  1 (y, t, t1, v) M+(t, t1) − R−  1 (y, t, t1, v) M−(t, t1),  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='17)  R1(t, t1, v) := R+  1 (y, t, t1, v) M+(t, t1) + R−  1 (y, t, t1, v) M−(t, t1),  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='18)  G1(t, t1, v) := R1(t, t1, v) + R∗  1(t1) − e  1  2 γ2(t1)Σrr(t,t1)  �  φr(t, t1)(y + Σrz(0, t) + B∗(t, t1)Σrr(0, t))  − B+(t, t1, v)Σrr(t, t1)  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='19)  Using the operator expansion method of Turfus [2021a] in the same manner as Turfus and Romero-Bermúdez [2021]  we obtain the following result.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='  Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='1 (Pricing Kernel).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' Making use of the above-deﬁned notation, the pricing kernel for (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='6) can be written  asymptotically in the limit as ϵ → 0 as  G(y, z, t;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' η, ζ, v) = D(t, v)e−µ∗(y,t,v)  ∞  �  n=0  Gn(y, z, t;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' η, ζ, v)  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='20)  3We have avoided being explicit about the range of t over which the norms are assessed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' A typical choice would be a weighted integral over  [0, T] for some ﬁnite T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='  4  with the Gn(·) = O(ϵn) and in particular  G0(y, z, t;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' η, ζ, v) = N2  �  η + Σrz(t, v) − φr(t, v)y, ζ − µ∗(y, t, v) + 1  2Σzz(t, v) − z;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' Σ(t, v)  �  ,  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='21)  G1(y, z, t;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' η, ζ, v) =  �� v  t  G1(t, t1, v)dt1 − Q(t, v)  � � ∂  ∂z − 1  �  G0(y, z, t;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' η, ζ, v),  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='22)  G2(y, z, t;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' η, ζ, v) =  � � v  t  � t2  t  G1(t, t1, v) G1(t, t2, v)dt1dt2  � ∂  ∂z − 1  �2  −  � v  t  G1(t, t1, v)dt1 Q(t, v)  � ∂  ∂z − 1  �2  + 1  2  �  Q2(t, v) −  � v  t  Σrz(t, t1)(γ(t1)R1(t, t1, v) − 1)dt1  � � ∂  ∂z − 1  �2  +  � v  t  R∗  2(t1)dt1  � ∂  ∂z − 1  ��  G0(y, z, t;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' η, ζ, v),  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='23)  with  Q(t, v) := Σrz(t, v)  φr(t, v)  � ∂  ∂y − B∗(t, v) ∂  ∂z  �  + Σzz(t, v) ∂  ∂z  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='24)  and N2(·, ·;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' Σ) a bivariate Gaussian probability density function with covariance Σ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' A proof of this result is given in Appendix A below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' Note in (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='23) that the shift operator in G1(t, t1, v) acts  on the y-variables in G1(t, t2, v).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='  What has effectively been achieved here is that representations of the O(1) drift and diffusion associated with z  and the O(ϵ1/2) Hull-White stochastic discounting, as captured by µ∗(y, t, v)+Q(t, v), are subtracted out of the time-  ordered exponential operator W(t, u) in (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='7) and incorporated directly into the modiﬁed Gaussian kernel G0(·;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' ·) on  which it acts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' In this way a zeroth order operator is replaced by the ﬁrst order operator W1(t, u) in (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='12).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' Only by  use of this device does the asymptotic expansion of the (modiﬁed) operator become possible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='  It will be observed that the leading-order contribution (n = 0) is in its functional form identical to the Hull-White  kernel of Turfus [2022], with the caveat that the mean reversion function φr(t, u) is adjusted up (reducing its impact)  by inclusion of the smile factor ψr(t, t1) in (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='7), with no impact from skew.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' This means that solutions based on our  expansion are likely to retain better accuracy even at longer maturities than those of Turfus and Romero-Bermúdez  [2021].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' Note that we could have expressed our results as a perturbation operator acting on the Hull-White kernel but  choose, for reasons of convenience of use, to multiply by the stochastic discounting operator in the ansatz (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='20) after  applying the perturbation operators term-by-term.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='  4  Fitting to the Forward Curve  Let us further deﬁne for future notational convenience  F1(t, T) :=  � T  t  G1(t, t1, T)dt1  =  � T  t  (R1(t, t1, T) + R∗  1(t1))dt1 − µ∗(y, t, T) + 1  2Σzz(t, T)  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='1)  F2(t, T) :=  � T  t  �� t2  t  G1(t, t1, T) G1(t, t2, T)dt1 − R∗  2(t2)  �  dt2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='2)  Note that y-shifts apply in the integral term in (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='2), but can in practice be ignored, since they give rise to terms  impacting at higher than second order;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' also that, in deriving (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='1), we have made use of the identity (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='18).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='  5  The calibration of our model to the forward interest rate market is achieved by considering zero coupon bond  prices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='  Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='1 (Calibration).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' Applying (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='20) to a unit payoff at T, the T-maturity zero coupon bond price associated  with the pricing kernel (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='20) is seen to be given asymptotically by  F T (y, t) ∼ D(t, T)e−µ∗(y,t,T ) (1 − F1(t, T) + F2(t, T)) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='3)  Differentiating the calibration condition F T (0, 0) = D(0, T) w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' T, applying this to second order accuracy and  setting T = t gives rise to the requirement that the ﬁrst two terms of (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='12) are given by  R∗  1(t) = −R+  1 (0, 0, t, t) + R−  1 (0, 0, t, t)  − ψr(0, t)  � t  0  φr(t1, t)Σrr(0, t1)(γ(t1)(R+  1 (0, 0, t1, t) + R−  1 (0, 0, t1, t)) − ψr(0, t1))dt1  = −ψr(0, t)  �sinh Y ∗(t, t)  γ(t)  +  � t  0  ψr(0, t1)φr(t1, t)Σrr(0, t1) (cosh Y ∗(t1, t) − 1) dt1  �  ,  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='4)  R∗  2(t) ∼ R∗  1(t)  � t  0  R∗  1(t1)dt1,  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='5)  where for t1 ∈ [0, t],  Y ∗(t1, t) := γ(t1)  �  y∗(t1) − B+(0, t1, t)Σrr(0, t1) − Σrz(0, t1)  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='6)  We observe that, excluding the bracketed expression which provides the main skew-smile adjustment, (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='3) is  essentially a Hull-White representation of the bond price making use of a modiﬁed mean reversion factor in place of  the usual φr(t, u) as the integrand in (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='7).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' A ﬁrst-order representation which should sufﬁce for many purposes, is  obtained by neglecting F2(t, T) in (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' Provided the leading-order skew-smile correction terms remain small, the  approximation should be a good one: the variable y would have to take on improbably large values for this not to be  the case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' Note that these results are, up to second order, equivalent to those presented in Turfus and Romero-Bermúdez  [2021], as might be expected since the model is unchanged here, only the method of building the expansion slightly  different.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='  5  Applications  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='1  Forward Rates  An expression for forward rates is easily deduced from our zero coupon bond formula.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='  Corollary 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='1 (Instantaneous Forward Rate).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' The instantaneous forward rate is given by  f T (y, t) = r(T) + ψr(t, T)φr(t, T)(y + Σrz(0, t) + B∗(t, T)Σrr(0, t))  + D(t, T)e−µ∗(y,t,T )  F T (y, t)  �  G1(t, T, T) −  � T  t  G1(t, t1, T) G1(t, T, T)dt1 + R∗  2(T)  �  + O(ϵ3),  (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='1)  with F T (y, t) as given by Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' The corresponding ﬁrst order version of this result is obtained by ignoring the  second two terms in parentheses and taking a ﬁrst order representation of F T (y, t).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' This result is obtained by noting that the instantaneous forward rate is given by f T (yt, t) where  f T (y, t) = − ∂  ∂T ln F T (y, t)  and making use of (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='  6  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='2  Option Pricing  We assume below that, in option pricing, the interest rate that is used as the underlying is the same one that is used in the  discounting of cash ﬂows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' If, particularly in the case of LIBOR, there is a spread over the risk-free rate, this situation  can effectively be managed by calibrating the model to the risk-free rate and subtracting the (assumed deterministic)  spread off of the strike (or coupon rate).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='  Compounded Rate Caplet Pricing  RFR cap and caplet prices are obtained to leading order from the following  theorem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='  Theorem 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='1 (RFR Caplet Price).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' Consider a caplet based on the compounded risk-free rate over a payment period  [T1, T2] and a payoff with strike K at time T2 of  �  e  � T2  T1 r(yt,t)dt − 1 − Kδ(T1, T2)  �+  =  �  D(T1, T2)−1ez2−z1 − κ−1�+  =: Pcaplet(z1, z2)  (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='2)  where zT1 = z1, zT2 = z2 and κ = (1 + Kδ(T1, T2))−1, with δ(·, ·) providing the relevant year fraction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' Using the  above-deﬁned notation and deﬁning the critical value of z2 − z1 at which the option comes into the money as  ∆z∗ = ln  �  κ−1D(T1, T2)  �  ,  (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='3)  the caplet PV will be given asymptotically with relative errors = O(ϵ2) by  PVCaplet ∼ D(0, T1)  �  1 −  � T1  0  ˜G1(0, t1, T1)dt1  �  Φ(d1(y, z − z1, 0))  �����  y=0,z=z1  − κ−1D(0, T2)  �  1 −  � T2  0  ˜G1(0, t1, T2)e−θ(y,0)H(T1−t1)dt1 − B∗(T1, T2)Σrz(0, T1)  �  Φ(d2(y, z − z1, 0))  �����  y=0,z=z1  − κ−1D(0, T2)  �  B∗2(T1, T2)Σrr(0, T1) + Σzz(T1, T2)N(d2(0, 0, 0)),  (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='4)  with Φ(·) a cumulative normal distribution function, N(·) the corresponding density and H(·) the Heaviside step  function, where we deﬁne  d1(y, w, t) := θ(y, t) + w − ∆z∗ + 1  2(B∗2(T1, T2)Σrr(t, T1) + Σzz(T1, T2))  �  B∗2(T1, T2)Σrr(t, T1) + Σzz(T1, T2)  (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='5)  d2(y, w, t) := d1(y, w, t) −  �  B∗2(T1, T2)Σrr(t, T1) + Σzz(T1, T2),  (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='6)  θ(y, t) := B∗(T1, T2)(φr(t, T1)y − Σrz(t, T1) + Σrz(0, T1)) + 1  2B∗2(T1, T2)φ2  r(t, T1)Σrr(0, t),  (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='7)  and ˜G1(t, t1, T2) is deﬁned analogously to G1(t, t1, T2) above except in that we re-deﬁne  ∆y(t, t1) = φr(T1 ∧ t1, T1 ∨ t1)Σrr(t, T1 ∧ t1)  φr(t, T1)  ,  (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='8)  ∆z(t, t1) =  �  Σrz(T1, t1) + B+(T1, t1, T2)Σrr(T1, t1)  �  1t1>T1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='  (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='9)  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' The proof of this result is set out in Appendix B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' Cap prices are of course obtained as an algebraic sum of  caplet prices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='  7  LIBOR Caplet Pricing  LIBOR or term-rate cap and caplet prices are obtained similarly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='  Theorem 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='2 (LIBOR Caplet Price).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' Consider a caplet based on the term rate over a payment period [T1, T2] and a  payoff with strike K at time T2 of  PLIBOR caplet(y1) :=  �  1/F T2(y1, T1) − κ−1�+  (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='10)  where yT1 = y1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' This gives rise to a T1-value of  VLIBOR caplet(y, T1) =  �  1 − κ−1F T2(y, T1)  �+  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='  Using the above-deﬁned notation, the caplet PV will be given asymptotically with relative errors = O(ϵ2) by  PVLIBOR Caplet ∼ D(0, T1)  �  1 −  � T1  0  ˜G1(0, t1, T1)dt1  �  Φ(d1(y, 0))  �����  y=0  − κ−1D(0, T2)  �  1 −  � T2  0  ˜G1(0, t1, T2)e−θ(y,0)H(T1−t1)dt1 − B∗(T1, T2)Σrz(0, T1)  �  Φ(d2(y, 0))  �����  y=0  − κ−1D(0, T2)  �  B∗2(T1, T2)Σrr(0, T1)N(d2(0, 0)),  (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='11)  where we deﬁne additionally  d1(y, t) := θ(y, t) − ∆z∗ + 1  2B∗2(T1, T2)Σrr(t, T1)  �  B∗2(T1, T2)Σrr(t, T1)  (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='12)  d2(y, t) := d1(y, t) −  �  B∗2(T1, T2)Σrr(t, T1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='  (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='13)  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' This result can be understood as a special case of Theorem 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='1 when a zero value is assigned to the volatility  σ(t) for t ∈ [T1, T2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='  Swaption Pricing  Swaption prices are obtained similarly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='  Theorem 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='3 (Swaption Price).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' Consider a payer swaption based on a LIBOR or compounded-rate swap with payment  periods [Ti−1, Ti] for i = 1, 2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' , n and a ﬁxed coupon K with payoff at time T0 given by the swap value at time T0  if this is in the money.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='  8  Using the above-deﬁned notation,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' the swaption PV will be given asymptotically with relative errors = O(ϵ2) by  PVSwaption ∼ D(0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' T0)  �  1 −  � T0  0  ˜G1(0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' t1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' T0)dt1  �  Φ(d(0)(y))  �����  y=0  − D(0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' Tn)  �  1 −  � Tn  0  ˜G1(0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' t1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' Tn)e−B∗(T0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='Tn)φr(0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='T0)yH(T0−t1)dt1 − B∗(T0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' Tn)Σrz(0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' T0)  �  Φ(d(n)(y))  �����  y=0  +  �  B∗2(T0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' Tn)Σrr(0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' T0)N(d(n)(0))  − K  n  �  i=1  δ(Ti−1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' Ti)D(0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' Ti)  � �  1 −  � Ti  0  ˜G1(0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' t1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' Ti)e−B∗(T0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='Ti)φr(0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='T0)yH(T0−t1)dt1 − B∗(T0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' Ti)Σrz(0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' T0)  �  Φ(d(i)(y))  �����  y=0  +  �  B∗2(T0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' Ti)Σrr(0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' T0)N(d(i)(0))  �  ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='  (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='14)  where we deﬁne additionally for i = 0, 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' , n  d(i)(y) := φr(0, T0)y − yc − Σrz(0, T0)  �  Σrr(0, T0)  −  �  B∗2(T0, Ti)Σrr(0, T0),  (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='15)  where yc is the value of yT0 at which the swap comes into the money.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' The proof of this result is analogous to that provided in Appendix B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' This follows from the similarity of the  swaption payoff:  PSwaption(y, T0) = 1 − F Tn(y, T0) − K  n  �  i=1  δ(Ti−1, Ti)F Ti(y, T0)  with Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='10).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' A key observation is that the value of a risk-free interest rate payment stream, starting at T0 with  ﬁnal payment at Tn and discounted at the risk-free interest rate is PV = F T0(y, t) − F Tn(y, t), i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' the difference  between the value of a unit payment at time T0 and one at time Tn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' We note further that this observation is equally  true of compounded-rate and term-rate swaptions, since the term-rate payment is by deﬁnition the expected value of a  compounded-rate payment, observed on its initial ﬁxing date.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='3  Implied Volatility Formulae  We look to translate the formulae set out in (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='4) and (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='11) above into expressions for effective/implied Hull-White  term variances.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' This has the advantage of making it more intuitively obvious how the smile and skew impact on the  caplet pricing as a function of moneyness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' Indeed, one of the ﬁrst things practitioners typically want to do with option  prices is to translate them into effective/implied volatility equivalents.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' A second advantage is that if, rather than using  our asymptotic formulae directly, we use the Hull-White formulae with our best estimate of the effective variance  substituted for the Hull-White variance, we naturally obtain better extrapolated behaviour far from the money, with  arbitrage avoided.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='4  4The quadratic expressions (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='26) and (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='32) obtained below may arguably give rise for values of ϵ of order unity to effective variance  speciﬁcations which are negative.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' But such circumstances are of no practical relevance and would in any event compromise the asymptotic approach  entirely, not just the implied volatility speciﬁcation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='  9  We note in passing that one of the main reasons for the popularity of the SABR model of Hagan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' [2002] was  precisely that the asymptotic representation of option prices was explicitly as a formula for the implied Black-Scholes  volatility.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' The approach we take is along the lines of that made use of by Alòs et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' [2015].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='  Effective Compounded Rates Variance  Starting with the expression (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='4) for the compounded caplet price, we  look to re-express this as  PVCaplet ∼ D(0, T1)Φ(d(1)(K, T1, T2)) − κ−1D(0, T2)Φ(d(2)(K, T1, T2))  (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='16)  with relative errors = O(ϵ2), where  d(1)(K, T1, T2)) := −∆z∗ + 1  2 (VC + v(K, T1, T2))  �  VC + v(K, T1, T2)  (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='17)  d(2)(K, T1, T2)) := d(1)(K, T1, T2) −  �  VC + v(K, T1, T2),  (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='18)  for some variance adjustment function v(K, T1, T2) deﬁned against a baseline compounded-rate term variance  VC = B∗2(T1, T2)Σrr(0, T1) + Σzz(T1, T2),  (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='19)  so that the effective variance is  Veffective = VC + v(K, T1, T2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='  (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='20)  To determine the appropriate functional form for v(K, T1, T2), we expand (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='4) and (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='16) as Taylor expansions  and equate terms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' To that end we note expanding (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='16) to ﬁrst order in terms of the small parameter v(K, T1, T2) that  PVCaplet ∼ D(0, T1)Φ(d(1)) − κ−1D(0, T2)  �  Φ(d(2)) − v(K, T1, T2)  2√VC  N(d(2))  �  ,  (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='21)  with d(j) given by dj(0, 0, 0), while the expansion of (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='4) gives rise with O(ϵ2) relative error to  D(0, T1)Φ(d(1)) − κ−1D(0, T2)Φ(d(2))  +  �  C1(T1, T2) − C2(T1, T2) d(2) + C3(T1, T2)  �  d(2)  2 − 1  ��  κ−1D(0, T2)N(d(2))  where  C1(T1, T2) :=  � T2  T1  (ψr(0, t1) cosh Y ∗(t1, T2) − ψr(T1, t1)) ΨC(T1, t1, T2) dt1  (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='22)  C2(T1, T2) := 1  2  � T2  T1  ψr(0, t1) sinh Y ∗(t1, T2)γ(t1)Ψ2  C(T1, t1, T2) dt1  (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='23)  C3(T1, T2) := 1  3!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='  � T2  T1  ψr(0, t1) cosh Y ∗(t1, T2)γ2(t1)Ψ3  C(T1, t1, T2) dt1,  (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='24)  with  ΨC(T1, t1, T2) := V  − 1  2  C  �  B∗(T1, T2)φr(T1, t1)Σrr(0, T1) + Σrz(T1, t1) + B+(T1, t1, T2)Σrr(T1, t1)  �  (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='25)  and Y ∗(·, ·) deﬁned by (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='6) above.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='  Equating terms in the two expansions, we conclude that we must have  v(K, T1, T2) ∼ 2V  1  2  C  �  C1(T1, T2) − C2(T1, T2) d(2) + C3(T1, T2)  �  d(2)  2 − 1  ��  ,  (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='26)  from which we deduce an effective compounding rate caplet term variance given by (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='20) with O(ϵ2) relative  error.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' It is at this point evident how the linear term involving C2(T1, T2) gives rise to the skew and the quadratic  term involving C3(T1, T2) to the smile.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' We suggest on this basis that taking the parameter ϵ to be given here by  max{|C2(T1, T2)|, C3(T1, T2)}/V  1  2  C would furnish a good guide as to the level of accuracy of the ﬁrst order effective  variance expansion, with relative errors being expected to be of magnitude ϵ2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='  10  Effective LIBOR Variance  Starting instead with the expression (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='11) for the LIBOR or term-rate caplet price, we  look to re-express this as  PVLIBOR Caplet ∼ D(0, T1)Φ(d(1)(K, T1, T2)) − κ−1D(0, T2)Φ(d(2)(K, T1, T2))  (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='27)  with relative errors = O(ϵ2), where  d(1)(K, T1, T2)) := −∆z∗ + 1  2 (VL + v(K, T1, T2))  �  VL + v(K, T1, T2)  (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='28)  d(2)(K, T1, T2)) := d(1)(K, T1, T2) −  �  VL + v(K, T1, T2),  (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='29)  for some variance adjustment function v(K, T1, T2) deﬁned against a baseline LIBOR term variance  VL := B∗2(T1, T2)Σrr(0, T1),  (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='30)  so that the effective variance is  Veffective = VL + v(K, T1, T2)  (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='31)  By a calculation analogous to the above, we conclude that we must have  v(K, T1, T2) ∼ 2V  1  2  L  �  C1(T1, T2) − C2(T1, T2) d(2) + C3(T1, T2)  �  d(2)  2 − 1  ��  ,  (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='32)  with d(j) given by dj(0, 0) and  C1(T1, T2) :=  � T2  T1  (ψr(0, t1) cosh Y ∗(t1, T2) − ψr(T1, t1)) ΨL(T1, t1) dt1,  (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='33)  C2(T1, T2) := 1  2  � T2  T1  ψr(0, t1) sinh Y ∗(t1, T2)γ(t1)Ψ2  L(T1, t1) dt1,  (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='34)  C3(T1, T2) := 1  3!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='  � T2  T1  ψr(0, t1) cosh Y ∗(t1, T2)γ2(t1)Ψ3  L(T1, t1) dt1,  (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='35)  with  ΨL(T1, t1) := φr(T1, t1)  �  Σrr(0, T1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='  (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='36)  Effective Swaption Variance  Starting instead with the expression (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='14) for the swaption price, we look to re-  express this as  PVSwaption ∼ D(0, T0)Φ( ˜d(0)(K, T)) − D(0, Tn)Φ( ˜d(n)(K, T)) − K  n  �  i=1  δ(Ti−1, Ti)D(0, Ti)Φ( ˜d(i)(K, T)),  (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='37)  with relative errors = O(ϵ2), where  ˜d(i)(K, T)) :=  −yc − Σrz(0, T0)  �  Σrr(0, T0) + ˜v(K, T)  − B∗(T0, Ti)  �  Σrr(0, T0) + ˜v(K, T)  (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='38)  for some variance adjustment function ˜v(K, T) with T := (T0, T1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' , Tn), with the effective short rate term variance  taken to be  Veffective = Σrr(0, T0) + ˜v(K, T).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='  (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='39)  11  Deﬁning ˜d(i) to be the result obtained by setting ˜v(K, T) = 0 in (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='38), we can expand (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='37) as  PVSwaption ∼ D(0, T0)Φ  �  ˜d(0)  �  − D(0, Tn)Φ  �  ˜d(n)  �  − K  n  �  i=1  δ(Ti−1, Ti)D(0, Ti)Φ  �  ˜d(i)  �  +  ˜v(K, T)  2  �  Σrr(0, T0)  n  �  i=1  (δin + Kδ(Ti−1, Ti))  �  1 + ∆ ˜d(i) ˜d(n)  �  B∗(T0, Ti)D(0, Ti)N  �  ˜d(n)  �  ,  (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='40)  where we have made use of the fact that  N  �  ˜d(i)  �  ∼  �  1 + ∆ ˜d(i) ˜d(n)  �  N  �  ˜d(n)  �  (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='41)  with  ∆ ˜d(i) := ˜d(n) − ˜d(i)  (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='42)  and δin the Kronecker delta.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' We observe that the sum in the second line of (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='40) can be written more compactly as  �  An + Bn ˜d(n)  �  N  �  ˜d(n)  �  Expanding (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='14) as in the previous cases leads to the conclusion that the second line in (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='40) must be equated with  n  �  i=1  �  C1(T0, Ti) − C2(T0, Ti) ˜d(i) + C3(T0, Ti)  �  ˜d2  (i) − 1  ��  (δin + Kδ(Ti−1, Ti)) D(0, Ti)N  �  ˜d(i)  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='  This can be written asymptotically, making use of (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='41), as  n  �  i=1  �  C1(T0, Ti) − C2(T0, Ti)  �  ˜d(n) − ∆ ˜d(i)  �  + C3(T0, Ti)  ��  ˜d(n) − ∆ ˜d(i)  �2  − 1  ��  (δin + Kδ(Ti−1, Ti))  �  1 + ∆ ˜d(i) ˜d(n)  �  D(0, Ti)N  �  ˜d(n)  �  ,  which we write more compactly as  �  Dn + En ˜d(n) + Fn  �  ˜d2  (n) − 1  ��  N  �  ˜d(n)  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='  Asymptotic matching then requires that ˜v(K, T) be chosen to satisfy  ˜v(K, T) ∼  2  �  Dn + En ˜d(n) + Fn  �  ˜d2  (n) − 1  ��  �  An + Bn ˜d(n)  � �  Σrr(0, T0)  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='  (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='43)  As can be seen, the effective term variance is on this occasion not quite quadratic in its dependence on log-moneyness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='  Further, the form of the denominator will cause it to give rise to singular behaviour for values of ˜d(n) sufﬁciently far  from the ATM level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' However, since the model would not in any event be calibrated to give credible results in such  extreme cases, this ought not to be a signiﬁcant limitation in practice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='  6  Numerical Calculations  Caplets  The above model has been calibrated to caplet market data capturing the skew and smile for SAR 6M  LIBOR rates in May 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' For the mean reversion, we choose a representative ﬁxed value of α(t) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' Choosing  other values made little difference to the results obtained.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' Since the model has three other disposable parameters  (σ(t), y∗(t) and γ(t)) it should be possible making use of (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='26) to match the ATM level, smile and skew of the  12  implied volatility surface at each maturity for which market data are provided.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' Indeed this is found to be the case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='5  The resulting ﬁt is illustrated in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' 1 and is seen to be excellent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' Results are expressed as σIV (K, T2), the constant  value of σ(t) which would have to be inserted in the Hull-White formula to replicate the price of a (6M tenor) caplet  with strike K and maturity T2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' For the smile, calibrated values of γ(t) ranged from around 300 at the short end to 40  for t = 10y while, for the skew, the corresponding values of γ(t)y∗(t) were 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='5 and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='08.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' The corresponding implied  volatility surface is illustrated in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
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+page_content='5  K  1e  2  2  3  4  5  6  7  IV(K, T2)  1e  3  T2 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='5  T2 = 1  T2 = 2  T2 = 5  T2 = 10  Figure 1: Implied volatilities for various caplet maturities T2  5In fact the ﬁtting was done to LIBOR caplet data treated as compounded-rate caplets, since the latter were not available and this approach  satisﬁed the exigency of convenient presentation of numerical results for compounded-rate formulae.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' In any event, it was found to be no more  difﬁcult to calibrate the model interpreting the data as being for LIBOR caplets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='  13  K  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
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+page_content='026  T2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
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+page_content='00  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
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+page_content='00  IV(K, T2) × 10  3  Figure 2: Caplet implied volatility surface  Values of σIV (K, T2) were also explicitly backed out from the compounded-rate caplet price formula (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' These  are shown for comparison in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' As can be seen, the ﬁt is similarly good close to the money but the asymptotic  caplet price formula clearly becomes unreliable for more extreme strikes so caution should be exercised in its direct  use to calculate prices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' Rather, the use of an asymptotic representation of the implied volatility surface, embedding as  it does the avoidance of arbitrage (negative option prices) for any reasonable strikes, is to be preferred.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='6  6For the same reason analytic option prices under the SABR model are always constructed indirectly from asymptotic representation of implied  volatilities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='  14  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
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+page_content='045  K  2  3  4  5  6  7  IV(K, T2)  1e  3  Solid: analytic using Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='26).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='  Dashed: numerical using Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' Dots: Mkt data  T2 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='5  T2 = 1  T2 = 2  T2 = 5  T2 = 10  Figure 3: Implied volatilities for various maturities  It is of interest to consider how much impact results from use of a compounded rate rather than a term rate as the  caplet underlying.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' This is illustrated in Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' 4 and 5 where PVs based on formulae (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='16) and (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='27) are compared.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='  As is evident, the impact is much greater for shorter maturities where T2 − T1 is comparable with T1, and becomes  rather insigniﬁcant when T2 − T1 ≪ T1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
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+page_content='0  PVCaplet × 103  O(  1) CMP T2 = 1  O(  1) LIBOR T2 = 1  O(  1) CMP T2 = 2  O(  1) LIBOR T2 = 2  Figure 4: Comparison of term-rate and compounded-rate caplet prices for short maturities  15  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
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+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='5  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='0  PVCaplet × 103  O(  1) CMP T2 = 5  O(  1) LIBOR T2 = 5  O(  1) CMP T2 = 10  O(  1) LIBOR T2 = 5  Figure 5: Comparison of term-rate and compounded-rate caplet prices for longer maturities  For completeness we also looked at instantaneous forward rates calculated in accordance with (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='1), with ﬁxing  date T = t + 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' Results are shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' Since these results incorporate second order terms, unlike the  caplet results shown above, they are expected to be highly accurate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' The impact of the skew/smile can be inferred by  comparing with the dashed lines (Hull-White).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' As expected, the model is seen to behave just like Hull-White with  forward rates linear in the underlying Gaussian variable y when this is small in magnitude.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='  4  2  0  2  4  y  (0, t)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
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+page_content='06  fT(y, t)  t = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='1 ,  (  2)  t = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='1, = y * = 0  t = 1 ,  (  2)  t = 1, = y * = 0  t = 2 ,  (  2)  t = 2, = y * = 0  t = 5 ,  (  2)  t = 5, = y * = 0  Figure 6: Forward rates for various observation dates t with payment date T = t + 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='  Swaptions  The implied volatility surface of swaptions with two payment periods of 3 months is shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
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+page_content='00  IV(K, T2) × 10  3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
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+page_content='9  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='0  IV(K, T2)  1e  2  Swaption 2 period, 3M  T2 = 1  T2 = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='5  T2 = 2  T2 = 3  T2 = 5  T2 = 7  T2 = 10  Figure 7: Swaption implied volatilities for various maturities  7  Conclusions  We have successfully extended the short rate model of Turfus and Romero-Bermúdez [2021] to address the pricing of  SOFR/SONIA/ESTR caplets based on compounded rates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' This we achieved by expressing the result as a perturbation  of the analytic kernel of Turfus [2022].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' The model is seen to have the following properties:  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' Convenient analytic representations are available for bond and option prices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' A single calibration addresses options of any maturity and tenor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' Option pricing takes account of volatility skew and smile.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' Prices can be calculated for LIBOR or term-rate options as well as for options on backward-looking compounded  rates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='  We believe our model to be unique in satisfying all of the above criteria.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='  The asymptotic expansion developed here provides the further beneﬁt of pricing forward rates and LIBOR caplets  more accurately than that of Turfus and Romero-Bermúdez [2021].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' The expression for forward rates is (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' Caplet  prices are best calculated noting that the effective Hull-White term variance is given by (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='20) and (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='26) for a  compounded-rate caplet and by (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='31) and (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='32) for a LIBOR or term-rate caplet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='  A  Proof of Pricing Kernel Result  We offer a sketch of the proof that (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='20) represents the pricing kernel for (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' We follow Turfus [2019, 2021a] in  introducing the following deﬁnitions and notation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='  17  Deﬁnition A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' The time-ordered exponential or Dyson series deﬁned for a linear operator L(t) by  ET  t (L(·)) = I +  ∞  �  n=1  �  t≤t1≤.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='≤tn≤T  L(t1) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' L(tn)dt1 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' dtn  = I +  ∞  �  n=1  � T  t  � T  t1  · ·  � T  tn−1  L(u) L(t2) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' L(tn)dtn .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' dt2dt1  = I +  ∞  �  n=1  � T  t  � tn  t  · ·  � t2  t  L(t1) L(t2) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' L(tn)dt1dt2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' dtn  (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='1)  generalises the exponentiation of the integral of a function f(t) to the case of a time-dependent linear operator L(t).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='  Deﬁnition A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' We deﬁne the commutator of an operator L(t) with an operator V(t) where both operators act on the  same function space by the following operator:  adL(t1)(V(t2)) := L(t1) V(t2) − V(t2) L(t1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='  (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='2)  We will have need to combine these two ideas in computing the time-ordered exponential of a commutator operator,  interpreted as follows:  Eu  t  �  adL(·)  �  (V(u)) = V(u) +  � u  t  adL(t1)(V(u))dt1 +  � u  t  � u  t2  adL(t2)  �  adL(t1)(V(u))  �  dt1dt2 + .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='  (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='3)  Proof of Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' We start by observing that, although r(y, t) − r(t) = O(ϵ  1  2 ), the term (r(y, t) − r(t))∂/∂z is  O(1) so prevents direct use of a naïve perturbation expansion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' Noting however that r(y, t) − r(t) ∼ y for small y  we can subtract out the asymptotic representation and look to handle it separately.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' To that end we write the evolution  operator associated with (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='6) as Ev  t (L0(·) + V0(·)) where  L0(t) = −α(t)y ∂  ∂y + 1  2σ2(t) ∂2  ∂y2 − r(t),  (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='4)  V0(t) = (r(y, t) − r(t))  � ∂  ∂z − 1  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='  (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='5)  Following Turfus and Romero-Bermúdez [2021] who apply the exponential expansion formula of Turfus [2021a] to a  closely analogous evolution operator, we can write the Green’s function solution of (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='6) as  G(y, z, t;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' η, ζ, v) = D(t, v) Ev  t (W(t, ·))N  �  η − φr(t, v)y  �  Σrr(t, v)  �  ,  (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='6)  where7  W(t, u) :=  �  R+(y, t, u)eγ(u)∆y(t,u) ∂  ∂y − R−(y, t, u)e−γ(u)∆y(t,u) ∂  ∂y + R∗(u)  � � ∂  ∂z − 1  �  ,  (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='7)  with  R±(y, t, u) := e  1  2 γ2(u)Σrr(t,u)±γ(u)(φr(t,u)y+y∗(u))  2γ(u)  ,  (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='8)  7Observe that the only difference at this stage compared to their result is in the inclusion of the derivative w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' z in (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='7).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' However there is  an important difference in the solution strategy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' By subtracting out of (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='14) below a Hull-White (linear) representation of the discounting rate in  addition to the z-drift, we are able to incorporate both directly into the analytic kernel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' So, rather than the stochastic discounting being represented  by a perturbation as in Turfus and Romero-Bermúdez [2021], it is only the difference between that and the Hull-White representation thereof which  is so represented.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='  18  Let us deﬁne  L1(t, u) := ψr(t, u)  �Σrr(t, u)  φr(t, u)  ∂  ∂y + Σrz(t, u) ∂  ∂z  � � ∂  ∂z − 1  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='  (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='9)  V1(t, u) := W(t, u) − L1(t, u).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='  (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='10)  We deduce  Ev  t (W(t, ·)) = Ev  t (W1(t, ·)) Ev  t (L1(t, ·)),  (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='11)  W1(t, u) = Eu  t  �  adL1(t,·)  �  (V1(t, u))  =  �  R+(y, t, u)eγ(u)(∆y(t,u) ∂  ∂y +Σrz(t,u)( ∂  ∂z −1))  − R−(y, t, u)e−γ(u)(∆y(t,u) ∂  ∂y +Σrz(t,u)( ∂  ∂z −1)) + R∗(u)  � � ∂  ∂z − 1  �  − L1(t, u).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='12)  Next deﬁning  L2(t, u) := ∂  ∂uµ∗(y, t, u)  � ∂  ∂z − 1  �  = ψr(t, u) (φr(t, u)(y + Σrz(0, t) + B∗(t, u)Σrr(0, t)))  � ∂  ∂z − 1  �  ,  (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='13)  V2(t, u) := W1(t, u) − L2(t, u).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='  (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='14)  we deduce  Ev  t (W1(t, ·)) = Ev  t (W2(t, ·)) Ev  t (L2(t, ·)),  (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='15)  W2(t, u) = Eu  t  �  adL2(t,·)  �  (V2(t, u))  =  �  R+(y, t, u)eγ(u)(∆y(t,u) ∂  ∂y +∆z(t,u)( ∂  ∂z −1))  − R−(y, t, u)e−γ(u)(∆y(t,u) ∂  ∂y +∆z(t,u)( ∂  ∂z −1)) + R∗(u)  � � ∂  ∂z − 1  �  − L3(t, u).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='  (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='16)  where  L3(t, u) := Eu  t  �  adL2(t,·)  �  (L1(t, u) + L2(t, u))  = L1(t, u) + L2(t, u) − B∗(t, u)ψr(t, u)Σrr(t, u)  φr(t, u)  � ∂  ∂z − 1  �2  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='  (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='17)  We observe, making use of the identity8  � v  t  B+(t, u, v)ψr(t, u)Σrr(t, u)du = 1  2Σzz(t, v),  (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='18)  that  � v  t  B∗(t, u)ψr(t, u)Σrr(t, u)  φr(t, u) du = B∗(t, v)Σrz(t, v)  φr(t, v) − 1  2Σzz(t, v),  (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='19)  whence we deduce  � v  t  L3(t, u)du =  �  µ∗(y, t, v) + Σrz(t, v)  φr(t, v)  ∂  ∂y + 1  2Σzz(t, v) ∂  ∂z  +  �1  2Σzz(t, v) − B∗(t, v)Σrz(t, v)  φr(t, v)  � � ∂  ∂z − 1  �� � ∂  ∂z − 1  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='  8This is readily proved by differentiating both sides w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='  19  Applying Ev  t (L2(t, ·)) Ev  t (L1(t, ·)) to the Gaussian kernel, so increasing its dimension from 1 to 2, gives rise to  G(y, z, t;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' η, ζ, v) = D(t, v) Ev  t (W2(t, ·))e−µ∗(y,t,v)G0(y, z, t;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' η, ζ, v),  (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='20)  with G0(·;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' ·) deﬁned by (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='21) above.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' It is convenient to move the exponential function to the left of this expression.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='  To this end we note that the exponential of a derivative acts as a shift operator, whence  e±γ(u)∆y(t,u) ∂  ∂y e−µ∗(y,t,v) = e−µ∗(y,t,v)e±γ(u)( ∂  ∂y −B∗(t,v))∆y(t,u),  L3(t, u) e−µ∗(y,t,v) = e−µ∗(y,t,v)  �  L3(t, u) − B∗(t, v)Σrr(t, u)  φr(t, u)  � ∂  ∂z − 1  ��  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='  We obtain  G(y, z, t;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' η, ζ, v) = D(t, v)e−µ∗(y,t,v) Ev  t (W3(t, ·, v))G0(y, z, t;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' η, ζ, v),  (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='21)  W3(t, u, v) =  �  R+  1 (y, t, u, v) M+(t, u) − R−  1 (y, t, u, v) M−(t, u) + R∗(u)  � � ∂  ∂z − 1  �  − L3(t, u) + B∗(t, v)ψr(t, u)Σrr(t, u)  φr(t, u)  � ∂  ∂z − 1  �  ,  (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='22)  with R±  1 (y, t, u, v) deﬁned by (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='13), where we have made use of the fact that  e±γ(u)(∆y(t,u) ∂  ∂y +∆z(t,u) ∂  ∂z) ≡ M±(t, u).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='  Expanding Ev  t (W3(t, ·, v)) as a power series in (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='21) and making use of the above identities, we obtain (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='20), with  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='21)–(3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='23) as the ﬁrst three terms, as claimed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' This completes the proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='  B  Proof of RFR Caplet Pricing Result  Proof of Theorem 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' Making use of (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='20), the ﬁrst order caplet value as of time T1 with yT1 = y and zT1 = z1 will  be  Vcaplet(y, T1) = lim  z→z1  ��  R2 G(y, z, T1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' η, ζ, T2)Pcaplet(z1, ζ)dηdζ  ∼ e−µ∗(y,T1,T2)  �  Σzz(T1, T2)  �  1 +  �� T2  T1  G1(T1, t1, T2)dt1 − Q(T1, T2)  � � ∂  ∂z − 1  ��  � ∞  z1+∆z∗  �  eζ−z1 − κ−1D(T1, T2)  �  N  �  ζ − µ∗(y, T1, T2) + 1  2Σzz(T1, T2) − z  �  Σzz(T1, T2)  �  dζ  �����  z=z1  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='  (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='1)  We see the z-dependence drops out at this stage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' Letting V (i,j) denote the result of applying Gi(·;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' ·) to the jth order  contribution to Vcaplet, we ﬁnd  V (0,0)(y, T1) = Φ(d1(y, 0, T1)) − κ−1D(T1, T2)e−µ∗(y,T1,T2)Φ(d2(y, 0, T1)),  with d1(·) and d2(·) deﬁned by (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='5) and (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='6), respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' Applying the ﬁrst-order operator and making use of the  identity  N(d1(y, 0, t)) − κ−1D(T1, T2)e−θ(y,t)N(d2(y, 0, t) = 0  (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='2)  20  yields at ﬁrst order9  V (1,0)(y, T1) = κ−1D(T1, T2)e−µ∗(y,T1,T2)  �� T2  T1  G1(T1, t1, T2)dt1 − Σzz(T1, T2) ∂  ∂z  �  Φ(d2(y, z − z1, T1))  ����  z=z1  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='  Here the effect of the shift operators is to transform  Φ(d2(y, 0, T1) → Φ(d2(y, ±γ(t1)∆z1(t1), T1),  where  ∆z1(t1) := Σrz(T1, t1) + B+(T1, t1, T2)Σrr(T1, t1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='  (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='3)  Combining this with the leading-order term (and noting that there is no ﬁrst-order payoff contribution), we obtain  Vcaplet(y, T1) ∼ V (0,0)(y, T1) + V (1,0)(y, T1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' Taking this in turn as the payoff at T1 and valuing as of time t ∈ [0, T1)  gives rise to  Vcaplet(y, t) =  ��  R2 G(y, z, t;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' η, ζ, T1)Vcaplet(η, T1)dηdζ  ∼ V (0,0)(y, t) + V (0,1)(y, t) + V (1,0)(y, t),  (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='4)  The ζ-integration is in this case trivial.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' In particular we have the quasi-Hull-White result  V (0,0)(y, t) = e−µ∗(y,t,T1) �  D(t, T1)Φ(d1(y, 0, t)) − κ−1D(t, T2)e−θ(y,t)Φ(d2(y, 0, t))  �  ,  (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='5)  whence  V (0,0)(0, 0) = D(0, T1)Φ(d1(0, 0, 0)) − κ−1D(0, T2)Φ(d2(0, 0, 0)),  (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='6)  Considering next the action of the ﬁrst-order Green’s function term on the leading-order term, we obtain  V (1,0)(y, t) = −e−µ∗(y,t,T1)  �� T1  t  G1(t, t1, T1)dt1 − Σrz(t, T1)  φr(t, T1)  ∂  ∂y  �  �  D(t, T1)Φ(d1(y, 0, t)) − κ−1D(t, T2)e−θ(y,t)Φ(d2(y, 0, t))  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='  (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='7)  Setting y = t = 0, we ﬁnd  V (1,0)(0, 0) ∼ −D(0, T1)  � T1  0  G1(0, t1, T1)dt1 Φ(d1(y, 0, 0))  �����  y=0  + κ−1D(0, T2)  � � T1  0  G1(0, t1, T2)dt1 e−θ(y,0) + B∗(T1, T2)Σrz(0, T1)  �  Φ(d2(y, 0, 0))  �����  y=0  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='8)  9We use the convention here that the integration in the operator expression is applied after the operator has been applied to the operand;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' likewise  for the assignment of the z-value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='  21  Considering next the action of the leading-order Green’s function term on the ﬁrst-order term V (1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='0)(y,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' T1),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' we obtain  V (0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='1)(y,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' t) ∼ κ−1D(t,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' T2)e−µ∗(y,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='t,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='T1)−θ(y,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='t)  � � T2  T1  R+(y − ∆y1(t),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' t,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' t1)e−γ(t1)(B+(T1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='t1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='T2)Σrr(T1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='t1)+Σrz(T1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='t1))  Φ(d2(y + γ(t1)φr(T1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' t1)∆y(t,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' T1),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' γ(t1)∆z1(t1),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' t))dt1  −  � T2  T1  R−(y + ∆y1(t),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' t,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' t1)eγ(t1)(B+(T1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='t1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='T2)Σrr(T1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='t1)+Σrz(T1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='t1))  Φ(d2(y − γ(t1)φr(T1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' t1)∆y(t,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' T1),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' −γ(t1)∆z1(t1),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' t))dt1  +  � � T2  T1  �  R∗  1(t1) + e  1  2 γ2(t1)Σrr(0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='t1)B+(T1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' t1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' T2)Σrr(t,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' t1)  �  dt1 − θ(y,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' t)  �  Φ(d2(y,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' 0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' t))  −  �  B∗2(T1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' T2)Σrr(t,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' T1) + Σzz(T1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' T2)N(d2(y,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' 0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' t))  �  ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='  (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='9)  with O(ϵ) relative errors, where  ∆y1(t) := Σrz(t, T1)  φr(t, T1) + B∗(T1, T2)Σrr(t, T1)  φr(t, T1) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='  (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='10)  We conclude, making use of the fact that µ∗(0, 0, T1) = θ(0, 0) = 0, that  V (0,1)(0, 0) ∼ κ−1D(0, T2)  � � T2  T1  R+  1 (0, 0, t1, T2)Φ(d2(γ(t1)φr(T1, t1)∆y(0, T1), γ(t1)∆z1(t1), 0))dt1  −  � T2  T1  R−  1 (0, 0, t1, T2)Φ(d2(−γ(t1)φr(T1, t1)∆y(0, T1), −γ(t1)∆z1(t1), 0))dt1  +  � T2  T1  R∗  1(t1)dt1Φ(d2(0, 0, 0))  −  �  B∗2(T1, T2)Σrr(0, T1) + Σzz(T1, T2)N(d2(0, 0, 0))  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='  (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='11)  We make use here of the identity that, for t ≤ T1 ≤ t1 ≤ T2,  Σrz(T1, t1) + B+(T1, t1, T2)Σrr(T1, t1) + φr(t, t1)∆y1(t, T1)  = Σrz(T1, t1) + B+(T1, t1, T2)Σrr(t, t1) + φr(T1, t1)(Σrz(t, T1) + B∗(T1, t1)Σrr(t, T1))  = Σrz(t, t1) + B+(t, t1, T2)Σrr(t, t1) − φr(t, t1)∆y2(t, t1)  where  ∆y2(t, t1) =  1  φr(t, t1)  � T2  T1  (ψr(t, u) − ψr(T1, t1))  (φr(u, t1)Σrr(T1, u)1u≤t1 + φr(T1, u)Σrr(t, T1)1u>t1) du.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='  (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='12)  We neglect this subdominant adjustment factor in our asymptotic estimate, arguing that the result would otherwise not  be consistent with the price of deep in-the-money forward contracts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' Combining all V (i,j)(0, 0) terms and simplifying  gives rise to (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' This completes the proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='  22  C  Calibration to Caplet market data  The calibration of the forward curve has already been explained in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' As mentioned before, for the mean reversion,  we choose a representative ﬁxed value of α(t) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' The calibration of σ(t), y∗(t) and γ(t) follows from matching  the analytical implied volatility formula to the implied volatilities quoted in the market for 6-month caps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' We take  piece-wise parametrisations for these parameters and calibrate on the available maturities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' The result of the calibration  is given in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='  0  2  4  6  8  10  t (y)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='000  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='001  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='002  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='003  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='004  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='005  0  2  4  6  8  10  t (y)  0  50  100  150  200  250  300  0  2  4  6  8  10  t (y)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='0000  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='0005  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='0010  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='0015  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='0020  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='0025  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='0030  y *  Figure 9: Piece-wise functions for σ(t), y∗(t) and γ(t) after calibration to market data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' The black dots indicate the  cap maturities used for calibration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='  References  E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' Alòs, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' De Santiago, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' Vives.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' Calibration of stochastic volatility models via second-order approximation: the  Heston case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' International Journal of Theoretical and Applied Finance, 18(6):1550036, 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' Antonov and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' Spector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' General Short-Rate Analytics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
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+page_content='  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
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+page_content=' Konikov, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
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+page_content=' Modern SABR Analytics: Formulas and Insights for Quants, Former  Physicists and Mathematicians.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
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+page_content=' ISBN 978-3030106553.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
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+page_content=' Black and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' Karasinski.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
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+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' Hagan, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' Kumar, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' Lesniewski, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
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+page_content=' Wilmott Magazine, July:  84–108, 2002.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content='  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
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+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
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+page_content=' Perturbation Methods in Credit Derivatives: Strategies for efﬁcient risk management.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
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+page_content=' ISBN 978-1-119-60961-2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
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+page_content=' Risky Caplet Pricing with Backward-Looking Rates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
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+page_content=' Caplet Pricing with Backward-Looking Rates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
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+page_content=' Turfus and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' Romero-Bermúdez.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
+page_content=' Analytic Short Rate Model with Smile and Skew.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
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+page_content=' What Short Rate Model Should I Use?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfT_yr/content/2301.01260v1.pdf'}
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+Think Twice: A Human-like Two-stage Conversational Agent for
+Emotional Response Generation
+Yushan Qian
+Tianjin University
+Tianjin, China
+yushanqian@tju.edu.cn
+Bo Wang
+Tianjin University
+Tianjin, China
+bo_wang@tju.edu.cn
+Shangzhao Ma
+Tianjin University
+Tianjin, China
+shangzhaoma@tju.edu.cn
+Wu Bin
+Quesoar Co. Ltd.
+Tianjin, China
+wubin@quesoar.com
+Shuo Zhang
+Quesoar Co. Ltd.
+Tianjin, China
+s@quesoar.com
+Dongming Zhao
+Artificial Intelligence Laboratory,
+China Mobile Communication Group
+Tianjin Co., Ltd.
+Tianjin, China
+waitman_840602@163.com
+Kun Huang
+Artificial Intelligence Laboratory,
+China Mobile Communication Group
+Tianjin Co., Ltd.
+Tianjin, China
+hknzh@126.com
+Yuexian Hou
+Tianjin University
+Tianjin, China
+yxhou@tju.edu.cn
+ABSTRACT
+Towards human-like dialogue systems, current emotional dialogue
+approaches jointly model emotion and semantics with a unified
+neural network. This strategy tends to generate safe responses
+due to the mutual restriction between emotion and semantics, and
+requires the rare large-scale emotion-annotated dialogue corpus. In-
+spired by the "think twice" behavior in human intelligent dialogue,
+we propose a two-stage conversational agent for the generation of
+emotional dialogue. Firstly, a dialogue model trained without the
+emotion-annotated dialogue corpus generates a prototype response
+that meets the contextual semantics. Secondly, the first-stage proto-
+type is modified by a controllable emotion refiner with the empathy
+hypothesis. Experimental results on the DailyDialog and Empathet-
+icDialogues datasets demonstrate that the proposed conversational
+agent outperforms the compared models in the emotion genera-
+tion and maintains the semantic performance in the automatic and
+human evaluations.
+KEYWORDS
+Emotional Dialogue, Dialogue Systems, Human Interaction
+ACM Reference Format:
+Yushan Qian, Bo Wang, Shangzhao Ma, Wu Bin, Shuo Zhang, Dongming
+Zhao, Kun Huang, and Yuexian Hou. 2023. Think Twice: A Human-like Two-
+stage Conversational Agent for Emotional Response Generation. In Proc.
+of the 22nd International Conference on Autonomous Agents and Multiagent
+Systems (AAMAS 2023), London, United Kingdom, May 29 – June 2, 2023,
+IFAAMAS, 10 pages.
+Proc. of the 22nd International Conference on Autonomous Agents and Multiagent Sys-
+tems (AAMAS 2023), A. Ricci, W. Yeoh, N. Agmon, B. An (eds.), May 29 – June 2, 2023,
+London, United Kingdom. © 2023 International Foundation for Autonomous Agents
+and Multiagent Systems (www.ifaamas.org). All rights reserved.
+1
+INTRODUCTION
+In the task of open-domain dialogue generation, emotional dialogue
+aims to generate responses involving the perception and expression
+of proper emotions. A large number of studies [29, 34, 37] have
+demonstrated that emotional dialogue can significantly improve
+users’ satisfaction in a human-machine conversation. Moreover,
+building a dialogue system with human emotions is one of the
+ultimate goals of artificial intelligence.
+Towards emotional dialogue systems, in addition to the early
+methods of manually compiling rules by professionals [42], existing
+statistical approaches are mainly based on neural network mod-
+els [1, 10, 20, 22, 24, 27, 43, 55–57]. With an end-to-end strategy,
+these neural network models jointly generate the semantics and
+emotions of the dialogue responses.
+However, current end-to-end emotional dialogue models still
+face several challenges. Firstly, in deep neural networks, the input
+emotion signals are often weakened through the complex learn-
+ing process. Secondly, in the joint generation model, the design to
+enhance emotions often restricts the semantic performance of gen-
+erated responses (e.g., safe responses). Thirdly, large-scale emotion-
+annotated dialogue corpora are rare for joint training of semantics
+and emotions with deep neural networks.
+In response to the above challenges, we propose to generate
+emotional responses with the idea of human intelligent dialogue
+behavior. When humans respond in a dialogue, the simultaneous
+processing of emotion and semantics can not ensure satisfying
+results. The intuitive emotion generated simultaneously with se-
+mantics is often arduous to ensure a response in the appropriate
+emotion. One source of the appropriate emotional response comes
+from an independent emotion selection after determining the se-
+mantics, i.e., thinking twice about appropriate emotions. In this
+independent emotion selection, a paramount strategy for humans to
+arXiv:2301.04907v1  [cs.CL]  12 Jan 2023
+
+Honey, it's time for 
+dinner.
+Shut up! The video is 
+starting.
+Please be quiet! the 
+video is starting.
+Honey, it's time for 
+dinner.
+Shut up! The video is 
+starting.
+Shut up! The video is 
+starting. Sorry, I’m 
+just too nervous.
+Rewrite
+Add
+Positive
+Negative
+Figure 1: The real-life examples of emotion adjustment in
+the human dialogue. The "think twice" strategy can be ob-
+served in human intelligent behavior and effectively im-
+proves the quality of emotional responses by rewriting ex-
+pressions or adding extra information. Bold tokens are the
+rewritten or added part.
+determine the appropriate emotion is the empathy strategy, which
+makes the emotion of the response consistent with that of the con-
+text [2, 24, 39]. As visualized in Figure 1, each response firstly has
+a proper semantic to respond to the context. Then, by recognizing
+the context’s emotional state, we can adjust the response emotion-
+ally and achieve a certain degree of empathy by responding to the
+partner’s emotion.
+Therefore, we design a human-like two-stage conversational
+agent for emotional response generation. Firstly, a prototype re-
+sponse with proper semantics is generated with a pre-trained model
+fine-tuned on dialogue corpus without emotion annotation. Then,
+the contextual emotional state is recognized by a dialogue emotion
+detector. According to the empathy hypothesis [24], the type of
+generated emotion is consistent with the contextual emotional state.
+Finally, the prototype is modified by a controllable emotion refiner
+to generate a final response that is both semantically relevant and
+emotionally appropriate.
+Specifically, towards effective refining for an emotional response
+in the second stage, we also refer to two human pragmatic strategies.
+First, humans express the same information in different ways with
+different vocabulary choices [36]. Therefore, we involve expected
+emotional attributes in the response by replacing the original emo-
+tional words or phrases instead of constructing a new sentence from
+scratch, i.e., the "rewriting" strategy. Second, there are also some
+implicit emotions reflected through the whole sentence instead of
+specific words. Consequently, we also adjust the emotion by adding
+extra sentences to the response, i.e., the "adding" strategy.
+In summary, our contributions are:
+• Inspired by human intelligent dialogue behavior, we propose
+a human-like two-stage conversational agent for emotional
+response generation. To the best of our knowledge, it is the
+first two-stage model specifically for emotional dialogue.
+• The proposed method effectively alleviates two problems
+of existing emotional dialogue approaches, i.e., weakening
+the emotion effect during the complex learning process and
+restricting the semantic generation to meet the emotion
+demand.
+• The proposed two-stage conversational agent reduces the
+demand for the sizeable emotion-annotated dialogue cor-
+pus. The training of the prototype response generator in the
+first stage only requires general dialogue corpora without
+emotion annotation, and the controllable emotion dialogue
+refiner is trained on non-dialogue and non-parallel emotion-
+annotated corpora.
+• The proposed method can be generalized to other existing
+end-to-end emotion dialogue generation models as post-
+processing for emotionalization. Even if some sentences have
+poor emotional expressions, there is no need to retrain the
+whole model and build new sentences from scratch.
+2
+METHODS
+2.1
+Preliminaries
+Formally, in this paper, the dialogue context is alternate utterances
+of two speakers, defined as 𝐶 = {𝑈1,𝑈2, . . . ,𝑈𝑛}, where 𝑛 denotes
+the number of utterances in a dialogue. The set of context emotions
+is 𝐸 = {𝑒1,𝑒2, . . . ,𝑒𝑛}, which corresponds to the dialogue context 𝐶.
+Our goal is to generate the next utterance 𝑈𝑛+1, which is coherent
+to the context and contains the appropriate emotion.
+As shown in Figure 2, our model consists of three parts: the
+Prototype Utterance Generator 𝐺, the Dialogue Emotion Detec-
+tor 𝐷, and the Controllable Emotion Refiner 𝑅. The Controllable
+Emotion Refiner 𝑅 has two modules, named "Rewrite" and "Add".
+The Prototype Utterance Generator 𝐺 takes the dialogue context
+𝐶 as input and generates a prototype response 𝑈𝑚. The Dialogue
+Emotion Detector 𝐷 takes the dialogue context 𝐶 as input and ob-
+tains the emotion state set 𝐸, which dynamically determines the
+response emotion 𝑒𝑛+1. The Controllable Emotion Refiner 𝑅 refines
+𝑈𝑚 according to 𝑒𝑛+1 by rewriting 𝑈𝑚 or adding extra sentences
+into 𝑈𝑚 with Rewrite Module and Add Module, respectively, and
+generates the final response 𝑅𝑒, which is 𝑈𝑛+1.
+2.2
+Prototype Utterance Generator
+We use DialoGPT [54] as the Prototype Utterance Generator to
+generate relevant, diverse, and contextually consistent responses.
+Large-scale pre-trained language models [5, 38, 54] have exten-
+sively promoted the research progress of the open-domain dialogue
+in recent years. The method of pre-training and fine-tuning can
+avoid training models from scratch, save computing resources, and
+achieve excellent results in downstream tasks.
+DialoGPT has a 12-to-48 layer Transformer with layer normal-
+ization like GPT-2 [38], which is trained on the 147M large-scale
+dialogue dataset from Reddit. All utterances of the context are
+spliced into a long sentence with “<|endoftext |>” as input. The
+conditional distribution of the target prototype utterance 𝑈𝑚 is the
+product of a series of conditional probabilities:
+𝑃(𝑈𝑚|𝐶) = �𝑆+𝑠𝑚
+𝑖=𝑆+1 𝑃(𝑡𝑖 |𝑡1,𝑡2, ...,𝑡𝑖−1),
+(1)
+
+Selector
+GLEU: r>a?r:a
+Stage 2： Controllable Emotion Refiner
+Prototype Response
+Generator
+Context  {U1,U2,…,Un}
+Rewrite Module
+Add Module
+p(en+1|Re)
+p(Re)
+Um
+en+1
+Re
+Dialogue Emotion Detector
+1
+2
+3
+P(Um|C)=∏𝑖=𝑆+1
+S+sm P(ti|t1, t2, … , ti-1)
+Stage 1： Prototype Generation
+Emotional Response
+1 1 1
+2 2 2
+3 3 3
+r
+a
+P(a|x)
+P(x)
+P(x|a)
+cx,ssrc
+L(θ)
+α(t)
+Figure 2: The overall architecture of the proposed two-stage conversational agent. The first stage includes Prototype Utterance
+Generator and Dialogue Emotion Detector, which generates prototype response 𝑈𝑚 and detects the contextual emotion state
+as the expected emotion 𝑒𝑛+1 of the final response, respectively. The second stage includes Rewrite Module, Add Module, and
+Selector. Rewrite Module and Add Module refine 𝑈𝑚 according to 𝑒𝑛+1, and the Selector selects the final response from the
+outputs of Rewrite Module and Add Module based on the GLEU score.
+where 𝐶 = {𝑈1,𝑈2, ...,𝑈𝑛}, 𝑛 is the number of utterances, 𝑈𝑖 =
+�
+𝑡1,𝑡2, ...,𝑡𝑠𝑖
+�, 𝑡𝑖 is each token in the utterance, 𝑠𝑖 is the length of
+each utterance, 𝑆 = 𝑠1 +𝑠2 +· · ·+𝑠𝑛 represents the number of tokens
+in all utterances, 𝑠𝑚 is the length of 𝑈𝑚.
+We use the maximum mutual information scoring function (MMI)
+and the top-k sampling [6] to reduce the generation of meaningless
+responses. The specific implementation is based on tools provided
+by Hugging Face1. We conduct fine-tuning on the training set for
+3 epochs with the batch size of 8 and the learning rate of 0.00001.
+Emotional labels in the training set will not be used. During the
+decoding process, we use the top-k (k=100) sampling and nucleus
+sampling (p=0.7) [13].
+2.3
+Dialogue Emotion Detector
+As an intuitive hypothesis of empathy, during emotional dialogues
+between two individuals, the listener usually tends to respond in
+a way that recognizes the speaker’s feelings [2, 24] and achieves
+a certain degree of empathy by calling the respondent’s emotions.
+In this work, we adopt this empathy hypothesis to determine the
+emotion of the response according to the emotion state of the
+context.
+To this end, the goal of the Dialogue Emotion Detector 𝐷 is to
+detect emotions in the dialogue context. According to the empathy
+hypothesis, 𝐷 determines the expected emotion of the Controllable
+Emotion Refiner by the recognized emotion distribution in the
+dialogue context.
+The Dialogue Emotion Detector 𝐷 is developed based on Dia-
+logueGCN [9], which regards each utterance in the dialogue as
+a node of the graph network. There are directed edges between
+utterances, and the sequence order of utterances determines the di-
+rection of each edge. These directed edges can model the emotional
+impact of what the speaker or the other people has said before. We
+1https://huggingface.co/models
+use Glove embedding and CNN to extract features of utterances
+and get the embedding of each utterance 𝑈𝑖, which is the vector of
+each node. There are 𝑏 utterances before each utterance, and there
+are 𝑎 utterances after it. The node of each utterance has edges with
+𝑎 + 𝑏 + 1 nodes (including itself). The weight 𝑎𝑖𝑗 of each edge is
+decided by the relationship between nodes as follows:
+𝛼𝑖𝑗 = softmax(𝑈𝑇
+𝑖 𝑊𝑢 [𝑈𝑖−𝑏, ...,𝑈𝑖+𝑎]),
+for
+𝑗 = 𝑖 − 𝑏, ...,𝑖 + 𝑎.
+(2)
+Further details about GCN construction are available in [9].
+Finally, the embedding from the sequence encoder 𝑠𝑞 and the
+speaker-level encoder 𝑠𝑝 are spliced together, and combined with
+the similarity-based attention mechanism to obtain the final embed-
+ding of the utterance node. Then we use a fully connected network
+to classify multiple emotion categories:
+𝐻 = [ℎ1,ℎ2, . . . ,ℎ𝑛],
+ℎ𝑖 = softmax([𝑠𝑞𝑖,𝑠𝑝𝑖]𝑇𝑊 𝐻)𝐻𝑇,
+𝑒𝑖 = argmax(softmax(FFN(ℎ𝑖))).
+(3)
+We use L2 regularization classification cross-entropy loss as the
+loss function and Adam [17] as the optimizer. We classify emotions
+in the emotion state set 𝑆 into two groups of negative emotions
+and positive emotions as in [27]. Following [2, 24], we assume
+that empathetic responses may mimic the user’s emotions to some
+extent. Therefore, the target emotion 𝑒𝑛+1 that we finally pass to
+the Controllable Emotion Refiner 𝑅 is defined as follows:
+𝑒𝑛+1 = positive,
+if
+𝑁𝑢𝑚𝑝𝑜𝑠 (𝐸) > 𝑁𝑢𝑚𝑛𝑒𝑔(𝐸),
+otherwise
+𝑒𝑛+1 = negative.
+(4)
+Where 𝐸 = {𝑒1,𝑒2, . . . ,𝑒𝑛} is the set of emotions in each dialogue.
+𝑁𝑢𝑚𝑝𝑜𝑠 and 𝑁𝑢𝑚𝑛𝑒𝑔 represent the number of positive emotions
+and negative emotions in 𝐸, respectively.
+
+2.4
+Controllable Emotion Refiner
+The Controllable Emotion Refiner 𝑅 takes the prototype response
+𝑈𝑚 and the target emotion 𝑒𝑛+1 as input, and generates the final
+response 𝑅𝑒. The goal we need to learn is defined as:
+𝑃(𝑅𝑒 |𝑈𝑚,𝑒𝑛+1) & Stype(𝑅𝑒) = 𝑒𝑛+1,
+(5)
+where “Stype” represents the emotion type.
+The Controllable Emotion Refiner 𝑅 consists of two modules,
+“Rewrite” and “Add”. The Rewrite Module transforms the emotion
+attribute of the 𝑈𝑚 by replacing the original emotion symbols in
+the sentence with symbols that express the target emotion. The
+Add module adjusts the emotion type by adding extra sentences.
+Rewrite Module. The Rewrite Module consists of two parts: the
+first one is the deletion part, which determines whether each token
+in the input is an emotion attribute word, learns the emotional part
+and non-emotional part in the input, and deletes the emotional part.
+We adopt the attention mechanism of Transformer to extract the
+attention score as the weight of each token [44]:
+𝛼(𝑡) = softmax(𝑄𝐾𝑇 ), 𝑓 𝑜𝑟 𝑡 ∈ 𝑈𝑚,
+(6)
+where 𝑄 and 𝐾 carry the original connotations of query and key
+vectors in the Transformer.
+The second is the generating part, which generates sentences
+with target emotion attributes. The generating part adopts the
+Transformer structure, based on the Hugging Face [49]. The input
+of generating part is the prototype response and the target emotion.
+The output is a sentence that conforms to the target emotion. With-
+out requiring the parallel corpus, the training goal of generating
+part is to minimize the following reconstruction loss:
+𝐿(𝜃) =
+∑︁
+𝑥,𝑠𝑠𝑟𝑐 ∈𝐷
+log𝑝(𝑥|𝑐𝑥,𝑠𝑠𝑟𝑐;𝜃),
+(7)
+where 𝐷 is the training dataset. Given a sentence 𝑥, the Rewrite
+Module model learns to reconstruct 𝑦 = 𝑥 with 𝑐𝑥, 𝑠𝑠𝑟𝑐. 𝑐𝑥 is the
+non-emotional content of 𝑥, and 𝑠𝑠𝑟𝑐 is the original style of the
+sentence.
+Add Module. The Add Module is developed based on the work
+of [4] to change the emotion polarity of the original sentence by
+adding extra sentences with the target emotion. Using Bayes’ theo-
+rem, we can use the model 𝑝(𝑥) and the model 𝑝(𝑎|𝑥) to express
+the model 𝑝(𝑥|𝑎):
+𝑝(𝑥|𝑎) ∝ 𝑝(𝑎|𝑥)𝑝(𝑥).
+(8)
+In order to obtain the required 𝑝(𝑥|𝑎) to generate the sentence
+based on attribute 𝑎, we already have a language model 𝑝(𝑥) that
+can generate fluent sentences. Furthermore, we build a classifier to
+determine whether the text 𝑥 generated by the language model has
+𝑎 attribute, that is, 𝑝(𝑎|𝑥), then 𝑝(𝑥|𝑎) can be obtained.
+The process of the Add Module has three steps:
+1. First, a forward pass is performed through the language model
+to compute the likelihood of the desired attribute using an attribute
+model that predicts 𝑝(𝑎|𝑥).
+2. Second, a backward pass updates the internal latent represen-
+tations of the language model, using gradients from the attribute
+model to increase the likelihood of the sentence having the desired
+attribute.
+Table 1: Two groups of emotions in the DailyDialog dataset
+according to positivity and negativity.
+Positive
+Negative
+happiness,
+surprise,
+other
+anger, disgust, fear,
+sadness
+Table 2: Two groups of emotions in the EmpatheticDia-
+logues dataset according to positivity and negativity.
+Positive
+Negative
+confident,
+joyful,
+grateful, impressed,
+proud, excited, trust-
+ing, hopeful, faithful,
+prepared,
+content,
+surprised, caring
+afraid, angry, annoyed, an-
+ticipating, anxious, apprehen-
+sive, ashamed, devastated, dis-
+appointed, disgusted, embar-
+rassed, furious, guilty, jealous,
+lonely, nostalgic, sad, senti-
+mental, terrified
+3. Third, re-sampling to generate a new word according to the
+obtained new output probability distribution.
+To generate more diverse sentences that conform to the language
+model, two methods are adopted to ensure that the language model
+of the generated sentence is as close as possible to the original
+language model: Kullback–Leibler (KL) Divergence and Post-norm
+Geometric Mean Fusion. About the language model, we use GPT2.
+Regarding the specific attribute discriminator 𝑝(𝑎|𝑥), we take the
+existing non-dialogue emotion-annotated corpus and pre-train a
+classifier.
+Selector. A Selector is designed to determine whether the re-
+sponse is from the Rewrite Module or the Add Module is selected as
+the final output. The Selector uses GLEU [30] as a basis for judging
+the overall effect of responses, which compares with the prototype
+response. [44] found that GLEU is more suitable for human score
+than BLEU score. The Selector selects the final response with a
+higher GLEU score.
+3
+EXPERIMENTS
+In this section, we introduce the datasets, baselines and evalua-
+tion metrics. The proposed conversational agent is experimentally
+compared with baselines and the experimental results are discussed.
+3.1
+Datasets
+We used the DailyDialog [23] and EmpatheticDialogues [39] datasets
+for the experiment. DailyDialog is a multi-round dialogue dataset
+for daily chat scenes. There are a total of 12,218 dialogues and
+103,607 utterances. Each dialogue has about 8 rounds. The topic
+and emotion in each utterance are labeled. There are seven types of
+emotion: anger, disgust, fear, happiness, sadness, surprise, and oth-
+ers. Refer to [27], we divided the 7 emotion types into two groups
+containing 3 positive and 4 negative emotions, respectively, as listed
+in Table 1. EmpatheticDialogues is a widely-used benchmark dataset
+for empathetic response generation, which is a large-scale multi-
+turn dataset containing 25k empathetic dialogues between crowd-
+sourcing workers. EmpatheticDialogues also provides an emotion
+
+label for each dialogue from 32 available emotions. Following [27],
+we divided the 32 emotion types into two groups containing 13 pos-
+itive and 19 negative emotions, respectively, as listed in Table 2. We
+focus on positive and negative emotions because the consistency of
+polarity level emotion is more popular in emotion study and robust
+in the application. Since our method and baselines are under the
+same assumption and processed in the same way during evaluation,
+the results are competitive and convincing.
+Considering the limited running space and to unify the number
+of rounds in each dialogue, we segment the original dialogues into
+sub dialogues having 4 rounds. Finally, for the DailyDialog dataset,
+the dialogue numbers of the training / validation / test set are 54,299
+/ 5,109 / 4,782, respectively. For the EmpatheticDialogues dataset,
+the dialogue numbers of the training / validation / test set are 18,383
+/ 2,810 / 3,320, respectively.
+3.2
+Compared Models
+To the best of our knowledge, this is an early work in the two-
+stage generation of emotional dialogue. In view of the empathy
+hypothesis, we compare our approach with a range of models used
+in related tasks, including general dialogue, emotional dialogue,
+and empathetic dialogue.
+Transformer [48]: The standard Transformer model that is
+trained to optimize NLL loss.
+Multi-TRS [39]: A multi-task Transformer model jointly trained
+by predicting the emotion and generating the response.
+Mojitalk [57]: An encoder-decoder based CVAE model incorpo-
+rated with emotion embedding.
+MoEL [24]: A Transformer-based model employs emotion-specific
+decoders whose outputs are aggregated and fed to a final decoder
+to generate the empathetic response.
+MIME [27]: A Transformer-based model that leverages emotion
+groups and emotion mimicry, which effectively blends emotions in
+positive and negative emotion groups and generates the empathetic
+response.
+EmpDG [20]: An interactive adversarial model consists of a gen-
+erator and a discriminator. The discriminator requires user feedback.
+Besides, the model exploits both the coarse-grained dialogue-level
+and fine-grained token-level emotions. Referring to [40], we only
+apply the empathetic generator to ensure consistent input and
+output in the test set for a fair comparison with other baselines.
+3.3
+Implementation Details
+We use the official codes of all baselines, especially, EmpDG only
+applies the empathetic generator (Multi-TRS2, Mojitalk3, MoEL4,
+MIME5, EmpDG6). We implement all the models using PyTorch
+except Mojitalk. All the baselines were trained on a V100 GPU with
+the batch size of 16 and the early stopping strategy. About the Adam
+optimizer, we set 𝛽1 = 0.9 and 𝛽2 = 0.98. For the emotion detection
+in the automatic evaluation, emotion pre-training model in Senta
+is “𝑒𝑟𝑛𝑖𝑒_2.0_𝑠𝑘𝑒𝑝_𝑙𝑎𝑟𝑔𝑒_𝑒𝑛”.
+2https://github.com/facebookresearch/EmpatheticDialogues
+3https://github.com/Claude-Zhou/MojiTalk
+4https://github.com/HLTCHKUST/MoEL
+5https://github.com/declare-lab/MIME
+6https://github.com/qtli/EmpDG
+3.4
+Evaluation Metrics
+3.4.1
+Automatic Evaluation. We apply the following evaluation
+metrics in the automatic evaluation:
+BLEU: Word-overlap scores with human responses [33]. We use
+BLEU-4, which is calculated with an NLG evaluation toolkit 7.
+Diversity: Dist-n measures the proportion of unique n-grams
+in the generated responses [25]. It is commonly used to evaluate
+whether the dialogue model can generate a diverse response as
+humans do. Low diversity often means the model tends to generate
+similar safe responses to different contexts. We refer to the work
+of [3] to calculate the Dist-1 and Dist-2 metrics.
+Emotion Accuracy (Acc): The emotion accuracy is defined as
+the proportion of consistent emotion polarities between generated
+responses and the ground truth. We use the Sentiment Knowledge
+Enhanced Pre-training for Sentiment Analysis (SKEP) model [45]
+proposed by Baidu as the emotion detector during the evaluation8.
+SKEP is a state-of-the-art emotion detector in 14 typical Chinese and
+English sentiment analysis tasks. We use it to automatically detect
+the emotion polarity of the responses generated by our proposed
+conversational agent and baselines.
+3.4.2
+Human Evaluation. We randomly sampled 100 dialogues and
+generated responses with our proposed conversational agent and
+baselines. We employed three human annotators to evaluate each
+response based on four aspects:
+Content(Con): Whether the response is appropriate for the
+context in the current dialogue. It is rated on a Likert scale (1: not
+at all, 3: somewhat, 5: very much).
+Emotion(Emo): Whether the response is appropriate for the
+context in the emotion polarity. 1 indicates the response is appro-
+priate, and 0 indicates the response is inappropriate.
+Emotion-intensity(Int): What the emotion intensity of the
+response is. 0 represents no emotion, 1 represents slight intensity,
+and 2 represents strong intensity.
+Fluency(Flu): Whether the response is readable and understand-
+able. It is rated on a Likert scale (1: not at all, 3: somewhat, 5: very
+much).
+3.5
+Main Results
+Both automatic and human evaluation results are shown in Table 3
+and Table 4 on the DailyDialog and EmpatheticDialogues datasets,
+respectively.
+For the performance of emotion generation, it can be observed
+that the proposed conversational agent outperforms baselines in
+Acc for the automatic evaluation and Emo for the human evalu-
+ation in two datasets, indicating the outstanding performance of
+our conversational agent in emotion generation. In addition, our
+conversational agent also achieves the best and second-best results
+in Int on the DailyDialog and EmpatheticDialogues datasets, re-
+spectively. which clearly verifies that the emotional effect of our
+model is more significant and sufficient compared with the SOTA
+end-to-end systems. This is because in the process of the two stages,
+7https://github.com/Maluuba/nlg-eval
+8https://github.com/baidu/Senta
+
+Table 3: Automatic and Human evaluations in the DailyDialog dataset (The significant improvement with p-value < 0.05 (t-test).
+Fleiss’s kappa for Human evaluation is 0.526, indicating "moderate agreement").
+Model
+Automatic Evaluation
+Human Evaluation
+BLEU-4
+Dist-1
+Dist-2
+Acc(%)
+Con
+Emo
+Int
+Flu
+Transformer
+0.44
+1.10
+5.84
+54.04
+3.54
+0.69
+0.49
+4.60
+Multi-TRS
+0.58
+1.17
+6.35
+54.29
+3.49
+0.75
+0.52
+4.35
+Mojitalk
+0.58
+4.99
+22.40
+53.99
+3.14
+0.79
+0.61
+4.21
+MoEL
+0.46
+1.51
+8.39
+55.44
+3.35
+0.77
+0.73
+4.67
+MIME
+0.54
+0.48
+1.79
+53.43
+3.42
+0.78
+0.68
+4.43
+EmpDG
+0.57
+1.12
+5.73
+56.02
+3.40
+0.79
+0.77
+4.47
+Our
+0.67
+9.71
+42.77
+57.36
+3.82
+0.84
+0.79
+4.45
+Table 4: Automatic and Human evaluations in the EmpatheticDialogues dataset (The significant improvement with p-value <
+0.05 (t-test). Fleiss’s kappa for Human evaluation is 0.462, indicating "moderate agreement").
+Model
+Automatic Evaluation
+Human Evaluation
+BLEU-4
+Dist-1
+Dist-2
+Acc(%)
+Con
+Emo
+Int
+Flu
+Transformer
+0.35
+0.64
+2.40
+62.29
+3.24
+0.62
+0.84
+4.86
+Multi-TRS
+0.35
+0.73
+2.77
+61.36
+3.30
+0.76
+0.98
+4.80
+Mojitalk
+0.23
+6.99
+33.52
+61.81
+2.74
+0.76
+1.03
+4.54
+MoEL
+0.34
+1.15
+7.28
+62.47
+3.44
+0.77
+1.04
+4.82
+MIME
+0.37
+0.89
+3.93
+61.87
+3.32
+0.80
+1.12
+4.86
+EmpDG
+0.39
+0.75
+2.50
+62.62
+3.33
+0.81
+1.05
+4.78
+Our
+0.39
+5.24
+22.37
+65.42
+3.65
+0.82
+1.11
+4.72
+Table 5: Ablation Analysis.
+Model
+DailyDialog
+EmpatheticDialogues
+BLEU-4
+Dist-1
+Dist-2
+Acc(%)
+BLEU-4
+Dist-1
+Dist-2
+Acc(%)
+Our
+0.67
+9.71
+42.77
+57.36
+0.39
+5.24
+22.37
+65.42
+w/o Add
+0.59
+7.48
+33.79
+56.04
+0.29
+4.07
+19.63
+65.33
+w/o Rewrite
+0.49
+7.93
+35.74
+55.88
+0.35
+4.95
+20.27
+65.78
+w/o DED
+0.63
+8.77
+39.27
+56.84
+—
+—
+—
+—
+the emotional effect of the response is separately determined and re-
+fined in the second stage without being influenced by the semantic
+generation in the first stage.
+For the performance of semantic generation, the proposed con-
+versational agent reaches the highest level in BLEU-4 and Con. In
+terms of Dist-1 and Dist-2, our conversational agent also scores
+moderately. These results confirm that the proposed conversational
+agent significantly improves emotional expression while maintain-
+ing appropriate semantics. We also note that our proposed conver-
+sational scores are ordinary in Flu, which is possibly due to the
+"adding" strategy increasing the sentence length and affecting the
+reading difficulty. This is a small limitation given that all models
+score above 4, which we will explore in the future.
+For the performance of compared baselines, MoEL has a low
+Bleu score and a high emotion accuracy score, which shows that
+this existing model loses semantic information when pursuing
+emotion features. Furthermore, all baselines except Mojitalk have
+low scores on diversity metrics, which indicates that there are a
+large number of safe responses in the generated responses. MoEL,
+Mojitalk, MIME, and EmpDG also have low scores in Con in the
+DailyDialog dataset, which is lower than Transformer. This may be
+primarily due to the mutual restriction of semantics and emotions,
+which reduces the output space.
+In Figure 3, for 100 human evaluation samples, we compared
+the correctness and significance of the emotion of the prototype
+response and the refined response generated by our proposed con-
+versational agent. The red and blue columns indicate correct (i.e.,
+coherent to the contextual emotion) and incorrect emotions, respec-
+tively. The length of the columns indicates the significance of the
+emotion. We can note that the number of red columns in the refined
+responses is more, and the length is longer, which illustrates that
+the refined responses improve the correctness and significance of
+the emotion in the prototype response.
+3.6
+Human A/B Test
+We conducted the human A/B test, which is shown in Table 7. We
+randomly sampled 100 response pairs and asked 3 annotators to
+choose the better response for each pair. A tie is allowed if both
+are good or bad. We can observe that responses generated by the
+proposed conversational agent are preferred by annotators than
+
+Table 6: Examples of generated responses by our proposed conversational agent and baselines. The corresponding contexts
+did not appear in the training set. Bold tokens are the refined part.
+Context
+Ground Truth Response
+Models
+Generated Response
+DailyDialog
+No, honey, why didn’t you go to cram school
+last night?
+Dad, I don’t want to talk about it now.
+Honey, if you don’t want to go to cram school,
+you should tell me the reason why.
+I’m sorry, dad. But I would
+rather stay at school than go
+to cram school.
+Transformer
+I do not think I can do that .
+Multi-TRS
+Yeah, I know, but I am sure I will.
+Mojitalk
+Well, be able to be a good point.
+Moel
+I do not know. I want to go to school.
+MIME
+That is true. But I do not know.
+EmpDG
+I am sorry. I can not wait to get out of the internet.
+Ours
+Sorry dad. I can’t do that again. I’m so busy.
+I could have Suzy stay at my place.
+I don’t want to do that to you, Karen.
+Why not?
+Your own kids would get
+Suzy’s cold. I think it would
+be better to have a good
+babysitter here.
+Transformer
+Yes, I think I would love to.
+Multi-TRS
+I am sorry. I must have to give her a girl.
+Mojitalk
+Well, I have a cold.
+Moel
+I do not know. I would like to. You?
+MIME
+I am not sure. I am not sure.
+EmpDG
+I am sorry, but I have no idea.
+Ours
+I’m sorry. I just can’t. I’ve got nothing to lose.
+I just want to make the best of what I have, and the best I can.
+EmpatheticDialogues
+Why does McDonalds always get my order wrong!
+I said no lettuce!
+Report to their management.
+Sometimes I think the management don’t even care!
+Just give it a trial.
+Transformer
+I am sorry to hear that. I hope they win.
+Multi-TRS
+I hope you get a better next time.
+Mojitalk
+That’s a great idea! I’m sure you’ll get his family, he has done issues as well.
+Moel
+I hope everything works out!
+MIME
+I am sorry to hear that. I hope you find a new job.
+EmpDG
+I do not know what I do.
+Ours
+It is a problem. I am not sure how to solve it. I feel very sorry.
+I visited an orphan once and it was such a surreal
+moment. It made me realise how thankful I should
+be for a family.
+That must have been and intense and emotional
+moment for you.
+Yes it definitely was. I went with intentions to
+teach the kid a few things but I ended up learning
+lots more from him.
+Uau, what a surreal moment.
+I always believe kids have a
+lot to teach us.
+Transformer
+I am sure he’ll be a good person.
+Multi-TRS
+I am glad you are able to find a new one.
+Mojitalk
+Me too. The original kids is really much now.
+Moel
+I am glad you are on the right?
+MIME
+That is great. I am glad you are happy for you.
+EmpDG
+I am sure you will do it.
+Ours
+I’m glad you had such a great experience.
+Figure 3: Compare the prototype response and refined re-
+sponse with respect to the correctness and significance of
+the emotion. The left and right columns indicate proto-
+type and refined responses, respectively. The red and blue
+columns indicate correct (i.e., coherent to the contextual
+emotion) and incorrect emotions, respectively. The length
+of the columns indicates the significance of the emotion.
+those generated by other models, which indicates that responses
+with appropriate emotions and diversity are more attractive to
+users.
+3.7
+Ablation Analysis
+In order to verify the effectiveness of our proposed conversational
+agent, we also conducted ablation studies. 1) w/o Add: The Add
+module is removed in the Controllable Emotion Refiner. We only
+consider using "rewriting" to refine the prototype response; 2) w/o
+Rewrite: The Rewrite module is removed in the Controllable Emo-
+tion Refiner, and we consider using "adding" to refine the prototype
+response; 3) w/o DED: The Dialogue Emotion Detector is removed
+and replaced by emotion recognition of a single utterance. This
+is only conducted in the DailyDialog dataset because the emotion
+annotation of the EmpatheticDialogues dataset is dialogue-level.
+As shown in Table 5, we can observe that removing the Add
+module or the Rewrite module both causes a drop in most metrics.
+This suggests that combining the "rewriting" and "adding" strat-
+egy is beneficial to generating appropriate responses in line with
+the human language characteristics of both explicit and implicit
+expression. Moreover, the dialogue emotion detector also plays an
+important role in emotional response generation, which is superior
+to concatenating the context into a long sentence or identifying a
+single utterance.
+
+Samples
+Correct Emotions
+Incorrect Emotions
+0.8
+0.6
+0.4
+0.2
+0
+0.2
+0.4
+0.6
+0.8
+1
+Significance score of emotion
+Prototype Response Samples Refined Response SamplesTable 7: Result of human A/B test. Fleiss’ kappa result for DailyDialog and EmpatheticDialogues is 0.612 and 0.496, indicating
+"substantial agreement" and "moderate agreement", respectively.
+Models
+DailyDialog
+EmpatheticDialogues
+Win
+Lose
+Tie
+Win
+Lose
+Tie
+Our vs Transformer
+45.0%
+34.7%
+20.3%
+56.3%
+27.3%
+16.3 %
+Our vs Multi-TRS
+46.0%
+31.0%
+23.0%
+52.3%
+28.0%
+19.7%
+Our vs Mojitalk
+56.3%
+26.0%
+17.7%
+53.3%
+26.0%
+20.7%
+Our vs MoEL
+44.7%
+31.0%
+24.3%
+46.7%
+19.3%
+14.0%
+Our vs MIME
+49.0%
+31.7%
+19.3%
+51.0%
+25.7%
+23.3%
+Our vs EmpDG
+42.0%
+32.0%
+26.0%
+48.0%
+31.7%
+26.3%
+3.8
+Case Study
+We sampled some generated responses from all seven models in
+Table 6. We can observe that responses generated by other baselines
+have emotional expressions, but the semantics are less appropri-
+ate in general. Although responses generated by Transformer are
+fluent, they often do not conform to the context. In contrast, the
+response of the proposed conversational agent not only inherits the
+contextual semantics but also involves rich and appropriate emo-
+tions at the same time. For example, the proposed conversational
+agent coherently transforms "It is a problem. I am not sure how to
+solve it." to "It is a problem. I am not sure how to solve it. I feel very
+sorry."
+4
+RELATED WORK
+Dialogue Emotion Recognition. Different from the emotion recog-
+nition of independent sentences, emotions in dialogue should be
+recognized by the context. Used context typically includes history
+utterances [35], history emotions [28] and mutual influence of
+speakers [12]. To model the context, utterances and speakers can
+be independently [12] or interactively [11] modeled by GRU. [9]
+uses GCN to solve the problem of context propagation in existing
+GRU-based methods. Commonsense knowledge [8], psychological
+knowledge [18], and cognitive theory of emotion [14] are also used
+to enhance dialogue emotion recognition.
+Emotional Dialogue. Emotional dialogue aims to generate
+emotional responses with two main strategies. One strategy is
+to specify a target emotion in advance [22, 43, 56, 57]. The advan-
+tage of this advantage is that the generated emotions are flexible
+and controllable, and its disadvantage is that large-scale emotion-
+annotated dialogue corpora are required. The other strategy is to
+utilize the dialogue context to learn emotions by itself [1], which
+is close to empathetic dialogue [7, 20, 21, 24, 27, 41] supposing
+that listeners can infer speakers’ emotions [39]. The advantage of
+this strategy is that it can utilize the existing large-scale dialogue
+corpora, and its disadvantage is that the emotions of generated
+responses are challenging to control. Furthermore, a promising
+task emotional support dialogue [26] has recently emerged, which
+provides valuable assistance to people in need [47].
+Controllable Text Generation. Controllable text generation
+aims to generate texts with controllable styles. Style is defined as to-
+kens belonging to a specific category or label [36]. Typical processes
+include training a large-scale conditional generation model from
+scratch, fine-tuning from a pre-trained language model, and replac-
+ing the key n-tuple to adjust the style of the generated sentence [4].
+As a kind of style, emotion has good practical significance for its
+controllable generation. Emotion controlled text generation is to
+redefine the text to contain the specific emotion without changing
+the contextual intention [15, 16, 31, 44, 50].
+The differences between the proposed conversational agent and
+existing methods are:
+(1) As far as we know, we are the first to study a two-stage emo-
+tion response paradigm in the field of emotional dialogue specially.
+(2) We refine the response with dynamically recognized dialogue
+emotion. However, current rewriting methods do not consider the
+dynamic acquisition of emotions.
+5
+CONCLUSIONS
+This paper designed a two-stage conversational agent in the field
+of emotional dialogue that generates content-related and emotional
+responses. The proposed conversational agent generates a semanti-
+cally coherent prototype in the first stage and emotionally refines
+the prototype response in the second stage. Extensive automatic
+and human evaluations have demonstrated that the proposed con-
+versational agent can generate high-quality emotional responses
+of appropriate semantics, and the training is free of the emotion-
+annotated dialogue corpus.
+In the future, to improve the proposed conversational agent, we
+will explore the flexible enhancement of other specific features
+besides the sentiment of the dialogue system, such as domain and
+style adaptation of existing dialogue models.
+REFERENCES
+[1] Nabiha Asghar, P. Poupart, J. Hoey, Xin Jiang, and Lili Mou. Affective neural
+response generation. ArXiv, abs/1709.03968, 2018.
+[2] Laurie Carr, Marco Iacoboni, Marie-Charlotte Dubeau, John C. Mazziotta, and
+Gian Luigi Lenzi. Neural mechanisms of empathy in humans: A relay from neural
+systems for imitation to limbic areas. Proceedings of the National Academy of
+Sciences, 100(9):5497–5502, 2003.
+[3] Chaotao Chen, Jinhua Peng, Fan Wang, Jun Xu, and Hua Wu. Generating multi-
+ple diverse responses with multi-mapping and posterior mapping selection. In
+Proceedings of the Twenty-Eighth International Joint Conference on Artificial Intel-
+ligence, IJCAI-19, pages 4918–4924. International Joint Conferences on Artificial
+Intelligence Organization, 7 2019.
+[4] Sumanth Dathathri, Andrea Madotto, Janice Lan, Jane Hung, Eric Frank, Piero
+Molino, Jason Yosinski, and Rosanne Liu. Plug and play language models: A
+simple approach to controlled text generation, 2019.
+[5] Jacob Devlin, Ming-Wei Chang, Kenton Lee, and Kristina Toutanova. BERT:
+Pre-training of deep bidirectional transformers for language understanding. In
+Proceedings of the 2019 Conference of the North American Chapter of the Association
+for Computational Linguistics: Human Language Technologies, Volume 1 (Long and
+
+Short Papers), pages 4171–4186, Minneapolis, Minnesota, June 2019. Association
+for Computational Linguistics.
+[6] Angela Fan, Mike Lewis, and Yann Dauphin. Hierarchical neural story generation.
+arXiv preprint arXiv:1805.04833, 2018.
+[7] Jun Gao, Yuhan Liu, Haolin Deng, Wei Wang, Yu Cao, Jiachen Du, and Ruifeng
+Xu. Improving empathetic response generation by recognizing emotion cause
+in conversations. In Marie-Francine Moens, Xuanjing Huang, Lucia Specia,
+and Scott Wen-tau Yih, editors, Findings of the Association for Computational
+Linguistics: EMNLP 2021, Virtual Event / Punta Cana, Dominican Republic, 16-20
+November, 2021, pages 807–819. Association for Computational Linguistics, 2021.
+[8] Deepanway Ghosal, Navonil Majumder, Alexander Gelbukh, Rada Mihalcea, and
+Soujanya Poria. COSMIC: COmmonSense knowledge for eMotion identification
+in conversations. In Findings of the Association for Computational Linguistics:
+EMNLP 2020, pages 2470–2481, Online, November 2020. Association for Compu-
+tational Linguistics.
+[9] Deepanway Ghosal, Navonil Majumder, Soujanya Poria, Niyati Chhaya, and
+Alexander Gelbukh. DialogueGCN: A graph convolutional neural network for
+emotion recognition in conversation. In Proceedings of the 2019 Conference on
+Empirical Methods in Natural Language Processing and the 9th International Joint
+Conference on Natural Language Processing (EMNLP-IJCNLP), pages 154–164,
+Hong Kong, China, November 2019. Association for Computational Linguistics.
+[10] Sayan Ghosh, Mathieu Chollet, Eugene Laksana, Louis-Philippe Morency, and
+Stefan Scherer. Affect-LM: A neural language model for customizable affective
+text generation. In Proceedings of the 55th Annual Meeting of the Association for
+Computational Linguistics (Volume 1: Long Papers), pages 634–642, Vancouver,
+Canada, July 2017. Association for Computational Linguistics.
+[11] Devamanyu Hazarika, Soujanya Poria, Rada Mihalcea, Erik Cambria, and Roger
+Zimmermann. ICON: Interactive conversational memory network for multimodal
+emotion detection. In Proceedings of the 2018 Conference on Empirical Methods
+in Natural Language Processing, pages 2594–2604, Brussels, Belgium, October-
+November 2018. Association for Computational Linguistics.
+[12] Devamanyu Hazarika, Soujanya Poria, Amir Zadeh, Erik Cambria, Louis-Philippe
+Morency, and Roger Zimmermann. Conversational memory network for emotion
+recognition in dyadic dialogue videos. In Proceedings of the 2018 Conference of the
+North American Chapter of the Association for Computational Linguistics: Human
+Language Technologies, Volume 1 (Long Papers), pages 2122–2132, New Orleans,
+Louisiana, June 2018. Association for Computational Linguistics.
+[13] Ari Holtzman, Jan Buys, Li Du, Maxwell Forbes, and Yejin Choi. The curious
+case of neural text degeneration. arXiv preprint arXiv:1904.09751, 2019.
+[14] Dou Hu, Lingwei Wei, and Xiaoyong Huai. Dialoguecrn: Contextual reasoning
+networks for emotion recognition in conversations. In Chengqing Zong, Fei
+Xia, Wenjie Li, and Roberto Navigli, editors, Proceedings of the 59th Annual
+Meeting of the Association for Computational Linguistics and the 11th International
+Joint Conference on Natural Language Processing, ACL/IJCNLP 2021, (Volume 1:
+Long Papers), Virtual Event, August 1-6, 2021, pages 7042–7052. Association for
+Computational Linguistics, 2021.
+[15] Zhiting Hu, Zichao Yang, Xiaodan Liang, Ruslan Salakhutdinov, and Eric P. Xing.
+Toward controlled generation of text. In Doina Precup and Yee Whye Teh, editors,
+Proceedings of the 34th International Conference on Machine Learning, volume 70
+of Proceedings of Machine Learning Research, pages 1587–1596. PMLR, 06–11 Aug
+2017.
+[16] N. Keskar, Bryan McCann, L. Varshney, Caiming Xiong, and R. Socher. Ctrl:
+A conditional transformer language model for controllable generation. ArXiv,
+abs/1909.05858, 2019.
+[17] Diederik P. Kingma and Jimmy Ba. Adam: A method for stochastic optimization,
+2017.
+[18] Jiangnan Li, Zheng Lin, Peng Fu, and Weiping Wang. Past, present, and future:
+Conversational emotion recognition through structural modeling of psycho-
+logical knowledge. In Marie-Francine Moens, Xuanjing Huang, Lucia Specia,
+and Scott Wen-tau Yih, editors, Findings of the Association for Computational
+Linguistics: EMNLP 2021, Virtual Event / Punta Cana, Dominican Republic, 16-20
+November, 2021, pages 1204–1214. Association for Computational Linguistics,
+2021.
+[19] Jiwei Li, Michel Galley, Chris Brockett, Jianfeng Gao, and Bill Dolan. A diversity-
+promoting objective function for neural conversation models. In Proceedings of
+the 2016 Conference of the North American Chapter of the Association for Compu-
+tational Linguistics: Human Language Technologies, pages 110–119, San Diego,
+California, June 2016. Association for Computational Linguistics.
+[20] Qintong Li, Hongshen Chen, Zhaochun Ren, Pengjie Ren, Zhaopeng Tu, and
+Zhumin Chen. Empdg: Multi-resolution interactive empathetic dialogue gen-
+eration. In Donia Scott, Núria Bel, and Chengqing Zong, editors, Proceedings
+of the 28th International Conference on Computational Linguistics, COLING 2020,
+Barcelona, Spain (Online), December 8-13, 2020, pages 4454–4466. International
+Committee on Computational Linguistics, 2020.
+[21] Qintong Li, Piji Li, Zhaochun Ren, Pengjie Ren, and Zhumin Chen. Knowledge
+bridging for empathetic dialogue generation. 2022.
+[22] Shifeng Li, Shi Feng, Daling Wang, Kaisong Song, Yifei Zhang, and Weichao Wang.
+Emoelicitor: An open domain response generation model with user emotional
+reaction awareness. In Christian Bessiere, editor, Proceedings of the Twenty-Ninth
+International Joint Conference on Artificial Intelligence, IJCAI-20, pages 3637–3643.
+International Joint Conferences on Artificial Intelligence Organization, 7 2020.
+Main track.
+[23] Yanran Li, Hui Su, Xiaoyu Shen, Wenjie Li, Ziqiang Cao, and Shuzi Niu. Daily-
+Dialog: A manually labelled multi-turn dialogue dataset. In Proceedings of the
+Eighth International Joint Conference on Natural Language Processing (Volume 1:
+Long Papers), pages 986–995, Taipei, Taiwan, November 2017. Asian Federation
+of Natural Language Processing.
+[24] Zhaojiang Lin, Andrea Madotto, Jamin Shin, Peng Xu, and Pascale Fung. MoEL:
+Mixture of empathetic listeners. In Proceedings of the 2019 Conference on Empirical
+Methods in Natural Language Processing and the 9th International Joint Conference
+on Natural Language Processing (EMNLP-IJCNLP), pages 121–132, Hong Kong,
+China, November 2019. Association for Computational Linguistics.
+[25] Chia-Wei Liu, Ryan Lowe, Iulian Serban, Mike Noseworthy, Laurent Charlin, and
+Joelle Pineau. How NOT to evaluate your dialogue system: An empirical study of
+unsupervised evaluation metrics for dialogue response generation. In Proceedings
+of the 2016 Conference on Empirical Methods in Natural Language Processing,
+pages 2122–2132, Austin, Texas, November 2016. Association for Computational
+Linguistics.
+[26] Siyang Liu, Chujie Zheng, Orianna Demasi, Sahand Sabour, Yu Li, Zhou Yu,
+Yong Jiang, and Minlie Huang. Towards emotional support dialog systems. In
+Chengqing Zong, Fei Xia, Wenjie Li, and Roberto Navigli, editors, Proceedings of
+the 59th Annual Meeting of the Association for Computational Linguistics and the
+11th International Joint Conference on Natural Language Processing, ACL/IJCNLP
+2021, (Volume 1: Long Papers), Virtual Event, August 1-6, 2021, pages 3469–3483.
+Association for Computational Linguistics, 2021.
+[27] Navonil Majumder, Pengfei Hong, Shanshan Peng, Jiankun Lu, Deepanway
+Ghosal, Alexander Gelbukh, Rada Mihalcea, and Soujanya Poria. MIME: MIM-
+icking emotions for empathetic response generation. In Proceedings of the 2020
+Conference on Empirical Methods in Natural Language Processing (EMNLP), pages
+8968–8979, Online, November 2020. Association for Computational Linguistics.
+[28] Navonil Majumder, Soujanya Poria, Devamanyu Hazarika, Rada Mihalcea,
+Alexander Gelbukh, and Erik Cambria. Dialoguernn: An attentive rnn for emo-
+tion detection in conversations. Proceedings of the AAAI Conference on Artificial
+Intelligence, 33(01):6818–6825, Jul. 2019.
+[29] Bilyana Martinovski and David R. Traum. Breakdown in human-machine in-
+teraction: the error is the clue. In ISCA tutorial and research workshop on Error
+handling in dialogue systems, August 2003 2003.
+[30] Courtney Napoles, Keisuke Sakaguchi, Matt Post, and Joel Tetreault. Gleu without
+tuning, 2016.
+[31] Kartikey Pant, Yash Verma, and R. Mamidi. Sentiinc: Incorporating sentiment
+information into sentiment transfer without parallel data. Advances in Information
+Retrieval, 12036:312 – 319, 2020.
+[32] Kishore Papineni, Salim Roukos, Todd Ward, and Wei-Jing Zhu. Bleu: a method
+for automatic evaluation of machine translation. In Proceedings of the 40th Annual
+Meeting of the Association for Computational Linguistics, pages 311–318, Philadel-
+phia, Pennsylvania, USA, July 2002. Association for Computational Linguistics.
+[33] Kishore Papineni, Salim Roukos, Todd Ward, and Wei-Jing Zhu. Bleu: a method
+for automatic evaluation of machine translation. In Proceedings of the 40th
+Annual Meeting of the Association for Computational Linguistics, July 6-12, 2002,
+Philadelphia, PA, USA, pages 311–318. ACL, 2002.
+[34] Timo Partala and V. Surakka. The effects of affective interventions in human-
+computer interaction. Interact. Comput., 16:295–309, 2004.
+[35] Soujanya Poria, Erik Cambria, Devamanyu Hazarika, Navonil Majumder, Amir
+Zadeh, and Louis-Philippe Morency. Context-dependent sentiment analysis in
+user-generated videos. In Proceedings of the 55th Annual Meeting of the Association
+for Computational Linguistics (Volume 1: Long Papers), pages 873–883, Vancouver,
+Canada, July 2017. Association for Computational Linguistics.
+[36] Shrimai Prabhumoye, Alan W Black, and Ruslan Salakhutdinov. Exploring
+controllable text generation techniques. In Proceedings of the 28th International
+Conference on Computational Linguistics, pages 1–14, Barcelona, Spain (Online),
+December 2020. International Committee on Computational Linguistics.
+[37] Helmut Prendinger, Junichiro Mori, and Mitsuru Ishizuka. Using human physi-
+ology to evaluate subtle expressivity of a virtual quizmaster in a mathematical
+game. International Journal of Human-Computer Studies, 62(2):231–245, 2005.
+Subtle expressivity for characters and robots.
+[38] Alec Radford, Jeff Wu, Rewon Child, David Luan, Dario Amodei, and Ilya
+Sutskever. Language models are unsupervised multitask learners. 2019.
+[39] Hannah Rashkin, Eric Michael Smith, Margaret Li, and Y-Lan Boureau. Towards
+empathetic open-domain conversation models: A new benchmark and dataset.
+In Proceedings of the 57th Annual Meeting of the Association for Computational
+Linguistics, pages 5370–5381, Florence, Italy, July 2019. Association for Computa-
+tional Linguistics.
+[40] Sahand Sabour, Chujie Zheng, and Minlie Huang. CEM: commonsense-aware
+empathetic response generation. CoRR, abs/2109.05739, 2021.
+[41] Sahand Sabour, Chujie Zheng, and Minlie Huang. CEM: commonsense-aware
+empathetic response generation. CoRR, abs/2109.05739, 2021.
+
+[42] M. Skowron. Affect listeners: Acquisition of affective states by means of conver-
+sational systems. In COST 2102 Training School, 2009.
+[43] Zhenqiao Song, Xiaoqing Zheng, Lu Liu, Mu Xu, and Xuanjing Huang. Gen-
+erating responses with a specific emotion in dialog. In Proceedings of the 57th
+Annual Meeting of the Association for Computational Linguistics, pages 3685–3695,
+Florence, Italy, July 2019. Association for Computational Linguistics.
+[44] A. Sudhakar, Bhargav Upadhyay, and A. Maheswaran. Transforming delete, re-
+trieve, generate approach for controlled text style transfer. ArXiv, abs/1908.09368,
+2019.
+[45] Hao Tian, Can Gao, Xinyan Xiao, Hao Liu, Bolei He, Hua Wu, Haifeng Wang, and
+feng wu. SKEP: Sentiment knowledge enhanced pre-training for sentiment analy-
+sis. In Proceedings of the 58th Annual Meeting of the Association for Computational
+Linguistics, pages 4067–4076, Online, July 2020. Association for Computational
+Linguistics.
+[46] Hao Tian, Can Gao, Xinyan Xiao, Hao Liu, Bolei He, Hua Wu, Haifeng Wang,
+and Feng Wu. SKEP: Sentiment knowledge enhanced pre-training for senti-
+ment analysis. In Proceedings of the 58th Annual Meeting of the Association for
+Computational Linguistics, pages 4067–4076, Online, July 2020. Association for
+Computational Linguistics.
+[47] Quan Tu, Yanran Li, Jianwei Cui, Bin Wang, Ji-Rong Wen, and Rui Yan. MISC: A
+mixed strategy-aware model integrating COMET for emotional support conver-
+sation. CoRR, abs/2203.13560, 2022.
+[48] Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones,
+Aidan N Gomez, Ł ukasz Kaiser, and Illia Polosukhin. Attention is all you need. In
+I. Guyon, U. V. Luxburg, S. Bengio, H. Wallach, R. Fergus, S. Vishwanathan, and
+R. Garnett, editors, Advances in Neural Information Processing Systems, volume 30.
+Curran Associates, Inc., 2017.
+[49] Thomas Wolf, Lysandre Debut, Victor Sanh, Julien Chaumond, Clement De-
+langue, Anthony Moi, Pierric Cistac, Tim Rault, Remi Louf, Morgan Funtowicz,
+Joe Davison, Sam Shleifer, Patrick von Platen, Clara Ma, Yacine Jernite, Julien
+Plu, Canwen Xu, Teven Le Scao, Sylvain Gugger, Mariama Drame, Quentin
+Lhoest, and Alexander Rush. Transformers: State-of-the-art natural language
+processing. In Proceedings of the 2020 Conference on Empirical Methods in Natural
+Language Processing: System Demonstrations, pages 38–45, Online, October 2020.
+Association for Computational Linguistics.
+[50] Xing Wu, Tao Zhang, Liangjun Zang, Jizhong Han, and Songlin Hu. Mask and
+infill: Applying masked language model for sentiment transfer. In IJCAI, 2019.
+[51] Jingjing Xu, X. Sun, Qi Zeng, Xuancheng Ren, X. Zhang, Houfeng Wang, and
+W. Li. Unpaired sentiment-to-sentiment translation: A cycled reinforcement
+learning approach. In ACL, 2018.
+[52] Yi Zhang, Jingjing Xu, Pengcheng Yang, and X. Sun. Learning sentiment memories
+for sentiment modification without parallel data. In EMNLP, 2018.
+[53] Yizhe Zhang, Michel Galley, Jianfeng Gao, Zhe Gan, Xiujun Li, Chris Brockett,
+and Bill Dolan. Generating informative and diverse conversational responses via
+adversarial information maximization. In S. Bengio, H. Wallach, H. Larochelle,
+K. Grauman, N. Cesa-Bianchi, and R. Garnett, editors, Advances in Neural Infor-
+mation Processing Systems, volume 31. Curran Associates, Inc., 2018.
+[54] Yizhe Zhang, Siqi Sun, Michel Galley, Yen-Chun Chen, Chris Brockett, Xiang Gao,
+Jianfeng Gao, Jingjing Liu, and Bill Dolan. DIALOGPT : Large-scale generative pre-
+training for conversational response generation. In Proceedings of the 58th Annual
+Meeting of the Association for Computational Linguistics: System Demonstrations,
+pages 270–278, Online, July 2020. Association for Computational Linguistics.
+[55] Peixiang Zhong, D. Wang, and C. Miao. An affect-rich neural conversational
+model with biased attention and weighted cross-entropy loss. In AAAI, 2019.
+[56] Hao Zhou, Minlie Huang, T. Zhang, Xiaoyan Zhu, and Bing Liu. Emotional
+chatting machine: Emotional conversation generation with internal and external
+memory. In AAAI, 2018.
+[57] Xianda Zhou and William Yang Wang. MojiTalk: Generating emotional responses
+at scale. In Proceedings of the 56th Annual Meeting of the Association for Computa-
+tional Linguistics (Volume 1: Long Papers), pages 1128–1137, Melbourne, Australia,
+July 2018. Association for Computational Linguistics.
+
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+page_content='Think Twice: A Human-like Two-stage Conversational Agent for  Emotional Response Generation  Yushan Qian  Tianjin University  Tianjin, China  yushanqian@tju.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
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+page_content='cn  Bo Wang  Tianjin University  Tianjin, China  bo_wang@tju.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
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+page_content='cn  Shangzhao Ma  Tianjin University  Tianjin, China  shangzhaoma@tju.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
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+page_content='cn  Wu Bin  Quesoar Co.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Ltd.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  Tianjin, China  wubin@quesoar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='com  Shuo Zhang  Quesoar Co.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Ltd.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  Tianjin, China  s@quesoar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='com  Dongming Zhao  Artificial Intelligence Laboratory,  China Mobile Communication Group  Tianjin Co.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=', Ltd.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  Tianjin, China  waitman_840602@163.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='com  Kun Huang  Artificial Intelligence Laboratory,  China Mobile Communication Group  Tianjin Co.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=', Ltd.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  Tianjin, China  hknzh@126.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='com  Yuexian Hou  Tianjin University  Tianjin, China  yxhou@tju.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='edu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='cn  ABSTRACT  Towards human-like dialogue systems, current emotional dialogue  approaches jointly model emotion and semantics with a unified  neural network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' This strategy tends to generate safe responses  due to the mutual restriction between emotion and semantics, and  requires the rare large-scale emotion-annotated dialogue corpus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' In-  spired by the "think twice" behavior in human intelligent dialogue,  we propose a two-stage conversational agent for the generation of  emotional dialogue.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Firstly, a dialogue model trained without the  emotion-annotated dialogue corpus generates a prototype response  that meets the contextual semantics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Secondly, the first-stage proto-  type is modified by a controllable emotion refiner with the empathy  hypothesis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Experimental results on the DailyDialog and Empathet-  icDialogues datasets demonstrate that the proposed conversational  agent outperforms the compared models in the emotion genera-  tion and maintains the semantic performance in the automatic and  human evaluations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  KEYWORDS  Emotional Dialogue, Dialogue Systems, Human Interaction  ACM Reference Format:  Yushan Qian, Bo Wang, Shangzhao Ma, Wu Bin, Shuo Zhang, Dongming  Zhao, Kun Huang, and Yuexian Hou.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' 2023.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Think Twice: A Human-like Two-  stage Conversational Agent for Emotional Response Generation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' In Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  of the 22nd International Conference on Autonomous Agents and Multiagent  Systems (AAMAS 2023), London, United Kingdom, May 29 – June 2, 2023,  IFAAMAS, 10 pages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' of the 22nd International Conference on Autonomous Agents and Multiagent Sys-  tems (AAMAS 2023), A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Ricci, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Yeoh, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Agmon, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' An (eds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' ), May 29 – June 2, 2023,  London, United Kingdom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' © 2023 International Foundation for Autonomous Agents  and Multiagent Systems (www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='ifaamas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='org).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' All rights reserved.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  1  INTRODUCTION  In the task of open-domain dialogue generation, emotional dialogue  aims to generate responses involving the perception and expression  of proper emotions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' A large number of studies [29, 34, 37] have  demonstrated that emotional dialogue can significantly improve  users’ satisfaction in a human-machine conversation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Moreover,  building a dialogue system with human emotions is one of the  ultimate goals of artificial intelligence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  Towards emotional dialogue systems, in addition to the early  methods of manually compiling rules by professionals [42], existing  statistical approaches are mainly based on neural network mod-  els [1, 10, 20, 22, 24, 27, 43, 55–57].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' With an end-to-end strategy,  these neural network models jointly generate the semantics and  emotions of the dialogue responses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  However, current end-to-end emotional dialogue models still  face several challenges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Firstly, in deep neural networks, the input  emotion signals are often weakened through the complex learn-  ing process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Secondly, in the joint generation model, the design to  enhance emotions often restricts the semantic performance of gen-  erated responses (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=', safe responses).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Thirdly, large-scale emotion-  annotated dialogue corpora are rare for joint training of semantics  and emotions with deep neural networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  In response to the above challenges, we propose to generate  emotional responses with the idea of human intelligent dialogue  behavior.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' When humans respond in a dialogue, the simultaneous  processing of emotion and semantics can not ensure satisfying  results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' The intuitive emotion generated simultaneously with se-  mantics is often arduous to ensure a response in the appropriate  emotion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' One source of the appropriate emotional response comes  from an independent emotion selection after determining the se-  mantics, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=', thinking twice about appropriate emotions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' In this  independent emotion selection, a paramount strategy for humans to  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='04907v1  [cs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content="CL]  12 Jan 2023  Honey, it's time for  dinner." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  Shut up!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' The video is  starting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  Please be quiet!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' the  video is starting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content="  Honey, it's time for  dinner." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  Shut up!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' The video is  starting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  Shut up!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' The video is  starting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Sorry, I’m  just too nervous.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  Rewrite  Add  Positive  Negative  Figure 1: The real-life examples of emotion adjustment in  the human dialogue.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' The "think twice" strategy can be ob-  served in human intelligent behavior and effectively im-  proves the quality of emotional responses by rewriting ex-  pressions or adding extra information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Bold tokens are the  rewritten or added part.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  determine the appropriate emotion is the empathy strategy, which  makes the emotion of the response consistent with that of the con-  text [2, 24, 39].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' As visualized in Figure 1, each response firstly has  a proper semantic to respond to the context.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Then, by recognizing  the context’s emotional state, we can adjust the response emotion-  ally and achieve a certain degree of empathy by responding to the  partner’s emotion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  Therefore, we design a human-like two-stage conversational  agent for emotional response generation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Firstly, a prototype re-  sponse with proper semantics is generated with a pre-trained model  fine-tuned on dialogue corpus without emotion annotation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Then,  the contextual emotional state is recognized by a dialogue emotion  detector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' According to the empathy hypothesis [24], the type of  generated emotion is consistent with the contextual emotional state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  Finally, the prototype is modified by a controllable emotion refiner  to generate a final response that is both semantically relevant and  emotionally appropriate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  Specifically, towards effective refining for an emotional response  in the second stage, we also refer to two human pragmatic strategies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  First, humans express the same information in different ways with  different vocabulary choices [36].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Therefore, we involve expected  emotional attributes in the response by replacing the original emo-  tional words or phrases instead of constructing a new sentence from  scratch, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=', the "rewriting" strategy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Second, there are also some  implicit emotions reflected through the whole sentence instead of  specific words.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Consequently, we also adjust the emotion by adding  extra sentences to the response, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=', the "adding" strategy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  In summary, our contributions are:  Inspired by human intelligent dialogue behavior, we propose  a human-like two-stage conversational agent for emotional  response generation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' To the best of our knowledge, it is the  first two-stage model specifically for emotional dialogue.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  The proposed method effectively alleviates two problems  of existing emotional dialogue approaches, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=', weakening  the emotion effect during the complex learning process and  restricting the semantic generation to meet the emotion  demand.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  The proposed two-stage conversational agent reduces the  demand for the sizeable emotion-annotated dialogue cor-  pus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' The training of the prototype response generator in the  first stage only requires general dialogue corpora without  emotion annotation, and the controllable emotion dialogue  refiner is trained on non-dialogue and non-parallel emotion-  annotated corpora.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  The proposed method can be generalized to other existing  end-to-end emotion dialogue generation models as post-  processing for emotionalization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Even if some sentences have  poor emotional expressions, there is no need to retrain the  whole model and build new sentences from scratch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  2  METHODS  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='1  Preliminaries  Formally, in this paper, the dialogue context is alternate utterances  of two speakers, defined as 𝐶 = {𝑈1,𝑈2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' ,𝑈𝑛}, where 𝑛 denotes  the number of utterances in a dialogue.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' The set of context emotions  is 𝐸 = {𝑒1,𝑒2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' ,𝑒𝑛}, which corresponds to the dialogue context 𝐶.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  Our goal is to generate the next utterance 𝑈𝑛+1, which is coherent  to the context and contains the appropriate emotion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  As shown in Figure 2, our model consists of three parts: the  Prototype Utterance Generator 𝐺, the Dialogue Emotion Detec-  tor 𝐷, and the Controllable Emotion Refiner 𝑅.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' The Controllable  Emotion Refiner 𝑅 has two modules, named "Rewrite" and "Add".' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  The Prototype Utterance Generator 𝐺 takes the dialogue context  𝐶 as input and generates a prototype response 𝑈𝑚.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' The Dialogue  Emotion Detector 𝐷 takes the dialogue context 𝐶 as input and ob-  tains the emotion state set 𝐸, which dynamically determines the  response emotion 𝑒𝑛+1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' The Controllable Emotion Refiner 𝑅 refines  𝑈𝑚 according to 𝑒𝑛+1 by rewriting 𝑈𝑚 or adding extra sentences  into 𝑈𝑚 with Rewrite Module and Add Module, respectively, and  generates the final response 𝑅𝑒, which is 𝑈𝑛+1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='2  Prototype Utterance Generator  We use DialoGPT [54] as the Prototype Utterance Generator to  generate relevant, diverse, and contextually consistent responses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  Large-scale pre-trained language models [5, 38, 54] have exten-  sively promoted the research progress of the open-domain dialogue  in recent years.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' The method of pre-training and fine-tuning can  avoid training models from scratch, save computing resources, and  achieve excellent results in downstream tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  DialoGPT has a 12-to-48 layer Transformer with layer normal-  ization like GPT-2 [38], which is trained on the 147M large-scale  dialogue dataset from Reddit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' All utterances of the context are  spliced into a long sentence with “<|endoftext |>” as input.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' The  conditional distribution of the target prototype utterance 𝑈𝑚 is the  product of a series of conditional probabilities:  𝑃(𝑈𝑚|𝐶) = �𝑆+𝑠𝑚  𝑖=𝑆+1 𝑃(𝑡𝑖 |𝑡1,𝑡2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=',𝑡𝑖−1),  (1)  Selector  GLEU: r>a?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='r:a  Stage 2： Controllable Emotion Refiner  Prototype Response  Generator  Context  {U1,U2,…,Un}  Rewrite Module  Add Module  p(en+1|Re)  p(Re)  Um  en+1  Re  Dialogue Emotion Detector  1  2  3  P(Um|C)=∏𝑖=𝑆+1  S+sm P(ti|t1, t2, … , ti-1)  Stage 1： Prototype Generation  Emotional Response  1 1 1  2 2 2  3 3 3  r  a  P(a|x)  P(x)  P(x|a)  cx,ssrc  L(θ)  α(t)  Figure 2: The overall architecture of the proposed two-stage conversational agent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' The first stage includes Prototype Utterance  Generator and Dialogue Emotion Detector, which generates prototype response 𝑈𝑚 and detects the contextual emotion state  as the expected emotion 𝑒𝑛+1 of the final response, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' The second stage includes Rewrite Module, Add Module, and  Selector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Rewrite Module and Add Module refine 𝑈𝑚 according to 𝑒𝑛+1, and the Selector selects the final response from the  outputs of Rewrite Module and Add Module based on the GLEU score.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  where 𝐶 = {𝑈1,𝑈2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=',𝑈𝑛}, 𝑛 is the number of utterances, 𝑈𝑖 =  �  𝑡1,𝑡2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=',𝑡𝑠𝑖  �, 𝑡𝑖 is each token in the utterance, 𝑠𝑖 is the length of  each utterance, 𝑆 = 𝑠1 +𝑠2 +· · ·+𝑠𝑛 represents the number of tokens  in all utterances, 𝑠𝑚 is the length of 𝑈𝑚.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  We use the maximum mutual information scoring function (MMI)  and the top-k sampling [6] to reduce the generation of meaningless  responses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' The specific implementation is based on tools provided  by Hugging Face1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' We conduct fine-tuning on the training set for  3 epochs with the batch size of 8 and the learning rate of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='00001.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  Emotional labels in the training set will not be used.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' During the  decoding process, we use the top-k (k=100) sampling and nucleus  sampling (p=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='7) [13].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='3  Dialogue Emotion Detector  As an intuitive hypothesis of empathy, during emotional dialogues  between two individuals, the listener usually tends to respond in  a way that recognizes the speaker’s feelings [2, 24] and achieves  a certain degree of empathy by calling the respondent’s emotions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  In this work, we adopt this empathy hypothesis to determine the  emotion of the response according to the emotion state of the  context.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  To this end, the goal of the Dialogue Emotion Detector 𝐷 is to  detect emotions in the dialogue context.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' According to the empathy  hypothesis, 𝐷 determines the expected emotion of the Controllable  Emotion Refiner by the recognized emotion distribution in the  dialogue context.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  The Dialogue Emotion Detector 𝐷 is developed based on Dia-  logueGCN [9], which regards each utterance in the dialogue as  a node of the graph network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' There are directed edges between  utterances, and the sequence order of utterances determines the di-  rection of each edge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' These directed edges can model the emotional  impact of what the speaker or the other people has said before.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' We  1https://huggingface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='co/models  use Glove embedding and CNN to extract features of utterances  and get the embedding of each utterance 𝑈𝑖, which is the vector of  each node.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' There are 𝑏 utterances before each utterance, and there  are 𝑎 utterances after it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' The node of each utterance has edges with  𝑎 + 𝑏 + 1 nodes (including itself).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' The weight 𝑎𝑖𝑗 of each edge is  decided by the relationship between nodes as follows:  𝛼𝑖𝑗 = softmax(𝑈𝑇  𝑖 𝑊𝑢 [𝑈𝑖−𝑏, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=',𝑈𝑖+𝑎]),  for  𝑗 = 𝑖 − 𝑏, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=',𝑖 + 𝑎.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  (2)  Further details about GCN construction are available in [9].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  Finally, the embedding from the sequence encoder 𝑠𝑞 and the  speaker-level encoder 𝑠𝑝 are spliced together, and combined with  the similarity-based attention mechanism to obtain the final embed-  ding of the utterance node.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Then we use a fully connected network  to classify multiple emotion categories:  𝐻 = [ℎ1,ℎ2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' ,ℎ𝑛],  ℎ𝑖 = softmax([𝑠𝑞𝑖,𝑠𝑝𝑖]𝑇𝑊 𝐻)𝐻𝑇,  𝑒𝑖 = argmax(softmax(FFN(ℎ𝑖))).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  (3)  We use L2 regularization classification cross-entropy loss as the  loss function and Adam [17] as the optimizer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' We classify emotions  in the emotion state set 𝑆 into two groups of negative emotions  and positive emotions as in [27].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Following [2, 24], we assume  that empathetic responses may mimic the user’s emotions to some  extent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Therefore, the target emotion 𝑒𝑛+1 that we finally pass to  the Controllable Emotion Refiner 𝑅 is defined as follows:  𝑒𝑛+1 = positive,  if  𝑁𝑢𝑚𝑝𝑜𝑠 (𝐸) > 𝑁𝑢𝑚𝑛𝑒𝑔(𝐸),  otherwise  𝑒𝑛+1 = negative.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  (4)  Where 𝐸 = {𝑒1,𝑒2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' ,𝑒𝑛} is the set of emotions in each dialogue.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  𝑁𝑢𝑚𝑝𝑜𝑠 and 𝑁𝑢𝑚𝑛𝑒𝑔 represent the number of positive emotions  and negative emotions in 𝐸, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='4  Controllable Emotion Refiner  The Controllable Emotion Refiner 𝑅 takes the prototype response  𝑈𝑚 and the target emotion 𝑒𝑛+1 as input, and generates the final  response 𝑅𝑒.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' The goal we need to learn is defined as:  𝑃(𝑅𝑒 |𝑈𝑚,𝑒𝑛+1) & Stype(𝑅𝑒) = 𝑒𝑛+1,  (5)  where “Stype” represents the emotion type.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  The Controllable Emotion Refiner 𝑅 consists of two modules,  “Rewrite” and “Add”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' The Rewrite Module transforms the emotion  attribute of the 𝑈𝑚 by replacing the original emotion symbols in  the sentence with symbols that express the target emotion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' The  Add module adjusts the emotion type by adding extra sentences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  Rewrite Module.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' The Rewrite Module consists of two parts: the  first one is the deletion part, which determines whether each token  in the input is an emotion attribute word, learns the emotional part  and non-emotional part in the input, and deletes the emotional part.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  We adopt the attention mechanism of Transformer to extract the  attention score as the weight of each token [44]:  𝛼(𝑡) = softmax(𝑄𝐾𝑇 ), 𝑓 𝑜𝑟 𝑡 ∈ 𝑈𝑚,  (6)  where 𝑄 and 𝐾 carry the original connotations of query and key  vectors in the Transformer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  The second is the generating part, which generates sentences  with target emotion attributes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' The generating part adopts the  Transformer structure, based on the Hugging Face [49].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' The input  of generating part is the prototype response and the target emotion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  The output is a sentence that conforms to the target emotion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' With-  out requiring the parallel corpus, the training goal of generating  part is to minimize the following reconstruction loss:  𝐿(𝜃) =  ∑︁  𝑥,𝑠𝑠𝑟𝑐 ∈𝐷  log𝑝(𝑥|𝑐𝑥,𝑠𝑠𝑟𝑐;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='𝜃),  (7)  where 𝐷 is the training dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Given a sentence 𝑥, the Rewrite  Module model learns to reconstruct 𝑦 = 𝑥 with 𝑐𝑥, 𝑠𝑠𝑟𝑐.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' 𝑐𝑥 is the  non-emotional content of 𝑥, and 𝑠𝑠𝑟𝑐 is the original style of the  sentence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  Add Module.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' The Add Module is developed based on the work  of [4] to change the emotion polarity of the original sentence by  adding extra sentences with the target emotion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Using Bayes’ theo-  rem, we can use the model 𝑝(𝑥) and the model 𝑝(𝑎|𝑥) to express  the model 𝑝(𝑥|𝑎):  𝑝(𝑥|𝑎) ∝ 𝑝(𝑎|𝑥)𝑝(𝑥).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  (8)  In order to obtain the required 𝑝(𝑥|𝑎) to generate the sentence  based on attribute 𝑎, we already have a language model 𝑝(𝑥) that  can generate fluent sentences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Furthermore, we build a classifier to  determine whether the text 𝑥 generated by the language model has  𝑎 attribute, that is, 𝑝(𝑎|𝑥), then 𝑝(𝑥|𝑎) can be obtained.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  The process of the Add Module has three steps:  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' First, a forward pass is performed through the language model  to compute the likelihood of the desired attribute using an attribute  model that predicts 𝑝(𝑎|𝑥).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Second, a backward pass updates the internal latent represen-  tations of the language model, using gradients from the attribute  model to increase the likelihood of the sentence having the desired  attribute.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  Table 1: Two groups of emotions in the DailyDialog dataset  according to positivity and negativity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  Positive  Negative  happiness,  surprise,  other  anger, disgust, fear,  sadness  Table 2: Two groups of emotions in the EmpatheticDia-  logues dataset according to positivity and negativity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  Positive  Negative  confident,  joyful,  grateful, impressed,  proud, excited, trust-  ing, hopeful, faithful,  prepared,  content,  surprised, caring  afraid, angry, annoyed, an-  ticipating, anxious, apprehen-  sive, ashamed, devastated, dis-  appointed, disgusted, embar-  rassed, furious, guilty, jealous,  lonely, nostalgic, sad, senti-  mental, terrified  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Third, re-sampling to generate a new word according to the  obtained new output probability distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  To generate more diverse sentences that conform to the language  model, two methods are adopted to ensure that the language model  of the generated sentence is as close as possible to the original  language model: Kullback–Leibler (KL) Divergence and Post-norm  Geometric Mean Fusion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' About the language model, we use GPT2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  Regarding the specific attribute discriminator 𝑝(𝑎|𝑥), we take the  existing non-dialogue emotion-annotated corpus and pre-train a  classifier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  Selector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' A Selector is designed to determine whether the re-  sponse is from the Rewrite Module or the Add Module is selected as  the final output.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' The Selector uses GLEU [30] as a basis for judging  the overall effect of responses, which compares with the prototype  response.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' [44] found that GLEU is more suitable for human score  than BLEU score.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' The Selector selects the final response with a  higher GLEU score.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  3  EXPERIMENTS  In this section, we introduce the datasets, baselines and evalua-  tion metrics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' The proposed conversational agent is experimentally  compared with baselines and the experimental results are discussed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='1  Datasets  We used the DailyDialog [23] and EmpatheticDialogues [39] datasets  for the experiment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' DailyDialog is a multi-round dialogue dataset  for daily chat scenes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' There are a total of 12,218 dialogues and  103,607 utterances.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Each dialogue has about 8 rounds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' The topic  and emotion in each utterance are labeled.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' There are seven types of  emotion: anger, disgust, fear, happiness, sadness, surprise, and oth-  ers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Refer to [27], we divided the 7 emotion types into two groups  containing 3 positive and 4 negative emotions, respectively, as listed  in Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' EmpatheticDialogues is a widely-used benchmark dataset  for empathetic response generation, which is a large-scale multi-  turn dataset containing 25k empathetic dialogues between crowd-  sourcing workers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' EmpatheticDialogues also provides an emotion  label for each dialogue from 32 available emotions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Following [27],  we divided the 32 emotion types into two groups containing 13 pos-  itive and 19 negative emotions, respectively, as listed in Table 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' We  focus on positive and negative emotions because the consistency of  polarity level emotion is more popular in emotion study and robust  in the application.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Since our method and baselines are under the  same assumption and processed in the same way during evaluation,  the results are competitive and convincing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  Considering the limited running space and to unify the number  of rounds in each dialogue, we segment the original dialogues into  sub dialogues having 4 rounds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Finally, for the DailyDialog dataset,  the dialogue numbers of the training / validation / test set are 54,299  / 5,109 / 4,782, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' For the EmpatheticDialogues dataset,  the dialogue numbers of the training / validation / test set are 18,383  / 2,810 / 3,320, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='2  Compared Models  To the best of our knowledge, this is an early work in the two-  stage generation of emotional dialogue.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' In view of the empathy  hypothesis, we compare our approach with a range of models used  in related tasks, including general dialogue, emotional dialogue,  and empathetic dialogue.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  Transformer [48]: The standard Transformer model that is  trained to optimize NLL loss.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  Multi-TRS [39]: A multi-task Transformer model jointly trained  by predicting the emotion and generating the response.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  Mojitalk [57]: An encoder-decoder based CVAE model incorpo-  rated with emotion embedding.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  MoEL [24]: A Transformer-based model employs emotion-specific  decoders whose outputs are aggregated and fed to a final decoder  to generate the empathetic response.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  MIME [27]: A Transformer-based model that leverages emotion  groups and emotion mimicry, which effectively blends emotions in  positive and negative emotion groups and generates the empathetic  response.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  EmpDG [20]: An interactive adversarial model consists of a gen-  erator and a discriminator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' The discriminator requires user feedback.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  Besides, the model exploits both the coarse-grained dialogue-level  and fine-grained token-level emotions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Referring to [40], we only  apply the empathetic generator to ensure consistent input and  output in the test set for a fair comparison with other baselines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='3  Implementation Details  We use the official codes of all baselines, especially, EmpDG only  applies the empathetic generator (Multi-TRS2, Mojitalk3, MoEL4,  MIME5, EmpDG6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' We implement all the models using PyTorch  except Mojitalk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' All the baselines were trained on a V100 GPU with  the batch size of 16 and the early stopping strategy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' About the Adam  optimizer, we set 𝛽1 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='9 and 𝛽2 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='98.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' For the emotion detection  in the automatic evaluation, emotion pre-training model in Senta  is “𝑒𝑟𝑛𝑖𝑒_2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='0_𝑠𝑘𝑒𝑝_𝑙𝑎𝑟𝑔𝑒_𝑒𝑛”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  2https://github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='com/facebookresearch/EmpatheticDialogues  3https://github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='com/Claude-Zhou/MojiTalk  4https://github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='com/HLTCHKUST/MoEL  5https://github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='com/declare-lab/MIME  6https://github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='com/qtli/EmpDG  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='4  Evaluation Metrics  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='1  Automatic Evaluation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' We apply the following evaluation  metrics in the automatic evaluation:  BLEU: Word-overlap scores with human responses [33].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' We use  BLEU-4, which is calculated with an NLG evaluation toolkit 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  Diversity: Dist-n measures the proportion of unique n-grams  in the generated responses [25].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' It is commonly used to evaluate  whether the dialogue model can generate a diverse response as  humans do.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Low diversity often means the model tends to generate  similar safe responses to different contexts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' We refer to the work  of [3] to calculate the Dist-1 and Dist-2 metrics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  Emotion Accuracy (Acc): The emotion accuracy is defined as  the proportion of consistent emotion polarities between generated  responses and the ground truth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' We use the Sentiment Knowledge  Enhanced Pre-training for Sentiment Analysis (SKEP) model [45]  proposed by Baidu as the emotion detector during the evaluation8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  SKEP is a state-of-the-art emotion detector in 14 typical Chinese and  English sentiment analysis tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' We use it to automatically detect  the emotion polarity of the responses generated by our proposed  conversational agent and baselines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='2  Human Evaluation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' We randomly sampled 100 dialogues and  generated responses with our proposed conversational agent and  baselines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' We employed three human annotators to evaluate each  response based on four aspects:  Content(Con): Whether the response is appropriate for the  context in the current dialogue.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' It is rated on a Likert scale (1: not  at all, 3: somewhat, 5: very much).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  Emotion(Emo): Whether the response is appropriate for the  context in the emotion polarity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' 1 indicates the response is appro-  priate, and 0 indicates the response is inappropriate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  Emotion-intensity(Int): What the emotion intensity of the  response is.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' 0 represents no emotion, 1 represents slight intensity,  and 2 represents strong intensity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  Fluency(Flu): Whether the response is readable and understand-  able.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' It is rated on a Likert scale (1: not at all, 3: somewhat, 5: very  much).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='5  Main Results  Both automatic and human evaluation results are shown in Table 3  and Table 4 on the DailyDialog and EmpatheticDialogues datasets,  respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  For the performance of emotion generation, it can be observed  that the proposed conversational agent outperforms baselines in  Acc for the automatic evaluation and Emo for the human evalu-  ation in two datasets, indicating the outstanding performance of  our conversational agent in emotion generation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' In addition, our  conversational agent also achieves the best and second-best results  in Int on the DailyDialog and EmpatheticDialogues datasets, re-  spectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' which clearly verifies that the emotional effect of our  model is more significant and sufficient compared with the SOTA  end-to-end systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' This is because in the process of the two stages,  7https://github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='com/Maluuba/nlg-eval  8https://github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='com/baidu/Senta  Table 3: Automatic and Human evaluations in the DailyDialog dataset (The significant improvement with p-value < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='05 (t-test).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  Fleiss’s kappa for Human evaluation is 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='526, indicating "moderate agreement").' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  Model  Automatic Evaluation  Human Evaluation  BLEU-4  Dist-1  Dist-2  Acc(%)  Con  Emo  Int  Flu  Transformer  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='44  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='10  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='84  54.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='04  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='54  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='69  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='49  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='60  Multi-TRS  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='58  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='17  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='35  54.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='29  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='49  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='75  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='52  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='35  Mojitalk  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='58  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='99  22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='40  53.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='99  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='14  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='79  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='61  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='21  MoEL  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='46  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='51  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='39  55.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='44  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='35  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='77  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='73  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='67  MIME  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='54  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='48  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='79  53.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='43  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='42  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='78  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='68  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='43  EmpDG  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='57  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='12  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='73  56.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='02  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='40  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='79  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='77  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='47  Our  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='67  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='71  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='77  57.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='36  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='82  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='84  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='79  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='45  Table 4: Automatic and Human evaluations in the EmpatheticDialogues dataset (The significant improvement with p-value <  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='05 (t-test).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Fleiss’s kappa for Human evaluation is 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='462, indicating "moderate agreement").' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  Model  Automatic Evaluation  Human Evaluation  BLEU-4  Dist-1  Dist-2  Acc(%)  Con  Emo  Int  Flu  Transformer  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
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+page_content='99  33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='52  61.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
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+page_content='34  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='15  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='28  62.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
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+page_content='86  EmpDG  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
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+page_content='78  Our  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
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+page_content='72  Table 5: Ablation Analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  Model  DailyDialog  EmpatheticDialogues  BLEU-4  Dist-1  Dist-2  Acc(%)  BLEU-4  Dist-1  Dist-2  Acc(%)  Our  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
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+page_content='42  w/o Add  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='59  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
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+page_content='07  19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
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+page_content='33  w/o Rewrite  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='49  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
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+page_content='74  55.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='88  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
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+page_content='27  65.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='78  w/o DED  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='63  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='77  39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='27  56.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='84  —  —  —  —  the emotional effect of the response is separately determined and re-  fined in the second stage without being influenced by the semantic  generation in the first stage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  For the performance of semantic generation, the proposed con-  versational agent reaches the highest level in BLEU-4 and Con.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' In  terms of Dist-1 and Dist-2, our conversational agent also scores  moderately.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' These results confirm that the proposed conversational  agent significantly improves emotional expression while maintain-  ing appropriate semantics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' We also note that our proposed conver-  sational scores are ordinary in Flu, which is possibly due to the  "adding" strategy increasing the sentence length and affecting the  reading difficulty.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' This is a small limitation given that all models  score above 4, which we will explore in the future.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  For the performance of compared baselines, MoEL has a low  Bleu score and a high emotion accuracy score, which shows that  this existing model loses semantic information when pursuing  emotion features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Furthermore, all baselines except Mojitalk have  low scores on diversity metrics, which indicates that there are a  large number of safe responses in the generated responses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' MoEL,  Mojitalk, MIME, and EmpDG also have low scores in Con in the  DailyDialog dataset, which is lower than Transformer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' This may be  primarily due to the mutual restriction of semantics and emotions,  which reduces the output space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  In Figure 3, for 100 human evaluation samples, we compared  the correctness and significance of the emotion of the prototype  response and the refined response generated by our proposed con-  versational agent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' The red and blue columns indicate correct (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=',  coherent to the contextual emotion) and incorrect emotions, respec-  tively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' The length of the columns indicates the significance of the  emotion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' We can note that the number of red columns in the refined  responses is more, and the length is longer, which illustrates that  the refined responses improve the correctness and significance of  the emotion in the prototype response.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='6  Human A/B Test  We conducted the human A/B test, which is shown in Table 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' We  randomly sampled 100 response pairs and asked 3 annotators to  choose the better response for each pair.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' A tie is allowed if both  are good or bad.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' We can observe that responses generated by the  proposed conversational agent are preferred by annotators than  Table 6: Examples of generated responses by our proposed conversational agent and baselines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' The corresponding contexts  did not appear in the training set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Bold tokens are the refined part.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  Context  Ground Truth Response  Models  Generated Response  DailyDialog  No, honey, why didn’t you go to cram school  last night?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  Dad, I don’t want to talk about it now.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  Honey, if you don’t want to go to cram school,  you should tell me the reason why.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  I’m sorry, dad.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' But I would  rather stay at school than go  to cram school.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  Transformer  I do not think I can do that .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  Multi-TRS  Yeah, I know, but I am sure I will.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  Mojitalk  Well, be able to be a good point.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  Moel  I do not know.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' I want to go to school.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  MIME  That is true.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' But I do not know.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  EmpDG  I am sorry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' I can not wait to get out of the internet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  Ours  Sorry dad.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' I can’t do that again.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' I’m so busy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  I could have Suzy stay at my place.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  I don’t want to do that to you, Karen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  Why not?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  Your own kids would get  Suzy’s cold.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' I think it would  be better to have a good  babysitter here.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  Transformer  Yes, I think I would love to.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  Multi-TRS  I am sorry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' I must have to give her a girl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  Mojitalk  Well, I have a cold.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  Moel  I do not know.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' I would like to.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' You?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  MIME  I am not sure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' I am not sure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  EmpDG  I am sorry, but I have no idea.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  Ours  I’m sorry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' I just can’t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' I’ve got nothing to lose.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  I just want to make the best of what I have, and the best I can.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  EmpatheticDialogues  Why does McDonalds always get my order wrong!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  I said no lettuce!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  Report to their management.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  Sometimes I think the management don’t even care!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  Just give it a trial.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  Transformer  I am sorry to hear that.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' I hope they win.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  Multi-TRS  I hope you get a better next time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  Mojitalk  That’s a great idea!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' I’m sure you’ll get his family, he has done issues as well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  Moel  I hope everything works out!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  MIME  I am sorry to hear that.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' I hope you find a new job.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  EmpDG  I do not know what I do.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  Ours  It is a problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' I am not sure how to solve it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' I feel very sorry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  I visited an orphan once and it was such a surreal  moment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' It made me realise how thankful I should  be for a family.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  That must have been and intense and emotional  moment for you.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  Yes it definitely was.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' I went with intentions to  teach the kid a few things but I ended up learning  lots more from him.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  Uau, what a surreal moment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  I always believe kids have a  lot to teach us.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  Transformer  I am sure he’ll be a good person.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  Multi-TRS  I am glad you are able to find a new one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  Mojitalk  Me too.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' The original kids is really much now.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  Moel  I am glad you are on the right?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  MIME  That is great.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' I am glad you are happy for you.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  EmpDG  I am sure you will do it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  Ours  I’m glad you had such a great experience.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  Figure 3: Compare the prototype response and refined re-  sponse with respect to the correctness and significance of  the emotion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' The left and right columns indicate proto-  type and refined responses, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' The red and blue  columns indicate correct (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=', coherent to the contextual  emotion) and incorrect emotions, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' The length  of the columns indicates the significance of the emotion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  those generated by other models, which indicates that responses  with appropriate emotions and diversity are more attractive to  users.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='7  Ablation Analysis  In order to verify the effectiveness of our proposed conversational  agent, we also conducted ablation studies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' 1) w/o Add: The Add  module is removed in the Controllable Emotion Refiner.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' We only  consider using "rewriting" to refine the prototype response;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' 2) w/o  Rewrite: The Rewrite module is removed in the Controllable Emo-  tion Refiner, and we consider using "adding" to refine the prototype  response;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' 3) w/o DED: The Dialogue Emotion Detector is removed  and replaced by emotion recognition of a single utterance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' This  is only conducted in the DailyDialog dataset because the emotion  annotation of the EmpatheticDialogues dataset is dialogue-level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  As shown in Table 5, we can observe that removing the Add  module or the Rewrite module both causes a drop in most metrics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  This suggests that combining the "rewriting" and "adding" strat-  egy is beneficial to generating appropriate responses in line with  the human language characteristics of both explicit and implicit  expression.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Moreover, the dialogue emotion detector also plays an  important role in emotional response generation, which is superior  to concatenating the context into a long sentence or identifying a  single utterance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  Samples  Correct Emotions  Incorrect Emotions  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
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+page_content='8  1  Significance score of emotion  Prototype Response Samples Refined Response SamplesTable 7: Result of human A/B test.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Fleiss’ kappa result for DailyDialog and EmpatheticDialogues is 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='612 and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='496, indicating  "substantial agreement" and "moderate agreement", respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
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+page_content='8  Case Study  We sampled some generated responses from all seven models in  Table 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' We can observe that responses generated by other baselines  have emotional expressions, but the semantics are less appropri-  ate in general.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Although responses generated by Transformer are  fluent, they often do not conform to the context.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' In contrast, the  response of the proposed conversational agent not only inherits the  contextual semantics but also involves rich and appropriate emo-  tions at the same time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' For example, the proposed conversational  agent coherently transforms "It is a problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' I am not sure how to  solve it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='" to "It is a problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' I am not sure how to solve it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' I feel very  sorry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='"  4  RELATED WORK  Dialogue Emotion Recognition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Different from the emotion recog-  nition of independent sentences, emotions in dialogue should be  recognized by the context.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Used context typically includes history  utterances [35], history emotions [28] and mutual influence of  speakers [12].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' To model the context, utterances and speakers can  be independently [12] or interactively [11] modeled by GRU.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' [9]  uses GCN to solve the problem of context propagation in existing  GRU-based methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Commonsense knowledge [8], psychological  knowledge [18], and cognitive theory of emotion [14] are also used  to enhance dialogue emotion recognition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  Emotional Dialogue.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Emotional dialogue aims to generate  emotional responses with two main strategies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' One strategy is  to specify a target emotion in advance [22, 43, 56, 57].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' The advan-  tage of this advantage is that the generated emotions are flexible  and controllable, and its disadvantage is that large-scale emotion-  annotated dialogue corpora are required.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' The other strategy is to  utilize the dialogue context to learn emotions by itself [1], which  is close to empathetic dialogue [7, 20, 21, 24, 27, 41] supposing  that listeners can infer speakers’ emotions [39].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' The advantage of  this strategy is that it can utilize the existing large-scale dialogue  corpora, and its disadvantage is that the emotions of generated  responses are challenging to control.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Furthermore, a promising  task emotional support dialogue [26] has recently emerged, which  provides valuable assistance to people in need [47].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  Controllable Text Generation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Controllable text generation  aims to generate texts with controllable styles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Style is defined as to-  kens belonging to a specific category or label [36].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Typical processes  include training a large-scale conditional generation model from  scratch, fine-tuning from a pre-trained language model, and replac-  ing the key n-tuple to adjust the style of the generated sentence [4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  As a kind of style, emotion has good practical significance for its  controllable generation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Emotion controlled text generation is to  redefine the text to contain the specific emotion without changing  the contextual intention [15, 16, 31, 44, 50].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  The differences between the proposed conversational agent and  existing methods are:  (1) As far as we know, we are the first to study a two-stage emo-  tion response paradigm in the field of emotional dialogue specially.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  (2) We refine the response with dynamically recognized dialogue  emotion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' However, current rewriting methods do not consider the  dynamic acquisition of emotions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  5  CONCLUSIONS  This paper designed a two-stage conversational agent in the field  of emotional dialogue that generates content-related and emotional  responses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' The proposed conversational agent generates a semanti-  cally coherent prototype in the first stage and emotionally refines  the prototype response in the second stage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Extensive automatic  and human evaluations have demonstrated that the proposed con-  versational agent can generate high-quality emotional responses  of appropriate semantics, and the training is free of the emotion-  annotated dialogue corpus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  In the future, to improve the proposed conversational agent, we  will explore the flexible enhancement of other specific features  besides the sentiment of the dialogue system, such as domain and  style adaptation of existing dialogue models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  REFERENCES  [1] Nabiha Asghar, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Poupart, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Hoey, Xin Jiang, and Lili Mou.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Affective neural  response generation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' ArXiv, abs/1709.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='03968, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  [2] Laurie Carr, Marco Iacoboni, Marie-Charlotte Dubeau, John C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Mazziotta, and  Gian Luigi Lenzi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Neural mechanisms of empathy in humans: A relay from neural  systems for imitation to limbic areas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Proceedings of the National Academy of  Sciences, 100(9):5497–5502, 2003.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  [3] Chaotao Chen, Jinhua Peng, Fan Wang, Jun Xu, and Hua Wu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Generating multi-  ple diverse responses with multi-mapping and posterior mapping selection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' In  Proceedings of the Twenty-Eighth International Joint Conference on Artificial Intel-  ligence, IJCAI-19, pages 4918–4924.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' International Joint Conferences on Artificial  Intelligence Organization, 7 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  [4] Sumanth Dathathri, Andrea Madotto, Janice Lan, Jane Hung, Eric Frank, Piero  Molino, Jason Yosinski, and Rosanne Liu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Plug and play language models: A  simple approach to controlled text generation, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  [5] Jacob Devlin, Ming-Wei Chang, Kenton Lee, and Kristina Toutanova.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' BERT:  Pre-training of deep bidirectional transformers for language understanding.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' In  Proceedings of the 2019 Conference of the North American Chapter of the Association  for Computational Linguistics: Human Language Technologies, Volume 1 (Long and  Short Papers), pages 4171–4186, Minneapolis, Minnesota, June 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Association  for Computational Linguistics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  [6] Angela Fan, Mike Lewis, and Yann Dauphin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Hierarchical neural story generation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  arXiv preprint arXiv:1805.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='04833, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  [7] Jun Gao, Yuhan Liu, Haolin Deng, Wei Wang, Yu Cao, Jiachen Du, and Ruifeng  Xu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Improving empathetic response generation by recognizing emotion cause  in conversations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' In Marie-Francine Moens, Xuanjing Huang, Lucia Specia,  and Scott Wen-tau Yih, editors, Findings of the Association for Computational  Linguistics: EMNLP 2021, Virtual Event / Punta Cana, Dominican Republic, 16-20  November, 2021, pages 807–819.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Association for Computational Linguistics, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  [8] Deepanway Ghosal, Navonil Majumder, Alexander Gelbukh, Rada Mihalcea, and  Soujanya Poria.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' COSMIC: COmmonSense knowledge for eMotion identification  in conversations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' In Findings of the Association for Computational Linguistics:  EMNLP 2020, pages 2470–2481, Online, November 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Association for Compu-  tational Linguistics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  [9] Deepanway Ghosal, Navonil Majumder, Soujanya Poria, Niyati Chhaya, and  Alexander Gelbukh.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' DialogueGCN: A graph convolutional neural network for  emotion recognition in conversation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' In Proceedings of the 2019 Conference on  Empirical Methods in Natural Language Processing and the 9th International Joint  Conference on Natural Language Processing (EMNLP-IJCNLP), pages 154–164,  Hong Kong, China, November 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Association for Computational Linguistics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  [10] Sayan Ghosh, Mathieu Chollet, Eugene Laksana, Louis-Philippe Morency, and  Stefan Scherer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Affect-LM: A neural language model for customizable affective  text generation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' In Proceedings of the 55th Annual Meeting of the Association for  Computational Linguistics (Volume 1: Long Papers), pages 634–642, Vancouver,  Canada, July 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Association for Computational Linguistics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  [11] Devamanyu Hazarika, Soujanya Poria, Rada Mihalcea, Erik Cambria, and Roger  Zimmermann.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' ICON: Interactive conversational memory network for multimodal  emotion detection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' In Proceedings of the 2018 Conference on Empirical Methods  in Natural Language Processing, pages 2594–2604, Brussels, Belgium, October-  November 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Association for Computational Linguistics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  [12] Devamanyu Hazarika, Soujanya Poria, Amir Zadeh, Erik Cambria, Louis-Philippe  Morency, and Roger Zimmermann.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Conversational memory network for emotion  recognition in dyadic dialogue videos.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' In Proceedings of the 2018 Conference of the  North American Chapter of the Association for Computational Linguistics: Human  Language Technologies, Volume 1 (Long Papers), pages 2122–2132, New Orleans,  Louisiana, June 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Association for Computational Linguistics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  [13] Ari Holtzman, Jan Buys, Li Du, Maxwell Forbes, and Yejin Choi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' The curious  case of neural text degeneration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' arXiv preprint arXiv:1904.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='09751, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  [14] Dou Hu, Lingwei Wei, and Xiaoyong Huai.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Dialoguecrn: Contextual reasoning  networks for emotion recognition in conversations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' In Chengqing Zong, Fei  Xia, Wenjie Li, and Roberto Navigli, editors, Proceedings of the 59th Annual  Meeting of the Association for Computational Linguistics and the 11th International  Joint Conference on Natural Language Processing, ACL/IJCNLP 2021, (Volume 1:  Long Papers), Virtual Event, August 1-6, 2021, pages 7042–7052.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Association for  Computational Linguistics, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  [15] Zhiting Hu, Zichao Yang, Xiaodan Liang, Ruslan Salakhutdinov, and Eric P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Xing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  Toward controlled generation of text.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' In Doina Precup and Yee Whye Teh, editors,  Proceedings of the 34th International Conference on Machine Learning, volume 70  of Proceedings of Machine Learning Research, pages 1587–1596.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' PMLR, 06–11 Aug  2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  [16] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Keskar, Bryan McCann, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Varshney, Caiming Xiong, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Socher.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Ctrl:  A conditional transformer language model for controllable generation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' ArXiv,  abs/1909.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='05858, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  [17] Diederik P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Kingma and Jimmy Ba.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Adam: A method for stochastic optimization,  2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  [18] Jiangnan Li, Zheng Lin, Peng Fu, and Weiping Wang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Past, present, and future:  Conversational emotion recognition through structural modeling of psycho-  logical knowledge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' In Marie-Francine Moens, Xuanjing Huang, Lucia Specia,  and Scott Wen-tau Yih, editors, Findings of the Association for Computational  Linguistics: EMNLP 2021, Virtual Event / Punta Cana, Dominican Republic, 16-20  November, 2021, pages 1204–1214.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Association for Computational Linguistics,  2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  [19] Jiwei Li, Michel Galley, Chris Brockett, Jianfeng Gao, and Bill Dolan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' A diversity-  promoting objective function for neural conversation models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' In Proceedings of  the 2016 Conference of the North American Chapter of the Association for Compu-  tational Linguistics: Human Language Technologies, pages 110–119, San Diego,  California, June 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Association for Computational Linguistics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  [20] Qintong Li, Hongshen Chen, Zhaochun Ren, Pengjie Ren, Zhaopeng Tu, and  Zhumin Chen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Empdg: Multi-resolution interactive empathetic dialogue gen-  eration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' In Donia Scott, Núria Bel, and Chengqing Zong, editors, Proceedings  of the 28th International Conference on Computational Linguistics, COLING 2020,  Barcelona, Spain (Online), December 8-13, 2020, pages 4454–4466.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' International  Committee on Computational Linguistics, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  [21] Qintong Li, Piji Li, Zhaochun Ren, Pengjie Ren, and Zhumin Chen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Knowledge  bridging for empathetic dialogue generation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  [22] Shifeng Li, Shi Feng, Daling Wang, Kaisong Song, Yifei Zhang, and Weichao Wang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  Emoelicitor: An open domain response generation model with user emotional  reaction awareness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' In Christian Bessiere, editor, Proceedings of the Twenty-Ninth  International Joint Conference on Artificial Intelligence, IJCAI-20, pages 3637–3643.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  International Joint Conferences on Artificial Intelligence Organization, 7 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  Main track.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  [23] Yanran Li, Hui Su, Xiaoyu Shen, Wenjie Li, Ziqiang Cao, and Shuzi Niu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Daily-  Dialog: A manually labelled multi-turn dialogue dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' In Proceedings of the  Eighth International Joint Conference on Natural Language Processing (Volume 1:  Long Papers), pages 986–995, Taipei, Taiwan, November 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Asian Federation  of Natural Language Processing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  [24] Zhaojiang Lin, Andrea Madotto, Jamin Shin, Peng Xu, and Pascale Fung.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' MoEL:  Mixture of empathetic listeners.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' In Proceedings of the 2019 Conference on Empirical  Methods in Natural Language Processing and the 9th International Joint Conference  on Natural Language Processing (EMNLP-IJCNLP), pages 121–132, Hong Kong,  China, November 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Association for Computational Linguistics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  [25] Chia-Wei Liu, Ryan Lowe, Iulian Serban, Mike Noseworthy, Laurent Charlin, and  Joelle Pineau.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' How NOT to evaluate your dialogue system: An empirical study of  unsupervised evaluation metrics for dialogue response generation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' In Proceedings  of the 2016 Conference on Empirical Methods in Natural Language Processing,  pages 2122–2132, Austin, Texas, November 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Association for Computational  Linguistics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  [26] Siyang Liu, Chujie Zheng, Orianna Demasi, Sahand Sabour, Yu Li, Zhou Yu,  Yong Jiang, and Minlie Huang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Towards emotional support dialog systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' In  Chengqing Zong, Fei Xia, Wenjie Li, and Roberto Navigli, editors, Proceedings of  the 59th Annual Meeting of the Association for Computational Linguistics and the  11th International Joint Conference on Natural Language Processing, ACL/IJCNLP  2021, (Volume 1: Long Papers), Virtual Event, August 1-6, 2021, pages 3469–3483.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  Association for Computational Linguistics, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  [27] Navonil Majumder, Pengfei Hong, Shanshan Peng, Jiankun Lu, Deepanway  Ghosal, Alexander Gelbukh, Rada Mihalcea, and Soujanya Poria.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' MIME: MIM-  icking emotions for empathetic response generation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' In Proceedings of the 2020  Conference on Empirical Methods in Natural Language Processing (EMNLP), pages  8968–8979, Online, November 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Association for Computational Linguistics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  [28] Navonil Majumder, Soujanya Poria, Devamanyu Hazarika, Rada Mihalcea,  Alexander Gelbukh, and Erik Cambria.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Dialoguernn: An attentive rnn for emo-  tion detection in conversations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Proceedings of the AAAI Conference on Artificial  Intelligence, 33(01):6818–6825, Jul.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  [29] Bilyana Martinovski and David R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Traum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Breakdown in human-machine in-  teraction: the error is the clue.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' In ISCA tutorial and research workshop on Error  handling in dialogue systems, August 2003 2003.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  [30] Courtney Napoles, Keisuke Sakaguchi, Matt Post, and Joel Tetreault.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Gleu without  tuning, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  [31] Kartikey Pant, Yash Verma, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Mamidi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Sentiinc: Incorporating sentiment  information into sentiment transfer without parallel data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Advances in Information  Retrieval, 12036:312 – 319, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  [32] Kishore Papineni, Salim Roukos, Todd Ward, and Wei-Jing Zhu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Bleu: a method  for automatic evaluation of machine translation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' In Proceedings of the 40th Annual  Meeting of the Association for Computational Linguistics, pages 311–318, Philadel-  phia, Pennsylvania, USA, July 2002.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Association for Computational Linguistics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  [33] Kishore Papineni, Salim Roukos, Todd Ward, and Wei-Jing Zhu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Bleu: a method  for automatic evaluation of machine translation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' In Proceedings of the 40th  Annual Meeting of the Association for Computational Linguistics, July 6-12, 2002,  Philadelphia, PA, USA, pages 311–318.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' ACL, 2002.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  [34] Timo Partala and V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Surakka.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' The effects of affective interventions in human-  computer interaction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Interact.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Comput.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=', 16:295–309, 2004.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  [35] Soujanya Poria, Erik Cambria, Devamanyu Hazarika, Navonil Majumder, Amir  Zadeh, and Louis-Philippe Morency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Context-dependent sentiment analysis in  user-generated videos.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' In Proceedings of the 55th Annual Meeting of the Association  for Computational Linguistics (Volume 1: Long Papers), pages 873–883, Vancouver,  Canada, July 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Association for Computational Linguistics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  [36] Shrimai Prabhumoye, Alan W Black, and Ruslan Salakhutdinov.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Exploring  controllable text generation techniques.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' In Proceedings of the 28th International  Conference on Computational Linguistics, pages 1–14, Barcelona, Spain (Online),  December 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' International Committee on Computational Linguistics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  [37] Helmut Prendinger, Junichiro Mori, and Mitsuru Ishizuka.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Using human physi-  ology to evaluate subtle expressivity of a virtual quizmaster in a mathematical  game.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' International Journal of Human-Computer Studies, 62(2):231–245, 2005.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  Subtle expressivity for characters and robots.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  [38] Alec Radford, Jeff Wu, Rewon Child, David Luan, Dario Amodei, and Ilya  Sutskever.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Language models are unsupervised multitask learners.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  [39] Hannah Rashkin, Eric Michael Smith, Margaret Li, and Y-Lan Boureau.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Towards  empathetic open-domain conversation models: A new benchmark and dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  In Proceedings of the 57th Annual Meeting of the Association for Computational  Linguistics, pages 5370–5381, Florence, Italy, July 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Association for Computa-  tional Linguistics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  [40] Sahand Sabour, Chujie Zheng, and Minlie Huang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' CEM: commonsense-aware  empathetic response generation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' CoRR, abs/2109.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='05739, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  [41] Sahand Sabour, Chujie Zheng, and Minlie Huang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' CEM: commonsense-aware  empathetic response generation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' CoRR, abs/2109.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='05739, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  [42] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Skowron.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Affect listeners: Acquisition of affective states by means of conver-  sational systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' In COST 2102 Training School, 2009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  [43] Zhenqiao Song, Xiaoqing Zheng, Lu Liu, Mu Xu, and Xuanjing Huang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Gen-  erating responses with a specific emotion in dialog.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' In Proceedings of the 57th  Annual Meeting of the Association for Computational Linguistics, pages 3685–3695,  Florence, Italy, July 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Association for Computational Linguistics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  [44] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Sudhakar, Bhargav Upadhyay, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Maheswaran.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Transforming delete, re-  trieve, generate approach for controlled text style transfer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' ArXiv, abs/1908.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='09368,  2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  [45] Hao Tian, Can Gao, Xinyan Xiao, Hao Liu, Bolei He, Hua Wu, Haifeng Wang, and  feng wu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' SKEP: Sentiment knowledge enhanced pre-training for sentiment analy-  sis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' In Proceedings of the 58th Annual Meeting of the Association for Computational  Linguistics, pages 4067–4076, Online, July 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Association for Computational  Linguistics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  [46] Hao Tian, Can Gao, Xinyan Xiao, Hao Liu, Bolei He, Hua Wu, Haifeng Wang,  and Feng Wu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' SKEP: Sentiment knowledge enhanced pre-training for senti-  ment analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' In Proceedings of the 58th Annual Meeting of the Association for  Computational Linguistics, pages 4067–4076, Online, July 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Association for  Computational Linguistics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  [47] Quan Tu, Yanran Li, Jianwei Cui, Bin Wang, Ji-Rong Wen, and Rui Yan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' MISC: A  mixed strategy-aware model integrating COMET for emotional support conver-  sation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' CoRR, abs/2203.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='13560, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  [48] Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones,  Aidan N Gomez, Ł ukasz Kaiser, and Illia Polosukhin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Attention is all you need.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' In  I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Guyon, U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Luxburg, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Bengio, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Wallach, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Fergus, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Vishwanathan, and  R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Garnett, editors, Advances in Neural Information Processing Systems, volume 30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  Curran Associates, Inc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=', 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  [49] Thomas Wolf, Lysandre Debut, Victor Sanh, Julien Chaumond, Clement De-  langue, Anthony Moi, Pierric Cistac, Tim Rault, Remi Louf, Morgan Funtowicz,  Joe Davison, Sam Shleifer, Patrick von Platen, Clara Ma, Yacine Jernite, Julien  Plu, Canwen Xu, Teven Le Scao, Sylvain Gugger, Mariama Drame, Quentin  Lhoest, and Alexander Rush.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Transformers: State-of-the-art natural language  processing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' In Proceedings of the 2020 Conference on Empirical Methods in Natural  Language Processing: System Demonstrations, pages 38–45, Online, October 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  Association for Computational Linguistics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  [50] Xing Wu, Tao Zhang, Liangjun Zang, Jizhong Han, and Songlin Hu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Mask and  infill: Applying masked language model for sentiment transfer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' In IJCAI, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  [51] Jingjing Xu, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Sun, Qi Zeng, Xuancheng Ren, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Zhang, Houfeng Wang, and  W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Li.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Unpaired sentiment-to-sentiment translation: A cycled reinforcement  learning approach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' In ACL, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  [52] Yi Zhang, Jingjing Xu, Pengcheng Yang, and X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Sun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Learning sentiment memories  for sentiment modification without parallel data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' In EMNLP, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  [53] Yizhe Zhang, Michel Galley, Jianfeng Gao, Zhe Gan, Xiujun Li, Chris Brockett,  and Bill Dolan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Generating informative and diverse conversational responses via  adversarial information maximization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' In S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Bengio, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Wallach, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Larochelle,  K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Grauman, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Cesa-Bianchi, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Garnett, editors, Advances in Neural Infor-  mation Processing Systems, volume 31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Curran Associates, Inc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=', 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  [54] Yizhe Zhang, Siqi Sun, Michel Galley, Yen-Chun Chen, Chris Brockett, Xiang Gao,  Jianfeng Gao, Jingjing Liu, and Bill Dolan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' DIALOGPT : Large-scale generative pre-  training for conversational response generation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' In Proceedings of the 58th Annual  Meeting of the Association for Computational Linguistics: System Demonstrations,  pages 270–278, Online, July 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Association for Computational Linguistics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  [55] Peixiang Zhong, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Wang, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Miao.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' An affect-rich neural conversational  model with biased attention and weighted cross-entropy loss.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' In AAAI, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  [56] Hao Zhou, Minlie Huang, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Zhang, Xiaoyan Zhu, and Bing Liu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Emotional  chatting machine: Emotional conversation generation with internal and external  memory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' In AAAI, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content='  [57] Xianda Zhou and William Yang Wang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' MojiTalk: Generating emotional responses  at scale.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' In Proceedings of the 56th Annual Meeting of the Association for Computa-  tional Linguistics (Volume 1: Long Papers), pages 1128–1137, Melbourne, Australia,  July 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
+page_content=' Association for Computational Linguistics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/HdE4T4oBgHgl3EQfHwzB/content/2301.04907v1.pdf'}
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+New isomeric transition in 36Mg: Bridging the N=20 and N=28 islands of inversion
+M. Madurga1, J.M. Christie1, Z. Xu1, R. Grzywacz1,2, A. Poves3, T. King1, A.
+Chester4, J. Farr1, I. Fletcher1, J. Heideman1, D. Hoskins1, A. Laminack2, S. Liddick4,5,
+S. Neupane1, S. Peng2, A.L. Richard4,†, K. Siegl1, P. Wagenknecht1, R. Yokoyama1
+1Dept. of Physics and Astronomy, University of Tennessee, Knoxville, Tennessee 37996, USA
+2Physics Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37830, USA
+3Departamento de F´ısica Te´orica, and IFT UAM-CSIC,
+Universidad Aut´onoma de Madrid, 28049, Madrid, Spain
+4National Superconducting Cyclotron Laboratory, Michigan State University, East Lansing, Michigan 48824, USA
+5Department of Chemistry, Michigan State University, East Lansing, Michigan 48824, USA∗
+(Dated: January 31, 2023)
+We observed a new isomeric gamma transition at 168 keV in 36Mg, with a half-life of T1/2=[130-
+500](±40)(+800
+−20 )sys ns. We propose that the observed transition de-excites a new 0+ isomeric state
+and populates the previously known ﬁrst 2+ state. The existence of this isomer is consistent with the
+predictions of the large-scale shell model calculations of 36Mg using the sdpf-u-mix interaction. The
+observed excitation energy of the second 0+ state is caused by the small energy separation between two
+prolate-deformed conﬁgurations where the intruder conﬁguration corresponds to two neutron excitations
+from the sd to the pf shell. Within this interpretation, 36Mg becomes the crossing point between nuclei
+in which ground state deformed/superdeformed conﬁgurations are caused by the dominance of N=20
+intruders (32,34Mg) and nuclei where deformed conﬁgurations are associated with N=28 intruders (38Mg
+and beyond). We found the lack of three-body monopole corrections in other effective interactions results
+in a predominance of N=20 intruder conﬁgurations past 38Mg incompatible with our observation. We
+conclude that 36Mg bridges the N=20 and N=28 islands of inversion, forming the so-called Big Island of
+Deformation.
+The Island of Inversion centered around magnesium
+isotopes with neutron “magic” number N=20 has at-
+tracted considerable interest [1–5] since its discovery [6].
+Negative-parity intruder states ascribed to excitations in-
+volving multiple particle-hole conﬁgurations between sd to
+the pf orbitals indicate a sudden quenching of the N=20
+shell closure. Nuclei inside the Island of Inversion are de-
+ﬁned by having ground states dominated by such particle-
+hole conﬁgurations [7]. The quenching of the N=20 and
+N=28 shell closures is driven by the diminishing effect
+of the T=0 component of the tensor force as the proton-
+neutron ratio becomes more asymmetric [8]. This forms
+a so-called Big Island of Deformation, where both neu-
+tron magic numbers N=20 and N=28 disappear in the
+magnesium isotopic chain.
+Recently developed interac-
+tions in the proton/neutron sd-pf valence space have had
+considerable success in reproducing the observed intruder
+and ground-state conﬁgurations of known Island of In-
+version nuclei. Some examples are effective interactions
+such as sdpf-m [9], sdpf-u-mix [5], or the new interac-
+tion EEdf1, developed from the chiral expansion at N3LO,
+which incorporates phenomenological three body forces of
+Fujita-Miyazawa type that are transformed into a medium-
+dependent two-body interaction [10]). As we shall see later
+the explicit three body global monopole term proposed
+with sdpf-u-mix is crucial to produce the right evolution
+∗ †Current address: Lawrence Livermore National Laboratory, Livermore,
+CA 94550.
+of the N=20 neutron closure towards N=28. Interestingly,
+each interaction predicts differing microscopic interpreta-
+tions of the N=20 and N=28 islands of inversion. In all
+cases but sdpf-u-mix, excited states crossing the N=20 shell
+closure are substantial in both islands of inversion. On the
+other hand, sdpf-u-mix predicts the N=20 shell closure is
+restored at 40Mg, postulating instead that deformation is
+driven exclusively by the breakdown of the N=28 subshell
+closure. There is currently no experimental data that can
+resolve these differing interpretations. Delineation of the
+boundaries of the islands of inversion towards the neutron
+drip-line is therefore essential to determine the disappear-
+ance and appearance of the N=20 and N=28 shell closures
+respectively [11]. Isomers, long lived excited states, offer
+an observable with which to track evolving nuclear prop-
+erties as we study nuclei between shell closures. The half-
+life of an isomeric state is fully determined by the transi-
+tion’s energy and its electromagnetic transition probabil-
+ity, in turn deﬁned by the wave-functions of the involved
+states. One such example are the so-called shape isomers,
+excited states arising from nuclear conﬁgurations of differ-
+ent shapes. Low energy excited 0+ states corresponding to
+prolate(oblate) deformed conﬁgurations [12] may become
+isomeric when decaying to the ﬁrst excited 2+ state corre-
+sponding to the ground state band of different deformation.
+As of the beginning of 2023, there is only one isomer
+conﬁrmed and published in either neon or magnesium iso-
+topes, the 0+
+2 state in 32Mg that decays to the 2+
+1 via a 172
+keV transition with T1/2 >10 ns [13, 14]. Shell model
+calculations using the sdpf-u-mix interaction [15] produce
+arXiv:2301.12002v1  [nucl-ex]  27 Jan 2023
+
+2
+500
+600
+700
+800
+900
+Time of Flight (arb)
+5000
+6000
+7000
+8000
+9000
+E (arb)
+∆
+0
+20
+40
+60
+80
+100
+Mg
+36
+Z=13
+Z=12
+Z=11
+Z=10
+FIG. 1. Two dimensional energy loss (∆E) v. time of ﬂight parti-
+cle identiﬁcation plot for all ion implants between Z=10 (bottom
+row) and Z=13 (top row). Magnesium-36 is highlighted by the
+red circle. We also searched for isomers in 25−29F isotopes (not
+shown).
+a ground state that is a mixture of deformed (2p-2h) and
+superdeformed (4p-4h) conﬁgurations and an isomeric 0+
+state which is dominated by superdeformed and spherical
+(0p-0h) components. Notice that sdpf-u-mix is the only in-
+teraction that locates the isomer close to its experimental
+excitation energy. In the same calculation, heavier magne-
+sium isotopes were expected to strongly favor quadrupole
+components before transitioning to the N=28 Island of In-
+version at 40Mg. This hypothesis is supported by the sys-
+tematics of the ﬁrst 2+ states in 34,36,38Mg [16–19] com-
+paring well with calculations [20].
+In this Letter we present the observation of a new iso-
+meric gamma transition at 168 keV in 36Mg, assigned to
+a second 0+ state feeding the ﬁrst 2+ state. The analysis
+of the time structure of 168 keV gamma-ray events follow-
+ing the ion implantation results in a half-life of T1/2=[130-
+500](±40)tran(+800
+−20 )sys ns. We present an interpretation
+of the nature of the new second 0+ state and the evolu-
+tion of intruder conﬁgurations in the magnesium isotopic
+chain from N=20 to N=28 using shell model calculations
+with the sdpf-u-mix interaction [5]. Our calculations indi-
+cate the isomer naturally arises from gradually restoring the
+N=20 shell closure as the neutron 0f7/2 orbital is occupied
+towards the N=28 subshell closure.
+Experiment. The experiment was performed at the Na-
+tional Superconducting Cyclotron Laboratory (NSCL) at
+Michigan State University. A 48Ca beam, 80 pnA average
+intensity at 140 MeV/u, was fragmented in a 846 mg/cm2
+thick Be target at the entrance of the fragment separator,
+A1900 [21], to produce the nuclei of interest, a ”cocktail”
+beam consisting of isotopes from boron (Z=5) to aluminum
+(Z=13). In order to identify the different species, we mea-
+sured the ion’s time-of-ﬂight between a scintillator located
+in the focal plane of A1900 and a Silicon detector (Si PIN)
+placed in front of our experimental setup. Combining with
+the energy loss in the Si PIN allowed us to perform parti-
+cle identiﬁcation (PID) in the beam, as shown in Fig. 1.
+We implanted the ”cocktail” beam in a 12-mm thick YSO
+detector (Ytrium, Silicon Oxide) [22] allowing for record-
+ing energies and timestamps of ion implantation and beta-
+decay events. The YSO detector was surrounded on one
+side by 48 VANDLE modules [23] providing a total neu-
+tron detection efﬁciency of 11% at 1 MeV. On the other
+side of the setup, three HPGe clovers from the CLARION
+array [24] resulting in gamma detection of 1.8% efﬁciency
+at 1 MeV.
+We searched for isomers in all Fluorine, Neon, Sodium,
+Magnesium, and Aluminum isotopes shown in Fig. 1 by
+analyzing the gamma rays emitted between 40 ns and 500
+ns after ion implantation, correlated to each individual iso-
+tope using the PID plot (Fig. 1). We excluded the ﬁrst 40
+ns in order to remove the Gaussian tail of the prompt im-
+plantation ”ﬂash”, mostly Bremsstrahlung x-ray. We did
+not identify isomeric transitions in any F, Ne, Na, Mg, or
+Al isotope except for 36Mg. In 36Mg, we observe a promi-
+nent gamma transition at 168 keV, see Fig. 2. The top
+right panel of Fig. 2 shows the gamma spectrum between
+500 and 750 keV. We marked several gamma lines corre-
+sponding to germanium (†) and iron (§) neutron inelastic
+scattering [25], as well as the 511 keV line corresponding
+to positron annihilation (#). Imposing total event multi-
+plicity one, we expect close to no background in the 600 to
+700 keV region. Therefore, we identiﬁed the 3(2) counts at
+665 keV to the de-excitation of the ﬁrst 2+ state in 36Mg
+[16, 17, 19, 26–28].Since the 2+ state in 36Mg was not
+observed to be isomeric, we propose the isomeric state
+in 36Mg decays to the 2+ state via emitting the 168 keV
+gamma ray. We calculated the number of counts we would
+observe if the new 168 keV line and the 665 keV line form
+a gamma cascade. We observe a total 10(3) counts in the
+168 keV peak, with background component estimated from
+neighboring bins to 5(2) counts. Using efﬁciencies of 2.7%
+at 168 keV and 2.23% at 665 keV we expect 4(1) counts at
+665 keV, within error bars of the observed 3(2) counts. In
+order to substantiate the spin and parity of the new state we
+consider the recent measurement of the quadrupole elec-
+tromagnetic transition strength for the 665 keV line [17]
+conﬁrmed that it corresponds to the 2+
+1 state. Considering
+the placement of the other known isomer in neutron rich
+magnesium isotopes (32Mg), the most likely explanation
+places the new 168 keV isomer as the de-excitation of a
+new 833 keV 0+ state directly to the known 665 2+
+1 state
+in 36Mg (top left inset in Fig. 2).
+We performed a log likelihood analysis of the gamma
+activity after ion implantation, see Fig.
+3.
+The left
+panel shows the time distribution of gamma events af-
+ter ion implantation for the photopeak gate (167 to 169
+
+3
+150
+200
+250
+300
+E (keV)
+0.0
+2.5
+5.0
+7.5
+10.0
+1/keV
+168(1)
+*
+*
+FIG. 2. Delayed gamma energy spectrum in coincidence with
+36Mg implantation events. The most prominent line corresponds
+to the new isomeric transition at 168 keV ( [*] marks background
+lines). The top left panel shows the 36Mg partial level scheme.
+The top right panel shows the gamma spectrum between 500 and
+750 keV, including the 36Mg 665 keV transition and other back-
+ground lines (see text for details).
+keV). The right panel shows the time distribution of
+background events (166<Eγ<167 keV and 169<Eγ<170
+keV). First, in order to estimate the component arising from
+the tail of the Gaussian distribution of the ion implanta-
+tion Bremsstrahlung ﬂash, we ﬁtted the time distribution of
+the background gate to an exponential function (Fig. 3b).
+Then, we constructed a double exponential distribution,
+corresponding to photopeak and background combined,
+50% each as per the gamma energy spectrum estimate. We
+ﬁtted the photopeak gate, obtaining T1/2=90(+410
+−50 ) ns. We
+also studied the systematic uncertainty due to the shape of
+the tail of the implantation ﬂash. In order to progressively
+remove the background tail, we performed ﬁts to samples
+starting at increasingly later times, between 50 ns to 100 ns.
+Finally, we calculated the shortest observable half-life con-
+sidering the transit time (500 ns) in A1900, and assuming
+an isomer population of 10% in the fragmentation reaction
+producing 36Mg, obtaining 130(40) ns. Given the statis-
+tical constraints due to the size of our sample, the limits
+imposed by the transit time in A1900, and the systematic
+effects mentioned above, we provide a half-life range for
+the 168 keV isomer, at 3σ conﬁdence level, of T1/2=[130-
+500](±40)tran(+800
+−20 )sys ns. The resulting half-life range
+corresponds to B(E2)= [12−50] (+30
+−1 )tran(+10
+−7 )sys e2fm4.
+Discussion. In the heavy Magnesium isotopes two neu-
+tron shell closures are washed out by the presence of in-
+truder states whose energy, fostered by the quadrupole cor-
+relations, make them dominant in the ground states, giving
+rise to the N=20 and N=28 Islands of Inversion. It is inter-
+esting to follow the location of the intruder conﬁgurations
+before mixing as the number of neutrons increase. We de-
+0
+50
+100
+150
+200
+?1
+0
+1
+2
+3
+counts
+isomer+background
+isomer
+background
+(a)
+Clover -  YSO Time (ns)
+0
+50
+100
+150
+200
+?1
+0
+1
+2
+3
+background
+(b)
+FIG. 3.
+(Left) Time distribution of gamma activity after ion
+implantation gated on the 168 keV photopeak with background
+(black-dashed, see right panel), isomer (blue) and combined (red)
+ﬁts overlayed. (Right) Distribution of gamma events gated on the
+Compton background surrounding the photopeak.
+note by x=0 the normal ﬁlling conﬁguration, and by x=0,
+2, 4, etc, the xp-xh neutron excitations across N=20. Their
+relative position gives us a clear hint of what will be the
+structure of the low lying states after full diagonalization,
+although the details of the spectroscopy depend on many
+other ingredients, in particular on the off-diagonal matrix
+elements between the states calculated at ﬁxed values of t
+differing in two units. As explained in ref. [5] we submit
+that the effective interaction for this wide region should in-
+clude a three body monopole correction of the form:
+δVpf = 1
+2npf(18
+A )1/3 75 keV
+(1)
+Which restores the N=20 closure in 40Mg as it is required
+by consistency and naturalness of the very shell model
+with conﬁguration interaction (SM-CI) approach (npf is
+the number of neutrons in the pf shell in the normal ﬁll-
+ing approximation). Notice however that in ref. [29] the
+EEdf1 interaction produces a completely different, and in
+our opinion un-natural, picture because the 0d3/2 orbit is
+only half ﬁlled already in 30Mg and remains so even in the
+42Mg ground state.
+We proceed now to carry on the SM-CI calculations us-
+ing the sdpf-u-mix interaction and valence space [5]. The
+calculations are performed with the code Antoine [30].
+As a ﬁrst step, we study the relative location of the 0+
+band heads of the x=0 and x=2 conﬁgurations. The re-
+sults are shown in the bottom panel of Fig. 4. It is seen
+that the intruder states cease to be clearly dominant at
+A=36.
+This is consistent with the fact that even if the
+0f7/2 and 1p3/2 neutron orbits would behave as a super-
+orbit of degeneracy 12, the maximum collectivity in Quasi-
+SU3 [20] is obtained for 6 neutrons. Besides, the increase
+of the quadrupole moment Q of the 6p-2h conﬁguration
+with respect to the 4p-0h one is small, therefore the gain
+in quadrupole correlation energy of the latter barely com-
+pensates its loss of monopole energy. As a consequence,
+the 6p-2h conﬁguration in 36Mg is not as dominant as the
+4p-2h one in 34Mg. Beyond N=24, the 6p-0h and 8p-0h
+
+ey891
+02
+833keV
+665keV4
+0
+25
+50
+75
+100
+wavefunction frac. (%)
+0p-0h
+2p-2h
+4p-4h
+30
+32
+34
+36
+38
+40
+A
+4
+2
+0
+2
+4
+E(2p2h)
+E(0p0h) (MeV)
+SDPF-U-MIX
+SDPF-M
+FIG. 4. (Bottom panel) Energy splitting between the normal ﬁll-
+ing conﬁguration and the intruder state corresponding to the pro-
+motion of two neutrons across the N=20 magic shell closure, in
+the heavy Magnesium isotopes, calculated with sdpf-u-mix (red)
+and sdpf-m (blue). (Upper panel) Percentage of np-nh conﬁg-
+urations in the theoretical wave functions of the ground states
+of the Magnesium isotopes, 0p-0h (blue), 2p-2h (orange), 4p-4h
+(green), using the sdpf-u-mix interaction.
+conﬁgurations are re-established as the main components
+in the ground states of 38Mg and 40Mg. This is in stark
+contrast with the calculation using the sdpf-m interaction
+shown in the bottom panel of Fig. 4. The intruder conﬁgu-
+rations (x=2) remain highly dominant in 36Mg, while they
+become degenerate with the 6p-0h normal-ﬁlling (x=0)
+state in 38Mg. We conclude sdpf-m cannot naturally repro-
+duce a low lying 0+
+2 in 36Mg, favoring 38Mg instead. The
+”softness” of the N=20 core in sdpf-m highlights the im-
+portance of the three-body monopole correction mentioned
+above to produce the trend in Mg isotopes, restoring the
+N=20 shell closure and 36Mg as the crossing point between
+normal-ﬁlling and excited conﬁgurations.
+It is precisely the crossing of the 4p-0h and 6p-2h conﬁg-
+urations in 36Mg what might explain the very low energy
+of the excited 0+. In the full calculation, sdpf-u-mix places
+the excited 0+ in 36Mg at 1.55 MeV, and produces a 36Mg
+which is triaxial with a low lying gamma band, not very
+compatible with existence of a 0+ isomer as seen in the
+present experiment.
+Given that the amplitude of the 8p-4h conﬁgurations is
+negligible, the problem can be translated into a two state
+model including only the 4p-0h and the 6p-2h states dis-
+cussed above. Notice that both are prolate deformed. If
+the energies of the 4p-0h and 6p-2h states were degener-
+ate before mixing (and this is nearly the case), the ﬁnal
+splitting of the two 0+ states would be roughly equal to
+2W, with W = ⟨4p − 0h(0+)|V |6p − 2h(0+)⟩. In fact,
+W=730 keV in 36Mg, and this sets a theoretical lower limit
+to the excitation energy of the isomer 0+, within the two
+state model. The value in the complete diagonalization is
+very much in line with this estimate. Thus, the only way to
+get the splitting right is via a reduction of the value of W,
+which is dominated by the off-diagonal pairing interaction
+between the sd and the pf-shell neutron orbits. Hence we
+are led to make an “ad hoc” 10% reduction of the off diago-
+nal pairing matrix elements for npf > 0, bringing W down
+to about 500 keV. With this choice, the resulting compo-
+sition of the ground states of the Magnesium isotopes is
+as depicted in the upper panel of Figure 4. We see the in-
+truder (x=2,4) conﬁgurations are dominant in 32,34,36Mg,
+while the normal-ﬁlling (x=0) states take the majority of
+the wavefunction in 30,38,40Mg. This trend is consistent
+with the restoration of the N=20 shell closure as we ap-
+proach the N=28 subshell, disfavoring particle-hole excita-
+tions across the N=20 shell gap.
+The spectroscopic results for 36Mg are gathered in Table
+I. The excitation energies are in good agreement with the
+TABLE I. Theoretical excitation energies (in MeV), Qspec in
+efm2 and B(E2)’s (in e2fm4), for 36Mg.
+Jπ
+E(th))
+Qspec
+Jπ(f)
+B(E2)
+0+
+1
+0.0
+2+
+1
+0.58
+-23
+0+
+1
+130
+0+
+2
+1.02
+2+
+1
+5
+2+
+2
+1.43
+-15
+0+
+1
+2
+2+
+2
+2+
+1
+1
+2+
+2
+0+
+2
+120
+4+
+1
+1.73
+-23
+2+
+1
+183
+4+
+1
+2+
+2
+1
+present experimental result for the 0+ isomer and with the
+results of reference [16] for the yrast 2+ and 4+. The crit-
+icality at the crossover goes beyond the value of the exci-
+tation energy of the 0+ isomer, because it implies as well a
+change of structure, from a triaxial solution to a case of two
+coexisting prolate bands, the lowest dominated by 6p-2h
+conﬁgurations and the excited one by 4p-0h conﬁgurations
+as can be seen in the E2 properties listed in Table I. A very
+prominent feature of them is that the cross-talk between the
+two bands is almost absent. In particular, the B(E2) from
+the isomer to the yrast 2+ is small, compatible with the ex-
+perimental value extracted from its lifetime. Let’s mention
+ﬁnally that the crossover from the dominance of the 0f7/2
+orbit to a massive occupation of the 1p3/2 orbit, takes place
+at N=24 as well, paving the way to the N=28 Island of In-
+version.
+Conclusions. We observed a new 168 keV isomer in
+36Mg, with a halﬂife of [130-500](±40)tran(+800
+−20 )sys ns
+at 3σ conﬁdence level. From the observation of a 665 keV
+gamma line in the prompt gamma spectrum, we deduce it
+corresponds to a new 0+ state at 833 keV de-exciting to the
+known 665 keV 2+ state [17]. To elucidate the microscopic
+
+5
+origin of this isomer we performed shell model calculations
+using the sdpf-u-mix interaction. We propose the observed
+low energy of the state arises from two coexisting prolate
+deformed conﬁgurations consisting of the normal-ﬁlling
+and intruder two-neutron excitations respectively. We pre-
+dict that, for N>20 Mg isotopes, as the neutron 0f7/2 or-
+bital is gradually ﬁlled, the N=20 shell closure is restored
+while the N=28 subshell closure is quenched. Therefore,
+the quasi-degeneracy between normal and intruder conﬁg-
+urations occurs only for 36Mg. In contrast, other effective
+interactions used in the region predict substantial quench-
+ing of the N=20 shell closure even past 38Mg. We postulate
+the discrepancy arises from the lack of three-body correc-
+tions to the monopole part of the effective interaction. The
+isomer presented in this Letter supports this latter picture,
+with 36Mg being the bridge between the island of inversion
+centered around 32Mg, due to the quenching of the N=20
+shell closure, and the island of inversion centered in 40Mg,
+due to the quenching of the N =28 subshell closure. As a di-
+rect consequence we anticipate no isomers will be present
+in 34,38Mg. Thanks to the large yields of magnesium iso-
+topes afforded at the recently commissioned FRIB facility
+in MSU (or RIKEN, Japan), this hypothesis may be tested
+in the near future.
+Acknowledgements. We thank Augusto Macchiavelli for
+the fruitful discussions during the preparation of this Let-
+ter. The isotope(s) used in this research was supplied by
+the Isotope Program within the Ofﬁce of Nuclear Physics
+in the Department of Energy’s Ofﬁce of Science.
+The
+Lanczos shell-model calculation using the sdpf-m inter-
+action was performed with the code KSHELL [31]. This
+research was sponsored in part by the National Nuclear
+Security Administration under the Stewardship Science
+Academic Alliances program through DOE Cooperative
+Agreements No.
+DE-NA0003899 and DE-NA0004068.
+This research was also sponsored by the Ofﬁce of Nu-
+clear Physics, U. S. Department of Energy under contract
+DE-FG02-96ER40983 (UT) and DE-SC0020451 (MSU).
+This research was sponsored in part by National Science
+Foundation under the contract NSF-MRI-1919735. This
+work was also supported by the National Nuclear Secu-
+rity Administration through the Nuclear Science and Secu-
+rity Consortium under Award No. DE-NA0003180 and the
+Stewardship Science Academic Alliances program through
+DOE Award No. DOE-DE-NA0003906.
+A.P. is supported by grants CEX2020-001007-S funded
+by MCIN/AEI/10.13039/501100011033 and PID2021-
+127890NB-I00.
+[1] A. Poves and J. Retamosa.
+The onset of deformation
+at the n = 20 neutron shell closure far from stability.
+Physics Letters B, 184(4):311–315, 1987.
+ISSN 0370-
+2693.
+doi:https://doi.org/10.1016/0370-2693(87)90171-
+7.
+URL
+https://www.sciencedirect.com/
+science/article/pii/0370269387901717.
+[2] E. K. Warburton, J. A. Becker, and B. A. Brown.
+Mass
+systematics for a=29–44 nuclei: The deformed a∼32 re-
+gion.
+Phys. Rev. C, 41:1147–1166, Mar 1990.
+doi:
+10.1103/PhysRevC.41.1147.
+URL https://link.
+aps.org/doi/10.1103/PhysRevC.41.1147.
+[3] K Heyde and J L Wood.
+Intruder states and shape co-
+existence in the region n approximately 20, z approx-
+imately 12.
+Journal of Physics G: Nuclear and Par-
+ticle Physics, 17(2):135, feb 1991.
+doi:10.1088/0954-
+3899/17/2/007.
+URL https://dx.doi.org/10.
+1088/0954-3899/17/2/007.
+[4] N.
+Fukunishi,
+T.
+Otsuka,
+and
+T.
+Sebe.
+Vanish-
+ing of the shell gap in n = 20 neutron-rich nuclei.
+Physics Letters B, 296(3):279–284, 1992.
+ISSN 0370-
+2693.
+doi:https://doi.org/10.1016/0370-2693(92)91320-
+9.
+URL
+https://www.sciencedirect.com/
+science/article/pii/0370269392913209.
+[5] E. Caurier, F. Nowacki, and A. Poves. Merging of the is-
+lands of inversion at n=20 and n=28. Physical Review C
+- Nuclear Physics, 90, 7 2014.
+ISSN 1089490X.
+doi:
+10.1103/PhysRevC.90.014302.
+[6] C. Thibault, R. Klapisch, C. Rigaud, A. M. Poskanzer,
+R. Prieels, L. Lessard, and W. Reisdorf. Direct measurement
+of the masses of 11Li and 26−32Na with an on-line mass
+spectrometer. Phys. Rev. C, 12:644–657, Aug 1975. doi:
+10.1103/PhysRevC.12.644. URL https://link.aps.
+org/doi/10.1103/PhysRevC.12.644.
+[7] G. Neyens,
+M. Kowalska,
+D. Yordanov,
+K. Blaum,
+P. Himpe, P. Lievens, S. Mallion, R. Neugart, N. Ver-
+meulen, Y. Utsuno, and T. Otsuka. Measurement of the spin
+and magnetic moment of 31Mg: Evidence for a strongly
+deformed intruder ground state.
+Phys. Rev. Lett., 94:
+022501, Jan 2005.
+doi:10.1103/PhysRevLett.94.022501.
+URL
+https://link.aps.org/doi/10.1103/
+PhysRevLett.94.022501.
+[8] Takaharu Otsuka, Toshio Suzuki, Rintaro Fujimoto, Hu-
+bert Grawe, and Yoshinori Akaishi.
+Evolution of nu-
+clear shells due to the tensor force.
+Physical Re-
+view Letters, 95, 12 2005.
+ISSN 00319007.
+doi:
+10.1103/PhysRevLett.95.232502.
+[9] Yutaka Utsuno, Takaharu Otsuka, Takahiro Mizusaki, and
+Michio Honma.
+Varying shell gap and deformation in
+n
+∼
+20 unstable nuclei studied by the monte carlo
+shell model.
+Phys. Rev. C, 60:054315, Oct 1999.
+doi:
+10.1103/PhysRevC.60.054315.
+URL https://link.
+aps.org/doi/10.1103/PhysRevC.60.054315.
+[10] Naofumi Tsunoda, Takaharu Otsuka, Noritaka Shimizu,
+Morten Hjorth-Jensen, Kazuo Takayanagi, and Toshio
+Suzuki. Exotic neutron-rich medium-mass nuclei with real-
+istic nuclear forces. Phys. Rev. C, 95:021304, Feb 2017. doi:
+10.1103/PhysRevC.95.021304.
+URL https://link.
+aps.org/doi/10.1103/PhysRevC.95.021304.
+[11] K. Fossez, J. Rotureau, N. Michel, and W. Nazarewicz.
+Continuum
+effects
+in
+neutron-drip-line
+oxygen
+iso-
+topes.
+Phys. Rev. C, 96:024308, Aug 2017.
+doi:
+10.1103/PhysRevC.96.024308.
+URL https://link.
+aps.org/doi/10.1103/PhysRevC.96.024308.
+[12] J. H. Hamilton, A. V. Ramayya, W. T. Pinkston, R. M.
+Ronningen, G. Garcia-Bermudez, H. K. Carter, R. L.
+
+6
+Robinson, H. J. Kim, and R. O. Sayer.
+Evidence
+for coexistence of spherical and deformed shapes in
+72Se.
+Phys. Rev. Lett., 32:239–243, Feb 1974.
+doi:
+10.1103/PhysRevLett.32.239.
+URL https://link.
+aps.org/doi/10.1103/PhysRevLett.32.239.
+[13] K.
+Wimmer,
+T.
+Kr¨oll,
+R.
+Kr¨ucken,
+V.
+Bildstein,
+R. Gernh¨auser, B. Bastin, N. Bree, J. Diriken, P. Van Dup-
+pen, M. Huyse, N. Patronis, P. Vermaelen, D. Voulot,
+J. Van de Walle, F. Wenander, L. M. Fraile, R. Chapman,
+B. Hadinia, R. Orlandi, J. F. Smith, R. Lutter, P. G. Thirolf,
+M. Labiche, A. Blazhev, M. Kalk¨uhler, P. Reiter, M. Sei-
+dlitz, N. Warr, A. O. Macchiavelli, H. B. Jeppesen, E. Fiori,
+G. Georgiev, G. Schrieder, S. Das Gupta, G. Lo Bianco,
+S. Nardelli, J. Butterworth, J. Johansen, and K. Riisager.
+Discovery of the shape coexisting 0+ state in 32Mg by
+a two neutron transfer reaction.
+Phys. Rev. Lett., 105:
+252501, Dec 2010. doi:10.1103/PhysRevLett.105.252501.
+URL
+https://link.aps.org/doi/10.1103/
+PhysRevLett.105.252501.
+[14] R. Elder, H. Iwasaki, J. Ash, D. Bazin, P. C. Ben-
+der,
+T. Braunroth,
+B. A. Brown,
+C. M. Campbell,
+H. L. Crawford,
+B. Elman,
+A. Gade,
+M. Grinder,
+N. Kobayashi, B. Longfellow, A. O. Macchiavelli, T. Mi-
+jatovi´c, J. Pereira, A. Revel, D. Rhodes, J. A. Tostevin,
+and D. Weisshaar.
+Intruder dominance in the 0+
+2 state
+of
+32Mg studied with a novel technique for in-ﬂight
+decays.
+Phys. Rev. C, 100:041301, Oct 2019.
+doi:
+10.1103/PhysRevC.100.041301. URL https://link.
+aps.org/doi/10.1103/PhysRevC.100.041301.
+[15] A. Poves. Shape coexistence: The shell model view. Jour-
+nal of Physics G: Nuclear and Particle Physics, 43, 1 2016.
+ISSN 13616471. doi:10.1088/0954-3899/43/2/024010.
+[16] P. Doornenbal, H. Scheit, S. Takeuchi, N. Aoi, K. Li,
+M. Matsushita, D. Steppenbeck, H. Wang, H. Baba,
+H. Crawford, C. R. Hoffman, R. Hughes, E. Ideguchi,
+N. Kobayashi, Y. Kondo, J. Lee, S. Michimasa, T. Mo-
+tobayashi, H. Sakurai, M. Takechi, Y. Togano, R. Win-
+kler, and K. Yoneda. In-beam gamma-ray spectroscopy of
+mg34,36,38: Merging the n=20 and n=28 shell quenching.
+Physical Review Letters, 111, 11 2013. ISSN 00319007.
+doi:10.1103/PhysRevLett.111.212502.
+[17] P. Doornenbal, H. Scheit, S. Takeuchi, N. Aoi, K. Li,
+M. Matsushita, D. Steppenbeck, H. Wang, H. Baba,
+E. Ideguchi, N. Kobayashi, Y. Kondo, J. Lee, S. Michi-
+masa, T. Motobayashi, A. Poves, H. Sakurai, M. Takechi,
+Y. Togano, and K. Yoneda. Mapping the deformation in the
+”island of inversion”: Inelastic scattering of ne 30 and mg
+36 at intermediate energies. Physical Review C, 93, 4 2016.
+ISSN 24699993. doi:10.1103/PhysRevC.93.044306.
+[18] H. L. Crawford, P. Fallon, A. O. Macchiavelli, R. M.
+Clark, B. A. Brown, J. A. Tostevin, D. Bazin, N. Aoi,
+P. Doornenbal, M. Matsushita, H. Scheit, D. Steppen-
+beck, S. Takeuchi, H. Baba, C. M. Campbell, M. Cromaz,
+E. Ideguchi, N. Kobayashi, Y. Kondo, G. Lee, I. Y. Lee,
+J. Lee, K. Li, S. Michimasa, T. Motobayashi, T. Naka-
+mura, S. Ota, S. Paschalis, M. Petri, T. Sako, H. Saku-
+rai, S. Shimoura, M. Takechi, Y. Togano, H. Wang, and
+K. Yoneda. Shell and shape evolution at n = 28: The 40Mg
+ground state.
+Phys. Rev. C, 89:041303, Apr 2014.
+doi:
+10.1103/PhysRevC.89.041303.
+URL https://link.
+aps.org/doi/10.1103/PhysRevC.89.041303.
+[19] H. L. Crawford, P. Fallon, A. O. Macchiavelli, P. Door-
+nenbal, N. Aoi, F. Browne, C. M. Campbell, S. Chen,
+R. M. Clark, M. L. Cort´es, M. Cromaz, E. Ideguchi,
+M. D. Jones, R. Kanungo, M. Maccormick, S. Momiyama,
+I. Murray, M. Niikura, S. Paschalis, M. Petri, H. Saku-
+rai, M. Salathe, P. Schrock, D. Steppenbeck, S. Takeuchi,
+Y. K. Tanaka, R. Taniuchi, H. Wang, and K. Wimmer. First
+spectroscopy of the near drip-line nucleus mg 40.
+Phys-
+ical Review Letters, 122, 2 2019. ISSN 10797114. doi:
+10.1103/PhysRevLett.122.052501.
+[20] Fr´ed´eric Nowacki,
+Alexandre Obertelli,
+and Alfredo
+Poves.
+The neutron-rich edge of the nuclear landscape:
+Experiment and theory.
+Progress in Particle and Nu-
+clear Physics, 120:103866, 2021.
+ISSN 0146-6410.
+doi:https://doi.org/10.1016/j.ppnp.2021.103866.
+URL
+https://www.sciencedirect.com/science/
+article/pii/S014664102100020X.
+[21] D. J. Morrissey, B. M. Sherrill, M. Steiner, A. Stolz, and
+I. Wiedenhoever.
+Commissioning the a1900 projectile
+fragment separator. Nuclear Instruments and Methods in
+Physics Research, Section B: Beam Interactions with Ma-
+terials and Atoms, 204:90–96, 5 2003. ISSN 0168583X.
+doi:10.1016/S0168-583X(02)01895-5.
+[22] R. Yokoyama, M. Singh, R. Grzywacz, A. Keeler, T. T.
+King, J. Agramunt, N. T. Brewer, S. Go, J. Heideman, J. Liu,
+S. Nishimura, P. Parkhurst, V. H. Phong, M. M. Rajabali,
+B. C. Rasco, K. P. Rykaczewski, D. W. Stracener, J. L.
+Tain, A. Tolosa-Delgado, K. Vaigneur, and M. Woli´nska-
+Cichocka. Segmented yso scintillation detectors as a new
+beta-implant detection tool for decay spectroscopy in frag-
+mentation facilities. Nuclear Instruments and Methods in
+Physics Research, Section A: Accelerators, Spectrometers,
+Detectors and Associated Equipment, 937:93–97, 9 2019.
+ISSN 01689002. doi:10.1016/j.nima.2019.05.026.
+[23] W. A. Peters, S. Ilyushkin, M. Madurga, C. Matei, S. V.
+Paulauskas, R. K. Grzywacz, D. W. Bardayan, C. R. Brune,
+J. Allen, J. M. Allen, Z. Bergstrom, J. Blackmon, N. T.
+Brewer, J. A. Cizewski, P. Copp, M. E. Howard, R. Ikeyama,
+R. L. Kozub, B. Manning, T. N. Massey, M. Matos,
+E. Merino, P. D. O’Malley, F. Raiola, C. S. Reingold,
+F. Sarazin, I. Spassova, S. Taylor, and D. Walter. Perfor-
+mance of the versatile array of neutron detectors at low en-
+ergy (vandle). Nuclear Instruments and Methods in Physics
+Research, Section A: Accelerators, Spectrometers, Detec-
+tors and Associated Equipment, 836:122–133, 11 2016.
+ISSN 01689002. doi:10.1016/j.nima.2016.08.054.
+[24] C J Gross, T N Ginter, D Shapira, W T Milner, J W Mc-
+connell, A N James, J W Johnson, J Mas, P F Mantica, R L
+Auble, J J Das, J L Blankenship, J H Hamilton, R L Robin-
+son, Y A Akovali, C Baktash, J C Batchelder, C R Bingham,
+M J Brinkman, H K Carter, R A Cunningham, T Davinson,
+J D Fox, A Galindo-Uribarri, R Grzywacz, J F Liang, B D
+Macdonald, J Mackenzie, S D Paul, A Piechaczek, D C Rad-
+ford, A V Ramayya, W Reviol, D Rudolph, K Rykaczewski,
+K S Toth, W Weintraub, C Williams, P J Woods, C.-H Yu,
+and E F Zganjar. Performance of the recoil mass spectrom-
+eter and its detector systems at the holi”eld radioactive ion
+beam facility. Nuclear Instruments and Methods in Physics
+Research A, 450:12–29, 2000.
+[25] Miloslava Baginova, Pavol Vojtyla, and Pavel P. Povinec.
+Investigation of neutron interactions with ge detectors. Nu-
+
+7
+clear Instruments and Methods in Physics Research, Sec-
+tion A: Accelerators, Spectrometers, Detectors and Associ-
+ated Equipment, 897:22–31, 7 2018. ISSN 01689002. doi:
+10.1016/j.nima.2018.04.036.
+[26] A. Gade, P. Adrich, D. Bazin, M. D. Bowen, B. A. Brown,
+C. M. Campbell, J. M. Cook, S. Ettenauer, T. Glasmacher,
+K. W. Kemper, S. McDaniel, A. Obertelli, T. Otsuka,
+A. Ratkiewicz, K. Siwek, J. R. Terry, J. A. Tostevin, Y. Ut-
+suno, and D. Weisshaar.
+Spectroscopy of mg36: Inter-
+play of normal and intruder conﬁgurations at the neutron-
+rich boundary of the ”island of inversion”.
+Physical
+Review Letters, 99, 8 2007.
+ISSN 00319007.
+doi:
+10.1103/PhysRevLett.99.072502.
+[27] N. Kobayashi, T. Nakamura, Y. Kondo, J. A. Tostevin,
+Y. Utsuno, N. Aoi, H. Baba, R. Barthelemy, M. A. Fami-
+ano, N. Fukuda, N. Inabe, M. Ishihara, R. Kanungo, S. Kim,
+T. Kubo, G. S. Lee, H. S. Lee, M. Matsushita, T. Moto-
+bayashi, T. Ohnishi, N. A. Orr, H. Otsu, T. Otsuka, T. Sako,
+H. Sakurai, Y. Satou, T. Sumikama, H. Takeda, S. Takeuchi,
+R. Tanaka, Y. Togano, and K. Yoneda. Observation of a
+p -wave one-neutron halo conﬁguration in mg 37. Phys-
+ical Review Letters, 112, 6 2014. ISSN 10797114. doi:
+10.1103/PhysRevLett.112.242501.
+[28] S. Michimasa,
+Y. Yanagisawa,
+K. Inafuku,
+N. Aoi,
+Z. Elekes, Zs F¨ul¨op, Y. Ichikawa, N. Iwasa, K. Kurita,
+M. Kurokawa, T. Machida, T. Motobayashi, T. Naka-
+mura, T. Nakabayashi, M. Notani, H. J. Ong, T. K. On-
+ishi, H. Otsu, H. Sakurai, M. Shinohara, T. Sumikama,
+S. Takeuchi, K. Tanaka, Y. Togano, K. Yamada, M. Yam-
+aguchi, and K. Yoneda. Quadrupole collectivity in island-
+of-inversion nuclei 28,30ne and 34,36mg. Physical Review
+C - Nuclear Physics, 89, 5 2014. ISSN 1089490X. doi:
+10.1103/PhysRevC.89.054307.
+[29] Naofumi Tsunoda, Takaharu Otsuka, Kazuo Takayanagi,
+Noritaka Shimizu, Toshio Suzuki, Yutaka Utsuno, Sota
+Yoshida, and Hideki Ueno. The impact of nuclear shape on
+the emergence of the neutron dripline. Nature, 587:66–71,
+11 2020. ISSN 14764687. doi:10.1038/s41586-020-2848-x.
+[30] E Caurier, G Mart´ınez-Pinedo, F Nowacki, A Poves, and
+A P Zuker. The shell model as a uniﬁed view of nuclear
+structure. 2005.
+[31] Noritaka Shimizu. Nuclear shell-model code for massive
+parallel computation, ”kshell”, 2013.
+URL https://
+arxiv.org/abs/1310.5431.
+
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+page_content=' Liddick4,5,  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' Neupane1, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' Peng2, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content='L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' Richard4,†, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' Siegl1, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' Wagenknecht1, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' Yokoyama1  1Dept.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' of Physics and Astronomy,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' University of Tennessee,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' Knoxville,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' Tennessee 37996,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' USA  2Physics Division,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' Oak Ridge National Laboratory,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' Oak Ridge,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' Tennessee 37830,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' USA  3Departamento de F´ısica Te´orica,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' and IFT UAM-CSIC,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content='  Universidad Aut´onoma de Madrid,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' 28049,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' Madrid,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' Spain  4National Superconducting Cyclotron Laboratory,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' Michigan State University,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' East Lansing,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' Michigan 48824,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' USA  5Department of Chemistry,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' Michigan State University,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' East Lansing,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' Michigan 48824,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' USA∗  (Dated: January 31,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' 2023)  We observed a new isomeric gamma transition at 168 keV in 36Mg,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' with a half-life of T1/2=[130-  500](±40)(+800  −20 )sys ns.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' We propose that the observed transition de-excites a new 0+ isomeric state  and populates the previously known ﬁrst 2+ state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' The existence of this isomer is consistent with the  predictions of the large-scale shell model calculations of 36Mg using the sdpf-u-mix interaction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' The  observed excitation energy of the second 0+ state is caused by the small energy separation between two  prolate-deformed conﬁgurations where the intruder conﬁguration corresponds to two neutron excitations  from the sd to the pf shell.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' Within this interpretation, 36Mg becomes the crossing point between nuclei  in which ground state deformed/superdeformed conﬁgurations are caused by the dominance of N=20  intruders (32,34Mg) and nuclei where deformed conﬁgurations are associated with N=28 intruders (38Mg  and beyond).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' We found the lack of three-body monopole corrections in other effective interactions results  in a predominance of N=20 intruder conﬁgurations past 38Mg incompatible with our observation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' We  conclude that 36Mg bridges the N=20 and N=28 islands of inversion, forming the so-called Big Island of  Deformation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content='  The Island of Inversion centered around magnesium  isotopes with neutron “magic” number N=20 has at-  tracted considerable interest [1–5] since its discovery [6].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content='  Negative-parity intruder states ascribed to excitations in-  volving multiple particle-hole conﬁgurations between sd to  the pf orbitals indicate a sudden quenching of the N=20  shell closure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' Nuclei inside the Island of Inversion are de-  ﬁned by having ground states dominated by such particle-  hole conﬁgurations [7].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' The quenching of the N=20 and  N=28 shell closures is driven by the diminishing effect  of the T=0 component of the tensor force as the proton-  neutron ratio becomes more asymmetric [8].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' This forms  a so-called Big Island of Deformation, where both neu-  tron magic numbers N=20 and N=28 disappear in the  magnesium isotopic chain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content='  Recently developed interac-  tions in the proton/neutron sd-pf valence space have had  considerable success in reproducing the observed intruder  and ground-state conﬁgurations of known Island of In-  version nuclei.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' Some examples are effective interactions  such as sdpf-m [9], sdpf-u-mix [5], or the new interac-  tion EEdf1, developed from the chiral expansion at N3LO,  which incorporates phenomenological three body forces of  Fujita-Miyazawa type that are transformed into a medium-  dependent two-body interaction [10]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' As we shall see later  the explicit three body global monopole term proposed  with sdpf-u-mix is crucial to produce the right evolution  ∗ †Current address: Lawrence Livermore National Laboratory, Livermore,  CA 94550.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content='  of the N=20 neutron closure towards N=28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' Interestingly,  each interaction predicts differing microscopic interpreta-  tions of the N=20 and N=28 islands of inversion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' In all  cases but sdpf-u-mix, excited states crossing the N=20 shell  closure are substantial in both islands of inversion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' On the  other hand, sdpf-u-mix predicts the N=20 shell closure is  restored at 40Mg, postulating instead that deformation is  driven exclusively by the breakdown of the N=28 subshell  closure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' There is currently no experimental data that can  resolve these differing interpretations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' Delineation of the  boundaries of the islands of inversion towards the neutron  drip-line is therefore essential to determine the disappear-  ance and appearance of the N=20 and N=28 shell closures  respectively [11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' Isomers, long lived excited states, offer  an observable with which to track evolving nuclear prop-  erties as we study nuclei between shell closures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' The half-  life of an isomeric state is fully determined by the transi-  tion’s energy and its electromagnetic transition probabil-  ity, in turn deﬁned by the wave-functions of the involved  states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' One such example are the so-called shape isomers,  excited states arising from nuclear conﬁgurations of differ-  ent shapes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' Low energy excited 0+ states corresponding to  prolate(oblate) deformed conﬁgurations [12] may become  isomeric when decaying to the ﬁrst excited 2+ state corre-  sponding to the ground state band of different deformation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content='  As of the beginning of 2023, there is only one isomer  conﬁrmed and published in either neon or magnesium iso-  topes, the 0+  2 state in 32Mg that decays to the 2+  1 via a 172  keV transition with T1/2 >10 ns [13, 14].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' Shell model  calculations using the sdpf-u-mix interaction [15] produce  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content='12002v1  [nucl-ex]  27 Jan 2023  2  500  600  700  800  900  Time of Flight (arb)  5000  6000  7000  8000  9000  E (arb)  ∆  0  20  40  60  80  100  Mg  36  Z=13  Z=12  Z=11  Z=10  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' Two dimensional energy loss (∆E) v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' time of ﬂight parti-  cle identiﬁcation plot for all ion implants between Z=10 (bottom  row) and Z=13 (top row).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' Magnesium-36 is highlighted by the  red circle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' We also searched for isomers in 25−29F isotopes (not  shown).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content='  a ground state that is a mixture of deformed (2p-2h) and  superdeformed (4p-4h) conﬁgurations and an isomeric 0+  state which is dominated by superdeformed and spherical  (0p-0h) components.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' Notice that sdpf-u-mix is the only in-  teraction that locates the isomer close to its experimental  excitation energy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' In the same calculation, heavier magne-  sium isotopes were expected to strongly favor quadrupole  components before transitioning to the N=28 Island of In-  version at 40Mg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' This hypothesis is supported by the sys-  tematics of the ﬁrst 2+ states in 34,36,38Mg [16–19] com-  paring well with calculations [20].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content='  In this Letter we present the observation of a new iso-  meric gamma transition at 168 keV in 36Mg, assigned to  a second 0+ state feeding the ﬁrst 2+ state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' The analysis  of the time structure of 168 keV gamma-ray events follow-  ing the ion implantation results in a half-life of T1/2=[130-  500](±40)tran(+800  −20 )sys ns.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' We present an interpretation  of the nature of the new second 0+ state and the evolu-  tion of intruder conﬁgurations in the magnesium isotopic  chain from N=20 to N=28 using shell model calculations  with the sdpf-u-mix interaction [5].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' Our calculations indi-  cate the isomer naturally arises from gradually restoring the  N=20 shell closure as the neutron 0f7/2 orbital is occupied  towards the N=28 subshell closure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content='  Experiment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' The experiment was performed at the Na-  tional Superconducting Cyclotron Laboratory (NSCL) at  Michigan State University.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' A 48Ca beam, 80 pnA average  intensity at 140 MeV/u, was fragmented in a 846 mg/cm2  thick Be target at the entrance of the fragment separator,  A1900 [21], to produce the nuclei of interest, a ”cocktail”  beam consisting of isotopes from boron (Z=5) to aluminum  (Z=13).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' In order to identify the different species, we mea-  sured the ion’s time-of-ﬂight between a scintillator located  in the focal plane of A1900 and a Silicon detector (Si PIN)  placed in front of our experimental setup.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' Combining with  the energy loss in the Si PIN allowed us to perform parti-  cle identiﬁcation (PID) in the beam, as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content='  We implanted the ”cocktail” beam in a 12-mm thick YSO  detector (Ytrium, Silicon Oxide) [22] allowing for record-  ing energies and timestamps of ion implantation and beta-  decay events.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' The YSO detector was surrounded on one  side by 48 VANDLE modules [23] providing a total neu-  tron detection efﬁciency of 11% at 1 MeV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' On the other  side of the setup, three HPGe clovers from the CLARION  array [24] resulting in gamma detection of 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content='8% efﬁciency  at 1 MeV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content='  We searched for isomers in all Fluorine, Neon, Sodium,  Magnesium, and Aluminum isotopes shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' 1 by  analyzing the gamma rays emitted between 40 ns and 500  ns after ion implantation, correlated to each individual iso-  tope using the PID plot (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' We excluded the ﬁrst 40  ns in order to remove the Gaussian tail of the prompt im-  plantation ”ﬂash”, mostly Bremsstrahlung x-ray.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' We did  not identify isomeric transitions in any F, Ne, Na, Mg, or  Al isotope except for 36Mg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' In 36Mg, we observe a promi-  nent gamma transition at 168 keV, see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' The top  right panel of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' 2 shows the gamma spectrum between  500 and 750 keV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' We marked several gamma lines corre-  sponding to germanium (†) and iron (§) neutron inelastic  scattering [25], as well as the 511 keV line corresponding  to positron annihilation (#).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' Imposing total event multi-  plicity one, we expect close to no background in the 600 to  700 keV region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' Therefore, we identiﬁed the 3(2) counts at  665 keV to the de-excitation of the ﬁrst 2+ state in 36Mg  [16, 17, 19, 26–28].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content='Since the 2+ state in 36Mg was not  observed to be isomeric, we propose the isomeric state  in 36Mg decays to the 2+ state via emitting the 168 keV  gamma ray.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' We calculated the number of counts we would  observe if the new 168 keV line and the 665 keV line form  a gamma cascade.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' We observe a total 10(3) counts in the  168 keV peak, with background component estimated from  neighboring bins to 5(2) counts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' Using efﬁciencies of 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content='7%  at 168 keV and 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content='23% at 665 keV we expect 4(1) counts at  665 keV, within error bars of the observed 3(2) counts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' In  order to substantiate the spin and parity of the new state we  consider the recent measurement of the quadrupole elec-  tromagnetic transition strength for the 665 keV line [17]  conﬁrmed that it corresponds to the 2+  1 state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' Considering  the placement of the other known isomer in neutron rich  magnesium isotopes (32Mg), the most likely explanation  places the new 168 keV isomer as the de-excitation of a  new 833 keV 0+ state directly to the known 665 2+  1 state  in 36Mg (top left inset in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' 2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content='  We performed a log likelihood analysis of the gamma  activity after ion implantation, see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content='  The left  panel shows the time distribution of gamma events af-  ter ion implantation for the photopeak gate (167 to 169  3  150  200  250  300  E (keV)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content='5  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content='0  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content='5  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content='0  1/keV  168(1) FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' Delayed gamma energy spectrum in coincidence with  36Mg implantation events.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' The most prominent line corresponds  to the new isomeric transition at 168 keV ( [*] marks background  lines).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' The top left panel shows the 36Mg partial level scheme.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content='  The top right panel shows the gamma spectrum between 500 and  750 keV, including the 36Mg 665 keV transition and other back-  ground lines (see text for details).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content='  keV).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' The right panel shows the time distribution of  background events (166<Eγ<167 keV and 169<Eγ<170  keV).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' First, in order to estimate the component arising from  the tail of the Gaussian distribution of the ion implanta-  tion Bremsstrahlung ﬂash, we ﬁtted the time distribution of  the background gate to an exponential function (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' 3b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content='  Then, we constructed a double exponential distribution,  corresponding to photopeak and background combined,  50% each as per the gamma energy spectrum estimate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' We  ﬁtted the photopeak gate, obtaining T1/2=90(+410  −50 ) ns.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' We  also studied the systematic uncertainty due to the shape of  the tail of the implantation ﬂash.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' In order to progressively  remove the background tail, we performed ﬁts to samples  starting at increasingly later times, between 50 ns to 100 ns.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content='  Finally, we calculated the shortest observable half-life con-  sidering the transit time (500 ns) in A1900, and assuming  an isomer population of 10% in the fragmentation reaction  producing 36Mg, obtaining 130(40) ns.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' Given the statis-  tical constraints due to the size of our sample, the limits  imposed by the transit time in A1900, and the systematic  effects mentioned above, we provide a half-life range for  the 168 keV isomer, at 3σ conﬁdence level, of T1/2=[130-  500](±40)tran(+800  −20 )sys ns.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' The resulting half-life range  corresponds to B(E2)= [12−50] (+30  −1 )tran(+10  −7 )sys e2fm4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content='  Discussion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' In the heavy Magnesium isotopes two neu-  tron shell closures are washed out by the presence of in-  truder states whose energy, fostered by the quadrupole cor-  relations, make them dominant in the ground states, giving  rise to the N=20 and N=28 Islands of Inversion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' It is inter-  esting to follow the location of the intruder conﬁgurations  before mixing as the number of neutrons increase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' We de-  0  50  100  150  200  ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content='1  0  1  2  3  counts  isomer+background  isomer  background  (a)  Clover -  YSO Time (ns)  0  50  100  150  200  ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content='1  0  1  2  3  background  (b)  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content='  (Left) Time distribution of gamma activity after ion  implantation gated on the 168 keV photopeak with background  (black-dashed, see right panel), isomer (blue) and combined (red)  ﬁts overlayed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' (Right) Distribution of gamma events gated on the  Compton background surrounding the photopeak.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content='  note by x=0 the normal ﬁlling conﬁguration, and by x=0,  2, 4, etc, the xp-xh neutron excitations across N=20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' Their  relative position gives us a clear hint of what will be the  structure of the low lying states after full diagonalization,  although the details of the spectroscopy depend on many  other ingredients, in particular on the off-diagonal matrix  elements between the states calculated at ﬁxed values of t  differing in two units.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' As explained in ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' [5] we submit  that the effective interaction for this wide region should in-  clude a three body monopole correction of the form:  δVpf = 1  2npf(18  A )1/3 75 keV  (1)  Which restores the N=20 closure in 40Mg as it is required  by consistency and naturalness of the very shell model  with conﬁguration interaction (SM-CI) approach (npf is  the number of neutrons in the pf shell in the normal ﬁll-  ing approximation).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' Notice however that in ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' [29] the  EEdf1 interaction produces a completely different, and in  our opinion un-natural, picture because the 0d3/2 orbit is  only half ﬁlled already in 30Mg and remains so even in the  42Mg ground state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content='  We proceed now to carry on the SM-CI calculations us-  ing the sdpf-u-mix interaction and valence space [5].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' The  calculations are performed with the code Antoine [30].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content='  As a ﬁrst step, we study the relative location of the 0+  band heads of the x=0 and x=2 conﬁgurations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' The re-  sults are shown in the bottom panel of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' It is seen  that the intruder states cease to be clearly dominant at  A=36.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content='  This is consistent with the fact that even if the  0f7/2 and 1p3/2 neutron orbits would behave as a super-  orbit of degeneracy 12, the maximum collectivity in Quasi-  SU3 [20] is obtained for 6 neutrons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' Besides, the increase  of the quadrupole moment Q of the 6p-2h conﬁguration  with respect to the 4p-0h one is small, therefore the gain  in quadrupole correlation energy of the latter barely com-  pensates its loss of monopole energy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' As a consequence,  the 6p-2h conﬁguration in 36Mg is not as dominant as the  4p-2h one in 34Mg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' Beyond N=24, the 6p-0h and 8p-0h  ey891  02  833keV  665keV4  0  25  50  75  100  wavefunction frac.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' (%)  0p-0h  2p-2h  4p-4h  30  32  34  36  38  40  A  4  2  0  2  4  E(2p2h)  E(0p0h) (MeV)  SDPF-U-MIX  SDPF-M  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' (Bottom panel) Energy splitting between the normal ﬁll-  ing conﬁguration and the intruder state corresponding to the pro-  motion of two neutrons across the N=20 magic shell closure, in  the heavy Magnesium isotopes, calculated with sdpf-u-mix (red)  and sdpf-m (blue).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' (Upper panel) Percentage of np-nh conﬁg-  urations in the theoretical wave functions of the ground states  of the Magnesium isotopes, 0p-0h (blue), 2p-2h (orange), 4p-4h  (green), using the sdpf-u-mix interaction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content='  conﬁgurations are re-established as the main components  in the ground states of 38Mg and 40Mg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' This is in stark  contrast with the calculation using the sdpf-m interaction  shown in the bottom panel of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' The intruder conﬁgu-  rations (x=2) remain highly dominant in 36Mg, while they  become degenerate with the 6p-0h normal-ﬁlling (x=0)  state in 38Mg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' We conclude sdpf-m cannot naturally repro-  duce a low lying 0+  2 in 36Mg, favoring 38Mg instead.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' The  ”softness” of the N=20 core in sdpf-m highlights the im-  portance of the three-body monopole correction mentioned  above to produce the trend in Mg isotopes, restoring the  N=20 shell closure and 36Mg as the crossing point between  normal-ﬁlling and excited conﬁgurations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content='  It is precisely the crossing of the 4p-0h and 6p-2h conﬁg-  urations in 36Mg what might explain the very low energy  of the excited 0+.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' In the full calculation, sdpf-u-mix places  the excited 0+ in 36Mg at 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content='55 MeV, and produces a 36Mg  which is triaxial with a low lying gamma band, not very  compatible with existence of a 0+ isomer as seen in the  present experiment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content='  Given that the amplitude of the 8p-4h conﬁgurations is  negligible, the problem can be translated into a two state  model including only the 4p-0h and the 6p-2h states dis-  cussed above.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' Notice that both are prolate deformed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' If  the energies of the 4p-0h and 6p-2h states were degener-  ate before mixing (and this is nearly the case), the ﬁnal  splitting of the two 0+ states would be roughly equal to  2W, with W = ⟨4p − 0h(0+)|V |6p − 2h(0+)⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' In fact,  W=730 keV in 36Mg, and this sets a theoretical lower limit  to the excitation energy of the isomer 0+, within the two  state model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' The value in the complete diagonalization is  very much in line with this estimate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' Thus, the only way to  get the splitting right is via a reduction of the value of W,  which is dominated by the off-diagonal pairing interaction  between the sd and the pf-shell neutron orbits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' Hence we  are led to make an “ad hoc” 10% reduction of the off diago-  nal pairing matrix elements for npf > 0, bringing W down  to about 500 keV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' With this choice, the resulting compo-  sition of the ground states of the Magnesium isotopes is  as depicted in the upper panel of Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' We see the in-  truder (x=2,4) conﬁgurations are dominant in 32,34,36Mg,  while the normal-ﬁlling (x=0) states take the majority of  the wavefunction in 30,38,40Mg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' This trend is consistent  with the restoration of the N=20 shell closure as we ap-  proach the N=28 subshell, disfavoring particle-hole excita-  tions across the N=20 shell gap.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content='  The spectroscopic results for 36Mg are gathered in Table  I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' The excitation energies are in good agreement with the  TABLE I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' Theoretical excitation energies (in MeV), Qspec in  efm2 and B(E2)’s (in e2fm4), for 36Mg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content='  Jπ  E(th))  Qspec  Jπ(f)  B(E2)  0+  1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content='0  2+  1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content='58  23  0+  1  130  0+  2  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content='02  2+  1  5  2+  2  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content='43  15  0+  1  2  2+  2  2+  1  1  2+  2  0+  2  120  4+  1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content='73  23  2+  1  183  4+  1  2+  2  1  present experimental result for the 0+ isomer and with the  results of reference [16] for the yrast 2+ and 4+.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' The crit-  icality at the crossover goes beyond the value of the exci-  tation energy of the 0+ isomer, because it implies as well a  change of structure, from a triaxial solution to a case of two  coexisting prolate bands, the lowest dominated by 6p-2h  conﬁgurations and the excited one by 4p-0h conﬁgurations  as can be seen in the E2 properties listed in Table I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' A very  prominent feature of them is that the cross-talk between the  two bands is almost absent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' In particular, the B(E2) from  the isomer to the yrast 2+ is small, compatible with the ex-  perimental value extracted from its lifetime.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' Let’s mention  ﬁnally that the crossover from the dominance of the 0f7/2  orbit to a massive occupation of the 1p3/2 orbit, takes place  at N=24 as well, paving the way to the N=28 Island of In-  version.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content='  Conclusions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' We observed a new 168 keV isomer in  36Mg, with a halﬂife of [130-500](±40)tran(+800  −20 )sys ns  at 3σ conﬁdence level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' From the observation of a 665 keV  gamma line in the prompt gamma spectrum, we deduce it  corresponds to a new 0+ state at 833 keV de-exciting to the  known 665 keV 2+ state [17].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' To elucidate the microscopic  5  origin of this isomer we performed shell model calculations  using the sdpf-u-mix interaction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' We propose the observed  low energy of the state arises from two coexisting prolate  deformed conﬁgurations consisting of the normal-ﬁlling  and intruder two-neutron excitations respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' We pre-  dict that, for N>20 Mg isotopes, as the neutron 0f7/2 or-  bital is gradually ﬁlled, the N=20 shell closure is restored  while the N=28 subshell closure is quenched.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' Therefore,  the quasi-degeneracy between normal and intruder conﬁg-  urations occurs only for 36Mg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' In contrast, other effective  interactions used in the region predict substantial quench-  ing of the N=20 shell closure even past 38Mg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' We postulate  the discrepancy arises from the lack of three-body correc-  tions to the monopole part of the effective interaction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' The  isomer presented in this Letter supports this latter picture,  with 36Mg being the bridge between the island of inversion  centered around 32Mg, due to the quenching of the N=20  shell closure, and the island of inversion centered in 40Mg,  due to the quenching of the N =28 subshell closure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' As a di-  rect consequence we anticipate no isomers will be present  in 34,38Mg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' Thanks to the large yields of magnesium iso-  topes afforded at the recently commissioned FRIB facility  in MSU (or RIKEN, Japan), this hypothesis may be tested  in the near future.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content='  Acknowledgements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' We thank Augusto Macchiavelli for  the fruitful discussions during the preparation of this Let-  ter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' The isotope(s) used in this research was supplied by  the Isotope Program within the Ofﬁce of Nuclear Physics  in the Department of Energy’s Ofﬁce of Science.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content='  The  Lanczos shell-model calculation using the sdpf-m inter-  action was performed with the code KSHELL [31].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' This  research was sponsored in part by the National Nuclear  Security Administration under the Stewardship Science  Academic Alliances program through DOE Cooperative  Agreements No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content='  DE-NA0003899 and DE-NA0004068.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content='  This research was also sponsored by the Ofﬁce of Nu-  clear Physics, U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' Department of Energy under contract  DE-FG02-96ER40983 (UT) and DE-SC0020451 (MSU).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content='  This research was sponsored in part by National Science  Foundation under the contract NSF-MRI-1919735.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' This  work was also supported by the National Nuclear Secu-  rity Administration through the Nuclear Science and Secu-  rity Consortium under Award No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' DE-NA0003180 and the  Stewardship Science Academic Alliances program through  DOE Award No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' DOE-DE-NA0003906.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content='  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content='P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' is supported by grants CEX2020-001007-S funded  by MCIN/AEI/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content='13039/501100011033 and PID2021-  127890NB-I00.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content='  [1] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' Poves and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' Retamosa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content='  The onset of deformation  at the n = 20 neutron shell closure far from stability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content='  Physics Letters B, 184(4):311–315, 1987.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content='  ISSN 0370-  2693.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content='  doi:https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content='1016/0370-2693(87)90171-  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content='  URL  https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content='sciencedirect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content='com/  science/article/pii/0370269387901717.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content='  [2] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' Warburton, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' Becker, and B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' Brown.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content='  Mass  systematics for a=29–44 nuclei: The deformed a∼32 re-  gion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content='  Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' C, 41:1147–1166, Mar 1990.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content='  doi:  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content='1103/PhysRevC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content='41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content='1147.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content='  URL https://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content='  aps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content='1103/PhysRevC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content='41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content='1147.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content='  [3] K Heyde and J L Wood.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content='  Intruder states and shape co-  existence in the region n approximately 20, z approx-  imately 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content='  Journal of Physics G: Nuclear and Par-  ticle Physics, 17(2):135, feb 1991.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content='  doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content='1088/0954-  3899/17/2/007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content='  URL https://dx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content='doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content='  1088/0954-3899/17/2/007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content='  [4] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content='  Fukunishi,  T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content='  Otsuka,  and  T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content='  Sebe.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content='  Vanish-  ing of the shell gap in n = 20 neutron-rich nuclei.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content='  Physics Letters B, 296(3):279–284, 1992.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content='  ISSN 0370-  2693.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content='  doi:https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content='1016/0370-2693(92)91320-  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content='  URL  https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
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+page_content='com/  science/article/pii/0370269392913209.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content='  [5] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' Caurier, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' Nowacki, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' Poves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' Merging of the is-  lands of inversion at n=20 and n=28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' Physical Review C  Nuclear Physics, 90, 7 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content='  ISSN 1089490X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content='  doi:  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content='1103/PhysRevC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content='90.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content='014302.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content='  [6] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' Thibault, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' Klapisch, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' Rigaud, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' Poskanzer,  R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
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+page_content=' C, 96:024308, Aug 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
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+page_content=' Aoi, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' Baba, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' Barthelemy, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' Fami-  ano, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' Fukuda, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' Inabe, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' Ishihara, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' Kanungo, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' Kim,  T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' Kubo, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' Lee, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' Lee, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' Matsushita, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' Moto-  bayashi, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' Ohnishi, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' Orr, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' Otsu, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' Otsuka, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' Sako,  H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' Sakurai, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' Satou, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' Sumikama, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' Takeda, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' Takeuchi,  R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' Tanaka, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' Togano, and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' Yoneda.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' Observation of a  p -wave one-neutron halo conﬁguration in mg 37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' Phys-  ical Review Letters, 112, 6 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' ISSN 10797114.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' doi:  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content='1103/PhysRevLett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content='112.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content='242501.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content='  [28] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' Michimasa,  Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' Yanagisawa,  K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' Inafuku,  N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' Aoi,  Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' Elekes, Zs F¨ul¨op, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' Ichikawa, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' Iwasa, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' Kurita,  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' Kurokawa, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' Machida, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' Motobayashi, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' Naka-  mura, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' Nakabayashi, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' Notani, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' Ong, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' On-  ishi, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' Otsu, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' Sakurai, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' Shinohara, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' Sumikama,  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' Takeuchi, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' Tanaka, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' Togano, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' Yamada, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' Yam-  aguchi, and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' Yoneda.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' Quadrupole collectivity in island-  of-inversion nuclei 28,30ne and 34,36mg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' Physical Review  C - Nuclear Physics, 89, 5 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' ISSN 1089490X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' doi:  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content='1103/PhysRevC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content='89.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content='054307.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content='  [29] Naofumi Tsunoda, Takaharu Otsuka, Kazuo Takayanagi,  Noritaka Shimizu, Toshio Suzuki, Yutaka Utsuno, Sota  Yoshida, and Hideki Ueno.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' The impact of nuclear shape on  the emergence of the neutron dripline.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' Nature, 587:66–71,  11 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' ISSN 14764687.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content='1038/s41586-020-2848-x.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content='  [30] E Caurier, G Mart´ınez-Pinedo, F Nowacki, A Poves, and  A P Zuker.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' The shell model as a uniﬁed view of nuclear  structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' 2005.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content='  [31] Noritaka Shimizu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content=' Nuclear shell-model code for massive  parallel computation, ”kshell”, 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content='  URL https://  arxiv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content='org/abs/1310.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
+page_content='5431.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/IdFLT4oBgHgl3EQfJC9S/content/2301.12002v1.pdf'}
diff --git a/ItE0T4oBgHgl3EQfRwDJ/content/tmp_files/2301.02213v1.pdf.txt b/ItE0T4oBgHgl3EQfRwDJ/content/tmp_files/2301.02213v1.pdf.txt
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+arXiv:2301.02213v1  [cs.LO]  5 Jan 2023
+Representable and diagonally representable
+weakening relation algebras⋆
+Peter Jipsen1[0000−0001−8608−808X] and Jaˇs ˇSemrl2[0000−0001−7440−8867]
+1 Chapman University jipsen@chapman.edu https://www1.chapman.edu/~jipsen/
+2 UCL (University College London) j.semrl@cs.ucl.ac.uk
+http://www0.cs.ucl.ac.uk/staff/jsemrl/
+Abstract. A binary relation deﬁned on a poset is a weakening relation
+if the partial order acts as a both-sided compositional identity. This is
+motivated by the weakening rule in sequent calculi and closely related to
+models of relevance logic. For a ﬁxed poset the collection of weakening
+relations is a subreduct of the full relation algebra on the underlying set
+of the poset. We present a two-player game for the class of representable
+weakening relation algebras akin to that for the class of representable
+relation algebras. This enables us to deﬁne classes of abstract weaken-
+ing relation algebras that approximate the quasivariety of representable
+weakening relation algebras. We give explicit ﬁnite axiomatisations for
+some of these classes. We deﬁne the class of diagonally representable
+weakening relation algebras and prove that it is a discriminator vari-
+ety. We also provide explicit representations for several small weakening
+relation algebras.
+Keywords: weakening relation algebra · relevance frames · Sugihara
+monoids · representation games
+1
+Introduction
+The full algebra of binary relations on X is
+Rel(X) = (P(X2), ∩, ∪, ∅, ⊤, ; , idX, ¬,⌣ )
+where ⊤ = X2, R;S is the composition of R, S , ¬R = X2\R, and R⌣ = {(x, y) |
+(y, x) ∈ R}. The class RRA of representable relation algebras = SP{Rel(X) | X
+is a set}. Tarski [22] proved that RRA is a variety and Monk [17] proved that
+RRA is not ﬁnitely axiomatisable. For more details see the books by Givant [5],
+[6] and Maddux [11].
+The set of weakening relations on a poset X = (X, ≤) is W(X) = {R ⊆ X2 |
+≤;R;≤ = R}. The full algebra of weakening relations on a poset X is
+wk(X) = (W(X, ≤), ∩, ∪, ∅, ⊤, ; , 1, ∼)
+⋆ This work was supported by the Engineering and Physical Sciences Research Council
+EP/S021566/1
+
+where 1 = ≤ and ∼R = ¬R⌣ is the complement-converse operation. The class
+of representable weakening relation algebras is
+RwkRA = SP{wk(X, ≤) | (X, ≤) is a poset}.
+Weakening relations are the analogue of binary relations when the category
+Set of sets and functions is replaced by the category Pos of partially ordered sets
+and order-preserving functions. Since sets can be considered as discrete posets
+(i.e. antichains, ordered by the identity relation), Pos contains Set as a full
+subcategory, which implies that weakening relations are a substantial generali-
+sation of binary relations. However, weakening relations do not allow ¬ or ⌣ as
+operations.
+They have applications in sequent calculi [2], quasi-proximity lattices/spaces
+[19] , order-enriched categories [10] , mathematical morphology [21], and program
+semantics, e.g. via separation logic [18] .
+The closely related algebras Wk(X) are deﬁned as the expansions of wk(X)
+by the Heyting implication R → S = {(x, y) | ∀u, v(u ≤ x & y ≤ v & uRv ⇒
+uSv)}. The SP-closure of these algebras is denoted by RWkRA and has been
+studied in [3], [4], [9], [20], [21]. It is a discriminator variety that has RRA of
+representable relation algebras as a proper subvariety. The algebras in RWkRA
+are generalised bunched implication algebras, and the algebras in RwkRA are
+all the subreducts of algebras in RWkRA, hence RwkRA is a quasivariety. We
+show that it is not a variety, but with respect to representability the two classes
+behave the same way.
+In Section 2 we deﬁne a representation game for RwkRA (which can be ex-
+tended to a game for RWkRA) and use it to give an explicit universal axioma-
+tisation for the class. Section 3 deﬁnes (Kripke) frames for weakening relation
+algebras and adapts the game to this setting. From an n-pebble version of this
+frame game we deﬁne a sequence of classes wkRAn that approximate RwkRA from
+above, similar to the sequence RAn that converges the RRA. In the next section
+we ﬁnd ﬁnite axiomatisation for wkRA2 and wkRA3. In Section 5 we deﬁne the
+class of representable diagonal weakening relation algebras and show that is a
+discriminator variety. Finally, in the last section we show that all associative
+algebras in wkRA3 with 6 elements or fewer are representable.
+2
+Representation game
+In this section we present a representation game for weakening relation algebras
+similar to those deﬁned for relation algebras, deﬁned in [8]. We begin by deﬁning
+some notation.
+Deﬁnition 1. A bounded cyclic involutive unital distributive lattice-ordered magma
+A = (A, ·, +, ⊥, ⊤, ; , 1, ∼) is an algebra such that
+(1) (A, ·, +, ⊥, ⊤) is a bounded distributive lattice
+(2) (s + t); (u + v) = s; u + s; v + t; u + t; v
+2
+
+(3) s;⊥ = ⊥ = ⊥;s
+(4) s;1 = s = 1;s
+(5) ∼(∼s) = s
+(6) ∼(s · t) = ∼s + ∼t
+for all s, t, u, v ∈ A. A representation of A is an injective homomorphism h : A →
+wk(X) for some poset X = (X, ≤) such that h(⊤) is an equivalence relation on
+X.
+Note that s ≤ t if and only if s + t = t, or equivalently ∼s · ∼t = ∼t which
+can be rewritten as ∼t ≤ ∼s, hence ∼ is order reversing. The adjective “cyclic”
+is included in the name to contrast it to the non-cyclic general case the are two
+unary operations ∼, − in the language that satisfy ∼−s = s = −∼s. In the
+cyclic case ∼, − have the same interpretation.
+Distributive lattice-ordered magmas are abbreviated as dℓ-magmas. Let A
+be a bounded cyclic involutive unital dℓ-magma. Additionally we deﬁne 0 = ∼1.
+Deﬁnition 2. A network (for A) is a tuple N = (N, λ) where N is a set of
+nodes and λ : N 2 → ℘(A) is a labelling function such that for all x, y ∈ N,
+1 ∈ λ(x, x) and ⊤ ∈ λ(x, y). Such a network is consistent if and only if for all
+x, y ∈ N we have that
+λ(x, y) ∩ {∼a | a ∈ λ(y, x)} = ∅.
+A network N = (N, λ) is a prenetwork of N ′ = (N ′, λ′) – denoted N ⊆ N ′ – if
+and only if N ⊆ N ′ and for all x, y ∈ N we have λ(x, y) ⊆ λ′(x, y).
+Observe that the prenetwork predicate is a partial order and that inconsis-
+tency is inherited from prenetworks.
+We now have the tools to deﬁne a two player game and prove that the exis-
+tence of a winning strategy for one of the players coincides with A’s membership
+in the class of RWkRA.
+Deﬁnition 3. An n-round representation game, denoted Γn(A), for some n ≤
+ω is a two player game played between the challenger ∀ (Abelard) and the
+responder ∃ (H´elo¨ıse) over n + 1 moves. After the ith move for 0 ≤ i ≤ n, ∃ will
+return a network Ni such that N0 ⊆ N1 ⊆ ... ⊆ Nn. The game is won by ∀ if ∃
+returns an inconsistent network. Otherwise ∃ wins.
+On the initialisation move ∀ picks a pair of elements a ≰ b ∈ A and ∃
+must return a network N0 with some (x, y) ∈ N 2
+0 such that a ∈ λ(x, y) and
+∼b ∈ λ(y, x).
+On the ith move for 0 < i ≤ n, ∀ may challenge ∃ with any of the following
+four moves.
+join move: ∀ picks x, y ∈ Ni−1, some a ∈ λi−1(x, y), and some b, c ∈ A such
+that a ≤ b + c. ∃ must return a Ni with b ∈ λi(x, y) or c ∈ λi(x, y).
+involution move: ∀ picks x, y ∈ Ni−1 and some a, b ∈ A such that b = ∼a.
+∃ must return a Ni with a ∈ λi(x, y) or b ∈ λi(y, x).
+3
+
+composition move: ∀ picks x, y, z ∈ Ni−1 and a ∈ λi−1(x, y), b ∈ λi−1(y, z). ∃
+must return a Ni with c ∈ λi(x, z) where c = a; b.
+witness move: ∀ picks x, y ∈ Ni−1, a ∈ λi−1(x, y), and b, c ∈ A such that a =
+b; c. ∃ must return a Ni with some z ∈ Ni such that b ∈ λi(x, z), c ∈ λi(z, y).
+Proposition 1. A is representable if and only if ∃ has a winning strategy for
+Γω(A).
+Proof. If A is representable, then ∃ can take some representation h over X. Let
+a ≰ b be the pair played on initialisation move. There will exist some maximal
+X′ ⊆ X such that ∃x, y ∈ X′ : (x, y) ∈ h(a)\h(b) and ∀z, w ∈ X′ : (z, w) ∈ h(⊤).
+On initialisation move, ∃ can return the network N = (X′, λ) where λ(x, y) =
+{c ∈ A | (x, y) ∈ h(c)}. Because h preserves all the operations in the language,
+all moves ∀ may call are trivially responded to by returning the same network
+after every move.
+If A is countable then ∀ can schedule his moves in a way that every move will
+be called eventually. Let N a,b
+0
+, N a,b
+1
+, N a,b
+2
+, ... be the networks during an ∃-winning
+play of Γω(A) where ∀ scheduled his moves in such a way and the initialisation
+move was called for the pair a ≰ b. Deﬁne N a,b
+ω
+as {x | ∃i < ω : j ≥ i ⇒ x ∈
+N a,b
+i
+}, λa,b
+ω (x, y) as {c | ∃i < ω : j ≥ i ⇒ (x, y ∈ N a,b
+j
+∧ c ∈ λa,b
+j (x, y))}, and a
+relation ≡ as {(x, y) ∈ (N a,b
+i
+)2 | 1 ∈ λa,b
+ω (x, y), 1 ∈ λa,b
+ω (y, x)}. It is symmetric
+by deﬁnition, reﬂexive because networks are deﬁned as having 1 ∈ λa,b
+ω (x, x) and
+transitive because all composition moves were called eventually and 1; 1 = 1.
+Therefore, we can deﬁne ha,b : A →
+�
+(Nω/≡)2�
+where for all c ∈ A we have
+ha,b(c) = {([x]≡, [y]≡) | c ∈ λa,b
+ω (x, y)}.
+Because of initialisation there exists a pair x, y ∈ N a,b
+ω
+with a ∈ λa,b
+ω (x, y) and
+as the network remains consistent and ∼b ∈ λa,b
+ω (y, x), we have b /∈ λa,b
+ω (x, y).
+Because every composition move was called and 1 is the identity for ;, we have
+b /∈ λa,b
+ω (x′, y′) for all x′ ∈ [x]≡, y′ ∈ [y]≡. Thus ([x]≡, [y]≡) is a pair that ensures
+that ha,b(a) ̸⊆ ha,b(b).
+⊤ is represented by ha,b as the top relation by the deﬁnition of a network
+and ⊥ is represented as the empty relation because if there was a pair (x, y) with
+⊥ ∈ λa,b
+ω (x, y) then by a series of composition moves every pair would include ⊥
+in its label. That would mean that the initialisation pair of points would include
+both a and b in its label.
+The join move ensures that join is represented correctly by ha,b, namely the
+join move ensures ha,b(c)+ha,b(d) ⊆ ha,b(c+d) because c ≤ (c+d)+(c+d) and
+ha,b(c)+ ha,b(d) ⊇ ha,b(c+ d) because c+ d ≤ c+ d and thus a pair in ha,b(c+ d)
+will also be in ha,b(c) or ha,b(d).
+Because an inconsistent network is never introduced we have that if ∼c ∈
+λa,b
+ω (x, y) then c ̸∈ λa,b
+ω (x, y). Because all composition moves are eventually called
+and 1 is the identity for ; that applies to the all the points in the relevant
+equivalence classes of ≡ and ha,b(∼c) ⊆ ∼ha,b(c). For ha,b(∼c) ⊇ ∼ha,b(c) if
+([x]≡, [y]≡) /∈ ha,b(∼c) then when the involution move was called for (y, x) and
+c, ∃ chose to have c ∈ λa,b
+ω (y, x).
+4
+
+If ([x]≡, [y]≡) ∈ ha,b(c) and ([y]≡, [z]≡) ∈ ha,b(d) then by composition moves
+of a; 1; b = a; b we have ([x]≡, [z]≡) ∈ ha,b(c; d) so ha,b(c); ha,b(d) ⊆ ha,b(c; d).
+For ha,b(c); ha,b(d) ⊇ ha,b(c; d), assume ([x]≡, [z]≡) ∈ ha,b(c; d) and without loss
+c; d ∈ λa,b
+ω (x, z). Because the relevant witness move was called there will exist a
+y such that ([x]≡, [y]≡) ∈ ha,b(c) and ([y]≡, [z]≡) ∈ ha,b(d).
+ha,b(1) is reﬂexive by the deﬁnition of a network, antisymmetric as the base
+was quotiented by ≡, and transitive as 1; 1 = 1 and all the composition moves
+were called eventually. Furthermore as the composition is represented by ha,b
+and 1 being the identity for composition, it is the case that for all c ∈ A, ha,b(c)
+is a weakening relation with respect to 1.
+ha,b is thus a homomorphism for A discriminating a ≰ b. Thus let h(c) for
+all c ∈ A be the disjoint union ˙�
+a≰b∈Aha,b(c). Because h is a homomorphism
+that discriminates all a ≰ b pairs, it is a representation.
+This generalises to uncountable algebras by the downward L¨owenheim Skolem
+Theorem since RWkRA is a pseudoelementary class.
+⊓⊔
+Next we show that the existence of a winning strategy for ∃ can be expressed
+by a universal ﬁrst-order sentence. For this result we deﬁne the following con-
+cepts.
+Deﬁnition 4. A term network is a network N = (N, λ) where N is a ﬁnite set
+of nodes and λ is a labelling function that maps every pair of nodes to a ﬁnite
+set of terms. We also require that for all x, y ∈ N, 1 ∈ λ(x, x) and ⊤ ∈ λ(x, y).
+For every term network N = (N, λ) we deﬁne a network N +,x,y,t = (N ∪
+{y}, λℓ) where x ∈ N, y ∈ N ⊎ {x+} (for some new node x+), t is a term in the
+language of RWkRA and for all z, w ∈ N ⊎ {x+}.
+λℓ(z, w) =
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+{1, ⊤}
+if x+ = z = w
+{⊤}
+if x+ = z ̸= w ̸= x or x+ = w ̸= z ̸= x, w ̸= y
+{t, ⊤}
+if z = x, w = y = x+
+λ(z, w) ∪ {t}
+if z = x, w = y ̸= x+
+λ(z, w)
+otherwise
+For variables a, b we deﬁne two initial term networks below.
+N 1,a,b =({x}, {(x, x) �→ {⊤, 1, a, ∼b}})
+N 2,a,b =({x, y}, {(x, x) �→ {⊤, 1}, (x, y) �→ {⊤, a},
+(y, x) �→ {⊤, ∼b}, (y, y) �→ {⊤, 1}})
+Proposition 2. For every n < ω there exists a ﬁrst-order formula σn that cor-
+responds to ∃ having a winning strategy for Γn(A).
+Proof. We show by induction that there exists a formula φn(N) for every 0 ≤
+n < ω, deﬁned for a ﬁnite term network N, with all the variables universally
+quantiﬁed that signiﬁes that the network can remain consistent for n more moves
+5
+
+of the representation game where ∃ plays conservatively, i.e., only adds the re-
+quested labels. It is easy to see that she has a winning strategy for the game if
+and only if she also has one for the conservative play.
+In the base case, φ0(N) deﬁned below signiﬁes consistency (remaining con-
+sistent for zero moves)
+φ0(N) =
+�
+x,y∈N
+�
+t∈λ(x,y)
+�
+t′∈λ(y,x)
+t ̸= ∼t′.
+In the induction case, we assume that φn(N ′), where N ′ is a term network
+with all variables universally quantiﬁed, is both necessary and suﬃcient for N ′ to
+be able to remain consistent for n moves. Then we show you can deﬁne φn+1(N)
+that extends the assumption to n + 1 moves. Although we use a, b here, the
+variable names should be unique when constructing these formulas.
+φn+1(N) =
+�
+x,y∈N
+�
+t∈λ(x,y)
+∀a, b
+�
+t ≤ a + b =⇒ (φn(N +,x,y,a) ∨ φn(N +,x,y,b))
+�
+∧
+�
+x,y∈N
+�
+t∈λ(x,y)
+∀a
+�
+φn(N +,x,y,a) ∨ φn(N +,y,x,∼a)
+�
+∧
+�
+x,y,z∈N
+�
+t∈λ(x,y)
+�
+t′∈λ(y,z)
+φn(N +,x,z,t;t′)
+∧
+�
+x,y∈N
+�
+t∈λ(x,y)
+∀a, b
+�
+t = a; b =⇒
+�
+z∈N⊎{x+}
+φn
+�
+(N +,x,z,a)+,z,y,b��
+We now have a formula φn(N) for every 0 ≤ n < ω that ensures ∃ can keep
+a universally quantiﬁed term network N consistent. Hence the formula
+σn = ∀a, b (a ≰ b =⇒ (φn(N 1,a,b) ∨ φn(N 2,a,b))
+ensures that ∃ has a winning strategy for a conservative game of length n.
+⊓⊔
+Corollary 3. Σ = {σ1, σ2, . . .} together with the axioms for cyclic distributive
+involutive semirings is a recursively enumerable theory that axiomatises RWkRA.
+3
+Frames, frame games, and ﬁnite pebble games
+In this section we present ﬁnite algebras as frames, similar to Routley-Meyer
+frames or relevance frames for relevance logic [1] and atom structures of atomic
+relation algebras [12]. We then deﬁne a modiﬁed version of the representation
+game that utilises frames.
+Finally, we deﬁne an n-pebble versions of the frame game. Analogous to the
+abstract classes of relation algebras RAω ⊆ . . . ⊆ RA3 ⊆ RA2, this gives rise to
+classes of weakening relation algebras wkRAω ⊆ . . . ⊆ wkRA3 ⊆ wkRA2. Clearly
+RAω, wkRAω are the classes of representable relation algebras and weakening
+6
+
+algebras, respectively. Furthermore, similarly to RA4, we say that wkRA4 is the
+class of weakening relation algebras.
+First, observe that the language of RwkRA does not include negation and
+hence the lattice need not be Boolean. As we will see in Section 6, the smallest
+representable non-Boolean algebra is a 4-element chain S4. Thus we cannot
+present ﬁnite weakening relation algebras using atoms. Instead, we make use
+of join-irreducibles.
+Deﬁnition 5. A non-⊥ element a of a representable weakening relation algebra
+is join-irreducible if and only if for all b, c if a = b + c then a = b or a = c. It is
+join-prime if and only if for all b, c if a ≤ b + c then a ≤ b or a ≤ c.
+Because · distributes over + we have that an element is join-irreducible if and
+only if it is join-prime. In the ﬁnite case every algebra will have join-irreducibles
+and every element is a join of join-irreducibles. (In general this is only true for
+perfect algebras. In fact, by deﬁnition, a distributive lattice is join-perfect if
+every element is a join of completely join-irreducible elements. This generalises
+the concept of atomic for Boolean algebras.)
+The element a in the result below is called the join-irreducible label of (x, y).
+Proposition 4. In a representation h of a ﬁnite representable weakening re-
+lation algebra A, for any pair (x, y) there exists a join-irreducible a ∈ A such
+that
+↑a = {s ∈ A | (x, y) ∈ h(s)}.
+Proof. A representation h maps joins to unions, hence the set {s | (x, y) ∈ h(s)}
+is upward closed and if (x, y) ∈ h(a+ b) then it is also in h(a) or h(b). Hence the
+base set of the representation is itself a union of upward closures of join-primes.
+Now if it is above ↑a and ↑b then it must be the case that (y, x) is in neither
+h(∼a) nor h(∼b) and thus (x, y) ∈ h(∼(∼a + ∼b)) = h(a · b). Thus the meet of
+all such join-irreducibles must also be a non-⊥ element that is join-prime and
+below all elements in the set.
+⊓⊔
+Although the converse operation is not deﬁned in our language, we can use
+the following trick to deﬁne a useful unary operation on the join-irreducibles.
+Deﬁnition 6. For every join-irreducible a in a ﬁnite algebra, deﬁne ˆa = ∼ �
+a≰s s
+where � is with respect to join (+).
+The join �
+s≰t t, deﬁned for all s in a ﬁnite algebra A, is usually denoted
+κ(s). If we take s ≤ s′ ∈ A we have s ≰ t ⇒ s′ ≰ t and thus κ(s) ≤ κ(s′), hence
+κ is order preserving. Because ∼ is order reversing and κ is order preserving we
+have that ˆ is order reversing.
+Proposition 5. In any ﬁnite bounded distributive involutive additive algebra A,
+if a is a join-irreducible, so is ˆa.
+7
+
+Proof. It is well known that κ(a) of a join-irreducible a in a lattice is meet
+irreducible and because ∼ is order reversing, that means that ˆa = ∼κ(a) is a
+join-irreducible.
+⊓⊔
+Proposition 6. If a pair (x, y) in a representation has the join-irreducible label
+a, then (y, x) has label ˆa. Moreover, ˆˆa = a.
+Proof. ∼s ∈ h(y, x) if and only if s /∈ h(x, y), i.e. a ≰ s. Thus, by the argument
+from Proposition 4 the join-irreducible label of (y, x) can be written as �
+a≰s ∼s
+where � is with respect to meet (·) and this is equivalent to ∼ �
+a≰s s by the
+De Morgan equivalence.
+⊓⊔
+Finally to characterise composition, we need to deﬁne a ternary predicate,
+similar to the set of allowed triangles in relation algebras.
+Deﬁnition 7. Let A be a ﬁnite bounded cyclic involutive dℓ-magma and deﬁne
+a ternary relation R on the set of join-irreducibles of A by
+R(a, b, c) if and only if a ≤ b; c.
+For relation algebras with atoms a, b, c the Peircian triangle law says that
+a ≤ b; c ⇐⇒ ˆa ≤ ˆc;ˆb ⇐⇒ b ≤ a; ˆc ⇐⇒ ˆb ≤ c; ˆa ⇐⇒ c ≤ ˆb; a ⇐⇒ ˆc ≤ ˆa; b.
+As we will see in the next section, this law does not hold for the class of repre-
+sentable weakening relation algebra frames. However, atom structures for rela-
+tion algebras generalise to the weakening setting as follows.
+Deﬁnition 8. A relevance frame F = (F, I, ≤, R, ˆ) is a structure with a carrier
+set F, a unary predicate I, a partial order predicate ≤, a ternary predicate R,
+and an order-reversing involution operation ˆ where for all a, b, c, d in F
+(1) a ≤ b ⇔ ∃e : I(e) ∧ R(a, e, b)
+(2) a ≤ b ⇔ ∃e : I(e) ∧ R(a, b, e)
+(3) a ≤ b ∧ R(b, c, d) ⇒ R(a, c, d)
+(4) b ≤ c ∧ R(a, b, d) ⇒ R(a, c, d)
+(5) c ≤ d ∧ R(a, b, c) ⇒ R(a, b, d)
+Proposition 7. A relevance frame F = (F, I, ≤, R, ˆ) deﬁnes a bounded invo-
+lutive unital dℓ-magma A = (A, ·, +, ⊥, ⊤, ; , 1, ∼) by taking (F, ≤) as the join-
+irreducibles of the lattice with their partial order and for all s, t ∈ A
+1 =
+�
+I(a)
+a,
+∼s =
+�
+ˆa≰s
+a,
+s; t =
+�
+b≤s,c≤t,R(a,b,c)
+a
+where a, b, c ∈ F.
+8
+
+Proof. A bounded distributive lattice can be deﬁned by its join-irreducibles and
+their ordering. To show that the magma is unital, we can see that no term
+of the join deﬁning the composition with the identity is above the identity by
+Deﬁnition 8(1)(2) and because ≤ is reﬂexive, there will exist, for every join-
+irreducible a term in the composition with the identity (on either side) equal to
+that join-irreducible. Thus 1 is precisely the identity. Composition is additive by
+deﬁnition. ∼ is an involution because a join-irreducible a ≤ ∼(∼s) if and only if
+ˆa ≰ ∼s which is true if and only if a = ˆˆa ≤ s. For the De Morgan equivalence,
+a ≤ ∼(∼s + ∼t) if and only if ˆa ≰ ∼s + ∼t, or equivalently ˆa ≰ ∼s ∧ ˆa ≰ ∼t
+which by deﬁnition is true if and only if a = ˆˆa ≤ s and a = ˆˆa ≤ t, or simply
+a ≤ s · t.
+⊓⊔
+Proposition 8. Every ﬁnite bounded cyclic involutive unital dℓ-magma has a
+unique equivalent relevance frame.
+Proof. Finite distributive lattices are determined by their poset of join-irreducibles,
+and from Proposition 5 they have a unique ˆ deﬁned on the join-irreducibles.
+The mapping to R is unique as Deﬁnition 8(3)(4)(5) ensure that R is downward
+closed in the ﬁrst argument and upward closed in the other arguments.
+⊓⊔
+Proposition 9. For ﬁnite algebras and ﬁnite frames, the mappings described in
+the previous two lemmas are inverses of each other.
+Proof. Finite distributive lattices correspond uniquely to their posets of join-
+irreducibles. The preservation of identity and the composition follow trivially
+from the deﬁnition. For ∼, ˆ observe that ∼κ(a) = ˆa ≰ s if and only if ∼s ≰
+κ(a) = �
+a≰ t, or equivalently a ≤ ∼s. For the converse note that ∼κ(a) =
+�
+ˆb≰κ(a) b = �
+a≤ˆb b = �
+b≤ˆa b = ˆa.
+⊓⊔
+Although we have deﬁned these frames for ﬁnite algebras, we can say that
+a possibly inﬁnite algebra is frame-deﬁnable if it can be deﬁned by a relevance
+frame. In the context of relation algebras, this corresponds to complete and
+atomic relation algebras. Similarly to that class, we will show that every non-
+frame deﬁnable algebra embeds into a frame deﬁnable algebra with equivalent
+representability.
+Proposition 10. Let A be a bounded cyclic involutive unital dℓ-magma. Then
+a frame F(A) can be deﬁned by taking the carrier set of all prime ﬁlters U ⊆ A,
+with U ≤ V if and only if V ⊆ U, ˆU = {∼s | s ∈ A \ U}, I(U) ⇔ 1 ∈ U and
+R(U, V, W) if and only if for all v ∈ V, w ∈ W we have v;w ∈ U.
+Proof. ≤ is clearly a partial order, for closure of ˆ note that A \ U is a prime
+ideal, so by the order reversing property of ∼, ˆU is a prime ﬁlter. Furthermore,
+all the unitality conditions are trivially preserved and by U ′ ≤ U if and only if
+U ⊆ U ′ we have downward closure of R in the ﬁrst argument and upward closure
+in the other two.
+⊓⊔
+9
+
+Proposition 11. A is representable if and only if the algebra deﬁned by F(A)
+is a representable weakening relation algebra. This algebra is called the canonical
+extension of A.
+Proof. Because A is a subalgebra of the algebra deﬁned by F(A), we know that
+the right to left implication is true. For the other direction, if A is representable,
+every (x, y) will have a prime ﬁlter U such that (x, y) ∈ h(a) if and only if
+a ∈ U to represent the lattice correctly. The prime ﬁlter deﬁning (y, x) will be
+exactly ˆU. The identity is also correctly represented as it is only above those
+prime ﬁlters that include it. Finally for ; we have shown that it suﬃces for ∃ to
+have a winning strategy for a game of any ﬁnite length. Thus at any point we
+need to show that the compositions are correctly represented if and only if all
+compositions ﬁnite meets are properly included in the relevant prime ﬁlter.
+⊓⊔
+Deﬁnition 9. A frame network N = (N, λ) is deﬁned for a frame F = (F, I, ≤
+, R, ˆ) with N being the set of nodes and λ : N 2 → F is the labelling function.
+The network is said to be consistent if and only if for all x, y ∈ N we have
+λ(x, y) = �
+λ(y, x) and for all x, y, z ∈ N we have R(λ(x, y), λ(x, z), λ(z, y)).
+We say for two frame networks N = (N, λ), N ′ = (N ′, λ′) that N ⊆ N ′
+if and only if N ⊆ N ′ and λ = λ′ ↾N 2 where ↾ denotes the restriction of the
+function to the domain in the subscript.
+Deﬁnition 10. An inﬁnite length frame game G(F) where F = (F, I, ≤, R, ˆ)
+is a relevance frame is deﬁned for two players ∀ and ∃.
+The game starts with ∀ picking a join-irreducible a and ∃ must return a frame
+network N0 = (N0, λ0) such that there exists x, y ∈ N0 such that λ0(x, y) = a.
+At the ith move for 0 < i < ω ∀ picks a pair x, y ∈ Ni−1 and a pair of
+join-irreducibles a, b such that R(λ(x, y), a, b) and for all a′ ≤ a, b′ ≤ b ∈ Ni−1 if
+R(λ(x, y), a′, b′) then a = a′ and b = b′. ∃ must return a network Ni = (Ni, λi)
+such that Ni−1 ⊆ Ni and ∃z ∈ Ni such that λ(x, z) = a, λ(z, y) = b.
+∀ wins if and only if ∃ returns an inconsistent network at any point in the
+game.
+Proposition 12. ∃ has a winning strategy for G(F(A)) if and only if she has
+a winning strategy for Γω(A).
+Proof. It suﬃces to prove that she has a winning strategy for the play where all
+moves are called eventually. Thus if she has a winning strategy for Γω(A), we
+know that the limit network will have the relevant prime ﬁlters as labels. Thus
+if a is the initial join-irreducible ∃ can map all her moves from the limit network
+of the play where the initialisation pair was a ≰ κ(a).
+For the converse, assume she has a winning strategy for G(F(A)). To respond
+to the initialisation move with s ≰ t there will exist a join-irreducible a such
+that a ≤ s but a ≰ t or rather t ≤ κ(a) so returning the initial network for a
+will ensure that a ≤ s and ˆa ≤ ˜t. Any witness move called can be responded to
+by minimal join-irreducible pairs, which makes any other witness moves called
+by ∀ redundant.
+⊓⊔
+10
+
+We now deﬁne for every 2 ≤ n ≤ ω the n-pebble equivalent version of the
+frame game as follows.
+Deﬁnition 11. The n-pebble inﬁnite move game Gn(F) for a frame F is deﬁned
+exactly as G(F), except before ∀ calls a witness move, he takes N ′ ⊆ Ni−1 such
+that |N ′| ≤ n and then proceeds to call the witness move.
+In particular, the frame game G is equivalent to Gω. Next we deﬁne wkRAn
+and wkRA analogous to RAn, the variety of all n-dimensional relation algebras,
+and RA, the variety of all (4-dimensional) relation algebras [13], [8].
+Deﬁnition 12. The class wkRAn is the class of all bounded cyclic involutive
+unital dℓ-magmas A for which ∃ has a winning strategy for Gn(F(A)). The
+class of weakening relation algebras wkRA is deﬁned as wkRA4.
+It follows that wkRAω is equivalent to RwkRA and wkRAω ⊆ . . . ⊆ wkRA4 ⊆
+wkRA3 ⊆ wkRA2.
+4
+Axiomatisation of the abstract classes
+In this section we provide ﬁnite axiomatisations for wkRA2 and wkRA3. We leave
+open the problem of whether, similarly to RA4 the axiomatisation for wkRA4
+consists of axioms of wkRA3 and associativity of ;.
+We begin by axiomatising wkRA2. This will be done using the axiomatisation
+of bounded cyclic involutive unital dℓ-magmas together with the theory Φ2,
+deﬁned below.
+Deﬁnition 13. Let Φ2 be the ﬁrst order theory given by the following quasiequa-
+tions:
+(1) s · ∼s ≤ 0
+(2) s ≤ t ⇔ s; ∼t · 1 ≤ 0
+(3) s ≤ t;u ∧ s;t ≤ ∼u ⇒ s · 1 ≤ 0
+(4) s ≤ t;u ∧ u;s ≤ ∼t ⇒ s · 1 ≤ 0
+(5) s ≤ t;u ∧ (s · 1 · t;v) + (1 · s · ∼v;u) ≤ 0 ⇒ s · 1 ≤ 0
+Before we prove the soundness and completeness, we introduce a ternary
+predicate for the language of frames Rmin from the equivalence below.
+Rmin(a, b, c) ⇔ R(a, b, c) ∧ ∀b′, c′ : (R(a, b′, c′) ∧ b′ ≤ b ∧ c′ ≤ c ⇒ b′ = b ∧ c′ = c)
+Note that since the union of a chain of prime ﬁlters is again a prime ﬁlter, frames
+of the form F(A) have the property that R(a, b, c) can be reﬁned to Rmin(a, b′, c′)
+for some prime ﬁlters b′ ≤ b and c′ ≤ c.
+Lemma 13. Let A be a bounded cyclic involutive unital dℓ-magma. A |= Φ2 if
+and only if F(A) satisﬁes
+11
+
+(1) ∀a∃b : I(b) ∧ ˆb = b ∧ R(b, a, ˆa)
+(2) ∀a, b : I(a) ∧ ˆa = a ∧ R(a, b,ˆb) ⇒ R(b, a, b)
+(3) ∀a, b : I(a) ∧ ˆa = a ∧ R(a, b,ˆb) ⇒ R(ˆb,ˆb, a)
+(4) ∀a, b, c : I(a) ∧ ˆa = a ∧ Rmin(a, b, c) ⇒ b = ˆc
+Proof. For the left to right implication, observe that for any join-irreducible a,
+we know that a ≰ κ(a) so (a; ∼κ(a) · 1) ≰ 0 by Φ2(2). Thus there must exist
+a join-irreducible b ≤ 1, b ≰ 0, b ≤ a;ˆa. Suppose b ̸= ˆb. Then there would exist
+some b ≤ s,ˆb ≰ s. Because ˆˆb = b we know that b ≤ ∼s and thus b ≤ s · ∼s ≤ 0,
+contradicting Φ2(1) and we have proven (1) follows from Φ2. For (2) assume we
+have a ≤ 1, ˆa = a then a ≰ ∼1 = 0. Thus a = a · 1 ≰ 0 and a ≤ b;∼κ(b) implies
+a;b ≰ ∼∼κ(b) or simply a ≤ a;b. By a similar argument we get (3). Finally if
+a ≤ b;c and a = a·1 ≤ b;c·1 ≰ 0 we have b ≰ ∼c. We also have that a·1 = a ≰ 0
+and a ≤ b;c so a · κ(b);c ≰ 0 or a · b;ˆb ≰ 0. In the former case that means that
+κ(b);c ≰ 0 and thus κ(b) ≤ ∼c or c ≤ ˆb and we are done. In the latter case
+it means that there exists a join-irreducible a′ ≤ a such that a ≰ 0 and thus
+a′ = ˆa′ as well as a′ ≤ b;ˆb ≤ b; c by monotinicity. Because a′ ≤ a ≤ ˆa′ = a′ we
+have a = a′ and by minimality ˆb = c.
+For the right to left implication note that if s · ∼s ≰ 0 then there exists some
+a ≤ s · ∼s not below 0. Thus ˆa ≤ 1 and we know there exists a join-irreducible
+b = ˆb, b ≤ a; ˆa ≤ (s·∼s);1 = s·∼s and that contradicts b = ˆb. Assume s ≰ t. That
+is true if there exists a join-irreducible a such that a ≤ s, ˆa ≤ ∼t. Thus there
+exists a join-irreducible b = b · 1 ≰ 0 below 1 · a; ˆa ≤ 1 · s;∼t and we conclude
+1 · s;∼t ≰ 0. If 1 · s;∼t ≰ 0 then there exist join-irreducibles a, b, c such that
+I(a), a = ˆa, b ≤ s, c ≤ ∼t and b, c also being minimal and hence ˆb = c. Therefore
+ˆb ≤ ∼t or simply s ≰ t. s·1 ≰ 0∧s ≤ t;u ⇒ s;t ≰ ∼u follows directly from (2) and
+its dual directly from (3). Finally s·1 ≰ 0 and s ≤ t; u iﬀ there exist some a, b, c in
+the corresponding frame such that a ≤ s · 1, b ≤ t, c ≤ u, I(a), ˆa = a, Rmin(a, b, c)
+and thus ˆb = c by (4). Observe that for every v either b ≤ v or ˆb ≤ ∼v and thus
+a ≤ t; v or a ≤ ∼v;u and the join of the two terms is not below 0.
+⊓⊔
+Theorem 14. wkRA2 is axiomatised by the basic axioms for bounded cyclic in-
+volutive unital dℓ-magmas and Φ2.
+Proof. By Lemma 13 this axiomatisation is equivalent to the frame conditions,
+enumerated (1)–(4). First we show these are sound for the two pebble game.
+If there existed a join-irreducible a with no b, I(b),ˆb = b with R(b, a, ˆa), then
+∀ would win on initialisation with a because if λ(x, y) = a, no consistent b
+would exist for λ(x, x). We show (4) next. If this didn’t hold for some a, b, c
+then ∀ could start by asking a on initial move. By order reversing of ˆ and the
+identity, a is the only join-irreducible to be set as λ(x, x) where λ(x, y) = a. For
+the second move, ∀ calls the witness b; c on (x, x) and we get an inconsistency
+because b ̸= ˆc. For (2) and (3) see that if R(a, b,ˆb) we have Rmin(a, b,ˆb) by order
+reversing properties of ˆ and (4). Thus if ∀ again starts by forcing λ(x, x) = a
+then calling the witness b;ˆb then both R(b, a, b), R(ˆb,ˆb, a) must hold to keep the
+network consistent.
+12
+
+To show completeness, it suﬃces to say that ∃ can respond to any initialisa-
+tion with a by returning a network with two nodes x, y with λ(x, y) = a, λ(y, x) =
+ˆa and by (1) there exists a b for a and b′ for ˆa to be set as λ(x, x) and λ(y, y)
+respectively and by (2)(3) all other triangles are also consistent. A witness move
+can only be called on a reﬂexive node (x, x) and that means that by (2)(3)(4)
+any witness will be consistent and by the same reasoning as with initialisation,
+∃ can put a label on λ(y, y) and keep the network consistent.
+⊓⊔
+In order to axiomatise wkRA3 we only need to add two well known axioms as
+well as a set of quasiequations. The ﬁrst axiom is called rotation for involutive
+semirings and the second one was found by Maddux in [15] as an axiom that
+holds for binary relations, but not for relevance logic frames.
+Deﬁnition 14. Let Φ3 be the ﬁrst order theory containing all the formulas in
+Φ2 as well as
+(1) s; t ≤ ∼u ⇒ t; u ≤ ∼s
+(2) s · t;u ≤ ((s;v) · t);u + t;(u · ∼v)
+(3) 1 · ∼s′;s · t;∼t′ ≤ 0 ⇒ s;t ≤ (s · s′);t + s;(t · t′)
+(4) 1 · s · 0 = ⊥ ⇒ (s · 1);(t;u) ≤ ((s · 1);t);u
+(5) 1 · u · 0 = ⊥ ⇒ (s;t);(u · 1) ≤ s;(t;(u · 1))
+Lemma 15. Let A be a bounded cyclic involutive unital dℓ-magma. A |= Φ3 if
+and only if for F(A) all the formulas from Lemma 13 hold as well as
+(1) ∀a, b, c : Rmin(a, b, c) ⇒ R(b, a, ˆc)
+(2) ∀a, b, c : R(a,ˆb, ˆc) ⇒ R(b, ˆc, ˆa)
+(3) ∀a, b, c : Rmin(a, b, c) ⇒ ∃d : d = ˆd ∧ I(d) ∧ R(d,ˆb, b) ∧ R(d, c, ˆc)
+(4) ∀a, b, c, d : d = ˆd ∧ I(d) ∧ R(a, d, a) ∧ Rmin(a, b, c) ⇒ R(b, d, b)
+(5) ∀a, b, c, d : d = ˆd ∧ I(d) ∧ R(a, a, d) ∧ Rmin(a, b, c) ⇒ R(c, c, d)
+Proof. For the left to right implication of (1) if a, b, c are join-irreducibles with
+a ≤ b;c as well as the minimality condition for b, c then see that a = a · b;c ≤
+(a;ˆc · b);c + b;(c · κ(c)). c · κ(c) is strictly below c and due to minimality of
+b, c for this composition a ≰ b;(c · κ(c)). Thus a ≤ (a;ˆc · b);c and again by
+minimality a;ˆc · b = b or simply R(b, a, ˆc). For (2) observe that a ≰ ˆb; ˆc is the
+same as ∼κ(b);∼κ(c) ≤ κ(a) and by rotate we get ∼κ(c);∼κ(a) ≤ κ(b) and
+∼κ(a);∼κ(b) ≤ κ(c) so R(a,ˆb, ˆc), R(b, ˆc, ˆa), R(c, ˆa,ˆb) are equivalent. For (3) if
+Rmin(a, b, c) then we know b;c ≰ (b·κ(b));c+b;(c·κ(b)) and thus 1·∼s′;s·t;∼t′ ≰ 0
+and we can ﬁnd a d satisfying I(d), ˆd = d, R(d,ˆb, b), R(d, c, ˆc). For (4) see that
+1 · d · 0 = ⊥ and thus a ≤ d;a ≤ d;(b;c) ≤ (d;b);c. By minimality b = d;b. By a
+similar argument we get (5).
+For the right to left implication, if s;t ≤ ∼u observe that for all join-
+irreducibles a, b, c such that a ≤ s, b ≤ t, c ≤ u we have a;b ≤ κ(ˆc) and thus
+¬R(ˆc, a, b) and by (2) we have ¬R(ˆa, b, c) and thus b;c ≤ κ(ˆa) = ∼a. If for all
+join-irreducibles a, b, c below s, t, u respectively that holds then t;u ≤ ∼s. To
+show s · t;u ≤ ((s;v) · t);u + t;(u · ∼v) take any a ≤ s · t;u and some minimal b, c
+13
+
+witnessing the t;u composition. Then all v will either have c ≤ ∼v or ˆc ≤ v, in
+either case the term is above a by monotonicity. Finally if s;t ≰ (s · s′);t · s;(t · t′)
+it means that s;t is non-empty and as such there exists some a ≤ s;t and some
+Rmin(a, b, c) and as such b ≰ s′ and c ≰ t′ and thus ˆb; b ≤ ∼s′;s and c;ˆc ≤ t;∼t′
+and there exists a d ≰ 0 such that d ≤ 1·∼s′;s·t;∼t′ and therefore the term can-
+not be below 0. Take any join-irreducible a ≤ (s · 1); t;u. There will exist a self-ˆ
+join-irreducible d ≤ s·1 such that d ≤ d; a and a minimal b, c below t, u such that
+a ≤ b; c and so we have by (4) b ≤ d; b and thus a ≤ b;c ≤ (d;b);c ≤ ((s · 1);t);u.
+The dual is shown similarly from (5).
+⊓⊔
+Theorem 16. wkRA3 is axiomatised by the basic axioms for bounded cyclic in-
+volutive unital dℓ-magmas and Φ3.
+Proof. First we show that all the formulas from Lemma 15 are sound. If we
+have a, b, c such that Rmin(a, b, c) then ∀ calls a on initialisation and calls the
+witness Rmin(a, b, c) on the λ(x, y) = a and ∃ must return such a network where
+λ(x, z) = a, λ(y, z) = ˆc so R(b, a, ˆc) must hold for consistency and we have
+(1). For (2) assume without loss that we have R(a,ˆb, ˆc) so there must be some
+minimal ˆb′ ≤ ˆb, ˆc′ ≤ ˆc to call the witness on the initial pair a. Observe that for
+consistency b ≤ b′ ≤ ˆc′; ˆa ≤ ˆc; ˆa by monotonicity. For (3) if ∀ initialises with a
+and calls the b, c witness, ∃ needs a join-irreducible d to put on the reﬂexive edge
+of the added node.
+From Lemma 13, Theorem 16 we have that ∃ can survive the initial move
+and we only need to examine the two possible witness moves, that on a non-
+reﬂexive edge in a two-node network and that on a reﬂexive edge. If a witness
+move Rmin(a, b, c) is called on a non-reﬂexive edge (x, y), check that all Peircian
+transformations of this triangle hold. By (1) we have R(b, a, ˆc) and through (2)
+we get R(ˆb, c, ˆa), R(ˆc, ˆa, b) from R(a, b, c) and R(ˆa, ˆc,ˆb), R(c,ˆb, a) from R(b, a, ˆc).
+For the reﬂexive edge on (z, z) you can see that ∃ can add λ(z, z) = d from(3)
+and by similar reasoning to Theorem 16 all triangles including (z, z) are con-
+sistent. Finally let λ(x, x) = d. By (4) R(b, d, b) and by (2) R( ˆd = d, b,ˆb). The
+consistency of other triangles follows from formulas in Lemma 13. Similarly we
+get consistency for λ(y, y). For the reﬂexive witness Rmin(d, a, ˆa) on (x, x) ob-
+serve due to order reversing of ˆ, ∃ can either ﬁnd a join-irreducible c such that
+Rmin(λ(x, y), a, c) or Rmin(λ(y, x), c, ˆa) and ∃ can use the same strategy as for
+the non-reﬂexive witness move.
+⊓⊔
+To axiomatise the class wkRA = wkRA4 we would at least need to add associa-
+tivity for composition. For RA, it is precisely the axioms for RA3 and composition
+that axiomatise RA4, however, whether this also holds for wkRA remains open.
+Problem 17. What axioms are necessary to axiomatise wkRA? Is it ﬁnitely ax-
+iomatisable?
+Problem 18. Let n > 4. RAn is not ﬁnitely axiomatisable [8]. Is the same true
+for wkRAn?
+14
+
+5
+Representable diagonal weakening relation algebras
+form a discriminator variety
+In this section we deﬁne representable diagonal weakening relation algebras as
+those relation algebras where 1 can be represented as an antichain. Thus in this
+section when we talk about the concrete binary relation 1, we mean the diagonal
+on X. The algebras with this property are the members of RwkRA that satisfy
+the identity 1 · 0 = ⊥.
+We show that the simple representable diagonal relation algebras have a
+discriminator term. A neat consequence is that, unlike representable weaken-
+ing relation algebras, representable diagonal weakening relation algebras can be
+deﬁned by an equational theory.
+Lemma 19. For all R ⊆ X2 we have 1 ·
+�
+R;(R ·∼R)
+�
+= ⊥ = 1 ·
+�
+∼R;(R ·∼R)
+�
+.
+Proof. Suppose there exists (x, x′) ∈ 1 · (R;(R · ∼R)). Because (x, x′) ∈ 1 we
+have x = x′. Thus there must exist a y to witness the composition by having
+(x, y) ∈ R, (y, x) ∈ R · ∼R. This means that (x, y) ∈ R and (y, x) ∈ ∼R and we
+have reached a contradiction.
+The second equation can be proven by a similar argument or by substitution
+of R with ∼R, the involution law, and the commutativity of meet.
+⊓⊔
+Let d1(R, S) = 1 ·
+�
+R;(S · ∼S)
+�
+and d2(R, S) = 1 ·
+�
+∼S;(R · ∼S)
+�
+.
+Lemma 20. If R \ S ̸= ∅ for R, S ⊆ X2 then d1(R, S) + d2(R, S) ̸= ⊥.
+Proof. Assume (x, y) ∈ R \ S and consider the two cases, (y, x) ∈ S and (y, x) /∈
+S. In the ﬁrst case, because (x, y) /∈ S we also have (y, x) ∈ ∼S and consequently
+(y, x) ∈ S · ∼S. Hence (x, x) ∈ R;(S · ∼S) and also by deﬁnition in 1 and thus
+(x, x) ∈ d1(R, S).
+In the second case (y, x) /∈ S and therefore (x, y) ∈ ∼S. Because (x, y) /∈ S,
+(y, x) /∈ ∼S. By composition (y, y) ∈ ∼S; (R·∼S) and by reﬂexivity of 1 we also
+have (y, y) ∈ 1 ·
+�
+∼S;(R · ∼S)
+�
+.
+In either case we have that at least one of d1(R, S), d2(R, S) is nonempty and
+thus their join is always nonempty given R \ S ̸= ∅.
+⊓⊔
+Theorem 21. Simple diagonal weakening relation algebras have a term d(a, b, c)
+such that
+d(a, b, c) =
+�
+c
+if a = b
+a
+otherwise
+Proof. It is easy to see that in simple weakening relation algebras ⊤; s; ⊤ =
+⊤ if s ̸= ⊥ and ⊤; s; ⊤ = ⊥ otherwise. By the lemmas above, we have for
+representable simple algebras that a = b if and only d1 + d2 = ⊥, where di =
+di(a, b) + di(b, a) for i = 1, 2. Thus d(a, b, c) = ⊤; (d1 + d2); ⊤ · a + ∼(⊤; (d1 +
+d2); ⊤) · c will equal to c if a = b and a otherwise.
+⊓⊔
+There are several ways to prove the following corollary. We outline the argu-
+ment that generates a recursively enumerable equational theory.
+15
+
+Corollary 22. Representable diagonal weakening relation algebras form a dis-
+criminator variety.
+Proof. The representation game deﬁned for weakening relation algebras only
+needs an additional move where ∃ is requested add 1 to λ(y, x) if 1 ∈ λ(x, y) and
+this game gives rise to a similar style of a recursive axiomatisation as presented
+in Proposition 2. If all variables are given unique names, the universal quantiﬁers
+can also be moved to the begining of all these formulas. Observe that although
+these formulas apply to all algebras, the game is played on the homomorphic
+image of the algebra where ⊤ maps to ⊤; a; ⊤ where σn = s ≰ t ⇒ (φn(N 1,s,t)∨
+φn(N 2,s,t)). Thus we can construct a term from any universally quantiﬁed ﬁrst
+order formula that is equal to ⊤; a; ⊤ if and only if the formula is true and ⊥
+otherwise. For equations t = t′ we take ⊤; a; ⊤ · ∼d(t, t′, ⊤; a; ⊤). If a term t
+corresponds to a formula, then ∼t · ⊤; a; ⊤ corresponds to its negation and for
+disjunctions we can take the join of the corresponding terms. Thus every formula
+σn has an equivalent equation.
+⊓⊔
+6
+Representing associative members of wkRA3 with
+weakening relations
+Sugihara monoids are commutative distributive idempotent involutive residuated
+lattices. This variety is semilinear, i.e., generated by linearly ordered algebras,
+and the structure of these algebras is well known. In particular, the Sugihara
+monoid Sn is a chain with n elements {a−k, a−k+1, . . . , a−1, a0, a1, . . . , ak−1, ak}
+if n = 2k + 1 is odd, and otherwise for even n, Sn = Sn+1 \ {a0}. The involution
+operation is given by ∼ai = a−i and the multiplication is ai;aj = a− max |i|,|j|. It
+follows that in the odd case the identity element is 1 = a0 and in the even case
+it is 1 = a1.
+Note that S2 is the 2-element Boolean algebra and that for even n, there is
+a surjective homomorphism from Sn to Sn−1 that identiﬁes a1 and a−1.
+It is proved in [14] that the even Sugihara chains can be represented by
+algebras of weakening relations. For S2 this is clear since S2 ∼= Rel(1). For S4 an
+inﬁnite base set is needed with a dense order. E.g., we can take (Q, ≤) be the
+poset of rational numbers with the standard order and check that S4 ∼= {∅, <, ≤
+, Q2} is a representation in Wk(Q, ≤).
+It follows from the consistency of networks that no nontrivial member of
+wkRA2 has an element that satisﬁes a = ∼a. Hence any ﬁnite member of wkRA
+has an even number of elements. In particular, the odd Sugihara chains do not
+have a representation by weakening relations. However they are in the variety
+generated by all algebras of weakening relations since they are homomorphic
+images of even Sugihara chains. This shows that RWkRA is not closed under
+homomorphic images, so it is a proper quasivariety.
+Let 2 = {0, 1} be the two element chain with 0 < 1. The algebra wk(2) is
+shown in Figure 2, and it has the following six elements: ∅, {(0, 1)}, {(0, 0), (0, 1)},
+{(0, 1), (1, 1)}, ≤, 2 × 2.
+16
+
+The point algebra P shown in Figure 1 (see also [7]) is a representable re-
+lation algebra with 3 atoms idQ, <, > where < is the strict order on the ra-
+tional numbers Q. It has two weakening subalgebras: S4 = {∅, <, ≤, ⊤} and
+W6,1 = {∅, idQ, <, ≤, <∪>, ⊤}. Like the point algebra, both of these algebras
+can only be represented on an inﬁnite set. Note that W6,1 is diagonally repre-
+sentable, while S4 is not.
+idQ
+>
+≥
+∅
+P
+<
+<∪>
+≤
+⊤ = Q2
+∅
+S4
+<
+≤ = ∼<
+⊤ = Q2
+idQ
+∅
+W6,1
+< = ∼≤
+<∪> = ∼idQ
+≤
+⊤ = Q2
+Fig. 1. The point algebra P, the weakening subalgebra S4 and the diagonally repre-
+sentable weakening subalgebra W6,1.
+Since wkRA3 is ﬁnitely axiomatised, one can use a model ﬁnder such as
+Mace4 [16] to compute all members of cardinality n for small values of n. Up to
+isomorphism there are 14 algebras with 6 elements or fewer in wkRA3 such that
+; is associative, shown in Figure 2. We now brieﬂy describe their representations
+by weakening relations.
+The ﬁrst 5 are symmetric representable relation algebras, hence they are
+diagonally representable weakening relation algebras.
+As mentioned above, the Sugihara algebra S4 and the algebra W6,1 are
+representable as subalgebras of the ∼-reduct of the point algebra (Figure 1).
+The algebra W6,2 is representable as ∼-subreduct of the complex algebra of Z7,
+where the element a = {1, 2, 4} and 1 = {0}.
+W6,3 is subdirectly embedded in a direct product of two copies of S4, hence
+it is representable over the union of two disjoint copies of Q.
+Similarly W6,4 is represented over X = ({0} × Q) ∪ ({1} × Q) with order
+(i, p) ≤ (j, q)
+⇐⇒ p < q or p = q, i = j. The identity 1 maps to ≤ and the
+element a maps to the relation {((i, p), (i, q)) | i = 0, 1, p < q}.
+The representation of W6,5 requires the union of {i} × Q for i ∈ {0, 1, 2}.
+The partial order ≤ is deﬁned in the same way and a is mapped to the relation
+{((i, p), (i, q)) | i = 0, 1, 2, p < q}.
+Finally W6,6 is represented over X = ({0} × Q) ∪ ({1} × Q) with order
+(i, p) ≤ (j, q) ⇐⇒ i = j and p ≤ q. The identity 1 maps to ≤ and the element
+a maps to the relation {((i, p), (i, q)) | i = 0, 1, p < q}.
+17
+
+1
+0 = 1
+2
+1
+0
+22
+1
+∼a
+a
+0
+A2
+0
+1
+02
+A3
+02
+0
+1
+S4
+1
+0
+W6,1
+02
+0
+∼a
+a
+1
+W6,2
+02
+0
+∼a
+a
+1
+W6,3
+1
+∼a
+a
+0
+W6,4
+∼a
+0
+02
+1
+0;a
+a
+W6,5
+∼a
+02
+0
+1
+0;a
+a
+W6,6
+02
+∼a
+0;a
+0
+1
+a
+wk(2)
+1
+∼a
+a
+0
+02
+S6
+∼a
+1
+0
+a
+Fig. 2. All algebras in wkRA4 up to 6 elements. Black nodes denote idempotent ele-
+ments (x;x = x) and 02 = 0;0.
+We gratefully acknowledge a very useful conversation with Roger Maddux
+regarding relevance frames, relevance logic and its connections with relation
+algebras. In particular, formulas (3.101), (3.102) in [15] provided key insights
+into the axiomatisation of wkRA3.
+References
+1. Bimb´o, K., Dunn, J.M., Maddux, R.D.: Relevance logics and relation algebras.
+Rev. Symb. Log. 2(1), 102–131 (2009), doi.org/10.1017/S1755020309090145
+2. Galatos,
+N.,
+Jipsen,
+P.:
+Distributive
+residuated
+frames
+and
+generalized
+bunched
+implication
+algebras.
+Algebra
+Universalis
+78(3),
+303–336
+(2017),
+doi.org/10.1007/s00012-017-0456-x
+3. Galatos,
+N.,
+Jipsen,
+P.:
+The
+structure
+of
+generalized
+BI-algebras
+and
+weakening
+relation
+algebras.
+Algebra
+Universalis
+81(3),
+35
+(2020),
+doi.org/10.1007/s00012-020-00663-9
+4. Galatos, N., Jipsen, P.: Weakening relation algebras and FL2-algebras. In: Fahren-
+berg, U., Jipsen, P., Winter, M. (eds.) Relational and Algebraic Methods in Com-
+puter Science. pp. 117–133. Springer International Publishing, Cham (2020)
+5. Givant, S.: Advanced Topics in Relation Algebras, vol. 2. Springer International
+Publishing (2017)
+6. Givant, S.: Introduction to Relation Algebras, vol. 1. Springer International Pub-
+lishing (2017)
+7. Hirsch, R.: Relation algebras of intervals. Artiﬁcial Intelligence 83(2), 267–295
+(1996), doi.org/10.1016/0004-3702(95)00042-9
+8. Hirsch, R., Hodkinson, I.: Relation algebras by games. Elsevier (2002)
+18
+
+9. Jipsen, P.: Relation algebras, idempotent semirings and generalized bunched im-
+plication algebras. In: Relational and algebraic methods in computer science, Lec-
+ture Notes in Comput. Sci., vol. 10226, pp. 144–158. Springer, Cham (2017),
+doi.org/10.1007/978-3-319-57418-9_9
+10. Kurz, A., Velebil, J.: Relation lifting, a survey. Journal of Logical and Algebraic
+Methods in Programming 85(4), 475–499 (2016)
+11. Maddux, R.: Relation Algebras, vol. 13. Elsevier (2006)
+12. Maddux, R.: Some varieties containing relation algebras. Trans. Amer. Math. Soc.
+272(2), 501–526 (1982), doi.org/10.2307/1998710
+13. Maddux, R.: A sequent calculus for relation algebras. Ann. Pure Appl. Logic 25(1),
+73–101 (1983), doi.org/10.1016/0168-0072(83)90055-6
+14. Maddux, R.D.: Relevance logic and the calculus of relations. Rev. Symb. Log. 3(1),
+41–70 (2010), doi.org/10.1017/S1755020309990293
+15. Maddux, R.D.: Tarskian classical relevant logic. In: Alasdair Urquhart on nonclas-
+sical and algebraic logic and complexity of proofs, Outst. Contrib. Log., vol. 22,
+pp. 67–161. Springer, Cham (2022), doi.org/10.1007/978-3-030-71430-7_3
+16. McCune, W.: Prover9 and Mace4, www.cs.unm.edu/~mccune/prover9/, (2005–
+2010)
+17. Monk, D.: On representable relation algebras. Michigan Math. J. 11, 207–210
+(1964), projecteuclid.org/euclid.mmj/1028999131
+18. Reynolds, J.C.: Separation logic: A logic for shared mutable data structures. In:
+Proceedings 17th Annual IEEE Symposium on Logic in Computer Science. pp.
+55–74. IEEE (2002)
+19. Smyth, M.: Stable compactiﬁcation i. Journal of the London Mathematical Society
+2(2), 321–340 (1992)
+20. Stell, J.G.: Relations on hypergraphs. In: Relational and algebraic methods in
+computer science, Lecture Notes in Comput. Sci., vol. 7560, pp. 326–341. Springer,
+Heidelberg (2012), doi.org/10.1007/978-3-642-33314-9_22
+21. Stell, J.G.: Symmetric Heyting relation algebras
+with applications to hy-
+pergraphs.
+J.
+Log.
+Algebr.
+Methods
+Program.
+84(3),
+440–455
+(2015),
+doi.org/10.1016/j.jlamp.2014.12.001
+22. Tarski, A.: Contributions to the theory of models. Journal of Symbolic Logic 21(4)
+(1956)
+19
+
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+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf,len=804
+page_content='arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='02213v1  [cs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='LO]  5 Jan 2023  Representable and diagonally representable  weakening relation algebras⋆  Peter Jipsen1[0000−0001−8608−808X] and Jaˇs ˇSemrl2[0000−0001−7440−8867]  1 Chapman University jipsen@chapman.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='edu https://www1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='chapman.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='edu/~jipsen/  2 UCL (University College London) j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='semrl@cs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='ucl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='ac.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='uk  http://www0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='cs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='ucl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='ac.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='uk/staff/jsemrl/  Abstract.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' A binary relation deﬁned on a poset is a weakening relation  if the partial order acts as a both-sided compositional identity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' This is  motivated by the weakening rule in sequent calculi and closely related to  models of relevance logic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' For a ﬁxed poset the collection of weakening  relations is a subreduct of the full relation algebra on the underlying set  of the poset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' We present a two-player game for the class of representable  weakening relation algebras akin to that for the class of representable  relation algebras.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' This enables us to deﬁne classes of abstract weaken-  ing relation algebras that approximate the quasivariety of representable  weakening relation algebras.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' We give explicit ﬁnite axiomatisations for  some of these classes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' We deﬁne the class of diagonally representable  weakening relation algebras and prove that it is a discriminator vari-  ety.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' We also provide explicit representations for several small weakening  relation algebras.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  Keywords: weakening relation algebra · relevance frames · Sugihara  monoids · representation games  1  Introduction  The full algebra of binary relations on X is  Rel(X) = (P(X2), ∩, ∪, ∅, ⊤, ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' , idX, ¬,⌣ )  where ⊤ = X2, R;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='S is the composition of R, S , ¬R = X2\\R, and R⌣ = {(x, y) |  (y, x) ∈ R}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' The class RRA of representable relation algebras = SP{Rel(X) | X  is a set}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' Tarski [22] proved that RRA is a variety and Monk [17] proved that  RRA is not ﬁnitely axiomatisable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' For more details see the books by Givant [5],  [6] and Maddux [11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  The set of weakening relations on a poset X = (X, ≤) is W(X) = {R ⊆ X2 |  ≤;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='R;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='≤ = R}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' The full algebra of weakening relations on a poset X is  wk(X) = (W(X, ≤), ∩, ∪, ∅, ⊤, ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' , 1, ∼)  ⋆ This work was supported by the Engineering and Physical Sciences Research Council  EP/S021566/1  where 1 = ≤ and ∼R = ¬R⌣ is the complement-converse operation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' The class  of representable weakening relation algebras is  RwkRA = SP{wk(X, ≤) | (X, ≤) is a poset}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  Weakening relations are the analogue of binary relations when the category  Set of sets and functions is replaced by the category Pos of partially ordered sets  and order-preserving functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' Since sets can be considered as discrete posets  (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' antichains, ordered by the identity relation), Pos contains Set as a full  subcategory, which implies that weakening relations are a substantial generali-  sation of binary relations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' However, weakening relations do not allow ¬ or ⌣ as  operations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  They have applications in sequent calculi [2], quasi-proximity lattices/spaces  [19] , order-enriched categories [10] , mathematical morphology [21], and program  semantics, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' via separation logic [18] .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  The closely related algebras Wk(X) are deﬁned as the expansions of wk(X)  by the Heyting implication R → S = {(x, y) | ∀u, v(u ≤ x & y ≤ v & uRv ⇒  uSv)}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' The SP-closure of these algebras is denoted by RWkRA and has been  studied in [3], [4], [9], [20], [21].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' It is a discriminator variety that has RRA of  representable relation algebras as a proper subvariety.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' The algebras in RWkRA  are generalised bunched implication algebras, and the algebras in RwkRA are  all the subreducts of algebras in RWkRA, hence RwkRA is a quasivariety.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' We  show that it is not a variety, but with respect to representability the two classes  behave the same way.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  In Section 2 we deﬁne a representation game for RwkRA (which can be ex-  tended to a game for RWkRA) and use it to give an explicit universal axioma-  tisation for the class.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' Section 3 deﬁnes (Kripke) frames for weakening relation  algebras and adapts the game to this setting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' From an n-pebble version of this  frame game we deﬁne a sequence of classes wkRAn that approximate RwkRA from  above, similar to the sequence RAn that converges the RRA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' In the next section  we ﬁnd ﬁnite axiomatisation for wkRA2 and wkRA3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' In Section 5 we deﬁne the  class of representable diagonal weakening relation algebras and show that is a  discriminator variety.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' Finally, in the last section we show that all associative  algebras in wkRA3 with 6 elements or fewer are representable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  2  Representation game  In this section we present a representation game for weakening relation algebras  similar to those deﬁned for relation algebras, deﬁned in [8].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' We begin by deﬁning  some notation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  Deﬁnition 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' A bounded cyclic involutive unital distributive lattice-ordered magma  A = (A, ·, +, ⊥, ⊤, ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' , 1, ∼) is an algebra such that  (1) (A, ·, +, ⊥, ⊤) is a bounded distributive lattice  (2) (s + t);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' (u + v) = s;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' u + s;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' v + t;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' u + t;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' v  2  (3) s;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='⊥ = ⊥ = ⊥;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='s  (4) s;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='1 = s = 1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='s  (5) ∼(∼s) = s  (6) ∼(s · t) = ∼s + ∼t  for all s, t, u, v ∈ A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' A representation of A is an injective homomorphism h : A →  wk(X) for some poset X = (X, ≤) such that h(⊤) is an equivalence relation on  X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  Note that s ≤ t if and only if s + t = t, or equivalently ∼s · ∼t = ∼t which  can be rewritten as ∼t ≤ ∼s, hence ∼ is order reversing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' The adjective “cyclic”  is included in the name to contrast it to the non-cyclic general case the are two  unary operations ∼, − in the language that satisfy ∼−s = s = −∼s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' In the  cyclic case ∼, − have the same interpretation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  Distributive lattice-ordered magmas are abbreviated as dℓ-magmas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' Let A  be a bounded cyclic involutive unital dℓ-magma.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' Additionally we deﬁne 0 = ∼1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  Deﬁnition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' A network (for A) is a tuple N = (N, λ) where N is a set of  nodes and λ : N 2 → ℘(A) is a labelling function such that for all x, y ∈ N,  1 ∈ λ(x, x) and ⊤ ∈ λ(x, y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' Such a network is consistent if and only if for all  x, y ∈ N we have that  λ(x, y) ∩ {∼a | a ∈ λ(y, x)} = ∅.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  A network N = (N, λ) is a prenetwork of N ′ = (N ′, λ′) – denoted N ⊆ N ′ – if  and only if N ⊆ N ′ and for all x, y ∈ N we have λ(x, y) ⊆ λ′(x, y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  Observe that the prenetwork predicate is a partial order and that inconsis-  tency is inherited from prenetworks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  We now have the tools to deﬁne a two player game and prove that the exis-  tence of a winning strategy for one of the players coincides with A’s membership  in the class of RWkRA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  Deﬁnition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' An n-round representation game, denoted Γn(A), for some n ≤  ω is a two player game played between the challenger ∀ (Abelard) and the  responder ∃ (H´elo¨ıse) over n + 1 moves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' After the ith move for 0 ≤ i ≤ n, ∃ will  return a network Ni such that N0 ⊆ N1 ⊆ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' ⊆ Nn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' The game is won by ∀ if ∃  returns an inconsistent network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' Otherwise ∃ wins.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  On the initialisation move ∀ picks a pair of elements a ≰ b ∈ A and ∃  must return a network N0 with some (x, y) ∈ N 2  0 such that a ∈ λ(x, y) and  ∼b ∈ λ(y, x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  On the ith move for 0 < i ≤ n, ∀ may challenge ∃ with any of the following  four moves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  join move: ∀ picks x, y ∈ Ni−1, some a ∈ λi−1(x, y), and some b, c ∈ A such  that a ≤ b + c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' ∃ must return a Ni with b ∈ λi(x, y) or c ∈ λi(x, y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  involution move: ∀ picks x, y ∈ Ni−1 and some a, b ∈ A such that b = ∼a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  ∃ must return a Ni with a ∈ λi(x, y) or b ∈ λi(y, x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  3  composition move: ∀ picks x, y, z ∈ Ni−1 and a ∈ λi−1(x, y), b ∈ λi−1(y, z).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' ∃  must return a Ni with c ∈ λi(x, z) where c = a;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  witness move: ∀ picks x, y ∈ Ni−1, a ∈ λi−1(x, y), and b, c ∈ A such that a =  b;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' ∃ must return a Ni with some z ∈ Ni such that b ∈ λi(x, z), c ∈ λi(z, y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  Proposition 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' A is representable if and only if ∃ has a winning strategy for  Γω(A).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' If A is representable, then ∃ can take some representation h over X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' Let  a ≰ b be the pair played on initialisation move.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' There will exist some maximal  X′ ⊆ X such that ∃x, y ∈ X′ : (x, y) ∈ h(a)\\h(b) and ∀z, w ∈ X′ : (z, w) ∈ h(⊤).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  On initialisation move, ∃ can return the network N = (X′, λ) where λ(x, y) =  {c ∈ A | (x, y) ∈ h(c)}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' Because h preserves all the operations in the language,  all moves ∀ may call are trivially responded to by returning the same network  after every move.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  If A is countable then ∀ can schedule his moves in a way that every move will  be called eventually.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' Let N a,b  0  , N a,b  1  , N a,b  2  , .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' be the networks during an ∃-winning  play of Γω(A) where ∀ scheduled his moves in such a way and the initialisation  move was called for the pair a ≰ b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' Deﬁne N a,b  ω  as {x | ∃i < ω : j ≥ i ⇒ x ∈  N a,b  i  }, λa,b  ω (x, y) as {c | ∃i < ω : j ≥ i ⇒ (x, y ∈ N a,b  j  ∧ c ∈ λa,b  j (x, y))}, and a  relation ≡ as {(x, y) ∈ (N a,b  i  )2 | 1 ∈ λa,b  ω (x, y), 1 ∈ λa,b  ω (y, x)}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' It is symmetric  by deﬁnition, reﬂexive because networks are deﬁned as having 1 ∈ λa,b  ω (x, x) and  transitive because all composition moves were called eventually and 1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' 1 = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  Therefore, we can deﬁne ha,b : A →  �  (Nω/≡)2�  where for all c ∈ A we have  ha,b(c) = {([x]≡, [y]≡) | c ∈ λa,b  ω (x, y)}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  Because of initialisation there exists a pair x, y ∈ N a,b  ω  with a ∈ λa,b  ω (x, y) and  as the network remains consistent and ∼b ∈ λa,b  ω (y, x), we have b /∈ λa,b  ω (x, y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  Because every composition move was called and 1 is the identity for ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=', we have  b /∈ λa,b  ω (x′, y′) for all x′ ∈ [x]≡, y′ ∈ [y]≡.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' Thus ([x]≡, [y]≡) is a pair that ensures  that ha,b(a) ̸⊆ ha,b(b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  ⊤ is represented by ha,b as the top relation by the deﬁnition of a network  and ⊥ is represented as the empty relation because if there was a pair (x, y) with  ⊥ ∈ λa,b  ω (x, y) then by a series of composition moves every pair would include ⊥  in its label.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' That would mean that the initialisation pair of points would include  both a and b in its label.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  The join move ensures that join is represented correctly by ha,b, namely the  join move ensures ha,b(c)+ha,b(d) ⊆ ha,b(c+d) because c ≤ (c+d)+(c+d) and  ha,b(c)+ ha,b(d) ⊇ ha,b(c+ d) because c+ d ≤ c+ d and thus a pair in ha,b(c+ d)  will also be in ha,b(c) or ha,b(d).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  Because an inconsistent network is never introduced we have that if ∼c ∈  λa,b  ω (x, y) then c ̸∈ λa,b  ω (x, y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' Because all composition moves are eventually called  and 1 is the identity for ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' that applies to the all the points in the relevant  equivalence classes of ≡ and ha,b(∼c) ⊆ ∼ha,b(c).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' For ha,b(∼c) ⊇ ∼ha,b(c) if  ([x]≡, [y]≡) /∈ ha,b(∼c) then when the involution move was called for (y, x) and  c, ∃ chose to have c ∈ λa,b  ω (y, x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  4  If ([x]≡, [y]≡) ∈ ha,b(c) and ([y]≡, [z]≡) ∈ ha,b(d) then by composition moves  of a;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' 1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' b = a;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' b we have ([x]≡, [z]≡) ∈ ha,b(c;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' d) so ha,b(c);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' ha,b(d) ⊆ ha,b(c;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' d).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  For ha,b(c);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' ha,b(d) ⊇ ha,b(c;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' d), assume ([x]≡, [z]≡) ∈ ha,b(c;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' d) and without loss  c;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' d ∈ λa,b  ω (x, z).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' Because the relevant witness move was called there will exist a  y such that ([x]≡, [y]≡) ∈ ha,b(c) and ([y]≡, [z]≡) ∈ ha,b(d).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  ha,b(1) is reﬂexive by the deﬁnition of a network, antisymmetric as the base  was quotiented by ≡, and transitive as 1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' 1 = 1 and all the composition moves  were called eventually.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' Furthermore as the composition is represented by ha,b  and 1 being the identity for composition, it is the case that for all c ∈ A, ha,b(c)  is a weakening relation with respect to 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  ha,b is thus a homomorphism for A discriminating a ≰ b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' Thus let h(c) for  all c ∈ A be the disjoint union ˙�  a≰b∈Aha,b(c).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' Because h is a homomorphism  that discriminates all a ≰ b pairs, it is a representation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  This generalises to uncountable algebras by the downward L¨owenheim Skolem  Theorem since RWkRA is a pseudoelementary class.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  ⊓⊔  Next we show that the existence of a winning strategy for ∃ can be expressed  by a universal ﬁrst-order sentence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' For this result we deﬁne the following con-  cepts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  Deﬁnition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' A term network is a network N = (N, λ) where N is a ﬁnite set  of nodes and λ is a labelling function that maps every pair of nodes to a ﬁnite  set of terms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' We also require that for all x, y ∈ N, 1 ∈ λ(x, x) and ⊤ ∈ λ(x, y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  For every term network N = (N, λ) we deﬁne a network N +,x,y,t = (N ∪  {y}, λℓ) where x ∈ N, y ∈ N ⊎ {x+} (for some new node x+), t is a term in the  language of RWkRA and for all z, w ∈ N ⊎ {x+}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  λℓ(z, w) =  \uf8f1  \uf8f4  \uf8f4  \uf8f4  \uf8f4  \uf8f4  \uf8f4  \uf8f2  \uf8f4  \uf8f4  \uf8f4  \uf8f4  \uf8f4  \uf8f4  \uf8f3  {1, ⊤}  if x+ = z = w  {⊤}  if x+ = z ̸= w ̸= x or x+ = w ̸= z ̸= x, w ̸= y  {t, ⊤}  if z = x, w = y = x+  λ(z, w) ∪ {t}  if z = x, w = y ̸= x+  λ(z, w)  otherwise  For variables a, b we deﬁne two initial term networks below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  N 1,a,b =({x}, {(x, x) �→ {⊤, 1, a, ∼b}})  N 2,a,b =({x, y}, {(x, x) �→ {⊤, 1}, (x, y) �→ {⊤, a},  (y, x) �→ {⊤, ∼b}, (y, y) �→ {⊤, 1}})  Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' For every n < ω there exists a ﬁrst-order formula σn that cor-  responds to ∃ having a winning strategy for Γn(A).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' We show by induction that there exists a formula φn(N) for every 0 ≤  n < ω, deﬁned for a ﬁnite term network N, with all the variables universally  quantiﬁed that signiﬁes that the network can remain consistent for n more moves  5  of the representation game where ∃ plays conservatively, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=', only adds the re-  quested labels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' It is easy to see that she has a winning strategy for the game if  and only if she also has one for the conservative play.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  In the base case, φ0(N) deﬁned below signiﬁes consistency (remaining con-  sistent for zero moves)  φ0(N) =  �  x,y∈N  �  t∈λ(x,y)  �  t′∈λ(y,x)  t ̸= ∼t′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  In the induction case, we assume that φn(N ′), where N ′ is a term network  with all variables universally quantiﬁed, is both necessary and suﬃcient for N ′ to  be able to remain consistent for n moves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' Then we show you can deﬁne φn+1(N)  that extends the assumption to n + 1 moves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' Although we use a, b here, the  variable names should be unique when constructing these formulas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  φn+1(N) =  �  x,y∈N  �  t∈λ(x,y)  ∀a, b  �  t ≤ a + b =⇒ (φn(N +,x,y,a) ∨ φn(N +,x,y,b))  �  ∧  �  x,y∈N  �  t∈λ(x,y)  ∀a  �  φn(N +,x,y,a) ∨ φn(N +,y,x,∼a)  �  ∧  �  x,y,z∈N  �  t∈λ(x,y)  �  t′∈λ(y,z)  φn(N +,x,z,t;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='t′)  ∧  �  x,y∈N  �  t∈λ(x,y)  ∀a, b  �  t = a;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' b =⇒  �  z∈N⊎{x+}  φn  �  (N +,x,z,a)+,z,y,b��  We now have a formula φn(N) for every 0 ≤ n < ω that ensures ∃ can keep  a universally quantiﬁed term network N consistent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' Hence the formula  σn = ∀a, b (a ≰ b =⇒ (φn(N 1,a,b) ∨ φn(N 2,a,b))  ensures that ∃ has a winning strategy for a conservative game of length n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  ⊓⊔  Corollary 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' Σ = {σ1, σ2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='} together with the axioms for cyclic distributive  involutive semirings is a recursively enumerable theory that axiomatises RWkRA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  3  Frames, frame games, and ﬁnite pebble games  In this section we present ﬁnite algebras as frames, similar to Routley-Meyer  frames or relevance frames for relevance logic [1] and atom structures of atomic  relation algebras [12].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' We then deﬁne a modiﬁed version of the representation  game that utilises frames.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  Finally, we deﬁne an n-pebble versions of the frame game.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' Analogous to the  abstract classes of relation algebras RAω ⊆ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' ⊆ RA3 ⊆ RA2, this gives rise to  classes of weakening relation algebras wkRAω ⊆ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' ⊆ wkRA3 ⊆ wkRA2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' Clearly  RAω, wkRAω are the classes of representable relation algebras and weakening  6  algebras, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' Furthermore, similarly to RA4, we say that wkRA4 is the  class of weakening relation algebras.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  First, observe that the language of RwkRA does not include negation and  hence the lattice need not be Boolean.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' As we will see in Section 6, the smallest  representable non-Boolean algebra is a 4-element chain S4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' Thus we cannot  present ﬁnite weakening relation algebras using atoms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' Instead, we make use  of join-irreducibles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  Deﬁnition 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' A non-⊥ element a of a representable weakening relation algebra  is join-irreducible if and only if for all b, c if a = b + c then a = b or a = c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' It is  join-prime if and only if for all b, c if a ≤ b + c then a ≤ b or a ≤ c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  Because · distributes over + we have that an element is join-irreducible if and  only if it is join-prime.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' In the ﬁnite case every algebra will have join-irreducibles  and every element is a join of join-irreducibles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' (In general this is only true for  perfect algebras.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' In fact, by deﬁnition, a distributive lattice is join-perfect if  every element is a join of completely join-irreducible elements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' This generalises  the concept of atomic for Boolean algebras.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=')  The element a in the result below is called the join-irreducible label of (x, y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  Proposition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' In a representation h of a ﬁnite representable weakening re-  lation algebra A, for any pair (x, y) there exists a join-irreducible a ∈ A such  that  ↑a = {s ∈ A | (x, y) ∈ h(s)}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' A representation h maps joins to unions, hence the set {s | (x, y) ∈ h(s)}  is upward closed and if (x, y) ∈ h(a+ b) then it is also in h(a) or h(b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' Hence the  base set of the representation is itself a union of upward closures of join-primes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  Now if it is above ↑a and ↑b then it must be the case that (y, x) is in neither  h(∼a) nor h(∼b) and thus (x, y) ∈ h(∼(∼a + ∼b)) = h(a · b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' Thus the meet of  all such join-irreducibles must also be a non-⊥ element that is join-prime and  below all elements in the set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  ⊓⊔  Although the converse operation is not deﬁned in our language, we can use  the following trick to deﬁne a useful unary operation on the join-irreducibles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  Deﬁnition 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' For every join-irreducible a in a ﬁnite algebra, deﬁne ˆa = ∼ �  a≰s s  where � is with respect to join (+).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  The join �  s≰t t, deﬁned for all s in a ﬁnite algebra A, is usually denoted  κ(s).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' If we take s ≤ s′ ∈ A we have s ≰ t ⇒ s′ ≰ t and thus κ(s) ≤ κ(s′), hence  κ is order preserving.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' Because ∼ is order reversing and κ is order preserving we  have that ˆ is order reversing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  Proposition 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' In any ﬁnite bounded distributive involutive additive algebra A,  if a is a join-irreducible, so is ˆa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  7  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' It is well known that κ(a) of a join-irreducible a in a lattice is meet  irreducible and because ∼ is order reversing, that means that ˆa = ∼κ(a) is a  join-irreducible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  ⊓⊔  Proposition 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' If a pair (x, y) in a representation has the join-irreducible label  a, then (y, x) has label ˆa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' Moreover, ˆˆa = a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' ∼s ∈ h(y, x) if and only if s /∈ h(x, y), i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' a ≰ s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' Thus, by the argument  from Proposition 4 the join-irreducible label of (y, x) can be written as �  a≰s ∼s  where � is with respect to meet (·) and this is equivalent to ∼ �  a≰s s by the  De Morgan equivalence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  ⊓⊔  Finally to characterise composition, we need to deﬁne a ternary predicate,  similar to the set of allowed triangles in relation algebras.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  Deﬁnition 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' Let A be a ﬁnite bounded cyclic involutive dℓ-magma and deﬁne  a ternary relation R on the set of join-irreducibles of A by  R(a, b, c) if and only if a ≤ b;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  For relation algebras with atoms a, b, c the Peircian triangle law says that  a ≤ b;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' c ⇐⇒ ˆa ≤ ˆc;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='ˆb ⇐⇒ b ≤ a;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' ˆc ⇐⇒ ˆb ≤ c;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' ˆa ⇐⇒ c ≤ ˆb;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' a ⇐⇒ ˆc ≤ ˆa;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  As we will see in the next section, this law does not hold for the class of repre-  sentable weakening relation algebra frames.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' However, atom structures for rela-  tion algebras generalise to the weakening setting as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  Deﬁnition 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' A relevance frame F = (F, I, ≤, R, ˆ) is a structure with a carrier  set F, a unary predicate I, a partial order predicate ≤, a ternary predicate R,  and an order-reversing involution operation ˆ where for all a, b, c, d in F  (1) a ≤ b ⇔ ∃e : I(e) ∧ R(a, e, b)  (2) a ≤ b ⇔ ∃e : I(e) ∧ R(a, b, e)  (3) a ≤ b ∧ R(b, c, d) ⇒ R(a, c, d)  (4) b ≤ c ∧ R(a, b, d) ⇒ R(a, c, d)  (5) c ≤ d ∧ R(a, b, c) ⇒ R(a, b, d)  Proposition 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' A relevance frame F = (F, I, ≤, R, ˆ) deﬁnes a bounded invo-  lutive unital dℓ-magma A = (A, ·, +, ⊥, ⊤, ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' , 1, ∼) by taking (F, ≤) as the join-  irreducibles of the lattice with their partial order and for all s, t ∈ A  1 =  �  I(a)  a,  ∼s =  �  ˆa≰s  a,  s;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' t =  �  b≤s,c≤t,R(a,b,c)  a  where a, b, c ∈ F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  8  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' A bounded distributive lattice can be deﬁned by its join-irreducibles and  their ordering.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' To show that the magma is unital, we can see that no term  of the join deﬁning the composition with the identity is above the identity by  Deﬁnition 8(1)(2) and because ≤ is reﬂexive, there will exist, for every join-  irreducible a term in the composition with the identity (on either side) equal to  that join-irreducible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' Thus 1 is precisely the identity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' Composition is additive by  deﬁnition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' ∼ is an involution because a join-irreducible a ≤ ∼(∼s) if and only if  ˆa ≰ ∼s which is true if and only if a = ˆˆa ≤ s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' For the De Morgan equivalence,  a ≤ ∼(∼s + ∼t) if and only if ˆa ≰ ∼s + ∼t, or equivalently ˆa ≰ ∼s ∧ ˆa ≰ ∼t  which by deﬁnition is true if and only if a = ˆˆa ≤ s and a = ˆˆa ≤ t, or simply  a ≤ s · t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  ⊓⊔  Proposition 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' Every ﬁnite bounded cyclic involutive unital dℓ-magma has a  unique equivalent relevance frame.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' Finite distributive lattices are determined by their poset of join-irreducibles,  and from Proposition 5 they have a unique ˆ deﬁned on the join-irreducibles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  The mapping to R is unique as Deﬁnition 8(3)(4)(5) ensure that R is downward  closed in the ﬁrst argument and upward closed in the other arguments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  ⊓⊔  Proposition 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' For ﬁnite algebras and ﬁnite frames, the mappings described in  the previous two lemmas are inverses of each other.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' Finite distributive lattices correspond uniquely to their posets of join-  irreducibles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' The preservation of identity and the composition follow trivially  from the deﬁnition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' For ∼, ˆ observe that ∼κ(a) = ˆa ≰ s if and only if ∼s ≰  κ(a) = �  a≰ t, or equivalently a ≤ ∼s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' For the converse note that ∼κ(a) =  �  ˆb≰κ(a) b = �  a≤ˆb b = �  b≤ˆa b = ˆa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  ⊓⊔  Although we have deﬁned these frames for ﬁnite algebras, we can say that  a possibly inﬁnite algebra is frame-deﬁnable if it can be deﬁned by a relevance  frame.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' In the context of relation algebras, this corresponds to complete and  atomic relation algebras.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' Similarly to that class, we will show that every non-  frame deﬁnable algebra embeds into a frame deﬁnable algebra with equivalent  representability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  Proposition 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' Let A be a bounded cyclic involutive unital dℓ-magma.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' Then  a frame F(A) can be deﬁned by taking the carrier set of all prime ﬁlters U ⊆ A,  with U ≤ V if and only if V ⊆ U, ˆU = {∼s | s ∈ A \\ U}, I(U) ⇔ 1 ∈ U and  R(U, V, W) if and only if for all v ∈ V, w ∈ W we have v;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='w ∈ U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' ≤ is clearly a partial order, for closure of ˆ note that A \\ U is a prime  ideal, so by the order reversing property of ∼, ˆU is a prime ﬁlter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' Furthermore,  all the unitality conditions are trivially preserved and by U ′ ≤ U if and only if  U ⊆ U ′ we have downward closure of R in the ﬁrst argument and upward closure  in the other two.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  ⊓⊔  9  Proposition 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' A is representable if and only if the algebra deﬁned by F(A)  is a representable weakening relation algebra.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' This algebra is called the canonical  extension of A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' Because A is a subalgebra of the algebra deﬁned by F(A), we know that  the right to left implication is true.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' For the other direction, if A is representable,  every (x, y) will have a prime ﬁlter U such that (x, y) ∈ h(a) if and only if  a ∈ U to represent the lattice correctly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' The prime ﬁlter deﬁning (y, x) will be  exactly ˆU.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' The identity is also correctly represented as it is only above those  prime ﬁlters that include it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' Finally for ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' we have shown that it suﬃces for ∃ to  have a winning strategy for a game of any ﬁnite length.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' Thus at any point we  need to show that the compositions are correctly represented if and only if all  compositions ﬁnite meets are properly included in the relevant prime ﬁlter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  ⊓⊔  Deﬁnition 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' A frame network N = (N, λ) is deﬁned for a frame F = (F, I, ≤  , R, ˆ) with N being the set of nodes and λ : N 2 → F is the labelling function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  The network is said to be consistent if and only if for all x, y ∈ N we have  λ(x, y) = �  λ(y, x) and for all x, y, z ∈ N we have R(λ(x, y), λ(x, z), λ(z, y)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  We say for two frame networks N = (N, λ), N ′ = (N ′, λ′) that N ⊆ N ′  if and only if N ⊆ N ′ and λ = λ′ ↾N 2 where ↾ denotes the restriction of the  function to the domain in the subscript.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  Deﬁnition 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' An inﬁnite length frame game G(F) where F = (F, I, ≤, R, ˆ)  is a relevance frame is deﬁned for two players ∀ and ∃.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  The game starts with ∀ picking a join-irreducible a and ∃ must return a frame  network N0 = (N0, λ0) such that there exists x, y ∈ N0 such that λ0(x, y) = a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  At the ith move for 0 < i < ω ∀ picks a pair x, y ∈ Ni−1 and a pair of  join-irreducibles a, b such that R(λ(x, y), a, b) and for all a′ ≤ a, b′ ≤ b ∈ Ni−1 if  R(λ(x, y), a′, b′) then a = a′ and b = b′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' ∃ must return a network Ni = (Ni, λi)  such that Ni−1 ⊆ Ni and ∃z ∈ Ni such that λ(x, z) = a, λ(z, y) = b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  ∀ wins if and only if ∃ returns an inconsistent network at any point in the  game.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  Proposition 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' ∃ has a winning strategy for G(F(A)) if and only if she has  a winning strategy for Γω(A).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' It suﬃces to prove that she has a winning strategy for the play where all  moves are called eventually.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' Thus if she has a winning strategy for Γω(A), we  know that the limit network will have the relevant prime ﬁlters as labels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' Thus  if a is the initial join-irreducible ∃ can map all her moves from the limit network  of the play where the initialisation pair was a ≰ κ(a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  For the converse, assume she has a winning strategy for G(F(A)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' To respond  to the initialisation move with s ≰ t there will exist a join-irreducible a such  that a ≤ s but a ≰ t or rather t ≤ κ(a) so returning the initial network for a  will ensure that a ≤ s and ˆa ≤ ˜t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' Any witness move called can be responded to  by minimal join-irreducible pairs, which makes any other witness moves called  by ∀ redundant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  ⊓⊔  10  We now deﬁne for every 2 ≤ n ≤ ω the n-pebble equivalent version of the  frame game as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  Deﬁnition 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' The n-pebble inﬁnite move game Gn(F) for a frame F is deﬁned  exactly as G(F), except before ∀ calls a witness move, he takes N ′ ⊆ Ni−1 such  that |N ′| ≤ n and then proceeds to call the witness move.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  In particular, the frame game G is equivalent to Gω.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' Next we deﬁne wkRAn  and wkRA analogous to RAn, the variety of all n-dimensional relation algebras,  and RA, the variety of all (4-dimensional) relation algebras [13], [8].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  Deﬁnition 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' The class wkRAn is the class of all bounded cyclic involutive  unital dℓ-magmas A for which ∃ has a winning strategy for Gn(F(A)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' The  class of weakening relation algebras wkRA is deﬁned as wkRA4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  It follows that wkRAω is equivalent to RwkRA and wkRAω ⊆ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' ⊆ wkRA4 ⊆  wkRA3 ⊆ wkRA2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  4  Axiomatisation of the abstract classes  In this section we provide ﬁnite axiomatisations for wkRA2 and wkRA3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' We leave  open the problem of whether, similarly to RA4 the axiomatisation for wkRA4  consists of axioms of wkRA3 and associativity of ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='.  We begin by axiomatising wkRA2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' This will be done using the axiomatisation  of bounded cyclic involutive unital dℓ-magmas together with the theory Φ2,  deﬁned below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  Deﬁnition 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' Let Φ2 be the ﬁrst order theory given by the following quasiequa-  tions:  (1) s · ∼s ≤ 0  (2) s ≤ t ⇔ s;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' ∼t · 1 ≤ 0  (3) s ≤ t;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='u ∧ s;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='t ≤ ∼u ⇒ s · 1 ≤ 0  (4) s ≤ t;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='u ∧ u;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='s ≤ ∼t ⇒ s · 1 ≤ 0  (5) s ≤ t;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='u ∧ (s · 1 · t;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='v) + (1 · s · ∼v;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='u) ≤ 0 ⇒ s · 1 ≤ 0  Before we prove the soundness and completeness, we introduce a ternary  predicate for the language of frames Rmin from the equivalence below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  Rmin(a, b, c) ⇔ R(a, b, c) ∧ ∀b′, c′ : (R(a, b′, c′) ∧ b′ ≤ b ∧ c′ ≤ c ⇒ b′ = b ∧ c′ = c)  Note that since the union of a chain of prime ﬁlters is again a prime ﬁlter, frames  of the form F(A) have the property that R(a, b, c) can be reﬁned to Rmin(a, b′, c′)  for some prime ﬁlters b′ ≤ b and c′ ≤ c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  Lemma 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' Let A be a bounded cyclic involutive unital dℓ-magma.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' A |= Φ2 if  and only if F(A) satisﬁes  11  (1) ∀a∃b : I(b) ∧ ˆb = b ∧ R(b, a, ˆa)  (2) ∀a, b : I(a) ∧ ˆa = a ∧ R(a, b,ˆb) ⇒ R(b, a, b)  (3) ∀a, b : I(a) ∧ ˆa = a ∧ R(a, b,ˆb) ⇒ R(ˆb,ˆb, a)  (4) ∀a, b, c : I(a) ∧ ˆa = a ∧ Rmin(a, b, c) ⇒ b = ˆc  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' For the left to right implication, observe that for any join-irreducible a,  we know that a ≰ κ(a) so (a;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' ∼κ(a) · 1) ≰ 0 by Φ2(2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' Thus there must exist  a join-irreducible b ≤ 1, b ≰ 0, b ≤ a;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='ˆa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' Suppose b ̸= ˆb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' Then there would exist  some b ≤ s,ˆb ≰ s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' Because ˆˆb = b we know that b ≤ ∼s and thus b ≤ s · ∼s ≤ 0,  contradicting Φ2(1) and we have proven (1) follows from Φ2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' For (2) assume we  have a ≤ 1, ˆa = a then a ≰ ∼1 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' Thus a = a · 1 ≰ 0 and a ≤ b;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='∼κ(b) implies  a;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='b ≰ ∼∼κ(b) or simply a ≤ a;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' By a similar argument we get (3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' Finally if  a ≤ b;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='c and a = a·1 ≤ b;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='c·1 ≰ 0 we have b ≰ ∼c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' We also have that a·1 = a ≰ 0  and a ≤ b;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='c so a · κ(b);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='c ≰ 0 or a · b;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='ˆb ≰ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' In the former case that means that  κ(b);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='c ≰ 0 and thus κ(b) ≤ ∼c or c ≤ ˆb and we are done.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' In the latter case  it means that there exists a join-irreducible a′ ≤ a such that a ≰ 0 and thus  a′ = ˆa′ as well as a′ ≤ b;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='ˆb ≤ b;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' c by monotinicity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' Because a′ ≤ a ≤ ˆa′ = a′ we  have a = a′ and by minimality ˆb = c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  For the right to left implication note that if s · ∼s ≰ 0 then there exists some  a ≤ s · ∼s not below 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' Thus ˆa ≤ 1 and we know there exists a join-irreducible  b = ˆb, b ≤ a;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' ˆa ≤ (s·∼s);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='1 = s·∼s and that contradicts b = ˆb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' Assume s ≰ t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' That  is true if there exists a join-irreducible a such that a ≤ s, ˆa ≤ ∼t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' Thus there  exists a join-irreducible b = b · 1 ≰ 0 below 1 · a;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' ˆa ≤ 1 · s;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='∼t and we conclude  1 · s;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='∼t ≰ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' If 1 · s;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='∼t ≰ 0 then there exist join-irreducibles a, b, c such that  I(a), a = ˆa, b ≤ s, c ≤ ∼t and b, c also being minimal and hence ˆb = c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' Therefore  ˆb ≤ ∼t or simply s ≰ t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' s·1 ≰ 0∧s ≤ t;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='u ⇒ s;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='t ≰ ∼u follows directly from (2) and  its dual directly from (3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' Finally s·1 ≰ 0 and s ≤ t;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' u iﬀ there exist some a, b, c in  the corresponding frame such that a ≤ s · 1, b ≤ t, c ≤ u, I(a), ˆa = a, Rmin(a, b, c)  and thus ˆb = c by (4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' Observe that for every v either b ≤ v or ˆb ≤ ∼v and thus  a ≤ t;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' v or a ≤ ∼v;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='u and the join of the two terms is not below 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  ⊓⊔  Theorem 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' wkRA2 is axiomatised by the basic axioms for bounded cyclic in-  volutive unital dℓ-magmas and Φ2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' By Lemma 13 this axiomatisation is equivalent to the frame conditions,  enumerated (1)–(4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' First we show these are sound for the two pebble game.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  If there existed a join-irreducible a with no b, I(b),ˆb = b with R(b, a, ˆa), then  ∀ would win on initialisation with a because if λ(x, y) = a, no consistent b  would exist for λ(x, x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' We show (4) next.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' If this didn’t hold for some a, b, c  then ∀ could start by asking a on initial move.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' By order reversing of ˆ and the  identity, a is the only join-irreducible to be set as λ(x, x) where λ(x, y) = a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' For  the second move, ∀ calls the witness b;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' c on (x, x) and we get an inconsistency  because b ̸= ˆc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' For (2) and (3) see that if R(a, b,ˆb) we have Rmin(a, b,ˆb) by order  reversing properties of ˆ and (4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' Thus if ∀ again starts by forcing λ(x, x) = a  then calling the witness b;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='ˆb then both R(b, a, b), R(ˆb,ˆb, a) must hold to keep the  network consistent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  12  To show completeness, it suﬃces to say that ∃ can respond to any initialisa-  tion with a by returning a network with two nodes x, y with λ(x, y) = a, λ(y, x) =  ˆa and by (1) there exists a b for a and b′ for ˆa to be set as λ(x, x) and λ(y, y)  respectively and by (2)(3) all other triangles are also consistent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' A witness move  can only be called on a reﬂexive node (x, x) and that means that by (2)(3)(4)  any witness will be consistent and by the same reasoning as with initialisation,  ∃ can put a label on λ(y, y) and keep the network consistent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  ⊓⊔  In order to axiomatise wkRA3 we only need to add two well known axioms as  well as a set of quasiequations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' The ﬁrst axiom is called rotation for involutive  semirings and the second one was found by Maddux in [15] as an axiom that  holds for binary relations, but not for relevance logic frames.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  Deﬁnition 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' Let Φ3 be the ﬁrst order theory containing all the formulas in  Φ2 as well as  (1) s;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' t ≤ ∼u ⇒ t;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' u ≤ ∼s  (2) s · t;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='u ≤ ((s;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='v) · t);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='u + t;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='(u · ∼v)  (3) 1 · ∼s′;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='s · t;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='∼t′ ≤ 0 ⇒ s;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='t ≤ (s · s′);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='t + s;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='(t · t′)  (4) 1 · s · 0 = ⊥ ⇒ (s · 1);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='(t;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='u) ≤ ((s · 1);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='t);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='u  (5) 1 · u · 0 = ⊥ ⇒ (s;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='t);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='(u · 1) ≤ s;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='(t;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='(u · 1))  Lemma 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' Let A be a bounded cyclic involutive unital dℓ-magma.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' A |= Φ3 if  and only if for F(A) all the formulas from Lemma 13 hold as well as  (1) ∀a, b, c : Rmin(a, b, c) ⇒ R(b, a, ˆc)  (2) ∀a, b, c : R(a,ˆb, ˆc) ⇒ R(b, ˆc, ˆa)  (3) ∀a, b, c : Rmin(a, b, c) ⇒ ∃d : d = ˆd ∧ I(d) ∧ R(d,ˆb, b) ∧ R(d, c, ˆc)  (4) ∀a, b, c, d : d = ˆd ∧ I(d) ∧ R(a, d, a) ∧ Rmin(a, b, c) ⇒ R(b, d, b)  (5) ∀a, b, c, d : d = ˆd ∧ I(d) ∧ R(a, a, d) ∧ Rmin(a, b, c) ⇒ R(c, c, d)  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' For the left to right implication of (1) if a, b, c are join-irreducibles with  a ≤ b;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='c as well as the minimality condition for b, c then see that a = a · b;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='c ≤  (a;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='ˆc · b);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='c + b;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='(c · κ(c)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' c · κ(c) is strictly below c and due to minimality of  b, c for this composition a ≰ b;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='(c · κ(c)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' Thus a ≤ (a;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='ˆc · b);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='c and again by  minimality a;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='ˆc · b = b or simply R(b, a, ˆc).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' For (2) observe that a ≰ ˆb;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' ˆc is the  same as ∼κ(b);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='∼κ(c) ≤ κ(a) and by rotate we get ∼κ(c);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='∼κ(a) ≤ κ(b) and  ∼κ(a);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='∼κ(b) ≤ κ(c) so R(a,ˆb, ˆc), R(b, ˆc, ˆa), R(c, ˆa,ˆb) are equivalent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' For (3) if  Rmin(a, b, c) then we know b;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='c ≰ (b·κ(b));' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='c+b;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='(c·κ(b)) and thus 1·∼s′;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='s·t;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='∼t′ ≰ 0  and we can ﬁnd a d satisfying I(d), ˆd = d, R(d,ˆb, b), R(d, c, ˆc).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' For (4) see that  1 · d · 0 = ⊥ and thus a ≤ d;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='a ≤ d;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='(b;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='c) ≤ (d;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='b);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' By minimality b = d;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' By a  similar argument we get (5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  For the right to left implication, if s;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='t ≤ ∼u observe that for all join-  irreducibles a, b, c such that a ≤ s, b ≤ t, c ≤ u we have a;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='b ≤ κ(ˆc) and thus  ¬R(ˆc, a, b) and by (2) we have ¬R(ˆa, b, c) and thus b;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='c ≤ κ(ˆa) = ∼a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' If for all  join-irreducibles a, b, c below s, t, u respectively that holds then t;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='u ≤ ∼s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' To  show s · t;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='u ≤ ((s;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='v) · t);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='u + t;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='(u · ∼v) take any a ≤ s · t;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='u and some minimal b, c  13  witnessing the t;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='u composition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' Then all v will either have c ≤ ∼v or ˆc ≤ v, in  either case the term is above a by monotonicity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' Finally if s;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='t ≰ (s · s′);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='t · s;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='(t · t′)  it means that s;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='t is non-empty and as such there exists some a ≤ s;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='t and some  Rmin(a, b, c) and as such b ≰ s′ and c ≰ t′ and thus ˆb;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' b ≤ ∼s′;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='s and c;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='ˆc ≤ t;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='∼t′  and there exists a d ≰ 0 such that d ≤ 1·∼s′;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='s·t;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='∼t′ and therefore the term can-  not be below 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' Take any join-irreducible a ≤ (s · 1);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' t;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' There will exist a self-ˆ  join-irreducible d ≤ s·1 such that d ≤ d;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' a and a minimal b, c below t, u such that  a ≤ b;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' c and so we have by (4) b ≤ d;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' b and thus a ≤ b;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='c ≤ (d;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='b);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='c ≤ ((s · 1);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='t);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  The dual is shown similarly from (5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  ⊓⊔  Theorem 16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' wkRA3 is axiomatised by the basic axioms for bounded cyclic in-  volutive unital dℓ-magmas and Φ3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' First we show that all the formulas from Lemma 15 are sound.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' If we  have a, b, c such that Rmin(a, b, c) then ∀ calls a on initialisation and calls the  witness Rmin(a, b, c) on the λ(x, y) = a and ∃ must return such a network where  λ(x, z) = a, λ(y, z) = ˆc so R(b, a, ˆc) must hold for consistency and we have  (1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' For (2) assume without loss that we have R(a,ˆb, ˆc) so there must be some  minimal ˆb′ ≤ ˆb, ˆc′ ≤ ˆc to call the witness on the initial pair a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' Observe that for  consistency b ≤ b′ ≤ ˆc′;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' ˆa ≤ ˆc;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' ˆa by monotonicity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' For (3) if ∀ initialises with a  and calls the b, c witness, ∃ needs a join-irreducible d to put on the reﬂexive edge  of the added node.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  From Lemma 13, Theorem 16 we have that ∃ can survive the initial move  and we only need to examine the two possible witness moves, that on a non-  reﬂexive edge in a two-node network and that on a reﬂexive edge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' If a witness  move Rmin(a, b, c) is called on a non-reﬂexive edge (x, y), check that all Peircian  transformations of this triangle hold.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' By (1) we have R(b, a, ˆc) and through (2)  we get R(ˆb, c, ˆa), R(ˆc, ˆa, b) from R(a, b, c) and R(ˆa, ˆc,ˆb), R(c,ˆb, a) from R(b, a, ˆc).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  For the reﬂexive edge on (z, z) you can see that ∃ can add λ(z, z) = d from(3)  and by similar reasoning to Theorem 16 all triangles including (z, z) are con-  sistent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' Finally let λ(x, x) = d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' By (4) R(b, d, b) and by (2) R( ˆd = d, b,ˆb).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' The  consistency of other triangles follows from formulas in Lemma 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' Similarly we  get consistency for λ(y, y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' For the reﬂexive witness Rmin(d, a, ˆa) on (x, x) ob-  serve due to order reversing of ˆ, ∃ can either ﬁnd a join-irreducible c such that  Rmin(λ(x, y), a, c) or Rmin(λ(y, x), c, ˆa) and ∃ can use the same strategy as for  the non-reﬂexive witness move.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  ⊓⊔  To axiomatise the class wkRA = wkRA4 we would at least need to add associa-  tivity for composition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' For RA, it is precisely the axioms for RA3 and composition  that axiomatise RA4, however, whether this also holds for wkRA remains open.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  Problem 17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' What axioms are necessary to axiomatise wkRA?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' Is it ﬁnitely ax-  iomatisable?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  Problem 18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' Let n > 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' RAn is not ﬁnitely axiomatisable [8].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' Is the same true  for wkRAn?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  14  5  Representable diagonal weakening relation algebras  form a discriminator variety  In this section we deﬁne representable diagonal weakening relation algebras as  those relation algebras where 1 can be represented as an antichain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' Thus in this  section when we talk about the concrete binary relation 1, we mean the diagonal  on X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' The algebras with this property are the members of RwkRA that satisfy  the identity 1 · 0 = ⊥.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  We show that the simple representable diagonal relation algebras have a  discriminator term.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' A neat consequence is that, unlike representable weaken-  ing relation algebras, representable diagonal weakening relation algebras can be  deﬁned by an equational theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  Lemma 19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' For all R ⊆ X2 we have 1 ·  �  R;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='(R ·∼R)  �  = ⊥ = 1 ·  �  ∼R;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='(R ·∼R)  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' Suppose there exists (x, x′) ∈ 1 · (R;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='(R · ∼R)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' Because (x, x′) ∈ 1 we  have x = x′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' Thus there must exist a y to witness the composition by having  (x, y) ∈ R, (y, x) ∈ R · ∼R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' This means that (x, y) ∈ R and (y, x) ∈ ∼R and we  have reached a contradiction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  The second equation can be proven by a similar argument or by substitution  of R with ∼R, the involution law, and the commutativity of meet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  ⊓⊔  Let d1(R, S) = 1 ·  �  R;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='(S · ∼S)  �  and d2(R, S) = 1 ·  �  ∼S;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='(R · ∼S)  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  Lemma 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' If R \\ S ̸= ∅ for R, S ⊆ X2 then d1(R, S) + d2(R, S) ̸= ⊥.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' Assume (x, y) ∈ R \\ S and consider the two cases, (y, x) ∈ S and (y, x) /∈  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' In the ﬁrst case, because (x, y) /∈ S we also have (y, x) ∈ ∼S and consequently  (y, x) ∈ S · ∼S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' Hence (x, x) ∈ R;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='(S · ∼S) and also by deﬁnition in 1 and thus  (x, x) ∈ d1(R, S).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  In the second case (y, x) /∈ S and therefore (x, y) ∈ ∼S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' Because (x, y) /∈ S,  (y, x) /∈ ∼S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' By composition (y, y) ∈ ∼S;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' (R·∼S) and by reﬂexivity of 1 we also  have (y, y) ∈ 1 ·  �  ∼S;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='(R · ∼S)  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  In either case we have that at least one of d1(R, S), d2(R, S) is nonempty and  thus their join is always nonempty given R \\ S ̸= ∅.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  ⊓⊔  Theorem 21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' Simple diagonal weakening relation algebras have a term d(a, b, c)  such that  d(a, b, c) =  �  c  if a = b  a  otherwise  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' It is easy to see that in simple weakening relation algebras ⊤;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' s;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' ⊤ =  ⊤ if s ̸= ⊥ and ⊤;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' s;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' ⊤ = ⊥ otherwise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' By the lemmas above, we have for  representable simple algebras that a = b if and only d1 + d2 = ⊥, where di =  di(a, b) + di(b, a) for i = 1, 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' Thus d(a, b, c) = ⊤;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' (d1 + d2);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' ⊤ · a + ∼(⊤;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' (d1 +  d2);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' ⊤) · c will equal to c if a = b and a otherwise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  ⊓⊔  There are several ways to prove the following corollary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' We outline the argu-  ment that generates a recursively enumerable equational theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  15  Corollary 22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' Representable diagonal weakening relation algebras form a dis-  criminator variety.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' The representation game deﬁned for weakening relation algebras only  needs an additional move where ∃ is requested add 1 to λ(y, x) if 1 ∈ λ(x, y) and  this game gives rise to a similar style of a recursive axiomatisation as presented  in Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' If all variables are given unique names, the universal quantiﬁers  can also be moved to the begining of all these formulas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' Observe that although  these formulas apply to all algebras, the game is played on the homomorphic  image of the algebra where ⊤ maps to ⊤;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' a;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' ⊤ where σn = s ≰ t ⇒ (φn(N 1,s,t)∨  φn(N 2,s,t)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' Thus we can construct a term from any universally quantiﬁed ﬁrst  order formula that is equal to ⊤;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' a;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' ⊤ if and only if the formula is true and ⊥  otherwise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' For equations t = t′ we take ⊤;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' a;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' ⊤ · ∼d(t, t′, ⊤;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' a;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' ⊤).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' If a term t  corresponds to a formula, then ∼t · ⊤;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' a;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' ⊤ corresponds to its negation and for  disjunctions we can take the join of the corresponding terms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' Thus every formula  σn has an equivalent equation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  ⊓⊔  6  Representing associative members of wkRA3 with  weakening relations  Sugihara monoids are commutative distributive idempotent involutive residuated  lattices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' This variety is semilinear, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=', generated by linearly ordered algebras,  and the structure of these algebras is well known.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' In particular, the Sugihara  monoid Sn is a chain with n elements {a−k, a−k+1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' , a−1, a0, a1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' , ak−1, ak}  if n = 2k + 1 is odd, and otherwise for even n, Sn = Sn+1 \\ {a0}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' The involution  operation is given by ∼ai = a−i and the multiplication is ai;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='aj = a− max |i|,|j|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' It  follows that in the odd case the identity element is 1 = a0 and in the even case  it is 1 = a1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  Note that S2 is the 2-element Boolean algebra and that for even n, there is  a surjective homomorphism from Sn to Sn−1 that identiﬁes a1 and a−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  It is proved in [14] that the even Sugihara chains can be represented by  algebras of weakening relations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' For S2 this is clear since S2 ∼= Rel(1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' For S4 an  inﬁnite base set is needed with a dense order.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=', we can take (Q, ≤) be the  poset of rational numbers with the standard order and check that S4 ∼= {∅, <, ≤  , Q2} is a representation in Wk(Q, ≤).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  It follows from the consistency of networks that no nontrivial member of  wkRA2 has an element that satisﬁes a = ∼a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' Hence any ﬁnite member of wkRA  has an even number of elements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' In particular, the odd Sugihara chains do not  have a representation by weakening relations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' However they are in the variety  generated by all algebras of weakening relations since they are homomorphic  images of even Sugihara chains.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' This shows that RWkRA is not closed under  homomorphic images, so it is a proper quasivariety.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  Let 2 = {0, 1} be the two element chain with 0 < 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' The algebra wk(2) is  shown in Figure 2, and it has the following six elements: ∅, {(0, 1)}, {(0, 0), (0, 1)},  {(0, 1), (1, 1)}, ≤, 2 × 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  16  The point algebra P shown in Figure 1 (see also [7]) is a representable re-  lation algebra with 3 atoms idQ, <, > where < is the strict order on the ra-  tional numbers Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' It has two weakening subalgebras: S4 = {∅, <, ≤, ⊤} and  W6,1 = {∅, idQ, <, ≤, <∪>, ⊤}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' Like the point algebra, both of these algebras  can only be represented on an inﬁnite set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' Note that W6,1 is diagonally repre-  sentable, while S4 is not.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  idQ  >  ≥  ∅  P  <  <∪>  ≤  ⊤ = Q2  ∅  S4  <  ≤ = ∼<  ⊤ = Q2  idQ  ∅  W6,1  < = ∼≤  <∪> = ∼idQ  ≤  ⊤ = Q2  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' The point algebra P, the weakening subalgebra S4 and the diagonally repre-  sentable weakening subalgebra W6,1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  Since wkRA3 is ﬁnitely axiomatised, one can use a model ﬁnder such as  Mace4 [16] to compute all members of cardinality n for small values of n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' Up to  isomorphism there are 14 algebras with 6 elements or fewer in wkRA3 such that  ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' is associative, shown in Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' We now brieﬂy describe their representations  by weakening relations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  The ﬁrst 5 are symmetric representable relation algebras, hence they are  diagonally representable weakening relation algebras.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  As mentioned above, the Sugihara algebra S4 and the algebra W6,1 are  representable as subalgebras of the ∼-reduct of the point algebra (Figure 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  The algebra W6,2 is representable as ∼-subreduct of the complex algebra of Z7,  where the element a = {1, 2, 4} and 1 = {0}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  W6,3 is subdirectly embedded in a direct product of two copies of S4, hence  it is representable over the union of two disjoint copies of Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  Similarly W6,4 is represented over X = ({0} × Q) ∪ ({1} × Q) with order  (i, p) ≤ (j, q)  ⇐⇒ p < q or p = q, i = j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' The identity 1 maps to ≤ and the  element a maps to the relation {((i, p), (i, q)) | i = 0, 1, p < q}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  The representation of W6,5 requires the union of {i} × Q for i ∈ {0, 1, 2}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  The partial order ≤ is deﬁned in the same way and a is mapped to the relation  {((i, p), (i, q)) | i = 0, 1, 2, p < q}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  Finally W6,6 is represented over X = ({0} × Q) ∪ ({1} × Q) with order  (i, p) ≤ (j, q) ⇐⇒ i = j and p ≤ q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' The identity 1 maps to ≤ and the element  a maps to the relation {((i, p), (i, q)) | i = 0, 1, p < q}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  17  1  0 = 1  2  1  0  22  1  ∼a  a  0  A2  0  1  02  A3  02  0  1  S4  1  0  W6,1  02  0  ∼a  a  1  W6,2  02  0  ∼a  a  1  W6,3  1  ∼a  a  0  W6,4  ∼a  0  02  1  0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='a  a  W6,5  ∼a  02  0  1  0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='a  a  W6,6  02  ∼a  0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='a  0  1  a  wk(2)  1  ∼a  a  0  02  S6  ∼a  1  0  a  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' All algebras in wkRA4 up to 6 elements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' Black nodes denote idempotent ele-  ments (x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='x = x) and 02 = 0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  We gratefully acknowledge a very useful conversation with Roger Maddux  regarding relevance frames, relevance logic and its connections with relation  algebras.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' In particular, formulas (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='101), (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='102) in [15] provided key insights  into the axiomatisation of wkRA3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  References  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' Bimb´o, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=', Dunn, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=', Maddux, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' : Relevance logics and relation algebras.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' Symb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' Log.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' 2(1), 102–131 (2009), doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='1017/S1755020309090145  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' Galatos,  N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=',  Jipsen,  P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=':  Distributive  residuated  frames  and  generalized  bunched  implication  algebras.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  Algebra  Universalis  78(3),  303–336  (2017),  doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='1007/s00012-017-0456-x  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' Galatos,  N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=',  Jipsen,  P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=':  The  structure  of  generalized  BI-algebras  and  weakening  relation  algebras.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  Algebra  Universalis  81(3),  35  (2020),  doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='1007/s00012-020-00663-9  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' Galatos, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=', Jipsen, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=': Weakening relation algebras and FL2-algebras.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' In: Fahren-  berg, U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=', Jipsen, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=', Winter, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' (eds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=') Relational and Algebraic Methods in Com-  puter Science.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' 117–133.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' Springer International Publishing, Cham (2020)  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' Givant, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=': Advanced Topics in Relation Algebras, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' Springer International  Publishing (2017)  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' Givant, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=': Introduction to Relation Algebras, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' Springer International Pub-  lishing (2017)  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' Hirsch, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=': Relation algebras of intervals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' Artiﬁcial Intelligence 83(2), 267–295  (1996), doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='1016/0004-3702(95)00042-9  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' Hirsch, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=', Hodkinson, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=': Relation algebras by games.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' Elsevier (2002)  18  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' Jipsen, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=': Relation algebras, idempotent semirings and generalized bunched im-  plication algebras.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' In: Relational and algebraic methods in computer science, Lec-  ture Notes in Comput.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=', vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' 10226, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' 144–158.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' Springer, Cham (2017),  doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='1007/978-3-319-57418-9_9  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' Kurz, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=', Velebil, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=': Relation lifting, a survey.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' Journal of Logical and Algebraic  Methods in Programming 85(4), 475–499 (2016)  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' Maddux, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=': Relation Algebras, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' Elsevier (2006)  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' Maddux, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=': Some varieties containing relation algebras.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' Trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' Amer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='  272(2), 501–526 (1982), doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='2307/1998710  13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' Maddux, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=': A sequent calculus for relation algebras.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' Ann.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' Pure Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' Logic 25(1),  73–101 (1983), doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='1016/0168-0072(83)90055-6  14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' Maddux, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' : Relevance logic and the calculus of relations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' Symb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' Log.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' 3(1),  41–70 (2010), doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='1017/S1755020309990293  15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' Maddux, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content='D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' : Tarskian classical relevant logic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
+page_content=' In: Alasdair Urquhart on nonclas-  sical and algebraic logic and complexity of proofs, Outst.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
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+page_content=' : Symmetric Heyting relation algebras  with applications to hy-  pergraphs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ItE0T4oBgHgl3EQfRwDJ/content/2301.02213v1.pdf'}
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+1
+Fairness Guaranteed and Auction-based x-haul and
+Cloud Resource Allocation in Multi-tenant O-RANs
+Sourav Mondal, Member, IEEE and Marco Rufﬁni, Senior Member, IEEE
+Abstract—The open-radio access network (O-RAN) embraces
+cloudiﬁcation and network function virtualization for base-
+band function processing by dis-aggregated radio units (RUs),
+distributed units (DUs), and centralized units (CUs). These enable
+the cloud-RAN vision in full, where multiple mobile network
+operators (MNOs) can install their proprietary or open RUs, but
+lease on-demand computational resources for DU-CU functions
+from commonly available open-clouds via open x-haul interfaces.
+In this paper, we propose and compare the performances of
+min-max fairness and Vickrey-Clarke-Groves (VCG) auction-based
+x-haul and DU-CU resource allocation mechanisms to create
+a multi-tenant O-RAN ecosystem that is sustainable for small,
+medium, and large MNOs. The min-max fair approach minimizes
+the maximum OPEX of RUs through cost-sharing proportional
+to their demands, whereas the VCG auction-based approach
+minimizes the total OPEX for all resources utilized while extracting
+truthful demands from RUs. We consider time-wavelength division
+multiplexed (TWDM) passive optical network (PON)-based x-
+haul interfaces where PON virtualization technique is used
+to ﬂexibly provide optical connections among RUs and edge-
+clouds at macro-cell RU locations as well as open-clouds at the
+central ofﬁce locations. Moreover, we design efﬁcient heuristics
+that yield signiﬁcantly better economic efﬁciency and network
+resource utilization than conventional greedy resource allocation
+algorithms and reinforcement learning-based algorithms.
+Index Terms—Min-max fairness, MORAN, multi-tenant open-
+radio access networks, resource allocation, VCG auction.
+I. INTRODUCTION
+The ﬁfth-generation (5G) radio access networks (RANs)
+are standardized to meet a diverse set of QoS requirements
+to support broadband, low-latency, and machine-type commu-
+nications. Applications like mixed reality, telesurgery, high-
+deﬁnition video streaming, and Industrial Internet-of-Things,
+to name a few, will be free from the spectrum crunch and
+network resource scarcity issues of the legacy RANs. However,
+the existing mobile networks with their “one size ﬁts all” archi-
+tecture lack sufﬁcient ﬂexibility and intelligence for efﬁcient
+catering of such requirements [1]. Therefore, the necessity for
+a major architectural revolution is envisaged for beyond 5G
+and sixth-generation (6G) RANs. Over the past few years,
+major mobile network operators (MNOs) across the globe
+are collaborating within the Open-RAN (O-RAN) Alliance to
+standardize an open and smart RAN architecture that can
+perform complex RAN management with the aid of software-
+deﬁned networking (SDN), network function virtualization
+(NFV), and edge computing (EC) technologies [2]. This ar-
+chitecture typically follows 3GPP recommendations where the
+S. Mondal and M. Rufﬁni are with CONNECT Centre for Future Networks
+and Communication, Trinity College Dublin, University of Dublin, Dublin 2,
+Ireland (e-mail: somondal@tcd.ie, marco.rufﬁni@tcd.ie).
+This work is ﬁnancially supported by EU H2020 EDGE/MSCA (grant
+713567) and Science Foundation Ireland (SFI) grants 17/CDA/4760 and
+13/RC/2077 P2.
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+Fig. 1: A schematic diagram showing O-RAN architecture with
+functions of RU, O-DU, and O-CU and their corresponding interfaces.
+RUs perform low-PHY functions (typically split 7.2 and 7.3),
+while high-PHY, MAC, RLC, RRC, and PDCP functions are
+processed by the DU-CUs that can be hosted on OLT-Clouds
+with commercial off-the-shelf (COTS) hardware, as shown in
+Fig. 1. Recently, the IEEE P1914.1 standardization working
+group was created to specify the next-generation front-haul
+interface (NGFI). The RU-DU interface is known as the NGFI-
+I, or the front-haul (maximum one-way latency bound = 100
+µsec), and the DU-CU interface is known as the NGFI-II or
+the mid-haul (maximum one-way latency bound = 1 msec)
+[3]. The interface beyond CU to the 5G core is known as the
+back-haul; hence, the general term x-haul is used.
+The incorporation of open clouds for DU-CU function
+processing over the open front/mid-haul interfaces in the
+O-RAN architecture creates new business opportunities for
+small, medium, and large MNOs as well as network service
+providers (NSPs) [4]. In turn, this creates a multi-tenant O-
+RAN ecosystem where several MNOs deploy their RUs with
+macro and small-cell coverage over a certain geographic area
+but procure front/mid-haul and DU-CU function processing
+resources from the open and shared resource pool provided by
+various NSPs [5]. The primary beneﬁt of this multi-tenant O-
+RAN architecture is minimization of the CAPEX and OPEX
+for the MNOs. The techno-economic analysis in [6] shows
+that ∼40% CAPEX and ∼15% OPEX over 5 years can
+be reduced by adopting SDN-based architectures for mobile
+network virtualization. In practice, government, municipality,
+or an alliance of MNOs can be the NSP that owns the open
+x-haul and cloud resources and distribute the resources among
+the MNOs. On the other hand, a competitive market model can
+also be created where the MNOs compete against each other
+or form opportunistic coalitions for procuring their required
+x-haul and cloud resources. These observations motivate us to
+propose efﬁcient resource allocation mechanisms that create a
+multi-tenant O-RAN ecosystem that is sustainable for small,
+medium, and large MNOs.
+The cloud servers installed at a central ofﬁce (CO) or optical
+line terminal (OLT) locations are referred to as OLT-Clouds,
+but their signiﬁcant intermediate distance may become disad-
+vantageous for supporting low-latency applications and front-
+This article is currently undergoing through review process for possible publication in IEEE Transactions in Communications.
+arXiv:2301.00597v1  [cs.NI]  2 Jan 2023
+
+0O2
+haul interfaces (typical PON length ≥ 10 km). This hurdle
+can be overcome by installing Edge-Clouds at macro-cell RU
+locations to host DU-CU and local core functions for some
+of the neighboring small-cell RUs [7]. Moreover, efﬁciently
+utilizing geographically distributed Edge-Clouds can lead to a
+better cost efﬁciency of a RAN than centralized OLT-Clouds.
+Nonetheless, the RUs supporting latency-tolerant broadband
+applications can be connected to OLT-Cloud and 5G core
+without such issues. Therefore, we consider the TWDM-PON
+architecture proposed in [8] as the x-haul interfaces to create
+a logical mesh topology that facilitates the small-cell RUs
+to be connected with OLT-Clouds at CO locations or Edge-
+Clouds at macro-cell RU locations in a ﬂexible manner. This
+architecture supports East-West communication along with
+traditional North-South communication and its efﬁciency over
+similar architectures in literature was also proven in [8].
+We critically observe that a large body of the existing litera-
+ture mainly focuses on allocating computational resources only
+and ignores communication resources of the x-haul interfaces.
+Moreover, while connecting RUs from different MNOs to
+either Edge-Cloud or OLT-Cloud over the open front/mid-
+haul interfaces, the OPEX of the RUs are calculated by
+either of the well-known methods like uniform sharing, utility
+maximization, min-max fairness, and proportional fairness [9].
+Note that this resource allocation problem can be considered
+as an assignment problem, but the RUs can not demand any
+speciﬁc amount of resources as in the conventional setting.
+Each RU only knows its front/mid-haul datarate and RU-
+DU-CU processing requirements corresponding to its split
+option. After all the RUs inform their respective front/mid-
+haul datarate to the NSP, sufﬁcient resources are allocated
+by the NSP such that the front/mid-haul data generated by
+the RUs in each slot duration (5G slot duration can be
+125, 250, 500, or 1000 µsec) are transmitted and processed
+within the maximum latency bounds. Therefore, in the uniform
+sharing approach, when the cost of total utilized resources is
+uniformly distributed among the RUs, inefﬁciency may arise
+if RUs with lower resource requirements pay higher prices.
+In the utility maximization approach, the proﬁt of the NSP
+is maximized while RUs are connected to Edge/OLT-Clouds.
+Hence, the RUs from wealthy MNOs will get priority and the
+RUs from poor MNOs may suffer from resource starvation
+at high-load conditions. The proportional fairness is a fair
+resource allocation method where fairness is achieved through
+maximization of a logarithmic utility function.
+Nevertheless, in this paper, we embrace the min-max fair-
+ness approach with proportional cost sharing method, where
+we connect the RUs to Edge/OLT-Clouds such that the maxi-
+mum OPEX of the RUs is minimized by allocating resources
+proportional to their demands and satisfy their latency re-
+quirements. Also, the RUs from different MNOs are fairly
+chosen for allocation such that poor MNOs do not suffer
+heavily during high-load conditions. We design this method
+for creating a multi-tenant O-RAN ecosystem where all the
+small, medium, and large MNOs get fair opportunities for
+OPEX minimization. However, the decisions made by this
+scheme strongly depend on the revealed resource demands of
+the RUs to the NSPs and the RUs may not be always truthful
+in revealing their resource demands if there exist opportunities
+to gain extra incentives from the market. This motivates
+us to design a Vickrey-Clarke-Groves (VCG) auction-based
+mechanism that allocates resources to RUs while minimizing
+the cost of total utilized resources but uses a special payment
+rule that enforces truthful revelation of resource requirements
+as a weakly dominant strategy equilibrium for the RUs [10].
+Our primary contributions in this paper are:
+(a) We propose a multi-tenant O-RAN architecture where RUs
+from small, medium, and large MNOs can be connected
+to Edge/OLT-Clouds for their DU-CU functions for low-
+latency and broadband applications in a sustainable man-
+ner over TWDM-PON-based front/mid-haul interfaces via
+East-West and North-South links.
+(b) We formulate an integer non-linear program (INLP) for
+the min-max fair resource allocation. In this formulation,
+we minimize the maximum cost for leasing front/mid-haul
+and DU-CU resources of each RU (resource allocation is
+proportional to demand) while satisfying the latency re-
+quirements of the low-latency and broadband applications.
+(c) We formulate a second INLP for the VCG auction-based
+resource allocation. In this formulation, we minimize the
+total cost for leasing front/mid-haul and DU-CU resources
+of all the RUs. Moreover, a payment rule is designed
+that ensures truthful revelation of resource demands of the
+RUs to prevent them from taking unfair advantages while
+paying for consumed resources.
+(d) We design polynomial-time algorithms for efﬁcient imple-
+mentation of the min-max fair and VCG auction formula-
+tions. Furthermore, we compare the economic efﬁciency
+and network resource utilization achieved by our proposed
+algorithms against state-of-the-art nearest-ﬁrst (greedy)
+and reinforcement learning-based (multi-arm bandit) al-
+gorithms through numerical evaluation to showcase their
+usefulness in practice.
+The rest of this paper is organized as follows. Section II
+reviews some related works. Section III describes the multi-
+tenant O-RAN architecture. Section IV presents the system
+model. Section V presents the min-max fairness, VCG auction,
+and baseline (greedy nearest-ﬁrst and reinforcement learning-
+based) methods. Section VI presents numerical evaluation
+results. Finally, Section VII provides the concluding remarks.
+II. REVIEW OF RELATED WORKS
+Resource allocation and management problems are funda-
+mental research challenges in any networking environment
+and a large volume of literature exists on this area spanning
+across all types of network scenarios [11]. The O-RAN for
+beyond 5G/6G mobile communication systems is no exception
+to this as its ﬂexibility in terms of bandwidth, latency, and QoS
+requirements introduces several interesting research challenges
+[12]. Before the O-RAN architecture was proposed, several
+resource allocation or radio resource head (RRH) to base-
+band unit (BBU) assignment problems were solved using
+mathematical optimization and game theoretic tools for the
+Cloud-RAN (C-RAN) architecture by the authors of [13]–
+[16]. The authors of [17] designed a dynamic two-stage
+
+3
+Macro RU
+Small RU
+Fig. 2: The proposed TWDM-PON-based multi-tenant O-RAN architecture where RUs from multiple MNOs (hexagonal macro-cell and
+circular small-cell coverage area are shown in blue, green, and orange for three different MNOs) can be connected to Edge-Cloud or CO
+OLT-Cloud via the North-South or East-West virtual-PONs (indicated by red A, B, C) for the respective DUs and CUs.
+mechanism for downlink resource allocation and BBU-RRH
+assignment in C-RAN. The authors of [18] investigated a
+joint RRH-BBU association and energy sharing problem to
+minimize brown energy usage. Again, the authors of [19]
+investigated the RRH-BBU mapping problem to minimize the
+network power consumption by reducing the number of active
+BBUs. Moreover, the authors of [20] studied the joint RRH
+clustering and RRU activation problem with QoS constraints
+to minimize the energy consumption of RRHs. The authors of
+[21] demonstrated a multi-vendor multi-standard PON for 5G
+x-haul that performs the control and management operations
+by SDN/NFV technologies.
+After the formation of the O-RAN Alliance, as the standard-
+ization of virtualized RAN started, researchers from academia
+and industry started to propose various interesting solutions
+to overcome O-RAN deployment and resource management
+challenges. Recently, the authors of [22] provided a very
+elaborate overview of the architecture and components of O-
+RAN, explored artiﬁcial intelligence (AI)-based use cases,
+and discussed various research opportunities across different
+engineering sectors. The authors of [23] provided detailed
+discussions on the ongoing O-RAN Alliance standardization
+activities with various analyses supported by a study of the
+trafﬁc steering use case in a modular way following the
+open networking approach. We also shared several insights
+on optical transmission network (OTN) and optical distributed
+network (ODN)-based front/mid-haul network design for O-
+RANs from our observations in [24]. Alongside these, the
+authors of [25] formulated a two-step mixed-integer pro-
+gramming problem for ﬁnding the optimal power allocation,
+physical resource block (PRB) assignment, the number of
+virtual network functions (VNFs), and the number of RUs. The
+authors of [26] modeled the RU-DU assignment problem as a
+2D bin packing problem and proposed a deep reinforcement
+learning-based self-play method to achieve efﬁcient RU-DU
+resource management. Moreover, the authors of [27] designed
+a team learning algorithm for implementing a near-real-
+time (near-RT) radio intelligent controller (RIC) of O-RAN.
+However, neither of the aforementioned works focused on
+the challenges of designing ﬂexible front/mid-haul interfaces
+between RUs and Edge/OLT-Clouds. Moreover, no compar-
+ative analysis is available between the conventional greedy
+heuristics and learning-based resource allocation algorithms.
+Another important aspect of the O-RAN architecture, which
+essentially evolves from the C-RAN architecture, is its natural
+ability to facilitate multi-tenancy, i.e., a pool of network
+resources can be shared among multiple MNOs [28]. The
+multi-operator RAN (MORAN) allows two or more MNOs
+to share every component of a RAN except the radio carriers,
+whereas the multi-operator core network (MOCN) allows two
+or more core networks to share the same RAN or the carriers
+[29]. In [30], the authors demonstrated a virtual network
+controller enabled multi-tenant virtual network on top of multi-
+technology OTNs. We also performed some initial studies
+on the resource allocation problem for multi-tenant O-RAN
+ecosystems in [31]. However, a more detailed investigation of
+system performance, economic analysis, and robust resource
+allocation mechanisms implementable in a practical competi-
+tive market scenario is required.
+III. MULTI-TENANT O-RAN ARCHITECTURE
+Fig. 2 shows the considered O-RAN architecture in a multi-
+tenant scenario where multiple MNOs install neighboring RUs
+with hexagonal macro-cell and circular small-cell coverage.
+
+B4BCXX4
+Each MNO pays a fee for leasing networking (i.e., for x-
+haul) and computing resources (i.e., DU-CU processing at
+Edge/OLT-Clouds) according to a certain payment scheme.
+Furthermore, all the MNOs need to pay a default price to
+the mediator, acting as the open platform provider to cover
+the cost of the resources required for RAN management and
+control plane operations. Recently, ITU-T has drafted recom-
+mendations for using TWDM-PONs as an optical front/mid-
+haul solution as TWDM-PONs can support 100 Gbps or more
+aggregated datarate (i.e., in upcoming standardization) which
+can be scaled further by combining additional wavelengths
+[32]. Moreover, other recent work has addressed PON slicing
+isolation [33] and compliance with service level agreement
+(SLAs) [34]. Thus, TWDM-PON-based interfaces are used
+to connect both the macro and small-cell RUs to a CO with
+multi-level reﬂective splitters. These splitters are designed so
+that they can be dynamically reconﬁgured to pass through or
+reﬂect back (i.e., towards the end points) the desired set of
+wavelengths (the concept is taken from [8]). The wavelengths
+that are passed through, establish the North-South commu-
+nication links (downlink: green, uplink: blue), whereas the
+reﬂected wavelengths establish the East-West communication
+links (downlink: purple, uplink: red). In terms of network
+hierarchy, each level-1 reﬂective splitter aggregates multiple
+RUs and each level-2 reﬂective splitter aggregates multiple
+level-1 reﬂective splitters and all their respective RUs for a
+cost-efﬁcient deployment. A set of level-1 reﬂective splitters
+are used to connect RUs and Edge-Clouds directly, while
+multiple level-1 reﬂective splitters are connected to a level-
+2 reﬂective splitter to reach through other PON branches.
+A local connectivity between small-cells and macro-cells via
+East-West communication links can be achieved by installing
+an Edge-OLT at the macro-cell, while the small-cells can
+host a simple ONU. Control signals via the North-South
+communication links can be sent to these Edge-OLTs at macro-
+cells and ONUs at small-cells to create virtual-PON instances
+that communicate via the East-West communication links. For
+example, three virtual-PON instances are shown in Fig. 2 and
+the ONUs and Edge-OLTs belonging to the same virtual-PON
+are labeled as A, B, and C in red. This direct communication
+enables ultra-low latency and ultra-low jitter communications
+as the signals remain in the optical domain while reﬂected
+back at the splitter. Note that ONUs in virtual-PON instance
+A communicate only via level-1 reﬂective splitter. The same
+occurs for instance C. However, ONUs in virtual-PON instance
+B can communicate via both level-1 and level-2 reﬂective split-
+ters (i.e., they extend across two PON branches). Both OLT
+and Edge-Clouds can host the DU-CU functions. Although the
+OLT-Clouds host the main 5G core, the Edge-Clouds can be
+used to host local 5G cores [7]. The back-haul trafﬁc can be
+routed to the remote data centers via metro and core networks.
+Fig. 3 shows the user plane and control plane interfaces of
+the proposed TWDM-PON-based multi-tenant O-RAN archi-
+tecture. The RUs for ultra-reliable and low-latency (uRLLC)
+services are prioritized to be connected to Edge-Clouds,
+whereas RUs for enhanced mobile broadband (eMBB) services
+can be ﬂexibly connected to Edge/OLT-Clouds. Although
+Fig. 1 shows the most general schematic to highlight the
+Fig. 3: A schematic diagram showing the user plane and control plane
+interfaces of the proposed TWDM-PON-based multi-tenant O-RAN
+architecture that supports uRLLC and eMBB services.
+ﬂexible RAN deployment options provided by the O-RAN
+architecture, we choose to place DU and CU functions at a
+common Edge/OLT-Cloud because this is the most efﬁcient
+conﬁguration for uRLLC and eMBB applications in our judg-
+ment. The near-RT RIC mainly interacts with DUs and CUs by
+the E2 interface whose control loops operate with a periodicity
+between 10 msec and 1 sec. The near-RT RIC consists of
+multiple applications called xApps for per-UE controlled load-
+balancing, resource block management, interference detection
+and mitigation, QoS management, connectivity management,
+and seamless handover control. Alongside this, the near-RT
+RIC is connected to the non-real time (non-RT) RIC by the
+A1 interface. This non-RT RIC is a component of the service
+management and orchestration (SMO) framework and consists
+of rApps to complement the near-RT RIC for intelligent RAN
+operation and optimization on a time scale larger than 1 sec.
+Therefore, our proposed resource allocation algorithms in this
+paper can be implemented as control mechanisms that involve
+the periodic exchange of information and decision between
+RUs, Near-RT RIC, and Non-RT RIC. We consider that the
+RUs report their incoming resource demands to SMO every
+1 sec over the O1 interface. Observing the information over
+a few seconds interval (operators decide based on the dy-
+namicity of trafﬁc), the rApps execute our proposed decision-
+making algorithms and pass on the decision to COs over the
+O1 interface. Accordingly, RUs are connected to Edge/OLT-
+Clouds over North-South or East-West TWDM-PON links. All
+the intermediate UE connectivity and handover management
+functions are taken care of by the xApps in near-RT RIC.
+IV. SYSTEM MODEL
+In
+this
+section,
+we
+describe
+the
+TWDM-PON-based
+front/mid-haul communication and RU-DU-CU function pro-
+cessing models considered for our problem formulation. The
+datarate for the front/mid-haul interface mainly depends on
+the split option chosen between RU and DU [35]. With
+Split-7.2, all the radio frequency processing, fast Fourier
+transform (FFT)/inverse FFT, cyclic preﬁx removal/addition,
+digital beamforming, and resource element mapping are done
+at the RU. The datarate can be calculated as follows [35]:
+W7.2 = NP × NRB × N SC
+RB×N SF
+sym × T −1
+SF
+× µ × NQ × 2 × ζ,
+(1)
+
+Periodic and bursty front /mid-haul trafficRandomly distributed back-haul traffic5
+where, NP denotes the number of antenna ports, NRB denotes
+the number of resource blocks (RB), N SC
+RB denotes the number
+of sub-carriers per RB, T −1
+SF denotes sub-frame duration, µ
+denotes the maximum RB utilization, NQ denotes the quan-
+tizer bit resolution per I/Q dimension, and ζ denotes the front-
+haul overhead. With Split-7.3, precoding, layer mapping, and
+modulation are also done with the aforementioned tasks and
+the datarate is calculated as follows:
+W7.3 = NL × NRB × N RB
+SC × N SF
+sym × T −1
+SF
+× µ × (1 − η) × NQ × log2(Mmod) × ζ,
+(2)
+where, NL denotes the number of spatial layers, η denotes
+resource overhead, and Mmod denotes the modulation order.
+Note that 3GPP recommends Split-7.3 mainly to be used
+for downlink transmission, but Split-7.2 can be used for
+both uplink and downlink [36]. As front/mid-haul data are
+transmitted as periodic bursts of Ethernet frames, the number
+of frames in a burst can be calculated as B = ⌈RD × δt/P⌉,
+where RD denotes the front/mid-haul datarate, δt denotes the
+burst interval duration, and P denotes the payload size of an
+Ethernet frame (1500 Bytes). Hence, the actual throughput
+of a ﬂow can be calculated by (B × F/δt), where F is
+the maximum Ethernet frame size (1542 Bytes). This data
+is transmitted over TWDM-PON and cooperative dynamic
+bandwidth allocation (Co-DBA) protocol [37] is used for
+coordinating RAN and PON capacity scheduling in the uplink
+transmission. Furthermore, it is crucial to note that sufﬁcient
+communication resources should be available for each RU to
+transmit each burst of front/mid-haul data to DU-CU without
+failure to ensure a successful end-to-end communication.
+The total RU-DU-CU function processing effort per slot in
+Giga operations per second (GOPS) is given by [38]:
+CRDC =
+�
+3Na + N 2
+a + 1
+3 × M × Ψ × NL
+�
+× NRB
+5
+, (3)
+where, Na denotes the number of MIMO antennas, M denotes
+the number of modulation bits, and Ψ denotes the coding rate.
+This total computational effort CRDC is distributed among RU,
+DU, and CU based on the chosen intermediate split options.
+For example, 40% processing is done by RU with Split-7.2, but
+50% processing is done by RU with Split-7.3. The remainder
+of the processing is done by the DU-CU and the total RU-
+DU-CU processing time can be computed by the polynomial
+expressions provided in [39].
+V. ASSIGNMENT OF RUS TO EDGE/OLT-CLOUDS
+HOSTING DU/CU FUNCTIONS
+In this section, we formulate two problems for connecting
+the RUs to some Edge/OLT-Cloud over front/mid-haul inter-
+faces that hosts both the corresponding DU and CU functions.
+We also design some efﬁcient heuristics for both the problem
+formulations that can be implemented in practice. We consider
+that both macro-cell and small-cell radio heads can support
+either or both uRLLC and eMBB applications. Therefore, two
+separate RUs can be created by slicing the total available radio
+resources, which need to be optimally connected to Edge-
+Cloud via East-West communication links or OLT-Cloud via
+North-South communication links. At ﬁrst, we formulate a
+min-max fair resource allocation problem that creates a multi-
+tenant O-RAN ecosystem where all the small, medium, and
+large MNOs get fair opportunities for OPEX minimization. In
+this scheme, each RU pays the price for allocated resources
+in proportion to their demand. However, to prevent afﬂuent
+MNOs from inﬂuencing the fairness of resource allocation by
+revealing a higher resource demand, we formulate a VCG
+auction-based resource allocation problem with a different
+allocation and payment rule that makes each RU pay a price
+that is independent of their respective resource demand but
+dependent on the resource demands of other RUs. Thus, the
+RUs cannot gain any incentive by revealing any false resource
+demand. Although this formulation ensures truthful resource
+demand revelation from all the RUs, it cannot guarantee a
+fair OPEX for all MNOs because it minimizes the OPEX
+of the overall network and does not consider the OPEX of
+RUs individually. Therefore, NSPs can choose the min-max
+fairness resource allocation mechanism where truthful demand
+revelation is possible through strict market regulations (e.g.,
+huge economic penalty or market ban on detection of false
+information). For an open and competitive market scenario,
+the NSPs can choose the VCG auction-based mechanism. In
+addition to these, we design a nearest-ﬁrst (greedy) and a
+reinforcement learning-based resource allocation mechanism
+for performance comparison.
+A. Min-Max Fairness Guaranteed Resource Allocation
+Our primary objective here is to allocate front/mid-haul
+and DU-CU resources for RUs such that the OPEX of RUs
+with worst/high values are minimized. We denote the set of
+uRLLC RUs by Ru = {1, 2, . . . , Ru} and the set of eMBB
+RUs by Rm = R \ Ru, where R = {1, 2, . . . , Ru, Ru +
+1, . . . , Ru + Rm}. Note that at each RU location, one RU for
+uRLLC services and one RU for eMBB services can coexist,
+whose data are scheduled to be transmitted at different PRBs
+within each slot. Also, we denote the set of Edge-Clouds by
+E = {1, 2, . . . , E}, and the set of OLT-Clouds by Q = Y \ E,
+where Y = {1, 2, . . . , E, E + 1, . . . , E + Q}. The binary
+variable xry denotes if an RU r ∈ R is connected to an
+Edge/OLT-Cloud y ∈ Y, i.e.,
+xry =
+�
+1;
+if RU r and Edge/OLT-Cloud y are connected
+0;
+otherwise.
+The parameter zry indicates if RU r ∈ R and Edge/OLT-
+Cloud y ∈ Y can be connected over a virtual-PON (East-
+West or North-South) when its value is 1. The parameters
+Cr, Cλ, and CP denote the default cost to the mediator (e),
+the cost for throughput used (e/Gbps), and the cost for cloud
+resources leased (e/GOPS) by each RU r, respectively. As
+the Edge-Clouds are located at some macro-cell RU location,
+they can be owned by the respective MNO, and the attached
+RUs from the same MNO do not need to pay the costs of
+computational resources. The neutral NSP can also own the
+Edge-Clouds, but it needs to provide some price discount to the
+respective MNOs. To incorporate these facts, we incorporate
+a discount factor γry ∈ [0, 1] where γry = 0 indicates full
+discount and γry = 1 indicates no discount. The parameters
+
+6
+W UL
+r
+and W DL
+r
+denote the uplink and downlink front/mid-
+haul datarate of RU r. The parameters BUL
+y
+, BDL
+y
+, ∀y ∈ E
+denote the maximum uplink, and downlink throughput of the
+East-West TWDM-PON links and BUL
+y
+and BDL
+y
+, ∀y ∈ Q
+denote the maximum uplink and downlink throughput of the
+North-South TWDM-PON links. The maximum throughput
+of each PON link can vary according to the number of
+conﬁgured wavelengths. The parameters ηUL
+r
+and ηDL
+r
+denote
+the required uplink and downlink GOPS/slot, HUL
+r
+and HDL
+r
+denote the available uplink and downlink GOPS/slot for RU
+processing. The parameters ΓUL
+r
+and ΓDL
+r
+denote the required
+GOPS/slot for DU-CU processing of RU r and GUL
+y
+, GDL
+y
+denote maximum available GOPS/slot at Edge/OLT-Clouds
+y. The parameter θry denotes the burst interval over which
+data are transmitted from ONUs connected to RU r in East-
+West or North-South TWDM-PONs. Finally, the parameters
+∆H
+r and ∆RDC
+r
+denote the maximum one-way front/mid-haul
+latencies and total RU-DU-CU processing for RU r. Now, we
+formulate the min-max fair resource allocation problem for a
+multi-tenant O-RAN ecosystem as follows:
+P1 : min
+xry max
+r
+�
+�
+�
+�
+y∈Y
+(Cr + CλBry + γryCP Gry) xry
+�
+�
+� (4)
+subject to
+xry ≤ zry, ∀r ∈ R, y ∈ Y,
+(5)
+�
+y∈Y xry ≤ 1, ∀r ∈ R,
+(6)
+Bry =
+�
+W UL
+r
+BUL
+y
+ε + �
+r xryW UL
+r
+�
++
+�
+W DL
+r
+BDL
+y
+ε + �
+r xryW DL
+r
+�
+,
+∀r ∈ R, y ∈ Y, (7)
+Gry =
+�
+ΓUL
+r
+GUL
+y
+ε + �
+r xryΓUL
+r
+�
++
+�
+ΓDL
+r
+GDL
+y
+ε + �
+r xryΓDL
+r
+�
+,
+∀r ∈ R, y ∈ Y, (8)
+xry
+�
+δry + Dry
+vl
+�
++
+�θT T I
+θry
+� ��
+r xryW UL
+r
+θry
+BUL
+y
+�
+≤ ∆H
+r ,
+∀r ∈ R, y ∈ Y, (9)
+xry
+�Dry
+vl
+�
++
+�θT T I
+θry
+� ��
+r xryW DL
+r
+θry
+BDL
+y
+�
+≤ ∆H
+r ,
+∀r ∈ R, y ∈ Y, (10)
+ηUL
+r
+HUL
+r
++
+��
+r xryΓUL
+r
+GUL
+y
+�
+≤ ∆RDC
+r
+θT T I
+, ∀r ∈ R, y ∈ Y,
+(11)
+ηDL
+r
+HDL
+r
++
+��
+r xryΓDL
+r
+GDL
+y
+�
+≤ ∆RDC
+r
+θT T I
+, ∀r ∈ R, y ∈ Y,
+(12)
+xry ∈ {0, 1}, ∀r ∈ R, y ∈ Y.
+(13)
+The objective function of the problem P1 is given by (4),
+which indicates the minimization of maximum OPEX of each
+RU r. The ﬁrst term is the default cost, the second term
+is the front/mid-haul throughput leasing cost, and the third
+term is the DU-CU function processing resources leasing
+cost. Note that the price for throughput and computational
+resources paid by each RU is proportional to their demands.
+The constraint (5) ensures that RU r can be associated with
+Edge/OLT-Cloud y only when an East-West or North-South
+TABLE I: Network Parameters and Sets
+Symbol
+Deﬁnition
+Ru
+Set of RUs for uRLLC services
+Rm
+Set of RUs for eMBB services
+R
+Set of all RUs present in the system (R = Ru ∪ Rm)
+E
+Set of Edge-Cloud locations
+Q
+Set of OLT-Cloud locations
+Y
+Set of all Edge/OLT-Cloud locations (Y = E ∪ Q)
+Dry
+Distance between RU r ∈ R and Edge/OLT-Cloud y ∈ Y
+Cr
+Default cost of participation to the mediator (e)
+Cλ
+Cost for throughput used (e/Gbps)
+CP
+Cost for cloud resources leased (e/GOPS)
+W UL/DL
+r
+The uplink and downlink front/mid-haul datarate of RU r
+ΓUL/DL
+r
+Required GOPS/slot for DU-CU processing of RU r
+BUL/DL
+y
+Maximum throughput of the TWDM-PON links
+GUL/DL
+y
+Maximum available GOPS/slot at Edge/OLT-Clouds y
+ηUL/DL
+r
+Required uplink and downlink GOPS/slot for RU processing
+HUL/DL
+r
+Available uplink and downlink GOPS/slot for RU processing
+∆H
+r
+Maximum one-way front/mid-haul latency of RU r
+∆RDC
+r
+Maximum RU-DU-CU processing latency of RU r
+θslot
+Transmit time slot of RU r
+θry
+Transmission burst interval of TWDM-PON uplinks
+δry
+The reduced waiting time for uplink data at ONUs
+vl
+Speed of light in optical ﬁber (2 × 108 m/s)
+connection exists and the constraint (6) restricts RU r to
+be connected to one Edge-Cloud or OLT-Cloud y at most.
+The constraints (7) indicates the allocated share of throughput
+to RU r over front/mid-haul interface to Edge/OLT-Cloud y.
+Similarly, the constraint (8) indicates the allocated share of
+GOPS to RU r for DU-CU processing at Edge/OLT-Cloud
+y. Note that a very small constant ε ≈ 0 is added to the
+denominator of each of the terms in (7)-(8) to avoid division
+by zero. Furthermore, the constraint (9) ensures that the uplink
+front/mid-haul latency from RU r to Edge/OLT-Cloud y is
+within ∆H
+r . The parameter δry denotes the average queuing
+latency of uplink data due (considering the use of the Co-DBA
+mechanism). The second term with xry indicates propagation
+latency where the parameter Dry denotes the distance from
+RU r to Edge/OLT-Cloud y and vl denotes speed of light
+within ﬁber (2 × 105 km/s). The third term indicates data
+transmission latency where data is transmitted in multiple
+bursts of duration θry within each TTI, θT T I. Similarly, con-
+straint (10) ensures that the downlink front/mid-haul latency
+from RU r to Edge/OLT-Cloud y is within ∆H
+r . Finally, the
+constraints (11)-(12) ensure the uplink and downlink RU-DU-
+CU processing latencies are within ∆RDC
+r
+, respectively. The
+ﬁrst term indicates the RU processing latency and the second
+and third terms indicate the DU-CU processing latencies at
+Edge/OLT-Cloud y, respectively.
+B. Heuristic for the Min-Max Fair Resource Allocation
+We observe that P1 is an NP-hard problem and the primary
+reason behind the NP-hardness is that the locations of active
+Edge/OLT-Clouds are not known when we start to connect
+RUs to Edge/OLT-Clouds. Note that the problem P1 has a
+unique structure that converts a multi-objective problem into
+a single-objective problem such that standard optimization
+methods can be employed. In this case, we convert the
+minimization problem of OPEXs of multiple RUs into a min-
+imization problem of the maximum OPEX of RUs. However,
+
+7
+the problem P1 is still very inconvenient to solve due to the
+presence of max{., .} function in the objective. Therefore, we
+need to reformulate this problem into an equivalent epigraph
+form as follows:
+Pr
+1 :
+min
+xry,M
+M
+(14)
+subject to
+M ≥
+�
+y∈Y (Cr + CλBry + γryCP Gry) xry,
+∀r ∈ R, (15)
+constraints (5) − (13).
+It is straightforward to show that an optimal solution for
+Pr
+1 is also a solution for P1 [40]. Nonetheless, as both these
+problems are INLP, the evaluation of an optimal solution
+cannot be guaranteed in polynomial time. Hence, a heuristic
+algorithm is required. In general, we understand that OPEX
+of each RU in (4) can be minimized if each front/mid-
+haul link and Edge/OLT-Cloud resources are leased by a
+maximum number of RUs while satisfying constraints (9)-(12).
+In addition, we observe the following interesting property of
+optimal solutions of Pr
+1.
+Proposition 1: An optimal solution of Pr
+1 can guarantee
+fairness if and only if the OPEX of an RU with lower resource
+requirements does not exceed the OPEX of an RU with higher
+resource requirements.
+Please refer to Appendix A for the proof. In general,
+we can achieve the best possible value of M if full-mesh
+connectivity is available among RU and Edge/OLT-Clouds.
+However, in practice, mostly partial-mesh connectivity can
+be observed, i.e., constraint (6) along with constraints (9)-
+(12) will have a strong inﬂuence on the solution. Nonetheless,
+in general, we are able to connect a higher number of RUs
+to Edge/OLT-Clouds if we start with lower resource require-
+ments. Based on the above insights, we design a heuristic
+algorithm, summarized as Algorithm 1. At ﬁrst, we sort the
+RUs in R in the increasing order of (max{W DL
+r
+, W UL
+r
+})
+and (max{ΓDL
+r
+, ΓUL
+r
+}). This step is crucial to maintain con-
+sistency with Proposition 1. We also order the RUs such
+that the percentage of ownership of MNOs is uniformly
+maintained. Then we start to iteratively connect each RU
+r to an Edge/OLT-Cloud y. For r = 1, we initialize the
+ﬂag assign ← 0, the dummy set ¯Y ← Y, and ﬁnd the
+nearest y′ = arg miny{Dry}, y′ ∈
+¯Y. If the constraints
+(5), (9)-(12) are satisﬁed for this y′, we set xry′
+← 1,
+assign ← 1, and calculate the corresponding OPEX value
+Cr = �
+y(Cr + CλBry + γryCP Gry)xry. If this is not
+successful, then we remove y′ from ¯Y and continue this
+process until ¯Y = ∅. In the subsequent iterations, i.e., for
+1 < r ≤ |R|, we ﬁnd all y ∈ Y that satisfy constraints (5),
+(9)-(12) for the current RU r and reinitialize the dummy set
+¯Y. If at least one such y exists, i.e., | ¯Y|≥ 1, then we calculate
+the dummy OPEX values Cry = (Cr + CλBry + γryCP Gry)
+if RU r was connected to each of the Edge/OLT-Cloud y.
+Then we ﬁnd y′ = arg miny{Cry}, y′ ∈ ¯Y, set xry′ ← 1,
+and calculate the updated values of Bry, Gry, and Cr for all
+RUs. The ﬁrst for loop iterates for |R| times to return xry
+and Cr while ﬁnding a suitable Edge/OLT-Cloud y from a
+set of maximum size |Y| at every iteration. Therefore, the
+Algorithm 1 Algorithm for min-max fair resource allocation
+Input: R, E, Y, Dry, BU/DL
+y
+, W U/DL
+r
+, ΓU/DL
+r
+, GU/DL
+r
+Output: Near-optimal solution: x∗
+ry and C∗
+r
+Initialize: Sort the elements of R in the increasing order
+of (max{W DL
+r
+, W UL
+r
+}) and/or (max{ΓDL
+r
+, ΓUL
+r
+}) while
+maintaining an uniform distribution of the percentage of
+ownership of MNOs;
+1: for r ← 1 to |R| do
+2:
+if r = 1 then
+▷ choose best possible r = 1
+3:
+Set ¯Y ← Y;
+4:
+Set assign ← 0;
+5:
+while assign ̸= 1 and ¯Y ̸= ∅ do
+6:
+Find y′ = arg miny{Dry}, y′ ∈ ¯Y;
+7:
+if constraints (5), (9)-(12) are satisﬁed then
+8:
+Set xry′ ← 1;
+9:
+Set assign ← 1;
+10:
+Calculate Bry, Gry, and Cr;
+11:
+else
+12:
+Set ¯Y ← ¯Y \ {y′};
+13:
+end if
+14:
+end while
+15:
+if assign ̸= 1 and ¯Y = ∅ then
+16:
+break;
+▷ infeasibility condition
+17:
+end if
+18:
+else if 1 < r ≤ |R| then
+19:
+Find all y ∈ Y such that constraints (5), (9)-(12)
+20:
+are satisﬁed for the current RU r and create ¯Y;
+21:
+if | ¯Y|≥ 1 then
+▷ if at least one such y exists
+22:
+Calculate all dummy OPEX values for RU r,
+23:
+Cry, if r was connected to each of y ∈ ¯Y;
+24:
+Find y′ = arg miny{Cry}, y′ ∈ ¯Y;
+25:
+Set xry′ ← 1;
+26:
+Update Bry, Gry, and Cr, ∀r with �
+y xry = 1;
+27:
+else
+28:
+Set Bry = 0, Gry = 0, and Cr = 0;
+29:
+end if
+30:
+end if
+31: end for
+32: return xry and Cr;
+worst-case time-complexity of this loop, as well as Algorithm
+1, is O(|R|×|Y|). Now, if we denote the optimal number of
+Edge/OLT-Cloud as Y ∗, then the number of remaining RUs yet
+to be connected at every iteration t of Algorithm 1 is at most
+Rt ≤ Rt−1(1−1/Y ∗). Thus, at the end of all |R| iterations, we
+must have 1 ≤ |R|×(1−1/Y ∗)Y|R| = |R|×(1−1/Y ∗)Y ∗×
+Y|R|
+Y ∗ .
+By using the Taylor series approximation (1 − 1/x)x ≈ 1/e,
+we get 1 ≤ |R|×(1/e)
+Y|R|
+Y ∗ , or Y|R| ≤ Y ∗ loge(|R|), where
+Y|R| denotes the number of active Edge/OLT-Clouds after all
+|R| iterations. Hence, the solution produced by Algorithm 1
+approximates the optimal solution by a factor of O(loge(|R|)).
+C. VCG Auction-based Resource Allocation
+Although the solution obtained from the min-max fairness
+method described in previous sub-sections is very efﬁcient, the
+solution is dependent on the private information like W UL
+r
+,
+W DL
+r
+, ΓUL
+r
+, and ΓDL
+r
+shared by the RUs to the NSP. To
+
+8
+prevent the RUs from sharing false information and gaining
+unfair incentives from the market, we design a VCG auction-
+based resource allocation method in this sub-section. Note
+that this problem is very close to an auction of multiple
+divisible items [41] but with speciﬁc unique characteristics.
+Each RU wants to connect to an Edge/OLT-Cloud via some
+East-West or North-South TWDM-PON link to avail sufﬁcient
+throughput and Edge/OLT-Cloud resources to successfully
+transmit its front/mid-haul data generated within each slot
+duration, satisfying the maximum latency bounds. Therefore,
+the private valuation function of each RU r is given as:
+Vr(xry) =
+�
+�
+�
+�
+�
+�
+�
+�
+�
+�
+�
+�
+�
+�
+�
+(CλBy + CP Gy)xry;
+if r is connected to
+some y with successful
+front/mid-haul data
+transmission,
+0;
+otherwise,
+where, By = (BUL
+y
++ BDL
+y
+) and Gy = (GUL
+y
++ GDL
+y
+). Note
+that if an RU gets connected to some Edge/OLT-Cloud but
+fails to transmit its front/mid-haul data, then also its valuation
+of resources is zero. We assume that the NSP wants a fair
+market competition and hence, keeps the cost parameters
+Cr, Cλ, and CP the same for all the competing MNOs. At
+ﬁrst, each RU r submits their front/mid-haul datarate and
+DU-CU processing requirements to the NSP as a message
+br = ( ˆW UL
+r
+, ˆW DL
+r
+, ˆΓUL
+r
+, ˆΓDL
+r
+). After receiving messages
+b = (b1, b2, . . . , b|R|) from all RUs, the NSP solves the follow-
+ing cost-minimization problem while connecting a maximum
+number of RUs to Edge/OLT-Clouds and the solution ˆx∗
+ry can
+be considered as the allocation rule [42].
+P2 :
+min
+xry,ty
+�
+�
+�
+�
+y∈Y
+(CλBy + CP Gy) ty
+�
+�
+�
+(16)
+subject to
+ty ≤ xry, ∀r ∈ R, y ∈ Y,
+(17)
+constraints (5) − (6), (9) − (13),
+where ty is a binary decision variable and the constraint (17)
+implies that ty is equal to 1 if at least one RU r is connected
+to the Edge/OLT-Cloud y.
+Proposition 2: The allocation rule ˆx∗
+ry derived as a solution
+of P2 is allocatively efﬁcient.
+Please refer to Appendix B for the proof. Although sev-
+eral other dominant-strategy truthful mechanisms exist in
+the quasi-linear setting1, only with Groves mechanisms, we
+can implement an allocative efﬁciency in dominant strategies
+among agents with arbitrary quasi-linear utilities. Observe that
+the valuation for resources of each RU r is non-zero only if
+it is connected to some Edge/OLT-Cloud y and gets sufﬁcient
+resources to transmit its front/mid-haul data generated in each
+slot within the maximum latency bounds. Otherwise, if an
+RU r is unallocated or fails to transmit its front/mid-haul data
+generated in each slot within the maximum latency bounds, its
+valuation is zero. Note that the same resources By and Gy are
+shared by multiple RUs that are allocated to Edge/OLT-Cloud
+1The utility of agent r with private valuation vr from obtaining a fraction
+x of a divisible good at a price p is ur(x, p) = vr(x) − p.
+y. Therefore, the net worth of resources allocated to each RU r,
+ˆCr varies within [0, (CλBy+CP Gy)]. This implies that if only
+one RU is connected to an Edge/OLT-Cloud y, then it must
+bear the cost of the consumed resources ˆCr = (CλBy+CP Gy)
+all alone. However, if multiple RUs are connected to an
+Edge/OLT-Cloud y, then the total cost is uniformly divided
+among them, i.e., ˆCr = [(CλBy +CP Gy)/�
+r ˆx∗
+ry]. Using this
+observation, we design a payment rule for the RUs similar to
+Clarke’s mechanism [42] as follows:
+Pr(xry, b) =
+�
+��
+j̸=r
+˜Cj(x−r∗
+jy (b−r), bj)
+�
+� −
+�
+��
+j̸=r
+˜Cj(x∗
+jy(b), bj)
+�
+�
+=
+�
+j̸=r
+�
+CλBy + CP Gy
+�
+k̸=r x∗
+ky
+�
+−
+�
+j̸=r
+�
+CλBy + CP Gy
+�
+k x∗
+ky
+�
+, (18)
+which can be interpreted as the total cost of all RUs other
+than r under an efﬁcient allocation when RU r is absent in
+the system minus the total cost of all RUs other than r under
+an efﬁcient allocation when RU r is present in the system.
+Note that ˆx−r∗
+jy
+or ˆx−r∗
+ky
+denote allocation rules when RU r is
+absent in the system.
+Theorem 1: The payment rule (18) ensures that truthful
+private information sharing to NSPs is a weakly dominant
+strategy for all RUs.
+Please refer to Appendix C for the proof. This also
+shows that the mechanism is weakly budget balanced as
+�
+r Pr(ˆx∗
+ry, b) ≥ 0. With the aforementioned allocation and
+payment rules, the utility of each RU r is deﬁned as follows:
+Ur(ˆx∗
+ry, b) = Vr(ˆx∗
+ry, b) − Pr(ˆx∗
+ry, b).
+(19)
+Therefore, the individual rationality of the RUs is always
+maintained in this mechanism as Ur(ˆx∗
+ry, b) ≥ 0. In addition
+to Pr(ˆx∗
+ry, b), each RU r also needs to pay the default cost
+Cr to the NSP if it is connected to some Edge/OLT-Cloud y.
+D. Heuristic for the VCG Auction-based Resource Allocation
+As computational efﬁciency is an important property for a
+mechanism design, we design a polynomial-time heuristic to
+solve the problem P2 as outlined in Algorithm 2 (page 30). We
+start to iteratively connect each RU r to an Edge/OLT-Cloud
+y. For r = 1, we initialize the ﬂag assign ← 0, the dummy
+set ¯Y ← Y, and ﬁnd the nearest y′ = arg miny{Dry}, y′ ∈ ¯Y.
+If the constraints (5), (9)-(12) are satisﬁed for this y′, we set
+ˆxry′ ← 1, ty′ ← 1, assign ← 1, and calculate the cost of total
+utilized resources Ctot = �
+y∈Y (CλBy + CP Gy) ty, which is
+also equal to ˆCr, the shared cost of RU r. If the assignment
+is not successful, then we remove y′ from ¯Y and continue
+this process until ¯Y = ∅. In the subsequent iterations, i.e., for
+1 < r ≤ |R|, we ﬁnd all y ∈ Y that satisfy constraints (5),
+(9)-(12) are satisﬁed for the current RU r and reinitialize the
+dummy set ¯Y. If at least one such y exists, i.e., | ¯Y|≥ 1, then
+we calculate the dummy costs of total utilized resources Ctot,y
+if RU r was connected to each of the Edge/OLT-Cloud y. Then
+we ﬁnd y′ = arg miny{Ctot,y}, y′ ∈ ¯Y, set ˆxry′ ← 1, ty′ ← 1,
+and calculate the updated value of Ctot. We also calculate the
+shared cost of RU r as [(CλBy +CP Gy)/�
+r ˆxry] for y = y′.
+
+9
+Algorithm 2 Algorithm for VCG auction-based allocation
+Input: R, E, Y, Dry, BU/DL
+y
+, W U/DL
+r
+, ΓU/DL
+r
+, GU/DL
+r
+Output: Near-optimal solution: x∗
+ry and C∗
+r
+Initialize: Sort the elements of R in the increasing order
+of (max{W DL
+r
+, W UL
+r
+}) and (max{ΓDL
+r
+, ΓUL
+r
+}) while
+maintaining an uniform distribution of the percentage of
+ownership of MNOs;
+1: for r ← 1 to |R| do
+2:
+if r = 1 then
+▷ choose best possible r = 1
+3:
+Set ¯Y ← Y;
+4:
+Set assign ← 0;
+5:
+while assign ̸= 1 and ¯Y ̸= ∅ do
+6:
+Find y′ = arg miny{Dry}, y′ ∈ ¯Y;
+7:
+if constraints (5), (9)-(12) are satisﬁed then
+8:
+Set xry′ ← 1 and ty′ ← 1;
+9:
+Set assign ← 1;
+10:
+Calculate Ctot and ˜Cr;
+11:
+else
+12:
+Set ¯Y ← ¯Y \ {y′};
+13:
+end if
+14:
+end while
+15:
+if assign ̸= 1 and ¯Y = ∅ then
+16:
+break;
+▷ infeasibility condition
+17:
+end if
+18:
+else if 1 < r ≤ |R| then
+19:
+Find all y ∈ Y such that constraints (5), (9)-(12)
+20:
+are satisﬁed for the current RU r and create ¯Y;
+21:
+if | ¯Y|≥ 1 then
+▷ if at least one such y exists
+22:
+Calculate all dummy cost values for RU r,
+23:
+Ctot,y, if r was connected to each of y ∈ ¯Y;
+24:
+Find y′ = arg miny{Ctot,y}, y′ ∈ ¯Y;
+25:
+Set xry′ ← 1 and ty′ ← 1;
+26:
+Update Ctot and ˜Cr, ∀r with �
+y xry = 1;
+27:
+else
+28:
+Set ˜Cr = 0 and keep Ctot unchanged;
+29:
+end if
+30:
+end if
+31: end for
+32: for r ← 1 to |R| do
+33:
+Set R ← R \ {r} and execute lines 1-31;
+34:
+Calculate Pr(xry, b) and Cr = Cr + Pr(xry, b);
+35:
+Set R ← R ∪ {r};
+▷ add r back to R
+36: end for
+37: return xry and Cr;
+Once the RU to Edge/OLT-Cloud allocation is complete, we
+calculate the payment rule. For this purpose, we solve P2 using
+steps 1-31 for another |R| times in the absence of each of the
+RUs from R. Thus, we can calculate Pr(ˆxry, b), the payment
+made by each RU r using (18) and the OPEX of the RU r
+can be calculated as ˆCr = Cr + Pr(ˆxry, b). Note that the ﬁrst
+for loop iterates for |R| times to return ˆx∗
+ry and tries to ﬁnd a
+suitable Edge/OLT-Cloud y from a set of maximum size |Y|
+at every iteration. Therefore, the worst-case time-complexity
+of this loop is O(|R|×|Y|). The second for loop iterates for
+|R| times to return ˆCr, but it executes the ﬁrst for loop with
+complexity O(|R|−1). Therefore, the overall time-complexity
+of Algorithm 2 is O(|R|2×|Y|). Also, similar to Algorithm
+1, it can shown that the solution produced by Algorithm 2
+approximates the optimal solution by a factor of O(loge(|R|)).
+E. Nearest-First (Greedy) and Reinforcement Learning-based
+Resource Allocation Mechanisms
+To create a performance baseline, we design a conven-
+tional nearest-ﬁrst (greedy) approach-based resource alloca-
+tion method. We select the RUs sequentially and attempt
+to associate them to their nearest Edge/OLT-Cloud subject
+to the network connectivity (5)-(6), communication latency
+(9)-(10), and processing latency (11)-(12) constraints, i.e.,
+y′ = arg min{Dry|y′ ∈ Y, (5) − (6), (9) − (12)}. For each
+RU r, if their most nearest Edge/OLT-Cloud y′ is unavailable,
+then we remove y′ from the list of Edge/OLT-Clouds and
+proceed to ﬁnd the next nearest Edge/OLT-Cloud. In this
+way, we iteratively try to assign each RU r to an Edge/OLT-
+Cloud y. Once the maximum possible RUs are assigned to all
+Edge/OLT-Clouds, we can calculate the OPEX of the assigned
+RUs as Cr = �
+y∈Y
+�
+Cr + Cλ ˜Bry + CP ˜Gry
+�
+xry, where the
+share of throughput and DU-CU function processing resources
+for each RU r are considered either as proportional sharing:
+˜Bry =
+�
+W UL
+r
+BUL
+y
+�
+r xryW UL
+r
+�
++
+�
+W DL
+r
+BDL
+y
+�
+r xryW DL
+r
+�
+,
+(20)
+˜Gry =
+�
+ΓUL
+r
+GUL
+y
+�
+r xryΓUL
+r
+�
++
+�
+ΓDL
+r
+GDL
+y
+�
+r xryΓDL
+r
+�
+,
+(21)
+or as uniform sharing:
+˜Bry =
+�
+BUL
+y
+�
+r xry
+�
++
+�
+BDL
+y
+�
+r xry
+�
+,
+(22)
+˜Gry =
+�
+GUL
+y
+�
+r xry
+�
++
+�
+GDL
+y
+�
+r xry
+�
+.
+(23)
+The OPEX of the unassigned RUs are considered equal
+to zero. All the steps of this algorithm are summarized in
+Algorithm 3 (page 30). We observe that the worst-case time-
+complexity of the ﬁrst for loop is O(|R|×|Y|) and the time-
+complexity of the second for loop is O(|R|). This implies that
+the overall time-complexity of Algorithm 3 is O(|R|×|Y|).
+In the reinforcement learning-based method, each RU r ran-
+domly selects an Edge/OLT-Cloud y and attempts to establish
+a front/mid-haul connection by following a multi-arm bandit
+algorithm [43]. The reward of each RU (Rr) is calculated as
+the average of ∆H
+r to front/mid-haul latency ratio and ∆RDC
+r
+to RU-DU-CU processing latency ratio. The RUs perform
+both exploration and exploitation (ϵ-greedy with ϵ = 0.3,
+i.e., explore strategies with probability 0.3, else exploit) to
+maximize its cumulative reward values and eventually ﬁnd the
+best Edge/OLT-Cloud. After RU to Edge/OLT-Cloud allocation
+is done, the OPEX of the RUs are calculated as above.
+VI. RESULTS AND DISCUSSIONS
+To evaluate our proposed frameworks, we consider a multi-
+tenant O-RAN deployment area of dimension 5×5 km2. In this
+area, 8 macro-cell RUs (coverage = 1 km) and 30 small-cell
+
+10
+Algorithm 3 Algorithm for nearest-ﬁrst resource allocation
+Input: R, E, Y, Dry, BU/DL
+y
+, W U/DL
+r
+, ΓU/DL
+r
+, GU/DL
+r
+Output: Near-optimal solution: x∗
+ry and C∗
+r
+Initialize: Sort the elements of R in the increasing order
+of (max{W DL
+r
+, W UL
+r
+}) and (max{ΓDL
+r
+, ΓUL
+r
+}) while
+maintaining an uniform distribution of the percentage of
+ownership of MNOs;
+1: for r ← 1 to |R| do
+2:
+Set ˜Y ← Y;
+3:
+Set assign ← 0;
+4:
+while assign ̸= 1 and ˜Y ̸= ∅ do
+5:
+Find y′ = arg miny{Dry}, y′ ∈ ˜Y;
+6:
+if constraints (5), (9)-(12) are satisﬁed then
+7:
+Set xry′ ← 1;
+8:
+Set assign ← 1;
+9:
+else
+10:
+Set ˜Y ← ˜Y \ {y′};
+11:
+end if
+12:
+end while
+13: end for
+14: for r ← 1 to |R| do
+15:
+if �
+y xry = 1 then
+16:
+Calculate ˜Bry, ˜Gry, and Cr;
+17:
+else
+18:
+Set ˜Bry = 0, ˜Gry = 0, and Cr = 0;
+19:
+end if
+20: end for
+21: return xry and Cr;
+RUs (coverage = 0.5 km) from three different MNOs coexist.
+The front/mid-haul datarate and RU-DU-CU processing efforts
+of the RUs vary over time depending on the RU conﬁgurations
+and the chosen split option. For example, if the RUs are
+conﬁgured with 2x2 MIMO, 2 layers, 50 MHz bandwidth, 15
+kHz sub-carrier spacing, MCS index 16, and slot duration =
+0.5 msec, the maximum uplink datarate with Split-7.2 is 2.304
+Gbps, and the maximum downlink datarate with Split-7.3 is
+0.432 Gbps. Each radio head’s total RU-DU-CU processing
+requirement is nearly 550 GOPS/slot. We consider that in
+each radio head, 25% resources are used for uRLLC services
+and 75% resources are used for eMBB services. The one-way
+front-haul link latency bound is ∼100 µsec and we choose the
+RU-DU-CU processing latency bound 325 µsec for uRLLC
+services and 975 µsec for eMBB services [44]. The reduced
+queueing latency of the uplink data at the ONUs is 15 µsec
+as Co-DBA is used for uplink transmission [45] and the data
+are transmitted as periodic bursts of duration 31.25 µsec [7].
+Each wavelength of the TWDM-PON can support a throughput
+of 25 Gbps and we can aggregate multiple such wavelengths
+to achieve a few hundred Gbps of total throughput. A group
+of RUs are connected to a level-1 reﬂective splitter (locations
+found through k-means clustering) and a few level-1 reﬂective
+splitters are connected to a level-2 reﬂective splitter located
+at the center of the area. We assume that the RUs can
+be connected to the OLT-Clouds via the North-South links
+and to the Edge-Clouds via creating East-West virtual-PON
+links. We arbitrarily assume that each RU pays a default cost
+(a) Min-max fairness vs. baseline algorithms
+(b) VCG auction vs. baseline algorithms
+Fig. 4: Comparison of the total number of active Edge/OLT-Clouds
+obtained by the optimal solution, heuristics, and baseline methods
+with more computational resources at Edge-Clouds than at OLT-
+Clouds.
+of e100/day to the NSP (other network economic pricing
+schemes can also be employed but beyond the scope of this
+paper), although it has very little effect on the results as it
+is not associated with any decision variables. In addition, the
+cost for throughput used is e0.5/Gbps [46], and the cost for
+leasing DU/CU resources is e1.5/GOPS [47].
+Firstly, we compare the optimal solutions of the min-max
+fairness and VCG auction-based resource allocation methods
+with their corresponding heuristics. In this evaluation, each
+Edge-Cloud has a maximum capacity of 4.5 × 104 GOPS/slot
+and each OLT-Cloud has a maximum capacity of 1.5 × 104
+GOPS/slot. These values are chosen such that a feasible
+benchmark solution can be obtained by the greedy baseline
+algorithm with front/mid-haul datarate demand upto 2 Gbps
+per RU. We use OCTERACT, a global optimal mixed-integer
+TABLE II: Network Evaluation Scenarios
+Scenario - I
+Scenario - II
+Scenario - III
+Edge
+OLT
+Edge
+OLT
+Edge
+OLT
+Maximum
+GOPS/slot
+1.5 × 104
+4.5 × 104
+3 × 104
+3 × 104
+4.5 × 104
+1.5 × 104
+Maximum
+throughput
+50 Gbps
+600 Gbps
+100 Gbps
+400 Gbps
+150 Gbps
+200 Gbps
+
+11
+(a) Scenario-I
+(b) Scenario-II
+(c) Scenario-III
+Fig. 5: Comparison of overall O-RAN outage probability and outage probability for small, medium, and large MNOs against increasing
+front/mid-haul datarate demand per RU with different Edge/OLT-Cloud resource distributions obtained by min-max fairness and baseline
+(greedy nearest-ﬁrst and reinforcement learning-based) algorithms.
+(a) Scenario-I
+(b) Scenario-II
+(c) Scenario-III
+Fig. 6: Comparison of overall O-RAN outage probability and outage probability for small, medium, and large MNOs against increasing
+front/mid-haul data per RU with different Edge/OLT-Cloud resource distributions obtained by VCG auction-based and baseline (greedy
+nearest-ﬁrst and reinforcement learning-based) algorithms.
+nonlinear programming solver integrated with the AMPL plat-
+form to evaluate the optimal solutions of our formulated INLPs
+in a computer with Intel Core i7 processor and 32 GB RAM.
+In Fig. 4(a), we compare the optimal solution of Pr
+1 against
+the solutions obtained using Algorithm 1, the greedy baseline
+Algorithm 3, and the reinforcement learning-based method.
+Again, in Fig. 4(b), we compare the optimal solution of P2
+against the solutions obtained using Algorithm 2, the greedy
+baseline Algorithm 3, and the reinforcement learning-based
+method with the same dataset. From these ﬁgures, we observe
+that the optimal solution of Pr
+1 is the highest performing
+during lower load conditions. The nearest-ﬁrst method makes
+several sub-optimal RU to Edge/OLT-Cloud assignments as it
+connects each RU to its nearest (based on intermediate North-
+South or East-West link distance) Edge/OLT-Cloud if the
+latency constraints are satisﬁed. The reinforcement learning-
+based method requires less computation than other methods,
+but each RU independently attempts to connect to some
+Edge/OLT-Cloud that gives a higher reward, in turn lower
+latency values. Thus, the RU to Edge/OLT-Cloud assignment
+does not incorporate minimization of overall network resource
+utilization. However, all the solutions at medium and higher
+load conditions become similar as network load increases,
+because a large percentage of the potential Edge/OLT-Clouds
+gets activated and the scope of sub-optimal RU to Edge/OLT-
+Cloud assignments reduces.
+Next, we compare the network outage probabilities (deﬁned
+as the ratio of the total number of RUs that could not be
+connected to some Edge/OLT-Cloud to the total number of
+RUs present in the network) achieved by our proposed meth-
+ods. We consider that the RUs are owned by three different
+MNOs where a small MNO-1 has 20%, a medium MNO-2 has
+30%, and a large MNO-3 has 50% ownership. Additionally, we
+consider three scenarios with different computational resource
+distributions among Edge-Clouds and OLT-Clouds as outlined
+in Table II. Figs. 5(a)-5(c) show the overall O-RAN outage
+probabilities obtained through the min-max fairness and base-
+line (greedy nearest-ﬁrst and reinforcement learning-based)
+algorithms. Similarly, Figs. 6(a)-6(c) show the overall O-RAN
+outage probabilities obtained through the VCG auction-based
+and baseline (greedy nearest-ﬁrst and reinforcement learning-
+based) algorithms. We observe that all the methods show zero
+outage probability as long as there are sufﬁcient front/mid-
+haul and Edge/OLT-Cloud resources to accommodate all the
+
+12
+(a) Scenario-I
+(b) Scenario-II
+(c) Scenario-III
+Fig. 7: Comparison of the total cost of leased resources (e) and OPEX reduction percentage for small, medium, and large MNOs against
+network load variation with different Edge/OLT-Cloud resource distributions obtained by min-max fairness and baseline (greedy nearest-ﬁrst
+and reinforcement learning-based) algorithms.
+(a) Scenario-I
+(b) Scenario-II
+(c) Scenario-III
+Fig. 8: Comparison of the total cost of leased resources (e) and OPEX reduction percentage for small, medium, and large MNOs against
+network load variation with different Edge/OLT-Cloud resource distributions obtained by VCG auction-based and baseline (greedy nearest-ﬁrst
+and reinforcement learning-based) algorithms.
+RUs. However, network outage probability increases fastest
+with the reinforcement learning-based method, followed by the
+nearest-ﬁrst baseline method due to their inefﬁcient utilization
+of network resources, but the outage probability increases rela-
+tively slower with the VCG auction-based method and slowest
+with the min-max fairness method. We also plot the outage
+probabilities of the small, medium, and large MNOs, which
+show that the outage probabilities of the small, medium, and
+large MNOs vary according to their percentage of ownership,
+i.e., the highest for the large MNO and smallest for the small
+MNO, in all scenarios.
+Finally, we compare the total cost of leased front/mid-
+haul and Edge/OLT-Cloud resources obtained by the min-max
+fairness and baseline (greedy nearest-ﬁrst and reinforcement
+learning-based) algorithms. In Figs. 7(a)-7(c), we observe that
+during the low-load conditions, the performance of the min-
+max fairness approach is signiﬁcantly better than the baseline
+(greedy nearest-ﬁrst and reinforcement learning-based) meth-
+ods. However, as the front/mid-haul datarate demand per RU
+increases, the performance of all algorithms becomes similar
+due to the saturation of available resources. Although the
+total cost of leased resources (right y-axis) increases as we
+place more resources at the Edge-Clouds, the percentage of
+OPEX savings decreases (left y-axis) as resource utilization
+increases for all the MNOs. In all scenarios, the OPEX saving
+percentage is highest for the small MNO and lowest for
+the large MNOs. Similarly, Figs. 8(a)-8(c) compare the total
+cost of leased resources (right y-axis) obtained and OPEX
+reduction percentages (left y-axis) by the VCG auction-based
+and baseline (greedy nearest-ﬁrst and reinforcement learning-
+based) algorithms. We observe that the total cost of leased
+resources obtained by the VCG auction-based algorithm is
+very similar to the min-max fairness algorithm, but the OPEX
+saving percentages for small and medium MNOs are not
+always lower than the large MNO because the cost of the
+leased resources is uniformly shared among the RUs. Thus,
+often the small and medium MNOs pay a much higher price
+than their actual resource requirements. These results justify
+that our proposed min-max fair resource allocation framework
+creates a multi-tenant O-RAN ecosystem that is sustainable
+for small, medium, and large MNOs.
+VII. CONCLUSION
+In this paper, we have proposed a multi-tenant O-RAN
+architecture where RUs from multiple MNOs can lease re-
+
+13
+sources for their DU-CU function processing from Edge/OLT-
+Clouds over TWDM-PON-based open front/mid-haul inter-
+faces. These TWDM-PONs use reﬂective splitters to facil-
+itate East-West communication links along with traditional
+North-South communication links for better mesh connectivity
+among the RUs and Edge/OLT-Clouds. We have proposed two
+methods for allocating front/mid-haul and DU-CU processing
+resources to RUs based on min-max fairness and VCG auction
+mechanisms. In turn, we have formulated the corresponding
+INLPs and have designed time-efﬁcient heuristic algorithms.
+Through numerical evaluation, we have investigated the per-
+formance of these frameworks against different distributions of
+cloud resources at Edge and OLT locations. We have shown
+that both min-max fairness and VCG auction-based meth-
+ods achieve a much lower network outage probability than
+the baseline (greedy nearest-ﬁrst and reinforcement learning-
+based) methods due to the efﬁcient utilization of network
+resources. However, although the VCG auction-based method
+can ensure the extraction of truthful information from the RUs,
+the min-max fairness method ensures that the OPEX of the
+RUs are proportional to their actual resource requirements.
+Moreover, we have shown that the min-max fairness method
+can reduce the OPEX of all MNOs by more than 20% (at
+high load) to nearly 75% (at low load). We believe that our
+proposed frameworks have successfully laid cornerstones for
+developing further O-RAN resource allocation strategies.
+APPENDIX A
+PROOF OF PROPOSITION 1
+Proof: We observe that if our main problem formulation
+P1 has an optimal solution x∗
+ry, then our reformulated problem
+Pr
+1 also has an optimal solution (x∗
+ry, M ∗). This implies that
+we have found the best possible M ∗ as the maximum value
+of �
+y∈Y (Cr + CλBry + CP Gry) xry for some r ∈ R but
+it is the minimum among all feasible values of M. In this
+sense, the solution x∗
+ry guarantees fairness for all r ∈ R.
+However, sometimes the network connectivity, communication
+latency, and computation latency constraints may play a very
+strong role to produce an optimal solution (x∗
+ry, M ∗) without
+maintaining fairness. Now, we analyze all possible network
+scenarios to show the validity of this proposition.
+Case 1: Constraints (6), (9)-(12) are relaxed.
+This is the trivial case when there is full-mesh connectivity
+among the RUs and Edge/OLT-Clouds and no strict latency
+bound exists. Therefore, any RU can be connected to any
+Edge/OLT-Cloud and the optimal solution will be dictated
+by the objective (4) and constraints (5) and (13). Therefore,
+the optimum value of M will be achieved only when all
+the RUs are connected to a single Edge/OLT-Cloud with
+min{BUL
+y
++ BDL
+y
+} and/or min{GUL
+y
++ GDL
+y
+}. It is also
+obvious from (4) that the OPEX of each RU will be directly
+proportional to their resource demands W UL
+r
+, W DL
+r
+, ΓUL
+r
+, and
+ΓDL
+r
+, which ensure fairness.
+Case 2: Constraint (6) is relaxed only.
+In this case, although there is full-mesh connectivity among
+the RUs and Edge/OLT-Clouds, strict communication and pro-
+cessing latency bounds are applied. Therefore, only a limited
+number of RUs can be connected to each Edge/OLT-Cloud
+to satisfy constraints (9)-(12). In this case, the best possible
+solution can be achieved only if all RUs can be connected to
+(one or multiple) Edge/OLT-Clouds with minimum total cost
+of resources. Without loss of generality, consider that there
+are total |R| number of RUs and 2 front/mid-haul links and
+Edge/OLT-Clouds. If the front/mid-haul and Edge/OLT-Cloud
+1 have sufﬁcient resources to host all |R| number of RUs, then
+there is no issue of fairness. However, if there are insufﬁcient
+resources in Edge/OLT-Cloud 1 and some RUs need to be
+assigned to Edge/OLT-Cloud 2, then it is best to choose RUs
+with higher resource demands. By following this method, the
+fairness of the shared cost of each RU assigned to either of
+the Edge/OLT-Cloud can be guaranteed. If we assign RUs in
+any other randomized way, fairness cannot be guaranteed. For
+example, if we can assign only the RU with the lowest demand
+to Edge/OLT-Cloud 2 and the rest of the RUs to Edge/OLT-
+Cloud 1, then the optimal value M ∗ remains the same (total
+cost of resources of front/mid-haul and Edge/OLT-Cloud 2),
+but the fairness is not maintained. Note that this argument
+remains valid even if we generalize our scenario with more
+than 2 Edge/OLT-Clouds.
+Case 3: Constraint (9)-(12) are relaxed only.
+In this case, usually, there is partial-mesh connectivity
+among the RUs and Edge/OLT-Clouds but communication and
+processing latency bounds are relaxed. Therefore, in spite of
+sufﬁcient resources being present, we cannot connect all the
+RUs to a single Edge/OLT-Cloud due to network connectivity
+constraints. This implies that the cost of shared resources of
+multiple RUs with the exact same resource demand may vary
+if they are connected to different Edge/OLT-Clouds by being
+forced by the network connectivity constraints. However, their
+shared costs will be proportionally fair in comparison with the
+other RUs connected to each Edge/OLT-Clouds. For example,
+let us consider two RUs with the exact same resource demands
+but allocated to two different Edge/OLT-Clouds and a different
+number of other RUs connected to these Edge/OLT-Clouds.
+Therefore, the OPEX values may be different for these RUs
+but their OPEX values will be fair in comparison to other RUs
+connected to their corresponding Edge/OLT-Clouds.
+Case 4: All constraints (6), (9)-(12) are active.
+This is the most general case and characteristics of all the
+previous cases can be observed. Depending on the dataset,
+either constraint (6) or constraints (9)-(12) will dictate the
+optimal solution. Although sufﬁcient resources may be present
+at some Edge/OLT-Cloud to serve a large number of RUs,
+constraint (6) might interfere. Therefore, in this case, also the
+cost of shared resources of multiple RUs with the exact same
+resource demand may vary if they are connected to different
+Edge/OLT-Clouds. However, the OPEX values of each RU will
+be proportionally fair to their resource demands in comparison
+with other RUs connected to each Edge/OLT-Clouds.
+In general, we observe by testing a number of diverse
+datasets that to obtain the best possible solution M ∗ while
+maintaining the fairness of the OPEX values of the RUs, we
+must start to assign RUs to Edge/OLT-Clouds in the increasing
+order of their resource requirements.
+
+14
+APPENDIX B
+PROOF OF PROPOSITION 2
+Proof: We consider a resource allocation mechanism is
+allocatively efﬁcient if it optimizes the sum of the valuations of
+the agents for each given type proﬁle of the agents [48]. Now,
+in our problem formulation P2, the total cost of front/mid-haul
+and Edge/OLT-Clouds are minimized. Although the binary
+variable ty indicates if an Edge/OLT-Cloud y is activated or
+not, the constraint ty ≤ xry, ∀r ∈ R, y ∈ Y makes this
+formulation equivalent to minimizing the sum of valuation
+functions Vr(xry) for all RUs. Therefore, our allocation rule
+ˆx∗
+ry derived as an optimal solution of P2 can be considered
+as allocatively efﬁcient.
+APPENDIX C
+PROOF OF THEOREM 1
+Proof: The proposed payment rule can be interpreted as
+the total value of all RUs other than r under an efﬁcient
+allocation when RU r is absent in the system minus the total
+value of all RUs other than r under an efﬁcient allocation
+when RU r is present in the system. Observe that each RU
+r is connected to an Edge/OLT-Cloud y based on the shared
+information br = ( ˆW UL
+r
+, ˆW DL
+r
+, ˆΓUL
+r
+, ˆΓDL
+r
+) from all RUs.
+Case 1: If the shared information br is higher than its
+actual requirement, then there is a risk that it might remain
+unallocated when the network is in high-load condition. Then
+the valuation, payment, and utility of the RU r are given by:
+Vr(ˆx∗
+ry) = 0,
+Pr(ˆx∗
+ry, b) = 0,
+Ur(ˆx∗
+ry, b) = 0.
+Case 2: If the shared information br is lower than its
+actual requirement, then the RU might get allocated to some
+Edge/OLT-Cloud, but due to insufﬁcient resources in the RU’s
+share, the front/mid-haul data generated per slot may fail to
+get delivered within the maximum one-way front/mid-haul
+latency requirements. In this case, the valuation is zero but
+the payment is non-zero, yielding a negative utility. Thus, the
+valuation, payment, and utility of the RU r are:
+Vr(ˆx∗
+ry) = 0,
+Pr(ˆx∗
+ry, b) =
+|R|
+�
+j=1,j̸=r
+�
+CλBy + CP Gy
+�
+k̸=r ˆx−r∗
+ky
+�
+−
+|R|
+�
+j=1,j̸=r
+�
+CλBy + CP Gy
+�
+k ˆx∗
+ky
+�
+,
+Ur(ˆx∗
+ry, b) = 0 − Pr(ˆx∗
+ry, b) < 0.
+Case 3: There may arise network scenarios where an RU r
+might get connected to some Edge/OLT-Cloud by sharing false
+information (both higher and lower) and its front/mid-haul
+data generated per slot is also successfully delivered within
+the maximum one-way front/mid-haul latency requirements.
+However, after the RU to Edge/OLT-Cloud allocation, when
+the payment amount is calculated for each RU r, only the
+total number of RUs connected to each Edge/OLT-Cloud y is
+used and the revealed front/mid-haul datarate does not have
+any role to play. Thus, the utility of the RU with true revealed
+information as well as false revealed information remains the
+same. In this case, the valuation, payment, and utility of the
+RU r are given below:
+Vr(ˆx∗
+ry) =
+�
+y
+(CλBy + CP Gy)ˆx∗
+ry,
+Pr(ˆx∗
+ry, b) =
+|R|
+�
+j=1,j̸=r
+�
+CλBy + CP Gy
+�
+k̸=r ˆx−r∗
+ky
+�
+−
+|R|
+�
+j=1,j̸=r
+�
+CλBy + CP Gy
+�
+k ˆx∗
+ky
+�
+,
+Ur(ˆx∗
+ry, b) = Vr(ˆx∗
+ry) − Pr(ˆx∗
+ry, b) ≥ 0.
+Therefore, any RU r can not gain any advantages in its
+utility with the payment rule by sharing false information with
+the NSP. This ensures that sharing truthful information with
+the NSP is a weakly dominant strategy for all the RUs.
+REFERENCES
+[1] W. Saad, M. Bennis, and M. Chen, “A Vision of 6G Wireless Systems:
+Applications, Trends, Technologies, and Open Research Problems,”
+IEEE Network, vol. 34, no. 3, pp. 134–142, 2020.
+[2] “O-RAN: Towards an Open and Smart RAN,” O-RAN Alliance, Tech.
+Rep., Oct 2018.
+[3] C.-L. I et al., “RAN Revolution With NGFI (xhaul) for 5G,” J. Lightw.
+Technol., vol. 36, no. 2, pp. 541–550, 2018.
+[4] L. Peterson et al., “Democratizing the Network Edge,” ACM SIGCOMM
+Comp. Commun. Rev., vol. 49, no. 2, p. 31–36, May 2019.
+[5] “The Open Road to 5G,” Samsung Networks, Tech. Rep., July
+2019. [Online]. Available: https://image-us.samsung.com/SamsungUS/
+samsungbusiness/pdfs/Open-RAN-The-Open-Road-to-5G.pdf
+[6] B. Naudts et al., “Techno-economic Analysis of Software Deﬁned
+Networking as Architecture for the Virtualization of a Mobile Network,”
+in 2012 European Workshop Softw. Deﬁned Netw., 2012, pp. 67–72.
+[7] T. Pfeiffer, P. Dom, S. Bidkar, F. Fredricx, K. Christodoulopoulos,
+and R. Bonk, “PON going beyond FTTH [Invited Tutorial],” J. Opt.
+Commun. Netw., vol. 14, no. 1, pp. A31–A40, 2022.
+[8] S. Das et al., “Virtualized EAST–WEST PON Architecture Supporting
+Low-latency Communication for Mobile Functional Split based on
+Multiaccess Edge Computing,” IEEE/OSA J. Opt. Commun. Netw.,
+vol. 12, no. 10, pp. D109–D119, 2020.
+[9] L. Massoulie and J. Roberts, “Bandwidth Sharing: Objectives and
+Algorithms,” IEEE/ACM Trans. Netw., vol. 10, no. 3, pp. 320–328, 2002.
+[10] D. Niyato, N. C. Luong, P. Wang, and Z. Han, “Second-Price Sealed-
+Bid Auction,” in Auction Theory for Computer Networks.
+Cambridge
+University Press, 2020, ch. 6, pp. 119–157.
+[11] L. Tan, Resource Allocation and Performance Optimization in Commu-
+nication Networks and the Internet.
+USA: CRC Press, Inc., 2017.
+[12] D. Wypi´or, M. Klinkowski, and I. Michalski, “Open RAN—Radio Ac-
+cess Network Evolution, Beneﬁts and Market Trends,” Applied Sciences,
+vol. 12, no. 1, 2022.
+[13] J. Yao and N. Ansari, “QoS-Aware Joint BBU-RRH Mapping and
+User Association in Cloud-RANs,” IEEE Trans. Green Commun. Netw.,
+vol. 2, no. 4, pp. 881–889, 2018.
+[14] M. Barahman et al., “A Fair Computational Resource Management
+Strategy in C-RAN,” in 2018 International Conference on Broadband
+Communications for Next Generation Networks and Multimedia Appli-
+cations (CoBCom), 2018, pp. 1–6.
+[15] N. Mharsi and M. Hadji, “Joint Optimization of Communication Latency
+and Resource Allocation in Cloud Radio Access Networks,” in 2018
+International Conf. on Smart Commun. in Netw. Technol. (SaCoNeT),
+2018, pp. 13–18.
+[16] M. Peng, Y. Yu, H. Xiang, and H. V. Poor, “Energy-Efﬁcient Resource
+Allocation Optimization for Multimedia Heterogeneous Cloud Radio
+Access Networks,” IEEE Transactions on Multimedia, vol. 18, no. 5,
+pp. 879–892, 2016.
+
+15
+[17] M. Y. Lyazidi, N. Aitsaadi, and R. Langar, “Dynamic resource allocation
+for Cloud-RAN in LTE with real-time BBU/RRH assignment,” in 2016
+IEEE Int. Conf. Commun. (ICC), 2016, pp. 1–6.
+[18] S. Guo, D. Zeng, L. Gu, and J. Luo, “When Green Energy Meets Cloud
+Radio Access Network: Joint Optimization Towards Brown Energy
+Minimization,” Mob. Netw. Appl., vol. 24, no. 3, p. 962–970, Jun. 2019.
+[19] K. Boulos, M. El Helou, and S. Lahoud, “RRH Clustering in Cloud
+Radio Access Networks,” in 2015 International Conference on Applied
+Research in Computer Science and Engineering (ICAR), 2015, pp. 1–6.
+[20] H. M. Soliman and A. Leon-Garcia, “QoS-aware Joint RRH Activation
+and Clustering in Cloud-RANs,” in 2016 IEEE Wireless Commun. Netw.
+Conf. (WCNC), 2016, pp. 1–6.
+[21] D. Liang, R. Gu, Q. Guo, and Y. Ji, “Demonstration of Multi-Vendor
+Multi-Standard PON Networks for Network Slicing in 5G-oriented
+Mobile Network,” in 2017 Asia Commun. Photon. Conf. (ACP), 2017.
+[22] L. Bonati, M. Polese, S. D’Oro, S. Basagni, and T. Melodia, “Open,
+Programmable, and Virtualized 5G Networks: State-of-the-Art and the
+Road Ahead,” Comput. Netw., vol. 182, p. 107516, 2020.
+[23] M. Dryja´nski, u. Kułacz, and A. Kliks, “Toward Modular and Flexible
+Open RAN Implementations in 6G Networks: Trafﬁc Steering Use Case
+and O-RAN xApps,” Sensors, vol. 21, no. 24, 2021.
+[24] S. Mondal and M. Rufﬁni, “Optical Front/Mid-haul with Open Access-
+Edge Server Deployment Framework for Sliced O-RAN,” IEEE Trans-
+actions on Network and Service Management, pp. 1–18, 2022.
+[25] M. K. Motalleb, V. Shah-Mansouri, S. Parsaeefard, and O. L. A. L´opez,
+“Resource Allocation in an Open RAN System using Network Slicing,”
+IEEE Transactions on Network and Service Management, pp. 1–1, 2022.
+[26] X. Wang, J. D. Thomas, R. J. Piechocki, S. Kapoor, R. Santos-
+Rodr´ıguez, and A. Parekh, “Self-play learning strategies for resource
+assignment in Open-RAN networks,” Computer Networks, vol. 206, p.
+108682, 2022.
+[27] H. Zhang, H. Zhou, and M. Erol-Kantarci, “Team Learning-Based
+Resource Allocation for Open Radio Access Network (O-RAN),” in
+ICC 2022 - IEEE International Conference on Communications, 2022,
+pp. 4938–4943.
+[28] M. Kassis et al., “Flexible Multi-Operator RAN Sharing: Experimen-
+tation and Validation Using Open Source 4G/5G Prototype,” in 2021
+Joint European Conf. Netw. and Commun. & 6G Summit (EuCNC/6G
+Summit), 2021, pp. 205–210.
+[29] M. Sauter, “Long Term Evolution (LTE) and LTE-Advanced Pro,” in
+From GSM to LTE-Advanced Pro and 5G.
+John Wiley & Sons Ltd.,
+2017, ch. 4, pp. 211–333.
+[30] R. Vilalta et al., “Network Virtualization Controller for Abstraction and
+Control of OpenFlow-enabled Multi-tenant Multi-technology Transport
+Networks,” in Opt. Netw. Commun. Conf. Exhibit. (OFC), 2015.
+[31] S. Mondal and M. Rufﬁni, “A Min-Max Fair Resource Allocation
+Framework for Optical x-haul and DU/CU in Multi-tenant O-RANs,”
+in 2022 IEEE Int. Conf. Commun. (ICC), May 2022, pp. 452–457.
+[32] “5G
+Wireless
+Fronthaul
+Requirements
+in
+a
+Passive
+Op-
+tical
+Network
+Context,”
+Telecommunication
+Standardization
+Sector
+of
+ITU
+(ITU-T),
+Tech.
+Rep.,
+Sep
+2020.
+[On-
+line].
+Available:
+https://www.itu.int/rec/dologin pub.asp?lang=e&id=
+T-REC-G.Sup66-202009-I!!PDF-E&type=items
+[33] M. Rufﬁni et al., “Virtual DBA: Virtualizing Passive Optical Networks
+to Enable Multi-service Operation in True Multi-tenant Environments,”
+IEEE/OSA J. Opt. Commun. Netw., vol. 12, no. 4, pp. B63–B73, 2020.
+[34] F. Slyne, S. Zeb, and M. Rufﬁni, “Stateful DBA Hypervisor Supporting
+SLAs with Low Latency and High Availability in Shared PON,” in 2021
+Opt. Netw. Commun. Conf. Exhibit. (OFC), 2021, pp. 1–3.
+[35] “Small
+Cell
+Virtualization
+Functional
+Splits
+and
+Use
+Cases,”
+2015.
+[Online].
+Available:
+https://scf.io/en/documents/159 - Small
+Cell Virtualization Functional Splits and Use Cases.php
+[36] “Study on new radio access technology: Radio access architecture
+and interfaces,” 2017, accessed: 2022-07-02. [Online]. Available:
+https://www.3gpp.org/DynaReport/38801.htm
+[37] T. Tashiro, S. Kuwano, J. Terada, T. Kawamura, N. Tanaka, S. Shige-
+matsu, and N. Yoshimoto, “A Novel DBA Scheme for TDM-PON based
+Mobile Fronthaul,” in 2014 Opt. Netw. Commun. Conf. Exhibit. (OFC),
+2014, pp. 1–3.
+[38] M. Shehata et al., “Multiplexing Gain and Processing Savings of 5G
+Radio-Access-Network Functional Splits,” IEEE Trans. Green Commun.
+Netw., vol. 2, no. 4, pp. 982–991, 2018.
+[39] S. Khatibi, K. Shah, and M. Roshdi, “Modelling of Computational
+Resources for 5G RAN,” in 2018 European Conference on Networks
+and Communications (EuCNC), 2018, pp. 1–5.
+[40] E. K. P. Chong and S. H. ˙Zak, “Multiobjective optimization,” in An
+Introduction to Optimization.
+John Wiley & Sons, Ltd, 2008, ch. 23,
+pp. 541–562.
+[41] L. M. Ausubel and P. Cramton, “Auctioning Many Divisible Goods,”
+Journal of the European Economics Association, vol. 2, pp. 480–493,
+2004.
+[42] Y. Narahari, “Vickrey-Clarke-Groves (VCG) Mechanisms,” in Game
+Theory and Mechanism Design.
+World Scientiﬁc Publishing Company
+Pvt. Ltd., 2014, ch. 18, pp. 267–284.
+[43] R. S. Sutton and A. G. Barto, Introduction to Reinforcement Learning,
+1st ed.
+Cambridge, MA, USA: MIT Press, 1998.
+[44] D. H. Hailu et al., “Mobile fronthaul transport options in C-RAN
+and emerging research directions: A comprehensive study,” Optical
+Switching and Networking, vol. 30, pp. 40–52, 2018.
+[45] Y. Nakayama et al., “Efﬁcient DWBA Algorithm for TWDM-PON with
+Mobile Fronthaul in 5G Networks,” in 2017 IEEE Global Commun.
+Conf. (GLOBECOM), 2017, pp. 1–6.
+[46] “Preliminary Fiber Network Design and Business Plan Framework,”
+Columbia Telecommunications Corporation, Tech. Rep., Jun 2005.
+[47] Y. Xiao et al., “Can Fine-Grained Functional Split Beneﬁt to the
+Converged Optical-Wireless Access Networks in 5G and Beyond?” IEEE
+Trans. Netw. Service Manag., vol. 17, no. 3, pp. 1774–1787, 2020.
+[48] Y. Narahari, Game Theory and Mechanism Design.
+World Scientiﬁc
+Publishing Company Pvt. Ltd., 2014.
+Sourav Mondal (GS’16–M’21) received PhD from
+the Department of Electrical and Electronic Engi-
+neering of the University of Melbourne in 2020. He
+received his M.Tech in Telecommunication Systems
+Engineering from the Department of Electronics
+and Electrical Communication Engineering, Indian
+Institute of Technology Kharagpur and B.Tech in
+Electronics and Communication Engineering from
+Kalyani Govt. Engineering College, afﬁliated to
+West Bengal University of Technology in 2014 and
+2012, respectively. He was employed as an Engineer
+in Qualcomm India Pvt. Ltd. from 2014 to 2016. Currently, he is working as
+an EDGE/Marie Skłodowska-Curie post-doctoral fellow at CONNECT Centre
+for Future Networks and Communication in Trinity College Dublin, Ireland.
+Marco Rufﬁni received the M.Eng. degree in
+telecommunications from the Polytechnic University
+of Marche, Italy, in 2002, and the Ph.D. degree
+Trinity College Dublin (TCD) in 2007, where he
+joined Trinity College Dublin in 2005, after working
+as a Research Scientist with Philips, Germany. He
+is Associate Professor and Fellow of Trinity College
+and he is Principal Investigator of both the IPIC
+Photonics Integration Centre and the CONNECT
+Telecommunications Research Centre. He is cur-
+rently involved in several Science Foundation Ireland
+and H2020 projects, including a new research infrastructure to build a beyond
+5G testbed in Dublin. Prof. Rufﬁni leads the Optical Network Architecture
+Group, TCD and has authored over 150 international publications, over ten
+patents and contributed to standards at the broadband forum. He has raised
+research funding in excess of e7M. His main research is in the area of 5G
+optical networks, where he carries out pioneering work on the convergence
+of ﬁxed-mobile and access-metro networks, and on the virtualization of next
+generation networks, and has been invited to share his vision through several
+keynote and talks at major international conferences across the world. He
+leads the new SFI funded Ireland’s Open Networking testbed infrastructure.
+
+一
\ No newline at end of file
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+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf,len=1030
+page_content='1  Fairness Guaranteed and Auction-based x-haul and  Cloud Resource Allocation in Multi-tenant O-RANs  Sourav Mondal, Member, IEEE and Marco Rufﬁni, Senior Member, IEEE  Abstract—The open-radio access network (O-RAN) embraces  cloudiﬁcation and network function virtualization for base-  band function processing by dis-aggregated radio units (RUs),  distributed units (DUs), and centralized units (CUs).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' These enable  the cloud-RAN vision in full, where multiple mobile network  operators (MNOs) can install their proprietary or open RUs, but  lease on-demand computational resources for DU-CU functions  from commonly available open-clouds via open x-haul interfaces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  In this paper, we propose and compare the performances of  min-max fairness and Vickrey-Clarke-Groves (VCG) auction-based  x-haul and DU-CU resource allocation mechanisms to create  a multi-tenant O-RAN ecosystem that is sustainable for small,  medium, and large MNOs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' The min-max fair approach minimizes  the maximum OPEX of RUs through cost-sharing proportional  to their demands, whereas the VCG auction-based approach  minimizes the total OPEX for all resources utilized while extracting  truthful demands from RUs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' We consider time-wavelength division  multiplexed (TWDM) passive optical network (PON)-based x-  haul interfaces where PON virtualization technique is used  to ﬂexibly provide optical connections among RUs and edge-  clouds at macro-cell RU locations as well as open-clouds at the  central ofﬁce locations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Moreover, we design efﬁcient heuristics  that yield signiﬁcantly better economic efﬁciency and network  resource utilization than conventional greedy resource allocation  algorithms and reinforcement learning-based algorithms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  Index Terms—Min-max fairness, MORAN, multi-tenant open-  radio access networks, resource allocation, VCG auction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' INTRODUCTION  The ﬁfth-generation (5G) radio access networks (RANs)  are standardized to meet a diverse set of QoS requirements  to support broadband, low-latency, and machine-type commu-  nications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Applications like mixed reality, telesurgery, high-  deﬁnition video streaming, and Industrial Internet-of-Things,  to name a few, will be free from the spectrum crunch and  network resource scarcity issues of the legacy RANs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' However,  the existing mobile networks with their “one size ﬁts all” archi-  tecture lack sufﬁcient ﬂexibility and intelligence for efﬁcient  catering of such requirements [1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Therefore, the necessity for  a major architectural revolution is envisaged for beyond 5G  and sixth-generation (6G) RANs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Over the past few years,  major mobile network operators (MNOs) across the globe  are collaborating within the Open-RAN (O-RAN) Alliance to  standardize an open and smart RAN architecture that can  perform complex RAN management with the aid of software-  deﬁned networking (SDN), network function virtualization  (NFV), and edge computing (EC) technologies [2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' This ar-  chitecture typically follows 3GPP recommendations where the  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Mondal and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Rufﬁni are with CONNECT Centre for Future Networks  and Communication, Trinity College Dublin, University of Dublin, Dublin 2,  Ireland (e-mail: somondal@tcd.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='ie, marco.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='rufﬁni@tcd.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='ie).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  This work is ﬁnancially supported by EU H2020 EDGE/MSCA (grant  713567) and Science Foundation Ireland (SFI) grants 17/CDA/4760 and  13/RC/2077 P2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' 1: A schematic diagram showing O-RAN architecture with  functions of RU, O-DU, and O-CU and their corresponding interfaces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  RUs perform low-PHY functions (typically split 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='2 and 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='3),  while high-PHY, MAC, RLC, RRC, and PDCP functions are  processed by the DU-CUs that can be hosted on OLT-Clouds  with commercial off-the-shelf (COTS) hardware, as shown in  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Recently, the IEEE P1914.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='1 standardization working  group was created to specify the next-generation front-haul  interface (NGFI).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' The RU-DU interface is known as the NGFI-  I, or the front-haul (maximum one-way latency bound = 100  µsec), and the DU-CU interface is known as the NGFI-II or  the mid-haul (maximum one-way latency bound = 1 msec)  [3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' The interface beyond CU to the 5G core is known as the  back-haul;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' hence, the general term x-haul is used.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  The incorporation of open clouds for DU-CU function  processing over the open front/mid-haul interfaces in the  O-RAN architecture creates new business opportunities for  small, medium, and large MNOs as well as network service  providers (NSPs) [4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' In turn, this creates a multi-tenant O-  RAN ecosystem where several MNOs deploy their RUs with  macro and small-cell coverage over a certain geographic area  but procure front/mid-haul and DU-CU function processing  resources from the open and shared resource pool provided by  various NSPs [5].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' The primary beneﬁt of this multi-tenant O-  RAN architecture is minimization of the CAPEX and OPEX  for the MNOs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' The techno-economic analysis in [6] shows  that ∼40% CAPEX and ∼15% OPEX over 5 years can  be reduced by adopting SDN-based architectures for mobile  network virtualization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' In practice, government, municipality,  or an alliance of MNOs can be the NSP that owns the open  x-haul and cloud resources and distribute the resources among  the MNOs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' On the other hand, a competitive market model can  also be created where the MNOs compete against each other  or form opportunistic coalitions for procuring their required  x-haul and cloud resources.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' These observations motivate us to  propose efﬁcient resource allocation mechanisms that create a  multi-tenant O-RAN ecosystem that is sustainable for small,  medium, and large MNOs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  The cloud servers installed at a central ofﬁce (CO) or optical  line terminal (OLT) locations are referred to as OLT-Clouds,  but their signiﬁcant intermediate distance may become disad-  vantageous for supporting low-latency applications and front-  This article is currently undergoing through review process for possible publication in IEEE Transactions in Communications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='00597v1  [cs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='NI]  2 Jan 2023  0O2  haul interfaces (typical PON length ≥ 10 km).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' This hurdle  can be overcome by installing Edge-Clouds at macro-cell RU  locations to host DU-CU and local core functions for some  of the neighboring small-cell RUs [7].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Moreover, efﬁciently  utilizing geographically distributed Edge-Clouds can lead to a  better cost efﬁciency of a RAN than centralized OLT-Clouds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  Nonetheless, the RUs supporting latency-tolerant broadband  applications can be connected to OLT-Cloud and 5G core  without such issues.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Therefore, we consider the TWDM-PON  architecture proposed in [8] as the x-haul interfaces to create  a logical mesh topology that facilitates the small-cell RUs  to be connected with OLT-Clouds at CO locations or Edge-  Clouds at macro-cell RU locations in a ﬂexible manner.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' This  architecture supports East-West communication along with  traditional North-South communication and its efﬁciency over  similar architectures in literature was also proven in [8].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  We critically observe that a large body of the existing litera-  ture mainly focuses on allocating computational resources only  and ignores communication resources of the x-haul interfaces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  Moreover, while connecting RUs from different MNOs to  either Edge-Cloud or OLT-Cloud over the open front/mid-  haul interfaces, the OPEX of the RUs are calculated by  either of the well-known methods like uniform sharing, utility  maximization, min-max fairness, and proportional fairness [9].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  Note that this resource allocation problem can be considered  as an assignment problem, but the RUs can not demand any  speciﬁc amount of resources as in the conventional setting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  Each RU only knows its front/mid-haul datarate and RU-  DU-CU processing requirements corresponding to its split  option.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' After all the RUs inform their respective front/mid-  haul datarate to the NSP, sufﬁcient resources are allocated  by the NSP such that the front/mid-haul data generated by  the RUs in each slot duration (5G slot duration can be  125, 250, 500, or 1000 µsec) are transmitted and processed  within the maximum latency bounds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Therefore, in the uniform  sharing approach, when the cost of total utilized resources is  uniformly distributed among the RUs, inefﬁciency may arise  if RUs with lower resource requirements pay higher prices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  In the utility maximization approach, the proﬁt of the NSP  is maximized while RUs are connected to Edge/OLT-Clouds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  Hence, the RUs from wealthy MNOs will get priority and the  RUs from poor MNOs may suffer from resource starvation  at high-load conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' The proportional fairness is a fair  resource allocation method where fairness is achieved through  maximization of a logarithmic utility function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  Nevertheless, in this paper, we embrace the min-max fair-  ness approach with proportional cost sharing method, where  we connect the RUs to Edge/OLT-Clouds such that the maxi-  mum OPEX of the RUs is minimized by allocating resources  proportional to their demands and satisfy their latency re-  quirements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Also, the RUs from different MNOs are fairly  chosen for allocation such that poor MNOs do not suffer  heavily during high-load conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' We design this method  for creating a multi-tenant O-RAN ecosystem where all the  small, medium, and large MNOs get fair opportunities for  OPEX minimization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' However, the decisions made by this  scheme strongly depend on the revealed resource demands of  the RUs to the NSPs and the RUs may not be always truthful  in revealing their resource demands if there exist opportunities  to gain extra incentives from the market.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' This motivates  us to design a Vickrey-Clarke-Groves (VCG) auction-based  mechanism that allocates resources to RUs while minimizing  the cost of total utilized resources but uses a special payment  rule that enforces truthful revelation of resource requirements  as a weakly dominant strategy equilibrium for the RUs [10].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  Our primary contributions in this paper are:  (a) We propose a multi-tenant O-RAN architecture where RUs  from small, medium, and large MNOs can be connected  to Edge/OLT-Clouds for their DU-CU functions for low-  latency and broadband applications in a sustainable man-  ner over TWDM-PON-based front/mid-haul interfaces via  East-West and North-South links.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  (b) We formulate an integer non-linear program (INLP) for  the min-max fair resource allocation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' In this formulation,  we minimize the maximum cost for leasing front/mid-haul  and DU-CU resources of each RU (resource allocation is  proportional to demand) while satisfying the latency re-  quirements of the low-latency and broadband applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  (c) We formulate a second INLP for the VCG auction-based  resource allocation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' In this formulation, we minimize the  total cost for leasing front/mid-haul and DU-CU resources  of all the RUs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Moreover, a payment rule is designed  that ensures truthful revelation of resource demands of the  RUs to prevent them from taking unfair advantages while  paying for consumed resources.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  (d) We design polynomial-time algorithms for efﬁcient imple-  mentation of the min-max fair and VCG auction formula-  tions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Furthermore, we compare the economic efﬁciency  and network resource utilization achieved by our proposed  algorithms against state-of-the-art nearest-ﬁrst (greedy)  and reinforcement learning-based (multi-arm bandit) al-  gorithms through numerical evaluation to showcase their  usefulness in practice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  The rest of this paper is organized as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Section II  reviews some related works.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Section III describes the multi-  tenant O-RAN architecture.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Section IV presents the system  model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Section V presents the min-max fairness, VCG auction,  and baseline (greedy nearest-ﬁrst and reinforcement learning-  based) methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Section VI presents numerical evaluation  results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Finally, Section VII provides the concluding remarks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' REVIEW OF RELATED WORKS  Resource allocation and management problems are funda-  mental research challenges in any networking environment  and a large volume of literature exists on this area spanning  across all types of network scenarios [11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' The O-RAN for  beyond 5G/6G mobile communication systems is no exception  to this as its ﬂexibility in terms of bandwidth, latency, and QoS  requirements introduces several interesting research challenges  [12].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Before the O-RAN architecture was proposed, several  resource allocation or radio resource head (RRH) to base-  band unit (BBU) assignment problems were solved using  mathematical optimization and game theoretic tools for the  Cloud-RAN (C-RAN) architecture by the authors of [13]–  [16].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' The authors of [17] designed a dynamic two-stage  3  Macro RU  Small RU  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' 2: The proposed TWDM-PON-based multi-tenant O-RAN architecture where RUs from multiple MNOs (hexagonal macro-cell and  circular small-cell coverage area are shown in blue, green, and orange for three different MNOs) can be connected to Edge-Cloud or CO  OLT-Cloud via the North-South or East-West virtual-PONs (indicated by red A, B, C) for the respective DUs and CUs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  mechanism for downlink resource allocation and BBU-RRH  assignment in C-RAN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' The authors of [18] investigated a  joint RRH-BBU association and energy sharing problem to  minimize brown energy usage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Again, the authors of [19]  investigated the RRH-BBU mapping problem to minimize the  network power consumption by reducing the number of active  BBUs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Moreover, the authors of [20] studied the joint RRH  clustering and RRU activation problem with QoS constraints  to minimize the energy consumption of RRHs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' The authors of  [21] demonstrated a multi-vendor multi-standard PON for 5G  x-haul that performs the control and management operations  by SDN/NFV technologies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  After the formation of the O-RAN Alliance, as the standard-  ization of virtualized RAN started, researchers from academia  and industry started to propose various interesting solutions  to overcome O-RAN deployment and resource management  challenges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Recently, the authors of [22] provided a very  elaborate overview of the architecture and components of O-  RAN, explored artiﬁcial intelligence (AI)-based use cases,  and discussed various research opportunities across different  engineering sectors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' The authors of [23] provided detailed  discussions on the ongoing O-RAN Alliance standardization  activities with various analyses supported by a study of the  trafﬁc steering use case in a modular way following the  open networking approach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' We also shared several insights  on optical transmission network (OTN) and optical distributed  network (ODN)-based front/mid-haul network design for O-  RANs from our observations in [24].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Alongside these, the  authors of [25] formulated a two-step mixed-integer pro-  gramming problem for ﬁnding the optimal power allocation,  physical resource block (PRB) assignment, the number of  virtual network functions (VNFs), and the number of RUs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' The  authors of [26] modeled the RU-DU assignment problem as a  2D bin packing problem and proposed a deep reinforcement  learning-based self-play method to achieve efﬁcient RU-DU  resource management.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Moreover, the authors of [27] designed  a team learning algorithm for implementing a near-real-  time (near-RT) radio intelligent controller (RIC) of O-RAN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  However, neither of the aforementioned works focused on  the challenges of designing ﬂexible front/mid-haul interfaces  between RUs and Edge/OLT-Clouds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Moreover, no compar-  ative analysis is available between the conventional greedy  heuristics and learning-based resource allocation algorithms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  Another important aspect of the O-RAN architecture, which  essentially evolves from the C-RAN architecture, is its natural  ability to facilitate multi-tenancy, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=', a pool of network  resources can be shared among multiple MNOs [28].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' The  multi-operator RAN (MORAN) allows two or more MNOs  to share every component of a RAN except the radio carriers,  whereas the multi-operator core network (MOCN) allows two  or more core networks to share the same RAN or the carriers  [29].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' In [30], the authors demonstrated a virtual network  controller enabled multi-tenant virtual network on top of multi-  technology OTNs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' We also performed some initial studies  on the resource allocation problem for multi-tenant O-RAN  ecosystems in [31].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' However, a more detailed investigation of  system performance, economic analysis, and robust resource  allocation mechanisms implementable in a practical competi-  tive market scenario is required.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' MULTI-TENANT O-RAN ARCHITECTURE  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' 2 shows the considered O-RAN architecture in a multi-  tenant scenario where multiple MNOs install neighboring RUs  with hexagonal macro-cell and circular small-cell coverage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  B4BCXX4  Each MNO pays a fee for leasing networking (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=', for x-  haul) and computing resources (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=', DU-CU processing at  Edge/OLT-Clouds) according to a certain payment scheme.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  Furthermore, all the MNOs need to pay a default price to  the mediator, acting as the open platform provider to cover  the cost of the resources required for RAN management and  control plane operations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Recently, ITU-T has drafted recom-  mendations for using TWDM-PONs as an optical front/mid-  haul solution as TWDM-PONs can support 100 Gbps or more  aggregated datarate (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=', in upcoming standardization) which  can be scaled further by combining additional wavelengths  [32].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Moreover, other recent work has addressed PON slicing  isolation [33] and compliance with service level agreement  (SLAs) [34].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Thus, TWDM-PON-based interfaces are used  to connect both the macro and small-cell RUs to a CO with  multi-level reﬂective splitters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' These splitters are designed so  that they can be dynamically reconﬁgured to pass through or  reﬂect back (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=', towards the end points) the desired set of  wavelengths (the concept is taken from [8]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' The wavelengths  that are passed through, establish the North-South commu-  nication links (downlink: green, uplink: blue), whereas the  reﬂected wavelengths establish the East-West communication  links (downlink: purple, uplink: red).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' In terms of network  hierarchy, each level-1 reﬂective splitter aggregates multiple  RUs and each level-2 reﬂective splitter aggregates multiple  level-1 reﬂective splitters and all their respective RUs for a  cost-efﬁcient deployment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' A set of level-1 reﬂective splitters  are used to connect RUs and Edge-Clouds directly, while  multiple level-1 reﬂective splitters are connected to a level-  2 reﬂective splitter to reach through other PON branches.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  A local connectivity between small-cells and macro-cells via  East-West communication links can be achieved by installing  an Edge-OLT at the macro-cell, while the small-cells can  host a simple ONU.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Control signals via the North-South  communication links can be sent to these Edge-OLTs at macro-  cells and ONUs at small-cells to create virtual-PON instances  that communicate via the East-West communication links.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' For  example, three virtual-PON instances are shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' 2 and  the ONUs and Edge-OLTs belonging to the same virtual-PON  are labeled as A, B, and C in red.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' This direct communication  enables ultra-low latency and ultra-low jitter communications  as the signals remain in the optical domain while reﬂected  back at the splitter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Note that ONUs in virtual-PON instance  A communicate only via level-1 reﬂective splitter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' The same  occurs for instance C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' However, ONUs in virtual-PON instance  B can communicate via both level-1 and level-2 reﬂective split-  ters (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=', they extend across two PON branches).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Both OLT  and Edge-Clouds can host the DU-CU functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Although the  OLT-Clouds host the main 5G core, the Edge-Clouds can be  used to host local 5G cores [7].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' The back-haul trafﬁc can be  routed to the remote data centers via metro and core networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' 3 shows the user plane and control plane interfaces of  the proposed TWDM-PON-based multi-tenant O-RAN archi-  tecture.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' The RUs for ultra-reliable and low-latency (uRLLC)  services are prioritized to be connected to Edge-Clouds,  whereas RUs for enhanced mobile broadband (eMBB) services  can be ﬂexibly connected to Edge/OLT-Clouds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Although  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' 1 shows the most general schematic to highlight the  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' 3: A schematic diagram showing the user plane and control plane  interfaces of the proposed TWDM-PON-based multi-tenant O-RAN  architecture that supports uRLLC and eMBB services.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  ﬂexible RAN deployment options provided by the O-RAN  architecture, we choose to place DU and CU functions at a  common Edge/OLT-Cloud because this is the most efﬁcient  conﬁguration for uRLLC and eMBB applications in our judg-  ment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' The near-RT RIC mainly interacts with DUs and CUs by  the E2 interface whose control loops operate with a periodicity  between 10 msec and 1 sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' The near-RT RIC consists of  multiple applications called xApps for per-UE controlled load-  balancing, resource block management, interference detection  and mitigation, QoS management, connectivity management,  and seamless handover control.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Alongside this, the near-RT  RIC is connected to the non-real time (non-RT) RIC by the  A1 interface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' This non-RT RIC is a component of the service  management and orchestration (SMO) framework and consists  of rApps to complement the near-RT RIC for intelligent RAN  operation and optimization on a time scale larger than 1 sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  Therefore, our proposed resource allocation algorithms in this  paper can be implemented as control mechanisms that involve  the periodic exchange of information and decision between  RUs, Near-RT RIC, and Non-RT RIC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' We consider that the  RUs report their incoming resource demands to SMO every  1 sec over the O1 interface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Observing the information over  a few seconds interval (operators decide based on the dy-  namicity of trafﬁc), the rApps execute our proposed decision-  making algorithms and pass on the decision to COs over the  O1 interface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Accordingly, RUs are connected to Edge/OLT-  Clouds over North-South or East-West TWDM-PON links.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' All  the intermediate UE connectivity and handover management  functions are taken care of by the xApps in near-RT RIC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' SYSTEM MODEL  In  this  section,  we  describe  the  TWDM-PON-based  front/mid-haul communication and RU-DU-CU function pro-  cessing models considered for our problem formulation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' The  datarate for the front/mid-haul interface mainly depends on  the split option chosen between RU and DU [35].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' With  Split-7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='2, all the radio frequency processing, fast Fourier  transform (FFT)/inverse FFT, cyclic preﬁx removal/addition,  digital beamforming, and resource element mapping are done  at the RU.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' The datarate can be calculated as follows [35]:  W7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='2 = NP × NRB × N SC  RB×N SF  sym × T −1  SF  × µ × NQ × 2 × ζ,  (1)  Periodic and bursty front /mid-haul trafficRandomly distributed back-haul traffic5  where, NP denotes the number of antenna ports, NRB denotes  the number of resource blocks (RB), N SC  RB denotes the number  of sub-carriers per RB, T −1  SF denotes sub-frame duration, µ  denotes the maximum RB utilization, NQ denotes the quan-  tizer bit resolution per I/Q dimension, and ζ denotes the front-  haul overhead.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' With Split-7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='3, precoding, layer mapping, and  modulation are also done with the aforementioned tasks and  the datarate is calculated as follows:  W7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='3 = NL × NRB × N RB  SC × N SF  sym × T −1  SF  × µ × (1 − η) × NQ × log2(Mmod) × ζ,  (2)  where, NL denotes the number of spatial layers, η denotes  resource overhead, and Mmod denotes the modulation order.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  Note that 3GPP recommends Split-7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='3 mainly to be used  for downlink transmission, but Split-7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='2 can be used for  both uplink and downlink [36].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' As front/mid-haul data are  transmitted as periodic bursts of Ethernet frames, the number  of frames in a burst can be calculated as B = ⌈RD × δt/P⌉,  where RD denotes the front/mid-haul datarate, δt denotes the  burst interval duration, and P denotes the payload size of an  Ethernet frame (1500 Bytes).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Hence, the actual throughput  of a ﬂow can be calculated by (B × F/δt), where F is  the maximum Ethernet frame size (1542 Bytes).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' This data  is transmitted over TWDM-PON and cooperative dynamic  bandwidth allocation (Co-DBA) protocol [37] is used for  coordinating RAN and PON capacity scheduling in the uplink  transmission.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Furthermore, it is crucial to note that sufﬁcient  communication resources should be available for each RU to  transmit each burst of front/mid-haul data to DU-CU without  failure to ensure a successful end-to-end communication.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  The total RU-DU-CU function processing effort per slot in  Giga operations per second (GOPS) is given by [38]:  CRDC =  �  3Na + N 2  a + 1  3 × M × Ψ × NL  �  × NRB  5  , (3)  where, Na denotes the number of MIMO antennas, M denotes  the number of modulation bits, and Ψ denotes the coding rate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  This total computational effort CRDC is distributed among RU,  DU, and CU based on the chosen intermediate split options.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  For example, 40% processing is done by RU with Split-7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='2, but  50% processing is done by RU with Split-7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' The remainder  of the processing is done by the DU-CU and the total RU-  DU-CU processing time can be computed by the polynomial  expressions provided in [39].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' ASSIGNMENT OF RUS TO EDGE/OLT-CLOUDS  HOSTING DU/CU FUNCTIONS  In this section, we formulate two problems for connecting  the RUs to some Edge/OLT-Cloud over front/mid-haul inter-  faces that hosts both the corresponding DU and CU functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  We also design some efﬁcient heuristics for both the problem  formulations that can be implemented in practice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' We consider  that both macro-cell and small-cell radio heads can support  either or both uRLLC and eMBB applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Therefore, two  separate RUs can be created by slicing the total available radio  resources, which need to be optimally connected to Edge-  Cloud via East-West communication links or OLT-Cloud via  North-South communication links.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' At ﬁrst, we formulate a  min-max fair resource allocation problem that creates a multi-  tenant O-RAN ecosystem where all the small, medium, and  large MNOs get fair opportunities for OPEX minimization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' In  this scheme, each RU pays the price for allocated resources  in proportion to their demand.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' However, to prevent afﬂuent  MNOs from inﬂuencing the fairness of resource allocation by  revealing a higher resource demand, we formulate a VCG  auction-based resource allocation problem with a different  allocation and payment rule that makes each RU pay a price  that is independent of their respective resource demand but  dependent on the resource demands of other RUs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Thus, the  RUs cannot gain any incentive by revealing any false resource  demand.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Although this formulation ensures truthful resource  demand revelation from all the RUs, it cannot guarantee a  fair OPEX for all MNOs because it minimizes the OPEX  of the overall network and does not consider the OPEX of  RUs individually.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Therefore, NSPs can choose the min-max  fairness resource allocation mechanism where truthful demand  revelation is possible through strict market regulations (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=',  huge economic penalty or market ban on detection of false  information).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' For an open and competitive market scenario,  the NSPs can choose the VCG auction-based mechanism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' In  addition to these, we design a nearest-ﬁrst (greedy) and a  reinforcement learning-based resource allocation mechanism  for performance comparison.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Min-Max Fairness Guaranteed Resource Allocation  Our primary objective here is to allocate front/mid-haul  and DU-CU resources for RUs such that the OPEX of RUs  with worst/high values are minimized.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' We denote the set of  uRLLC RUs by Ru = {1, 2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' , Ru} and the set of eMBB  RUs by Rm = R \\ Ru, where R = {1, 2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' , Ru, Ru +  1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' , Ru + Rm}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Note that at each RU location, one RU for  uRLLC services and one RU for eMBB services can coexist,  whose data are scheduled to be transmitted at different PRBs  within each slot.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Also, we denote the set of Edge-Clouds by  E = {1, 2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' , E}, and the set of OLT-Clouds by Q = Y \\ E,  where Y = {1, 2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' , E, E + 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' , E + Q}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' The binary  variable xry denotes if an RU r ∈ R is connected to an  Edge/OLT-Cloud y ∈ Y, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=',  xry =  �  1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  if RU r and Edge/OLT-Cloud y are connected  0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  otherwise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  The parameter zry indicates if RU r ∈ R and Edge/OLT-  Cloud y ∈ Y can be connected over a virtual-PON (East-  West or North-South) when its value is 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' The parameters  Cr, Cλ, and CP denote the default cost to the mediator (e),  the cost for throughput used (e/Gbps), and the cost for cloud  resources leased (e/GOPS) by each RU r, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' As  the Edge-Clouds are located at some macro-cell RU location,  they can be owned by the respective MNO, and the attached  RUs from the same MNO do not need to pay the costs of  computational resources.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' The neutral NSP can also own the  Edge-Clouds, but it needs to provide some price discount to the  respective MNOs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' To incorporate these facts, we incorporate  a discount factor γry ∈ [0, 1] where γry = 0 indicates full  discount and γry = 1 indicates no discount.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' The parameters  6  W UL  r  and W DL  r  denote the uplink and downlink front/mid-  haul datarate of RU r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' The parameters BUL  y  , BDL  y  , ∀y ∈ E  denote the maximum uplink, and downlink throughput of the  East-West TWDM-PON links and BUL  y  and BDL  y  , ∀y ∈ Q  denote the maximum uplink and downlink throughput of the  North-South TWDM-PON links.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' The maximum throughput  of each PON link can vary according to the number of  conﬁgured wavelengths.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' The parameters ηUL  r  and ηDL  r  denote  the required uplink and downlink GOPS/slot, HUL  r  and HDL  r  denote the available uplink and downlink GOPS/slot for RU  processing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' The parameters ΓUL  r  and ΓDL  r  denote the required  GOPS/slot for DU-CU processing of RU r and GUL  y  , GDL  y  denote maximum available GOPS/slot at Edge/OLT-Clouds  y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' The parameter θry denotes the burst interval over which  data are transmitted from ONUs connected to RU r in East-  West or North-South TWDM-PONs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Finally, the parameters  ∆H  r and ∆RDC  r  denote the maximum one-way front/mid-haul  latencies and total RU-DU-CU processing for RU r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Now,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' we  formulate the min-max fair resource allocation problem for a  multi-tenant O-RAN ecosystem as follows:  P1 : min  xry max  r  �  �  �  �  y∈Y  (Cr + CλBry + γryCP Gry) xry  �  �  � (4)  subject to  xry ≤ zry,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' ∀r ∈ R,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' y ∈ Y,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  (5)  �  y∈Y xry ≤ 1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' ∀r ∈ R,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  (6)  Bry =  �  W UL  r  BUL  y  ε + �  r xryW UL  r  �  +  �  W DL  r  BDL  y  ε + �  r xryW DL  r  �  ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  ∀r ∈ R,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' y ∈ Y,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' (7)  Gry =  �  ΓUL  r  GUL  y  ε + �  r xryΓUL  r  �  +  �  ΓDL  r  GDL  y  ε + �  r xryΓDL  r  �  ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  ∀r ∈ R,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' y ∈ Y,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' (8)  xry  �  δry + Dry  vl  �  +  �θT T I  θry  � ��  r xryW UL  r  θry  BUL  y  �  ≤ ∆H  r ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  ∀r ∈ R,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' y ∈ Y,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' (9)  xry  �Dry  vl  �  +  �θT T I  θry  � ��  r xryW DL  r  θry  BDL  y  �  ≤ ∆H  r ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  ∀r ∈ R,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' y ∈ Y,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' (10)  ηUL  r  HUL  r  +  ��  r xryΓUL  r  GUL  y  �  ≤ ∆RDC  r  θT T I  ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' ∀r ∈ R,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' y ∈ Y,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  (11)  ηDL  r  HDL  r  +  ��  r xryΓDL  r  GDL  y  �  ≤ ∆RDC  r  θT T I  ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' ∀r ∈ R,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' y ∈ Y,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  (12)  xry ∈ {0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' 1},' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' ∀r ∈ R,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' y ∈ Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  (13)  The objective function of the problem P1 is given by (4),  which indicates the minimization of maximum OPEX of each  RU r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' The ﬁrst term is the default cost, the second term  is the front/mid-haul throughput leasing cost, and the third  term is the DU-CU function processing resources leasing  cost.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Note that the price for throughput and computational  resources paid by each RU is proportional to their demands.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='The constraint (5) ensures that RU r can be associated with  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='Edge/OLT-Cloud y only when an East-West or North-South  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='TABLE I: Network Parameters and Sets  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='Symbol  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='Deﬁnition  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='Ru  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='Set of RUs for uRLLC services  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='Rm  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='Set of RUs for eMBB services  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='R  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='Set of all RUs present in the system (R = Ru ∪ Rm)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='E  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='Set of Edge-Cloud locations  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='Q  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='Set of OLT-Cloud locations  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='Y  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='Set of all Edge/OLT-Cloud locations (Y = E ∪ Q)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='Dry  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='Distance between RU r ∈ R and Edge/OLT-Cloud y ∈ Y  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='Cr  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='Default cost of participation to the mediator (e)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='Cλ  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='Cost for throughput used (e/Gbps)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='CP  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='Cost for cloud resources leased (e/GOPS)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='W UL/DL  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='r  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='The uplink and downlink front/mid-haul datarate of RU r  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='ΓUL/DL  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='r  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='Required GOPS/slot for DU-CU processing of RU r  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='BUL/DL  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='y  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='Maximum throughput of the TWDM-PON links  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='GUL/DL  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='y  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='Maximum available GOPS/slot at Edge/OLT-Clouds y  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='ηUL/DL  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='r  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='Required uplink and downlink GOPS/slot for RU processing  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='HUL/DL  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='r  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='Available uplink and downlink GOPS/slot for RU processing  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='∆H  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='r  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='Maximum one-way front/mid-haul latency of RU r  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='∆RDC  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='r  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='Maximum RU-DU-CU processing latency of RU r  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='θslot  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='Transmit time slot of RU r  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='θry  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='Transmission burst interval of TWDM-PON uplinks  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='δry  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='The reduced waiting time for uplink data at ONUs  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='vl  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='Speed of light in optical ﬁber (2 × 108 m/s)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='connection exists and the constraint (6) restricts RU r to  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='be connected to one Edge-Cloud or OLT-Cloud y at most.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  The constraints (7) indicates the allocated share of throughput  to RU r over front/mid-haul interface to Edge/OLT-Cloud y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  Similarly, the constraint (8) indicates the allocated share of  GOPS to RU r for DU-CU processing at Edge/OLT-Cloud  y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Note that a very small constant ε ≈ 0 is added to the  denominator of each of the terms in (7)-(8) to avoid division  by zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Furthermore, the constraint (9) ensures that the uplink  front/mid-haul latency from RU r to Edge/OLT-Cloud y is  within ∆H  r .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' The parameter δry denotes the average queuing  latency of uplink data due (considering the use of the Co-DBA  mechanism).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' The second term with xry indicates propagation  latency where the parameter Dry denotes the distance from  RU r to Edge/OLT-Cloud y and vl denotes speed of light  within ﬁber (2 × 105 km/s).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' The third term indicates data  transmission latency where data is transmitted in multiple  bursts of duration θry within each TTI, θT T I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Similarly, con-  straint (10) ensures that the downlink front/mid-haul latency  from RU r to Edge/OLT-Cloud y is within ∆H  r .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Finally, the  constraints (11)-(12) ensure the uplink and downlink RU-DU-  CU processing latencies are within ∆RDC  r  , respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' The  ﬁrst term indicates the RU processing latency and the second  and third terms indicate the DU-CU processing latencies at  Edge/OLT-Cloud y, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Heuristic for the Min-Max Fair Resource Allocation  We observe that P1 is an NP-hard problem and the primary  reason behind the NP-hardness is that the locations of active  Edge/OLT-Clouds are not known when we start to connect  RUs to Edge/OLT-Clouds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Note that the problem P1 has a  unique structure that converts a multi-objective problem into  a single-objective problem such that standard optimization  methods can be employed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' In this case, we convert the  minimization problem of OPEXs of multiple RUs into a min-  imization problem of the maximum OPEX of RUs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' However,  7  the problem P1 is still very inconvenient to solve due to the  presence of max{.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=', .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='} function in the objective.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Therefore, we  need to reformulate this problem into an equivalent epigraph  form as follows:  Pr  1 :  min  xry,M  M  (14)  subject to  M ≥  �  y∈Y (Cr + CλBry + γryCP Gry) xry,  ∀r ∈ R, (15)  constraints (5) − (13).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  It is straightforward to show that an optimal solution for  Pr  1 is also a solution for P1 [40].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Nonetheless, as both these  problems are INLP, the evaluation of an optimal solution  cannot be guaranteed in polynomial time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Hence, a heuristic  algorithm is required.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' In general, we understand that OPEX  of each RU in (4) can be minimized if each front/mid-  haul link and Edge/OLT-Cloud resources are leased by a  maximum number of RUs while satisfying constraints (9)-(12).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  In addition, we observe the following interesting property of  optimal solutions of Pr  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  Proposition 1: An optimal solution of Pr  1 can guarantee  fairness if and only if the OPEX of an RU with lower resource  requirements does not exceed the OPEX of an RU with higher  resource requirements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  Please refer to Appendix A for the proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' In general,  we can achieve the best possible value of M if full-mesh  connectivity is available among RU and Edge/OLT-Clouds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  However, in practice, mostly partial-mesh connectivity can  be observed, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=', constraint (6) along with constraints (9)-  (12) will have a strong inﬂuence on the solution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Nonetheless,  in general, we are able to connect a higher number of RUs  to Edge/OLT-Clouds if we start with lower resource require-  ments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Based on the above insights, we design a heuristic  algorithm, summarized as Algorithm 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' At ﬁrst, we sort the  RUs in R in the increasing order of (max{W DL  r  , W UL  r  })  and (max{ΓDL  r  , ΓUL  r  }).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' This step is crucial to maintain con-  sistency with Proposition 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' We also order the RUs such  that the percentage of ownership of MNOs is uniformly  maintained.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Then we start to iteratively connect each RU  r to an Edge/OLT-Cloud y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' For r = 1, we initialize the  ﬂag assign ← 0, the dummy set ¯Y ← Y, and ﬁnd the  nearest y′ = arg miny{Dry}, y′ ∈  ¯Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' If the constraints  (5), (9)-(12) are satisﬁed for this y′, we set xry′  ← 1,  assign ← 1, and calculate the corresponding OPEX value  Cr = �  y(Cr + CλBry + γryCP Gry)xry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' If this is not  successful, then we remove y′ from ¯Y and continue this  process until ¯Y = ∅.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' In the subsequent iterations, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=', for  1 < r ≤ |R|, we ﬁnd all y ∈ Y that satisfy constraints (5),  (9)-(12) for the current RU r and reinitialize the dummy set  ¯Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' If at least one such y exists, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=', | ¯Y|≥ 1, then we calculate  the dummy OPEX values Cry = (Cr + CλBry + γryCP Gry)  if RU r was connected to each of the Edge/OLT-Cloud y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  Then we ﬁnd y′ = arg miny{Cry}, y′ ∈ ¯Y, set xry′ ← 1,  and calculate the updated values of Bry, Gry, and Cr for all  RUs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' The ﬁrst for loop iterates for |R| times to return xry  and Cr while ﬁnding a suitable Edge/OLT-Cloud y from a  set of maximum size |Y| at every iteration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Therefore, the  Algorithm 1 Algorithm for min-max fair resource allocation  Input: R, E, Y, Dry, BU/DL  y  , W U/DL  r  , ΓU/DL  r  , GU/DL  r  Output: Near-optimal solution: x∗  ry and C∗  r  Initialize: Sort the elements of R in the increasing order  of (max{W DL  r  , W UL  r  }) and/or (max{ΓDL  r  , ΓUL  r  }) while  maintaining an uniform distribution of the percentage of  ownership of MNOs;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  1: for r ← 1 to |R| do  2:  if r = 1 then  ▷ choose best possible r = 1  3:  Set ¯Y ← Y;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  4:  Set assign ← 0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  5:  while assign ̸= 1 and ¯Y ̸= ∅ do  6:  Find y′ = arg miny{Dry}, y′ ∈ ¯Y;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  7:  if constraints (5), (9)-(12) are satisﬁed then  8:  Set xry′ ← 1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  9:  Set assign ← 1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  10:  Calculate Bry, Gry, and Cr;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  11:  else  12:  Set ¯Y ← ¯Y \\ {y′};' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  13:  end if  14:  end while  15:  if assign ̸= 1 and ¯Y = ∅ then  16:  break;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  ▷ infeasibility condition  17:  end if  18:  else if 1 < r ≤ |R| then  19:  Find all y ∈ Y such that constraints (5), (9)-(12)  20:  are satisﬁed for the current RU r and create ¯Y;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  21:  if | ¯Y|≥ 1 then  ▷ if at least one such y exists  22:  Calculate all dummy OPEX values for RU r,  23:  Cry, if r was connected to each of y ∈ ¯Y;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  24:  Find y′ = arg miny{Cry}, y′ ∈ ¯Y;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  25:  Set xry′ ← 1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  26:  Update Bry, Gry, and Cr, ∀r with �  y xry = 1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  27:  else  28:  Set Bry = 0, Gry = 0, and Cr = 0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  29:  end if  30:  end if  31: end for  32: return xry and Cr;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  worst-case time-complexity of this loop, as well as Algorithm  1, is O(|R|×|Y|).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Now, if we denote the optimal number of  Edge/OLT-Cloud as Y ∗, then the number of remaining RUs yet  to be connected at every iteration t of Algorithm 1 is at most  Rt ≤ Rt−1(1−1/Y ∗).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Thus, at the end of all |R| iterations, we  must have 1 ≤ |R|×(1−1/Y ∗)Y|R| = |R|×(1−1/Y ∗)Y ∗×  Y|R|  Y ∗ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  By using the Taylor series approximation (1 − 1/x)x ≈ 1/e,  we get 1 ≤ |R|×(1/e)  Y|R|  Y ∗ , or Y|R| ≤ Y ∗ loge(|R|), where  Y|R| denotes the number of active Edge/OLT-Clouds after all  |R| iterations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Hence, the solution produced by Algorithm 1  approximates the optimal solution by a factor of O(loge(|R|)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' VCG Auction-based Resource Allocation  Although the solution obtained from the min-max fairness  method described in previous sub-sections is very efﬁcient, the  solution is dependent on the private information like W UL  r  ,  W DL  r  , ΓUL  r  , and ΓDL  r  shared by the RUs to the NSP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' To  8  prevent the RUs from sharing false information and gaining  unfair incentives from the market, we design a VCG auction-  based resource allocation method in this sub-section.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Note  that this problem is very close to an auction of multiple  divisible items [41] but with speciﬁc unique characteristics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  Each RU wants to connect to an Edge/OLT-Cloud via some  East-West or North-South TWDM-PON link to avail sufﬁcient  throughput and Edge/OLT-Cloud resources to successfully  transmit its front/mid-haul data generated within each slot  duration, satisfying the maximum latency bounds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Therefore,  the private valuation function of each RU r is given as:  Vr(xry) =  �  �  �  �  �  �  �  �  �  �  �  �  �  �  �  (CλBy + CP Gy)xry;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  if r is connected to  some y with successful  front/mid-haul data  transmission,  0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  otherwise,  where, By = (BUL  y  + BDL  y  ) and Gy = (GUL  y  + GDL  y  ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Note  that if an RU gets connected to some Edge/OLT-Cloud but  fails to transmit its front/mid-haul data, then also its valuation  of resources is zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' We assume that the NSP wants a fair  market competition and hence, keeps the cost parameters  Cr, Cλ, and CP the same for all the competing MNOs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' At  ﬁrst, each RU r submits their front/mid-haul datarate and  DU-CU processing requirements to the NSP as a message  br = ( ˆW UL  r  , ˆW DL  r  , ˆΓUL  r  , ˆΓDL  r  ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' After receiving messages  b = (b1, b2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' , b|R|) from all RUs, the NSP solves the follow-  ing cost-minimization problem while connecting a maximum  number of RUs to Edge/OLT-Clouds and the solution ˆx∗  ry can  be considered as the allocation rule [42].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  P2 :  min  xry,ty  �  �  �  �  y∈Y  (CλBy + CP Gy) ty  �  �  �  (16)  subject to  ty ≤ xry, ∀r ∈ R, y ∈ Y,  (17)  constraints (5) − (6), (9) − (13),  where ty is a binary decision variable and the constraint (17)  implies that ty is equal to 1 if at least one RU r is connected  to the Edge/OLT-Cloud y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  Proposition 2: The allocation rule ˆx∗  ry derived as a solution  of P2 is allocatively efﬁcient.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  Please refer to Appendix B for the proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Although sev-  eral other dominant-strategy truthful mechanisms exist in  the quasi-linear setting1, only with Groves mechanisms, we  can implement an allocative efﬁciency in dominant strategies  among agents with arbitrary quasi-linear utilities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Observe that  the valuation for resources of each RU r is non-zero only if  it is connected to some Edge/OLT-Cloud y and gets sufﬁcient  resources to transmit its front/mid-haul data generated in each  slot within the maximum latency bounds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Otherwise, if an  RU r is unallocated or fails to transmit its front/mid-haul data  generated in each slot within the maximum latency bounds, its  valuation is zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Note that the same resources By and Gy are  shared by multiple RUs that are allocated to Edge/OLT-Cloud  1The utility of agent r with private valuation vr from obtaining a fraction  x of a divisible good at a price p is ur(x, p) = vr(x) − p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Therefore, the net worth of resources allocated to each RU r,  ˆCr varies within [0, (CλBy+CP Gy)].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' This implies that if only  one RU is connected to an Edge/OLT-Cloud y, then it must  bear the cost of the consumed resources ˆCr = (CλBy+CP Gy)  all alone.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' However, if multiple RUs are connected to an  Edge/OLT-Cloud y, then the total cost is uniformly divided  among them, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=', ˆCr = [(CλBy +CP Gy)/�  r ˆx∗  ry].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Using this  observation,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' we design a payment rule for the RUs similar to  Clarke’s mechanism [42] as follows:  Pr(xry,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' b) =  �  ��  j̸=r  ˜Cj(x−r∗  jy (b−r),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' bj)  �  � −  �  ��  j̸=r  ˜Cj(x∗  jy(b),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' bj)  �  �  =  �  j̸=r  �  CλBy + CP Gy  �  k̸=r x∗  ky  �  −  �  j̸=r  �  CλBy + CP Gy  �  k x∗  ky  �  ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' (18)  which can be interpreted as the total cost of all RUs other  than r under an efﬁcient allocation when RU r is absent in  the system minus the total cost of all RUs other than r under  an efﬁcient allocation when RU r is present in the system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  Note that ˆx−r∗  jy  or ˆx−r∗  ky  denote allocation rules when RU r is  absent in the system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  Theorem 1: The payment rule (18) ensures that truthful  private information sharing to NSPs is a weakly dominant  strategy for all RUs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  Please refer to Appendix C for the proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' This also  shows that the mechanism is weakly budget balanced as  �  r Pr(ˆx∗  ry, b) ≥ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' With the aforementioned allocation and  payment rules, the utility of each RU r is deﬁned as follows:  Ur(ˆx∗  ry, b) = Vr(ˆx∗  ry, b) − Pr(ˆx∗  ry, b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  (19)  Therefore, the individual rationality of the RUs is always  maintained in this mechanism as Ur(ˆx∗  ry, b) ≥ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' In addition  to Pr(ˆx∗  ry, b), each RU r also needs to pay the default cost  Cr to the NSP if it is connected to some Edge/OLT-Cloud y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Heuristic for the VCG Auction-based Resource Allocation  As computational efﬁciency is an important property for a  mechanism design, we design a polynomial-time heuristic to  solve the problem P2 as outlined in Algorithm 2 (page 30).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' We  start to iteratively connect each RU r to an Edge/OLT-Cloud  y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' For r = 1, we initialize the ﬂag assign ← 0, the dummy  set ¯Y ← Y, and ﬁnd the nearest y′ = arg miny{Dry}, y′ ∈ ¯Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  If the constraints (5), (9)-(12) are satisﬁed for this y′, we set  ˆxry′ ← 1, ty′ ← 1, assign ← 1, and calculate the cost of total  utilized resources Ctot = �  y∈Y (CλBy + CP Gy) ty, which is  also equal to ˆCr, the shared cost of RU r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' If the assignment  is not successful, then we remove y′ from ¯Y and continue  this process until ¯Y = ∅.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' In the subsequent iterations, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=', for  1 < r ≤ |R|, we ﬁnd all y ∈ Y that satisfy constraints (5),  (9)-(12) are satisﬁed for the current RU r and reinitialize the  dummy set ¯Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' If at least one such y exists, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=', | ¯Y|≥ 1, then  we calculate the dummy costs of total utilized resources Ctot,y  if RU r was connected to each of the Edge/OLT-Cloud y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Then  we ﬁnd y′ = arg miny{Ctot,y}, y′ ∈ ¯Y, set ˆxry′ ← 1, ty′ ← 1,  and calculate the updated value of Ctot.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' We also calculate the  shared cost of RU r as [(CλBy +CP Gy)/�  r ˆxry] for y = y′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  9  Algorithm 2 Algorithm for VCG auction-based allocation  Input: R, E, Y, Dry, BU/DL  y  , W U/DL  r  , ΓU/DL  r  , GU/DL  r  Output: Near-optimal solution: x∗  ry and C∗  r  Initialize: Sort the elements of R in the increasing order  of (max{W DL  r  , W UL  r  }) and (max{ΓDL  r  , ΓUL  r  }) while  maintaining an uniform distribution of the percentage of  ownership of MNOs;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  1: for r ← 1 to |R| do  2:  if r = 1 then  ▷ choose best possible r = 1  3:  Set ¯Y ← Y;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  4:  Set assign ← 0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  5:  while assign ̸= 1 and ¯Y ̸= ∅ do  6:  Find y′ = arg miny{Dry}, y′ ∈ ¯Y;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  7:  if constraints (5), (9)-(12) are satisﬁed then  8:  Set xry′ ← 1 and ty′ ← 1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  9:  Set assign ← 1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  10:  Calculate Ctot and ˜Cr;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  11:  else  12:  Set ¯Y ← ¯Y \\ {y′};' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  13:  end if  14:  end while  15:  if assign ̸= 1 and ¯Y = ∅ then  16:  break;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  ▷ infeasibility condition  17:  end if  18:  else if 1 < r ≤ |R| then  19:  Find all y ∈ Y such that constraints (5), (9)-(12)  20:  are satisﬁed for the current RU r and create ¯Y;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  21:  if | ¯Y|≥ 1 then  ▷ if at least one such y exists  22:  Calculate all dummy cost values for RU r,  23:  Ctot,y, if r was connected to each of y ∈ ¯Y;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  24:  Find y′ = arg miny{Ctot,y}, y′ ∈ ¯Y;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  25:  Set xry′ ← 1 and ty′ ← 1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  26:  Update Ctot and ˜Cr, ∀r with �  y xry = 1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  27:  else  28:  Set ˜Cr = 0 and keep Ctot unchanged;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  29:  end if  30:  end if  31: end for  32: for r ← 1 to |R| do  33:  Set R ← R \\ {r} and execute lines 1-31;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  34:  Calculate Pr(xry, b) and Cr = Cr + Pr(xry, b);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  35:  Set R ← R ∪ {r};' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  ▷ add r back to R  36: end for  37: return xry and Cr;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  Once the RU to Edge/OLT-Cloud allocation is complete, we  calculate the payment rule.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' For this purpose, we solve P2 using  steps 1-31 for another |R| times in the absence of each of the  RUs from R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Thus, we can calculate Pr(ˆxry, b), the payment  made by each RU r using (18) and the OPEX of the RU r  can be calculated as ˆCr = Cr + Pr(ˆxry, b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Note that the ﬁrst  for loop iterates for |R| times to return ˆx∗  ry and tries to ﬁnd a  suitable Edge/OLT-Cloud y from a set of maximum size |Y|  at every iteration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Therefore, the worst-case time-complexity  of this loop is O(|R|×|Y|).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' The second for loop iterates for  |R| times to return ˆCr, but it executes the ﬁrst for loop with  complexity O(|R|−1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Therefore, the overall time-complexity  of Algorithm 2 is O(|R|2×|Y|).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Also, similar to Algorithm  1, it can shown that the solution produced by Algorithm 2  approximates the optimal solution by a factor of O(loge(|R|)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Nearest-First (Greedy) and Reinforcement Learning-based  Resource Allocation Mechanisms  To create a performance baseline, we design a conven-  tional nearest-ﬁrst (greedy) approach-based resource alloca-  tion method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' We select the RUs sequentially and attempt  to associate them to their nearest Edge/OLT-Cloud subject  to the network connectivity (5)-(6), communication latency  (9)-(10), and processing latency (11)-(12) constraints, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=',  y′ = arg min{Dry|y′ ∈ Y, (5) − (6), (9) − (12)}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' For each  RU r, if their most nearest Edge/OLT-Cloud y′ is unavailable,  then we remove y′ from the list of Edge/OLT-Clouds and  proceed to ﬁnd the next nearest Edge/OLT-Cloud.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' In this  way, we iteratively try to assign each RU r to an Edge/OLT-  Cloud y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Once the maximum possible RUs are assigned to all  Edge/OLT-Clouds,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' we can calculate the OPEX of the assigned  RUs as Cr = �  y∈Y  �  Cr + Cλ ˜Bry + CP ˜Gry  �  xry,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' where the  share of throughput and DU-CU function processing resources  for each RU r are considered either as proportional sharing:  ˜Bry =  �  W UL  r  BUL  y  �  r xryW UL  r  �  +  �  W DL  r  BDL  y  �  r xryW DL  r  �  ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  (20)  ˜Gry =  �  ΓUL  r  GUL  y  �  r xryΓUL  r  �  +  �  ΓDL  r  GDL  y  �  r xryΓDL  r  �  ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  (21)  or as uniform sharing:  ˜Bry =  �  BUL  y  �  r xry  �  +  �  BDL  y  �  r xry  �  ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  (22)  ˜Gry =  �  GUL  y  �  r xry  �  +  �  GDL  y  �  r xry  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  (23)  The OPEX of the unassigned RUs are considered equal  to zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' All the steps of this algorithm are summarized in  Algorithm 3 (page 30).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' We observe that the worst-case time-  complexity of the ﬁrst for loop is O(|R|×|Y|) and the time-  complexity of the second for loop is O(|R|).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' This implies that  the overall time-complexity of Algorithm 3 is O(|R|×|Y|).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  In the reinforcement learning-based method, each RU r ran-  domly selects an Edge/OLT-Cloud y and attempts to establish  a front/mid-haul connection by following a multi-arm bandit  algorithm [43].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' The reward of each RU (Rr) is calculated as  the average of ∆H  r to front/mid-haul latency ratio and ∆RDC  r  to RU-DU-CU processing latency ratio.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' The RUs perform  both exploration and exploitation (ϵ-greedy with ϵ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='3,  i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=', explore strategies with probability 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='3, else exploit) to  maximize its cumulative reward values and eventually ﬁnd the  best Edge/OLT-Cloud.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' After RU to Edge/OLT-Cloud allocation  is done, the OPEX of the RUs are calculated as above.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  VI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' RESULTS AND DISCUSSIONS  To evaluate our proposed frameworks, we consider a multi-  tenant O-RAN deployment area of dimension 5×5 km2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' In this  area, 8 macro-cell RUs (coverage = 1 km) and 30 small-cell  10  Algorithm 3 Algorithm for nearest-ﬁrst resource allocation  Input: R, E, Y, Dry, BU/DL  y  , W U/DL  r  , ΓU/DL  r  , GU/DL  r  Output: Near-optimal solution: x∗  ry and C∗  r  Initialize: Sort the elements of R in the increasing order  of (max{W DL  r  , W UL  r  }) and (max{ΓDL  r  , ΓUL  r  }) while  maintaining an uniform distribution of the percentage of  ownership of MNOs;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  1: for r ← 1 to |R| do  2:  Set ˜Y ← Y;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  3:  Set assign ← 0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  4:  while assign ̸= 1 and ˜Y ̸= ∅ do  5:  Find y′ = arg miny{Dry}, y′ ∈ ˜Y;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  6:  if constraints (5), (9)-(12) are satisﬁed then  7:  Set xry′ ← 1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  8:  Set assign ← 1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  9:  else  10:  Set ˜Y ← ˜Y \\ {y′};' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  11:  end if  12:  end while  13: end for  14: for r ← 1 to |R| do  15:  if �  y xry = 1 then  16:  Calculate ˜Bry, ˜Gry, and Cr;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  17:  else  18:  Set ˜Bry = 0, ˜Gry = 0, and Cr = 0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  19:  end if  20: end for  21: return xry and Cr;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  RUs (coverage = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='5 km) from three different MNOs coexist.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  The front/mid-haul datarate and RU-DU-CU processing efforts  of the RUs vary over time depending on the RU conﬁgurations  and the chosen split option.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' For example, if the RUs are  conﬁgured with 2x2 MIMO, 2 layers, 50 MHz bandwidth, 15  kHz sub-carrier spacing, MCS index 16, and slot duration =  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='5 msec, the maximum uplink datarate with Split-7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='2 is 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='304  Gbps, and the maximum downlink datarate with Split-7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='3 is  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='432 Gbps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Each radio head’s total RU-DU-CU processing  requirement is nearly 550 GOPS/slot.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' We consider that in  each radio head, 25% resources are used for uRLLC services  and 75% resources are used for eMBB services.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' The one-way  front-haul link latency bound is ∼100 µsec and we choose the  RU-DU-CU processing latency bound 325 µsec for uRLLC  services and 975 µsec for eMBB services [44].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' The reduced  queueing latency of the uplink data at the ONUs is 15 µsec  as Co-DBA is used for uplink transmission [45] and the data  are transmitted as periodic bursts of duration 31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='25 µsec [7].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  Each wavelength of the TWDM-PON can support a throughput  of 25 Gbps and we can aggregate multiple such wavelengths  to achieve a few hundred Gbps of total throughput.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' A group  of RUs are connected to a level-1 reﬂective splitter (locations  found through k-means clustering) and a few level-1 reﬂective  splitters are connected to a level-2 reﬂective splitter located  at the center of the area.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' We assume that the RUs can  be connected to the OLT-Clouds via the North-South links  and to the Edge-Clouds via creating East-West virtual-PON  links.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' We arbitrarily assume that each RU pays a default cost  (a) Min-max fairness vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' baseline algorithms  (b) VCG auction vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' baseline algorithms  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' 4: Comparison of the total number of active Edge/OLT-Clouds  obtained by the optimal solution, heuristics, and baseline methods  with more computational resources at Edge-Clouds than at OLT-  Clouds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  of e100/day to the NSP (other network economic pricing  schemes can also be employed but beyond the scope of this  paper), although it has very little effect on the results as it  is not associated with any decision variables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' In addition, the  cost for throughput used is e0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='5/Gbps [46], and the cost for  leasing DU/CU resources is e1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='5/GOPS [47].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  Firstly, we compare the optimal solutions of the min-max  fairness and VCG auction-based resource allocation methods  with their corresponding heuristics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' In this evaluation, each  Edge-Cloud has a maximum capacity of 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='5 × 104 GOPS/slot  and each OLT-Cloud has a maximum capacity of 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='5 × 104  GOPS/slot.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' These values are chosen such that a feasible  benchmark solution can be obtained by the greedy baseline  algorithm with front/mid-haul datarate demand upto 2 Gbps  per RU.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' We use OCTERACT, a global optimal mixed-integer  TABLE II: Network Evaluation Scenarios  Scenario - I  Scenario - II  Scenario - III  Edge  OLT  Edge  OLT  Edge  OLT  Maximum  GOPS/slot  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='5 × 104  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='5 × 104  3 × 104  3 × 104  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='5 × 104  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='5 × 104  Maximum  throughput  50 Gbps  600 Gbps  100 Gbps  400 Gbps  150 Gbps  200 Gbps  11  (a) Scenario-I  (b) Scenario-II  (c) Scenario-III  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' 5: Comparison of overall O-RAN outage probability and outage probability for small, medium, and large MNOs against increasing  front/mid-haul datarate demand per RU with different Edge/OLT-Cloud resource distributions obtained by min-max fairness and baseline  (greedy nearest-ﬁrst and reinforcement learning-based) algorithms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  (a) Scenario-I  (b) Scenario-II  (c) Scenario-III  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' 6: Comparison of overall O-RAN outage probability and outage probability for small, medium, and large MNOs against increasing  front/mid-haul data per RU with different Edge/OLT-Cloud resource distributions obtained by VCG auction-based and baseline (greedy  nearest-ﬁrst and reinforcement learning-based) algorithms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  nonlinear programming solver integrated with the AMPL plat-  form to evaluate the optimal solutions of our formulated INLPs  in a computer with Intel Core i7 processor and 32 GB RAM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' 4(a), we compare the optimal solution of Pr  1 against  the solutions obtained using Algorithm 1, the greedy baseline  Algorithm 3, and the reinforcement learning-based method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  Again, in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' 4(b), we compare the optimal solution of P2  against the solutions obtained using Algorithm 2, the greedy  baseline Algorithm 3, and the reinforcement learning-based  method with the same dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' From these ﬁgures, we observe  that the optimal solution of Pr  1 is the highest performing  during lower load conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' The nearest-ﬁrst method makes  several sub-optimal RU to Edge/OLT-Cloud assignments as it  connects each RU to its nearest (based on intermediate North-  South or East-West link distance) Edge/OLT-Cloud if the  latency constraints are satisﬁed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' The reinforcement learning-  based method requires less computation than other methods,  but each RU independently attempts to connect to some  Edge/OLT-Cloud that gives a higher reward, in turn lower  latency values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Thus, the RU to Edge/OLT-Cloud assignment  does not incorporate minimization of overall network resource  utilization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' However, all the solutions at medium and higher  load conditions become similar as network load increases,  because a large percentage of the potential Edge/OLT-Clouds  gets activated and the scope of sub-optimal RU to Edge/OLT-  Cloud assignments reduces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  Next, we compare the network outage probabilities (deﬁned  as the ratio of the total number of RUs that could not be  connected to some Edge/OLT-Cloud to the total number of  RUs present in the network) achieved by our proposed meth-  ods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' We consider that the RUs are owned by three different  MNOs where a small MNO-1 has 20%, a medium MNO-2 has  30%, and a large MNO-3 has 50% ownership.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Additionally, we  consider three scenarios with different computational resource  distributions among Edge-Clouds and OLT-Clouds as outlined  in Table II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' 5(a)-5(c) show the overall O-RAN outage  probabilities obtained through the min-max fairness and base-  line (greedy nearest-ﬁrst and reinforcement learning-based)  algorithms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Similarly, Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' 6(a)-6(c) show the overall O-RAN  outage probabilities obtained through the VCG auction-based  and baseline (greedy nearest-ﬁrst and reinforcement learning-  based) algorithms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' We observe that all the methods show zero  outage probability as long as there are sufﬁcient front/mid-  haul and Edge/OLT-Cloud resources to accommodate all the  12  (a) Scenario-I  (b) Scenario-II  (c) Scenario-III  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' 7: Comparison of the total cost of leased resources (e) and OPEX reduction percentage for small, medium, and large MNOs against  network load variation with different Edge/OLT-Cloud resource distributions obtained by min-max fairness and baseline (greedy nearest-ﬁrst  and reinforcement learning-based) algorithms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  (a) Scenario-I  (b) Scenario-II  (c) Scenario-III  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' 8: Comparison of the total cost of leased resources (e) and OPEX reduction percentage for small, medium, and large MNOs against  network load variation with different Edge/OLT-Cloud resource distributions obtained by VCG auction-based and baseline (greedy nearest-ﬁrst  and reinforcement learning-based) algorithms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  RUs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' However, network outage probability increases fastest  with the reinforcement learning-based method, followed by the  nearest-ﬁrst baseline method due to their inefﬁcient utilization  of network resources, but the outage probability increases rela-  tively slower with the VCG auction-based method and slowest  with the min-max fairness method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' We also plot the outage  probabilities of the small, medium, and large MNOs, which  show that the outage probabilities of the small, medium, and  large MNOs vary according to their percentage of ownership,  i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=', the highest for the large MNO and smallest for the small  MNO, in all scenarios.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  Finally, we compare the total cost of leased front/mid-  haul and Edge/OLT-Cloud resources obtained by the min-max  fairness and baseline (greedy nearest-ﬁrst and reinforcement  learning-based) algorithms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' In Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' 7(a)-7(c), we observe that  during the low-load conditions, the performance of the min-  max fairness approach is signiﬁcantly better than the baseline  (greedy nearest-ﬁrst and reinforcement learning-based) meth-  ods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' However, as the front/mid-haul datarate demand per RU  increases, the performance of all algorithms becomes similar  due to the saturation of available resources.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Although the  total cost of leased resources (right y-axis) increases as we  place more resources at the Edge-Clouds, the percentage of  OPEX savings decreases (left y-axis) as resource utilization  increases for all the MNOs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' In all scenarios, the OPEX saving  percentage is highest for the small MNO and lowest for  the large MNOs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Similarly, Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' 8(a)-8(c) compare the total  cost of leased resources (right y-axis) obtained and OPEX  reduction percentages (left y-axis) by the VCG auction-based  and baseline (greedy nearest-ﬁrst and reinforcement learning-  based) algorithms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' We observe that the total cost of leased  resources obtained by the VCG auction-based algorithm is  very similar to the min-max fairness algorithm, but the OPEX  saving percentages for small and medium MNOs are not  always lower than the large MNO because the cost of the  leased resources is uniformly shared among the RUs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Thus,  often the small and medium MNOs pay a much higher price  than their actual resource requirements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' These results justify  that our proposed min-max fair resource allocation framework  creates a multi-tenant O-RAN ecosystem that is sustainable  for small, medium, and large MNOs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  VII.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' CONCLUSION  In this paper, we have proposed a multi-tenant O-RAN  architecture where RUs from multiple MNOs can lease re-  13  sources for their DU-CU function processing from Edge/OLT-  Clouds over TWDM-PON-based open front/mid-haul inter-  faces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' These TWDM-PONs use reﬂective splitters to facil-  itate East-West communication links along with traditional  North-South communication links for better mesh connectivity  among the RUs and Edge/OLT-Clouds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' We have proposed two  methods for allocating front/mid-haul and DU-CU processing  resources to RUs based on min-max fairness and VCG auction  mechanisms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' In turn, we have formulated the corresponding  INLPs and have designed time-efﬁcient heuristic algorithms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  Through numerical evaluation, we have investigated the per-  formance of these frameworks against different distributions of  cloud resources at Edge and OLT locations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' We have shown  that both min-max fairness and VCG auction-based meth-  ods achieve a much lower network outage probability than  the baseline (greedy nearest-ﬁrst and reinforcement learning-  based) methods due to the efﬁcient utilization of network  resources.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' However, although the VCG auction-based method  can ensure the extraction of truthful information from the RUs,  the min-max fairness method ensures that the OPEX of the  RUs are proportional to their actual resource requirements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  Moreover, we have shown that the min-max fairness method  can reduce the OPEX of all MNOs by more than 20% (at  high load) to nearly 75% (at low load).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' We believe that our  proposed frameworks have successfully laid cornerstones for  developing further O-RAN resource allocation strategies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  APPENDIX A  PROOF OF PROPOSITION 1  Proof: We observe that if our main problem formulation  P1 has an optimal solution x∗  ry, then our reformulated problem  Pr  1 also has an optimal solution (x∗  ry, M ∗).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' This implies that  we have found the best possible M ∗ as the maximum value  of �  y∈Y (Cr + CλBry + CP Gry) xry for some r ∈ R but  it is the minimum among all feasible values of M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' In this  sense, the solution x∗  ry guarantees fairness for all r ∈ R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  However, sometimes the network connectivity, communication  latency, and computation latency constraints may play a very  strong role to produce an optimal solution (x∗  ry, M ∗) without  maintaining fairness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Now, we analyze all possible network  scenarios to show the validity of this proposition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  Case 1: Constraints (6), (9)-(12) are relaxed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  This is the trivial case when there is full-mesh connectivity  among the RUs and Edge/OLT-Clouds and no strict latency  bound exists.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Therefore, any RU can be connected to any  Edge/OLT-Cloud and the optimal solution will be dictated  by the objective (4) and constraints (5) and (13).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Therefore,  the optimum value of M will be achieved only when all  the RUs are connected to a single Edge/OLT-Cloud with  min{BUL  y  + BDL  y  } and/or min{GUL  y  + GDL  y  }.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' It is also  obvious from (4) that the OPEX of each RU will be directly  proportional to their resource demands W UL  r  , W DL  r  , ΓUL  r  , and  ΓDL  r  , which ensure fairness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  Case 2: Constraint (6) is relaxed only.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  In this case, although there is full-mesh connectivity among  the RUs and Edge/OLT-Clouds, strict communication and pro-  cessing latency bounds are applied.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Therefore, only a limited  number of RUs can be connected to each Edge/OLT-Cloud  to satisfy constraints (9)-(12).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' In this case, the best possible  solution can be achieved only if all RUs can be connected to  (one or multiple) Edge/OLT-Clouds with minimum total cost  of resources.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Without loss of generality, consider that there  are total |R| number of RUs and 2 front/mid-haul links and  Edge/OLT-Clouds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' If the front/mid-haul and Edge/OLT-Cloud  1 have sufﬁcient resources to host all |R| number of RUs, then  there is no issue of fairness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' However, if there are insufﬁcient  resources in Edge/OLT-Cloud 1 and some RUs need to be  assigned to Edge/OLT-Cloud 2, then it is best to choose RUs  with higher resource demands.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' By following this method, the  fairness of the shared cost of each RU assigned to either of  the Edge/OLT-Cloud can be guaranteed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' If we assign RUs in  any other randomized way, fairness cannot be guaranteed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' For  example, if we can assign only the RU with the lowest demand  to Edge/OLT-Cloud 2 and the rest of the RUs to Edge/OLT-  Cloud 1, then the optimal value M ∗ remains the same (total  cost of resources of front/mid-haul and Edge/OLT-Cloud 2),  but the fairness is not maintained.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Note that this argument  remains valid even if we generalize our scenario with more  than 2 Edge/OLT-Clouds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  Case 3: Constraint (9)-(12) are relaxed only.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  In this case, usually, there is partial-mesh connectivity  among the RUs and Edge/OLT-Clouds but communication and  processing latency bounds are relaxed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Therefore, in spite of  sufﬁcient resources being present, we cannot connect all the  RUs to a single Edge/OLT-Cloud due to network connectivity  constraints.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' This implies that the cost of shared resources of  multiple RUs with the exact same resource demand may vary  if they are connected to different Edge/OLT-Clouds by being  forced by the network connectivity constraints.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' However, their  shared costs will be proportionally fair in comparison with the  other RUs connected to each Edge/OLT-Clouds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' For example,  let us consider two RUs with the exact same resource demands  but allocated to two different Edge/OLT-Clouds and a different  number of other RUs connected to these Edge/OLT-Clouds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  Therefore, the OPEX values may be different for these RUs  but their OPEX values will be fair in comparison to other RUs  connected to their corresponding Edge/OLT-Clouds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  Case 4: All constraints (6), (9)-(12) are active.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  This is the most general case and characteristics of all the  previous cases can be observed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Depending on the dataset,  either constraint (6) or constraints (9)-(12) will dictate the  optimal solution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Although sufﬁcient resources may be present  at some Edge/OLT-Cloud to serve a large number of RUs,  constraint (6) might interfere.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Therefore, in this case, also the  cost of shared resources of multiple RUs with the exact same  resource demand may vary if they are connected to different  Edge/OLT-Clouds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' However, the OPEX values of each RU will  be proportionally fair to their resource demands in comparison  with other RUs connected to each Edge/OLT-Clouds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  In general, we observe by testing a number of diverse  datasets that to obtain the best possible solution M ∗ while  maintaining the fairness of the OPEX values of the RUs, we  must start to assign RUs to Edge/OLT-Clouds in the increasing  order of their resource requirements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  14  APPENDIX B  PROOF OF PROPOSITION 2  Proof: We consider a resource allocation mechanism is  allocatively efﬁcient if it optimizes the sum of the valuations of  the agents for each given type proﬁle of the agents [48].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Now,  in our problem formulation P2, the total cost of front/mid-haul  and Edge/OLT-Clouds are minimized.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Although the binary  variable ty indicates if an Edge/OLT-Cloud y is activated or  not, the constraint ty ≤ xry, ∀r ∈ R, y ∈ Y makes this  formulation equivalent to minimizing the sum of valuation  functions Vr(xry) for all RUs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Therefore, our allocation rule  ˆx∗  ry derived as an optimal solution of P2 can be considered  as allocatively efﬁcient.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  APPENDIX C  PROOF OF THEOREM 1  Proof: The proposed payment rule can be interpreted as  the total value of all RUs other than r under an efﬁcient  allocation when RU r is absent in the system minus the total  value of all RUs other than r under an efﬁcient allocation  when RU r is present in the system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Observe that each RU  r is connected to an Edge/OLT-Cloud y based on the shared  information br = ( ˆW UL  r  , ˆW DL  r  , ˆΓUL  r  , ˆΓDL  r  ) from all RUs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  Case 1: If the shared information br is higher than its  actual requirement, then there is a risk that it might remain  unallocated when the network is in high-load condition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Then  the valuation, payment, and utility of the RU r are given by:  Vr(ˆx∗  ry) = 0,  Pr(ˆx∗  ry, b) = 0,  Ur(ˆx∗  ry, b) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  Case 2: If the shared information br is lower than its  actual requirement, then the RU might get allocated to some  Edge/OLT-Cloud, but due to insufﬁcient resources in the RU’s  share, the front/mid-haul data generated per slot may fail to  get delivered within the maximum one-way front/mid-haul  latency requirements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' In this case, the valuation is zero but  the payment is non-zero, yielding a negative utility.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Thus, the  valuation, payment, and utility of the RU r are:  Vr(ˆx∗  ry) = 0,  Pr(ˆx∗  ry, b) =  |R|  �  j=1,j̸=r  �  CλBy + CP Gy  �  k̸=r ˆx−r∗  ky  �  −  |R|  �  j=1,j̸=r  �  CλBy + CP Gy  �  k ˆx∗  ky  �  ,  Ur(ˆx∗  ry, b) = 0 − Pr(ˆx∗  ry, b) < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  Case 3: There may arise network scenarios where an RU r  might get connected to some Edge/OLT-Cloud by sharing false  information (both higher and lower) and its front/mid-haul  data generated per slot is also successfully delivered within  the maximum one-way front/mid-haul latency requirements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  However, after the RU to Edge/OLT-Cloud allocation, when  the payment amount is calculated for each RU r, only the  total number of RUs connected to each Edge/OLT-Cloud y is  used and the revealed front/mid-haul datarate does not have  any role to play.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Thus, the utility of the RU with true revealed  information as well as false revealed information remains the  same.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' In this case, the valuation, payment, and utility of the  RU r are given below:  Vr(ˆx∗  ry) =  �  y  (CλBy + CP Gy)ˆx∗  ry,  Pr(ˆx∗  ry, b) =  |R|  �  j=1,j̸=r  �  CλBy + CP Gy  �  k̸=r ˆx−r∗  ky  �  −  |R|  �  j=1,j̸=r  �  CλBy + CP Gy  �  k ˆx∗  ky  �  ,  Ur(ˆx∗  ry, b) = Vr(ˆx∗  ry) − Pr(ˆx∗  ry, b) ≥ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  Therefore, any RU r can not gain any advantages in its  utility with the payment rule by sharing false information with  the NSP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' This ensures that sharing truthful information with  the NSP is a weakly dominant strategy for all the RUs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  REFERENCES  [1] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Saad, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Bennis, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Chen, “A Vision of 6G Wireless Systems:  Applications, Trends, Technologies, and Open Research Problems,”  IEEE Network, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' 34, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' 3, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' 134–142, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  [2] “O-RAN: Towards an Open and Smart RAN,” O-RAN Alliance, Tech.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  Rep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=', Oct 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  [3] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='-L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' I et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=', “RAN Revolution With NGFI (xhaul) for 5G,” J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Lightw.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  Technol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=', vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' 36, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' 2, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' 541–550, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  [4] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Peterson et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=', “Democratizing the Network Edge,” ACM SIGCOMM  Comp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=', vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' 49, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' 2, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' 31–36, May 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  [5] “The Open Road to 5G,” Samsung Networks, Tech.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Rep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=', July  2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' [Online].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Available: https://image-us.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='samsung.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='com/SamsungUS/  samsungbusiness/pdfs/Open-RAN-The-Open-Road-to-5G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='pdf  [6] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Naudts et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=', “Techno-economic Analysis of Software Deﬁned  Networking as Architecture for the Virtualization of a Mobile Network,”  in 2012 European Workshop Softw.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Deﬁned Netw.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=', 2012, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' 67–72.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  [7] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Pfeiffer, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Dom, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Bidkar, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Fredricx, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Christodoulopoulos,  and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Bonk, “PON going beyond FTTH [Invited Tutorial],” J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Opt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Netw.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=', vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' 14, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' 1, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' A31–A40, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  [8] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Das et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=', “Virtualized EAST–WEST PON Architecture Supporting  Low-latency Communication for Mobile Functional Split based on  Multiaccess Edge Computing,” IEEE/OSA J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Opt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Netw.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=',  vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' 12, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' 10, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' D109–D119, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  [9] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Massoulie and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Roberts, “Bandwidth Sharing: Objectives and  Algorithms,” IEEE/ACM Trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Netw.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=', vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' 10, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' 3, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' 320–328, 2002.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  [10] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Niyato, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Luong, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Wang, and Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Han, “Second-Price Sealed-  Bid Auction,” in Auction Theory for Computer Networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  Cambridge  University Press, 2020, ch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' 6, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' 119–157.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  [11] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Tan, Resource Allocation and Performance Optimization in Commu-  nication Networks and the Internet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  USA: CRC Press, Inc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=', 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  [12] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Wypi´or, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Klinkowski, and I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Michalski, “Open RAN—Radio Ac-  cess Network Evolution, Beneﬁts and Market Trends,” Applied Sciences,  vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' 12, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' 1, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  [13] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Yao and N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Ansari, “QoS-Aware Joint BBU-RRH Mapping and  User Association in Cloud-RANs,” IEEE Trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Green Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Netw.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=',  vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' 2, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' 4, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' 881–889, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  [14] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Barahman et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=', “A Fair Computational Resource Management  Strategy in C-RAN,” in 2018 International Conference on Broadband  Communications for Next Generation Networks and Multimedia Appli-  cations (CoBCom), 2018, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' 1–6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  [15] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Mharsi and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Hadji, “Joint Optimization of Communication Latency  and Resource Allocation in Cloud Radio Access Networks,” in 2018  International Conf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' on Smart Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' in Netw.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Technol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' (SaCoNeT),  2018, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' 13–18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  [16] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Peng, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Yu, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Xiang, and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Poor, “Energy-Efﬁcient Resource  Allocation Optimization for Multimedia Heterogeneous Cloud Radio  Access Networks,” IEEE Transactions on Multimedia, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' 18, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' 5,  pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' 879–892, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  15  [17] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Lyazidi, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Aitsaadi, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Langar, “Dynamic resource allocation  for Cloud-RAN in LTE with real-time BBU/RRH assignment,” in 2016  IEEE Int.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Conf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' (ICC), 2016, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' 1–6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  [18] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Guo, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Zeng, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Gu, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Luo, “When Green Energy Meets Cloud  Radio Access Network: Joint Optimization Towards Brown Energy  Minimization,” Mob.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Netw.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=', vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' 24, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' 3, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' 962–970, Jun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  [19] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Boulos, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' El Helou, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Lahoud, “RRH Clustering in Cloud  Radio Access Networks,” in 2015 International Conference on Applied  Research in Computer Science and Engineering (ICAR), 2015, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' 1–6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  [20] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Soliman and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Leon-Garcia, “QoS-aware Joint RRH Activation  and Clustering in Cloud-RANs,” in 2016 IEEE Wireless Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Netw.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  Conf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' (WCNC), 2016, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' 1–6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  [21] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Liang, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Gu, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Guo, and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Ji, “Demonstration of Multi-Vendor  Multi-Standard PON Networks for Network Slicing in 5G-oriented  Mobile Network,” in 2017 Asia Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Photon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Conf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' (ACP), 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  [22] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Bonati, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Polese, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' D’Oro, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Basagni, and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Melodia, “Open,  Programmable, and Virtualized 5G Networks: State-of-the-Art and the  Road Ahead,” Comput.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Netw.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=', vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' 182, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' 107516, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  [23] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Dryja´nski, u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Kułacz, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Kliks, “Toward Modular and Flexible  Open RAN Implementations in 6G Networks: Trafﬁc Steering Use Case  and O-RAN xApps,” Sensors, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' 21, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' 24, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  [24] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Mondal and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Rufﬁni, “Optical Front/Mid-haul with Open Access-  Edge Server Deployment Framework for Sliced O-RAN,” IEEE Trans-  actions on Network and Service Management, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' 1–18, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  [25] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Motalleb, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Shah-Mansouri, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Parsaeefard, and O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' L´opez,  “Resource Allocation in an Open RAN System using Network Slicing,”  IEEE Transactions on Network and Service Management, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' 1–1, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  [26] X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Wang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Thomas, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Piechocki, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Kapoor, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Santos-  Rodr´ıguez, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Parekh, “Self-play learning strategies for resource  assignment in Open-RAN networks,” Computer Networks, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' 206, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  108682, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  [27] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Zhang, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Zhou, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Erol-Kantarci, “Team Learning-Based  Resource Allocation for Open Radio Access Network (O-RAN),” in  ICC 2022 - IEEE International Conference on Communications, 2022,  pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' 4938–4943.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  [28] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Kassis et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=', “Flexible Multi-Operator RAN Sharing: Experimen-  tation and Validation Using Open Source 4G/5G Prototype,” in 2021  Joint European Conf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Netw.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' and Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' & 6G Summit (EuCNC/6G  Summit), 2021, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' 205–210.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  [29] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Sauter, “Long Term Evolution (LTE) and LTE-Advanced Pro,” in  From GSM to LTE-Advanced Pro and 5G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  John Wiley & Sons Ltd.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=',  2017, ch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' 4, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' 211–333.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  [30] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Vilalta et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=', “Network Virtualization Controller for Abstraction and  Control of OpenFlow-enabled Multi-tenant Multi-technology Transport  Networks,” in Opt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Netw.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Conf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Exhibit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' (OFC), 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  [31] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Mondal and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Rufﬁni, “A Min-Max Fair Resource Allocation  Framework for Optical x-haul and DU/CU in Multi-tenant O-RANs,”  in 2022 IEEE Int.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Conf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' (ICC), May 2022, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' 452–457.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  [32] “5G  Wireless  Fronthaul  Requirements  in  a  Passive  Op-  tical  Network  Context,”  Telecommunication  Standardization  Sector  of  ITU  (ITU-T),  Tech.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  Rep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=',  Sep  2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  [On-  line].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  Available:  https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='itu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='int/rec/dologin pub.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='asp?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='lang=e&id=  T-REC-G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='Sup66-202009-I!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='PDF-E&type=items  [33] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Rufﬁni et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=', “Virtual DBA: Virtualizing Passive Optical Networks  to Enable Multi-service Operation in True Multi-tenant Environments,”  IEEE/OSA J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Opt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Netw.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=', vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' 12, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' 4, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' B63–B73, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  [34] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Slyne, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Zeb, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Rufﬁni, “Stateful DBA Hypervisor Supporting  SLAs with Low Latency and High Availability in Shared PON,” in 2021  Opt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Netw.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Conf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Exhibit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' (OFC), 2021, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' 1–3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  [35] “Small  Cell  Virtualization  Functional  Splits  and  Use  Cases,”  2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  [Online].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  Available:  https://scf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='io/en/documents/159 - Small  Cell Virtualization Functional Splits and Use Cases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='php  [36] “Study on new radio access technology: Radio access architecture  and interfaces,” 2017, accessed: 2022-07-02.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' [Online].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Available:  https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='3gpp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='org/DynaReport/38801.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='htm  [37] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Tashiro, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Kuwano, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Terada, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Kawamura, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Tanaka, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Shige-  matsu, and N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Yoshimoto, “A Novel DBA Scheme for TDM-PON based  Mobile Fronthaul,” in 2014 Opt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Netw.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Conf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Exhibit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' (OFC),  2014, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' 1–3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  [38] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Shehata et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=', “Multiplexing Gain and Processing Savings of 5G  Radio-Access-Network Functional Splits,” IEEE Trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Green Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  Netw.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=', vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' 2, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' 4, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' 982–991, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  [39] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Khatibi, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Shah, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Roshdi, “Modelling of Computational  Resources for 5G RAN,” in 2018 European Conference on Networks  and Communications (EuCNC), 2018, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' 1–5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  [40] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Chong and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' ˙Zak, “Multiobjective optimization,” in An  Introduction to Optimization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  John Wiley & Sons, Ltd, 2008, ch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' 23,  pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' 541–562.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  [41] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Ausubel and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Cramton, “Auctioning Many Divisible Goods,”  Journal of the European Economics Association, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' 2, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' 480–493,  2004.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  [42] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Narahari, “Vickrey-Clarke-Groves (VCG) Mechanisms,” in Game  Theory and Mechanism Design.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  World Scientiﬁc Publishing Company  Pvt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Ltd.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=', 2014, ch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' 18, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' 267–284.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  [43] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Sutton and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Barto, Introduction to Reinforcement Learning,  1st ed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  Cambridge, MA, USA: MIT Press, 1998.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  [44] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Hailu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=', “Mobile fronthaul transport options in C-RAN  and emerging research directions: A comprehensive study,” Optical  Switching and Networking, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' 30, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' 40–52, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  [45] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Nakayama et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=', “Efﬁcient DWBA Algorithm for TWDM-PON with  Mobile Fronthaul in 5G Networks,” in 2017 IEEE Global Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  Conf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' (GLOBECOM), 2017, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' 1–6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  [46] “Preliminary Fiber Network Design and Business Plan Framework,”  Columbia Telecommunications Corporation, Tech.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Rep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=', Jun 2005.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  [47] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Xiao et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=', “Can Fine-Grained Functional Split Beneﬁt to the  Converged Optical-Wireless Access Networks in 5G and Beyond?”' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' IEEE  Trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Netw.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Service Manag.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=', vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' 17, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' 3, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' 1774–1787, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  [48] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Narahari, Game Theory and Mechanism Design.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  World Scientiﬁc  Publishing Company Pvt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Ltd.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=', 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  Sourav Mondal (GS’16–M’21) received PhD from  the Department of Electrical and Electronic Engi-  neering of the University of Melbourne in 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' He  received his M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='Tech in Telecommunication Systems  Engineering from the Department of Electronics  and Electrical Communication Engineering, Indian  Institute of Technology Kharagpur and B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='Tech in  Electronics and Communication Engineering from  Kalyani Govt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Engineering College, afﬁliated to  West Bengal University of Technology in 2014 and  2012, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' He was employed as an Engineer  in Qualcomm India Pvt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Ltd.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' from 2014 to 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Currently, he is working as  an EDGE/Marie Skłodowska-Curie post-doctoral fellow at CONNECT Centre  for Future Networks and Communication in Trinity College Dublin, Ireland.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  Marco Rufﬁni received the M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='Eng.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' degree in  telecommunications from the Polytechnic University  of Marche, Italy, in 2002, and the Ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' degree  Trinity College Dublin (TCD) in 2007, where he  joined Trinity College Dublin in 2005, after working  as a Research Scientist with Philips, Germany.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' He  is Associate Professor and Fellow of Trinity College  and he is Principal Investigator of both the IPIC  Photonics Integration Centre and the CONNECT  Telecommunications Research Centre.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' He is cur-  rently involved in several Science Foundation Ireland  and H2020 projects, including a new research infrastructure to build a beyond  5G testbed in Dublin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Prof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' Rufﬁni leads the Optical Network Architecture  Group, TCD and has authored over 150 international publications, over ten  patents and contributed to standards at the broadband forum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' He has raised  research funding in excess of e7M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' His main research is in the area of 5G  optical networks, where he carries out pioneering work on the convergence  of ﬁxed-mobile and access-metro networks, and on the virtualization of next  generation networks, and has been invited to share his vision through several  keynote and talks at major international conferences across the world.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content=' He  leads the new SFI funded Ireland’s Open Networking testbed infrastructure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
+page_content='  一' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdAyT4oBgHgl3EQftfm7/content/2301.00597v1.pdf'}
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+arXiv:2301.02698v1  [stat.AP]  6 Jan 2023
+Testing exponentiality using extropy of upper
+record values
+Santosh Kumar Chaudhary* and Nitin Gupta**
+Department of Mathematics, Indian Institute of Technology
+Kharagpur, West Bengal 721302, India.
+Abstract
+We are giving one characterization result of exponential distribution using
+extropy of nth upper k-record value. We introduce test statistics based on
+the proposed characterization result that will be used to test exponentiality.
+The critical value and power of the test have been calculated using monte
+Carlo simulation. The test is applied to seven real-life data sets to verify its
+applicability in practice.
+Keyword: Exponential distribution, Extropy, Record values, Testing ex-
+ponentiality.
+Mathematical Subject Classiﬁcation: 62B10, 62E10, 62G10, 62G30.
+1
+Introduction
+Let X1, X2, ..., XN be a random sample of size N from a population with
+unknown probability density function(pdf) f and cumulative distribution
+function (cdf) F. We consider X as a non-negative random variable.
+A
+probability distribution is said to be exponential with parameter λ if
+f(x) = λe−λx, x > 0, λ > 0.
+(1.1)
+Here, we are interested in testing whether a distribution is exponential. That
+is, H0 : X has exponential(λ) distribution against H1 : X does not have
+exponential(λ) distribution .
+Extropy of X is deﬁned by Lad et al. (2015) is
+J(X) = −1
+2
+� ∞
+0
+f 2(x)dx.
+(1.2)
+* Corresponding author E-mail: skchaudhary1994@kgpian.iitkgp.ac.in
+** E-mail: nitin.gupta@maths.iitkgp.ac.in
+
+2
+S.K.Chaudhary and N.Gupta
+The cumulative residual extropy (CRE) of X is deﬁned by Jahanshahi et al.
+(2020) is
+ξJ(X) = −1
+2
+� ∞
+0
+¯F 2
+X(x)dx.
+(1.3)
+The cumulative past extropy (CPE) of X is deﬁned as
+¯ξJ(X) = −1
+2
+� ∞
+0
+F 2
+X(x)dx.
+(1.4)
+Let X1, X2, . . . , XN, . . . be a sequence of independent and identically dis-
+tributed (iid) random variables from an absolutely continuous cdf F and pdf
+f. Let Xr:N be rth order statistics for 0 ≤ r ≤ N which is rth smallest in the
+sequence X1, X2, . . . , XN. Sequence of upper record time U(k) is deﬁned as
+U(1) = 1, U(k + 1) = min{j : j > U(k); Xj > U X
+k }, k = 1, 2, 3, . . . and the
+kth upper record value Uk is deﬁned as Uk = XU(k). The pdf of kth upper
+record value Uk is given as:
+fUk(x) =
+1
+Γ(k)(− log ¯F(x))k−1f(x),
+(1.5)
+where ¯F(x) = 1 − F(x) is a survival function of X and Γ(k) = (k − 1)! is
+a complete gamma function. An analogous deﬁnition can be given to lower
+k-record value (see Arnold et al.(1998))[1]. The pdf of kth lower record value
+Lk is
+fLk(x) =
+1
+Γ(k)(− log F(x))k−1f(x).
+(1.6)
+The pdf of the nth upper k-record value Un,k and the nth lower k-record
+value Ln,k respectively are given by (see Arnold et al.(1998 [1], 2008 [2]) )
+fUn,k(x) =
+kn
+Γ(n)(− log ¯F(x))n−1( ¯F(x))k−1fX(x),
+(1.7)
+and
+fLn,k(x) =
+kn
+Γ(n)(− log FX(x))n−1(FX(x))k−1fX(x).
+(1.8)
+The cdf of Un,k and Ln,k, respectively, are
+FUn,k(x) = 1 − ¯F k
+X(x)
+n−1
+�
+i=0
+(−k log ¯FX(x))i
+i!
+,
+(1.9)
+and
+FLn,k(x) = F k
+X(x)
+n−1
+�
+i=0
+(−k log FX(x))i
+i!
+.
+(1.10)
+
+S.K.Chaudhary and N.Gupta
+3
+Xiong et al. (2020)[12] proposed test statistics based on the characteriza-
+tion of exponential distribution using extropy of upper k-record value. Jose
+and Sathar (2022)[5] proposed test statistics based on the characterization
+of exponential distribution using extropy of nth lower k-record value. In
+this paper, we present some more characterization of exponential distribu-
+tion and introduce test statistics based on that characterization.
+Section
+2 of this paper discusses some examples and theorems for the exponential
+distribution. In Section 3, we obtain test statistics for testing exponentiality.
+2
+Characterization of exponential distribution
+Let us discuss some examples before we proceed to the main result of this
+section.
+Example 1 When X is exponential random variable with parameter λ > 0,
+and cdf FX(x) = 1 − e−λx, x > 0, then extropy of X,
+J(X) = −1
+2
+� ∞
+0
+f 2(x)dx = −1
+2
+� ∞
+0
+λ2e−2λxdx = −λ
+4.
+Example 2 (Xiong et al. (2020)[12]) When X is exponential random vari-
+able with parameter λ > 0, and cdf FX(x) = 1 − e−λx, x > 0, then extropy
+of U X
+k
+is
+J(U X
+k ) = −λΓ(2k − 1)
+22kΓ2(k)
+= Γ(2k − 1)
+22k−2Γ2(k)J(X)
+Theorem 2.1 of Xiong et al. (2020)[12] tells that a non-negative random
+variable X has an exponential distribution with a rate parameter λ > 0 if
+and only if
+J(U X
+k ) = Γ(2k − 1)
+22k−2Γ2(k)J(X), k = 1, 2, . . . .
+Also, Xiong et al. (2020)[12] proposed a goodness of ﬁt test for exponential-
+ity based on the above characteristics and analysed the performance of the
+proposed test statistics.
+Example 3 (Jose and Sathar (2022)[5]) When X is exponential random
+variable with parameter λ > 0, and cdf FX(x) = 1 − e−λx, x > 0, then
+
+4
+S.K.Chaudhary and N.Gupta
+extropy of J(Ln,k) is
+J(Ln,k) =−λkΓ(2n − 1)
+22nΓ2(n)
+��
+2k
+2k − 1
+�2n−1
+− 1
+�
+=kJ(X)Γ(2n − 1)
+22n−2Γ2(n)
+��
+2k
+2k − 1
+�2n−1
+− 1
+�
+.
+Theorem 2.1 of Jose and Sathar (2022)[5] proved that a non-negative random
+variable X has an exponential distribution with a rate parameter λ > 0 if
+and only if
+J(Ln,k) = kJ(X)Γ(2n − 1)
+22n−2Γ2(n)
+��
+2k
+2k − 1
+�2n−1
+− 1
+�
+.
+Also, Jose and Sathar (2022)[5] proposed a test for exponentiality based on
+the above characteristics and analysed the performance of the proposed test
+statistics.
+The following example is obtained as a particular case of Example 3.
+Example 4 (Jose and Sathar (2022)[5]) When X is exponential random
+variable with parameter λ > 0, and cdf FX(x) = 1 − e−λx, x > 0, then
+extropy of J(LX
+k ) is
+J(LX
+k ) =−λΓ(2k − 1)(22k−1 − 1)
+22kΓ2(k)
+=Γ(2k − 1)(22k−1 − 1)
+22k−2Γ2(k)
+J(X)
+Example 5 When X is exponential random variable with parameter λ > 0,
+and cdf FX(x) = 1 − e−λx, x > 0. The extropy of Un,k is
+J(Un,k) = −1
+2
+� ∞
+0
+f 2
+Un,k(x)dx
+= −1
+2
+� ∞
+0
+� kn
+Γ(n)(− log ¯F(x))n−1( ¯F(x))k−1fX(x)
+�2
+dx
+= −1
+2
+k2n
+Γ2(n)
+� ∞
+0
+�
+(− log ¯F(x))2n−2( ¯F(x))2k−2f 2
+X(x)
+�
+dx.
+
+S.K.Chaudhary and N.Gupta
+5
+Since X has exponential distribution. Therefore putting ¯F(x) = e−λx, f(x) =
+λe−λx and J(X) = −λ
+4 , we have
+J(Un,k) =−1
+2
+k2n
+Γ2(n)
+� ∞
+0
+(λx)2n−2(e−λx)2k−2λ2e−2λxdx
+=−λkΓ(2n − 1)
+22nΓ2(n)
+=kΓ(2n − 1)
+22n−2Γ2(n)J(X).
+Example 6 When X is exponential random variable with parameter λ > 0,
+and cdf FX(x) = 1−e−λx, x > 0. The CRE of nth upper k-record value Un,k
+is
+ξJ(Un,k) =−1
+2
+� ∞
+0
+¯F 2
+Un,k(x)dx
+=−1
+2
+� ∞
+0
+�
+¯F k(x)
+n−1
+�
+i=0
+�
+−k log ¯F(x)
+�i
+i!
+�2
+dx
+Since X has exponential distribution. Therefore putting ¯F(x) = e−λx and
+J(X) = −λ
+4 , we get
+ξJ(Un,k) = −1
+2
+� ∞
+0
+�
+(e−λx)k
+n−1
+�
+i=0
+�
+−k log e−λx�i
+i!
+�2
+dx
+= −1
+2
+n−1
+�
+i=0
+n−1
+�
+j=0
+(kλ)i+j
+i!j!
+� ∞
+0
+e−2kλxxi+jdx
+= −1
+4λk
+n−1
+�
+i=0
+n−1
+�
+j=0
+(i + j)!
+i!j!
+�1
+2
+�i+j
+=
+1
+16kJ(X)
+n−1
+�
+j=0
+n−1
+�
+i=0
+(i + j)!
+i!j!
+�1
+2
+�i+j
+.
+We state the following lemma from Goﬀman and Pedrick (2017) [6] which
+helps us to establish a characterization result for the exponential distribu-
+tion.
+Lemma 1 (Goﬀman and Pedrick (2017) [6]) A complete orthonormal sys-
+tem for the space L2(0, +∞) is given by the sequence of Laguerre function
+
+6
+S.K.Chaudhary and N.Gupta
+φn(x) = e
+−x
+2 Ln(x)
+n! , n ≥ 0, where Ln(x) is the Laguerre polynomial deﬁned
+as the sum of coeﬃcients of e−x in the nth derivative of xne−x, that is
+Ln(x) = ex dn
+dxn (xne−x) = �n
+i=0(−1)i�n
+i
+�
+n(n−1) . . . (i+1)xi. The meaning of
+the completeness of Laguerre functions in L2(0, +∞) is that if f ∈ L2(0, +∞)
+and
+� +∞
+0
+f(x)e− x
+2 Ln(x)dx = 0 for all n ≥ 0, then f is zero almost every-
+where.
+Remark 1 Lemma 1 is also used to prove Theorem 3.7 in Qiu (2017) [9],
+Theorem 2.1 in Xiong et al. (2020) [12] and Theorem 2.1 in Jose and Sathar
+(2022) [5].
+Theorem 1 A non-negative random variable X has an exponential distri-
+bution with rate parameter λ > 0 if and only if
+J(Un,k) = kΓ(2n − 1)
+22n−2Γ2(n)J(X), k = 1, 2, . . . .
+Proof: Proof of necessity follows from Example 5. The proof of suﬃciency
+is similar to the proof of Theorem 2.1 of Jose and Sathar (2022)[5] and we
+present here. Suppose X is a non negative random variable such that
+J(Un,k) = kΓ(2n − 1)
+22n−2Γ2(n)J(X).
+Using deﬁnition of extropy given in (1.2) and pdf of Un,k given in (1.7), we
+have,
+� ∞
+0
+�
+log( ¯F(x))
+�2n−2 ( ¯F(x))2k−2f 2(x)dx = −2J(X)Γ(2n − 1)
+22n−2k2n−1
+.
+Now, after substituting log( ¯F(x)) = −u, we get
+� ∞
+0
+u2n−2(e−u)2k−1f( ¯F −1(e−u))du = −4J(X)Γ(2n − 1)
+(2k)2n−1
+.
+(2.1)
+Using the result Γ(α)
+kα =
+� ∞
+0 e−kuuα−1du, expression (2.1) reduces to
+� ∞
+0
+e−2kuu2n−2{euf( ¯F −1(e−u)) + 4J(X)}du = 0.
+(2.2)
+We can write the above equation as
+� ∞
+0
+un−1e−u(2k+ 1
+2){e2uf( ¯F −1(e−u)) + 4euJ(X)}e− u
+2 Ln(u) = 0,
+(2.3)
+
+S.K.Chaudhary and N.Gupta
+7
+where Ln(u) is Lagurre polynomial deﬁned in lemma 1. Therefore,
+un−1e−u(2k+ 1
+2 ){e2uf( ¯F −1(e−u)) + 4euJ(X)} ∈ L2(0, +∞). Using the com-
+pleteness property in lemma 1, we get,
+e2uf( ¯F −1(e−u)) + 4euJ(X) = 0
+that is, euf( ¯F −1(e−u)) + 4J(X) = 0.
+(2.4)
+If we take v = e−u then expression 2.4 reduces to
+f( ¯F −1(v)) + 4vJ(X) = 0.
+(2.5)
+Further, substituting, t = ¯F −1(v), and using ¯F(0) = 1, we get
+¯F(t) = e4J(X)t, t > 0.
+Hence, random variable X has an exponential distribution with rate param-
+eter −4J(X).
+3
+Test Statistics
+We introduce a test statistics ∆n,k for testing exponentiality by using The-
+orem 1 as given below
+∆n,k = J(Un,k) − kΓ(2n − 1)
+22n−2Γ2(n)J(X)
+(3.1)
+From Theorem 1, ∆n,k = 0 for all k = 1, 2, 3, . . . if and only if X is ex-
+ponential. Therefore, ∆n,k is suitable to consider test statistics in testing
+the exponentiality of X. For computation purposes, we choose n=2 and k=2
+for further discussion. One may choose another value for n and k, but the
+procedure remains the same. Now, Test statistics is
+∆2,2 = J(U2,2) − J(X)
+(3.2)
+An estimator of ∆2,2 is
+∆2,2
+�
+= J(U2,2)
+�
+− J(X)
+�
+(3.3)
+Remark 2 The test statistics Ek introduced by Xiong et al.(2020) [12] is a
+particular case of our proposed test statistics ∆n,k.
+
+8
+S.K.Chaudhary and N.Gupta
+Remark 3 Test statistics proposed by Xiong et al.(2020) [12] is
+Ek = J(U X
+k ) − Γ(2k − 1)
+22k−2Γ2(k)J(X).
+For simplicity of calculation, they choose k=2, We get E2 = J(U X
+2 )− 1
+2J(X)
+but the estimator considered in Xiong et al.(2020) [12] for testing is E2
+�
+=
+J(U X
+2 )
+�
+− J(X)
+�
+. The test statistics and estimator should be E2 = J(U X
+2 ) −
+1
+2J(X) and E2
+�
+= J(U X
+2 )
+�
+− 1
+2J(X)
+�
+respectively.
+The Extropy of X can be expressed as
+J(X) = −1
+2
+� ∞
+0
+f 2(x)dx = −1
+2
+� 1
+0
+� d
+duF −1(u)
+�−1
+du
+Qui and Jia (2018) [7] introduced the sample estimator of J(X) by J(X)
+�
+as:
+J(X)
+�
+= −1
+2N
+N
+�
+i=1
+cim/N
+Xi+m:N − Xi−m:N
+where X1:N, X2:N, X3:N, . . . , XN:N are order statistics based on X1, X2, X3,
+. . . , XN, and
+ci =
+
+
+
+
+
+1 + i−1
+m
+if 1 ≤ i ≤ m,
+2
+if m + 1 ≤ i ≤ N − m,
+1 + N−i
+m
+if N − m + 1 ≤ i ≤ N.
+The window size m is positive integer smaller than N
+2 , and if i − m < 1
+then Xi−m:N = X1:N and if i + m > N then Xi+m:N = XN:N.
+Extropy of Un,k can be expressed as
+J(Un,k) = −1
+2
+� ∞
+0
+f 2
+Un,k(x)dx
+= −k2n
+2Γ2(n)
+� ∞
+0
+�
+(log ¯F(x))2n−2( ¯F(x))2k−2f 2
+X(x)
+�
+dx
+After Substituting u = F(x), we get
+J(Un,k) = −k2n
+2Γ2(n)
+� 1
+0
+�
+(log(1 − u))2n−2((1 − u))2k−2
+� d
+duF −1(u)
+�−1�
+du
+J(U2,2) = − 8
+� 1
+0
+�
+(log(1 − u))2((1 − u))2
+� d
+duF −1(u)
+�−1�
+du
+
+S.K.Chaudhary and N.Gupta
+9
+Vasicek (1976), [10] developed a concept to ﬁnd an estimator, and in accor-
+dance with that, an estimator of J(U2,2) will be produced by substituting the
+empirical distribution function F
+�
+N for the distribution function F and using
+the diﬀerence operator in place of a diﬀerential operator. The derivative of
+F −1(u) with respect to u, that is, dF −1(u)
+du
+will be estimated as
+Xi+m:N − Xi−m:N
+F
+�
+N(Xi+m:N) − F
+�
+N(Xi−m:N
+= Xi+m:N − Xi−m:N
+i+m
+N
+− i−m
+N
+= Xi+m:N − Xi−m:N
+2m/N
+.
+Analogous to Vasicek (1976) [10], Park (1999) [3], Xiong et al.(2020) [12],
+Jose and Sathar (2022) [5], we write estimator of J(Un,k) and J(U2,2), re-
+spectively, as follows,
+J(Un,k)
+�
+=
+−k2n
+2NΓ2(n)
+N
+�
+i=1
+�
+(log(1 −
+i
+N + 1))2n−2((1 −
+i
+N + 1))2k−2
+�
+2m/N
+Xi+m:N − Xi−m:N
+��
+J(U2,2)
+�
+=−8
+N
+N
+�
+i=1
+�
+(log(1 −
+i
+N + 1))2(1 −
+i
+N + 1)2
+�
+2m/N
+Xi+m:N − Xi−m:N
+��
+A reasonable estimator of ∆2,2 is obtained as
+∆2,2
+�
+= J(U2,2)
+�
+− J(X)
+�
+= −8
+N
+N
+�
+i=1
+�
+(log(1 −
+i
+N + 1))2(1 −
+i
+N + 1)2
+�
+2m/N
+Xi+m:N − Xi−m:N
+��
++ 1
+2N
+N
+�
+i=1
+cim/N
+Xi+m:N − Xi−m:N
+= − 1
+2N
+N
+�
+i=1
+�
+32
+�
+log(1 −
+i
+N + 1)
+�2 �
+1 −
+i
+N + 1
+�2
+− ci
+�
+m/N
+Xi+m:N − Xi−m:N
+The following Theorem says ∆
+�
+2,2 is a consistent estimator of ∆2,2 and
+proof follows from lines of proof of Theorem 1 of Vasicek (1976) [10]
+Theorem 2 Assume that X1, X2, ..., XN is a random sample of size N
+taken from a population with pdf f and cdf F. Also, let the variance of the
+random variable be ﬁnite. Then ∆
+�
+2,2 converges in probability to ∆2,2, that is,
+∆
+�
+2,2 is consistent estimator of ∆2,2, as N −→ ∞, m −→ ∞ and m
+N −→ 0.
+Note that the test statistics proposed by Park (1999) [3], Xiong et al.
+(2020) [12], Xiong et al. (2021) [11], Jose and Sathar (2022a [8]) and Jose
+and Sathar ( 2022b [5] ) are consistent due to the method given in Vasicek
+(1976) [10].
+
+10
+S.K.Chaudhary and N.Gupta
+Theorem 3 Let X1, X2, ..., XN be a sequence of iid random variables and
+let Yi = aXi +b, a > 0, b ∈ R, i = 1, 2, ..., N. Denote the estimator for ∆2,2
+based on Xi and Yi by ∆X
+2,2
+�
+and ∆Y
+2,2
+�
+, respectively. Then
+(i) E(∆Y
+2,2)
+�
+= 1
+aE(∆X
+2,2)
+�
+(ii) Var(∆Y
+2,2)
+�
+=
+1
+a2 V ar(∆X
+2,2)
+�
+(iii) MSE(∆Y
+2,2)
+�
+=
+1
+a3 MSE(∆X
+2,2)
+�
+where E(X), V ar(X) and MSE(X) represent expectation, variance and
+mean square error of random variable X, respectively.
+Proof:
+∆Y
+2,2
+�
+= − 1
+2N
+N
+�
+i=1
+�
+32
+�
+log(1 −
+i
+N + 1)
+�2 �
+1 −
+i
+N + 1
+�2
+− ci
+�
+m/N
+Yi+m:N − Yi−m:N
+= − 1
+2N
+N
+�
+i=1
+�
+32
+�
+log(1 −
+i
+N + 1)
+�2 �
+1 −
+i
+N + 1
+�2
+− ci
+�
+m/N
+aXi+m:N − aXi−m:N
+= 1
+a∆X
+2,2
+�
+Thus, proof is completed because of ∆Y
+2,2
+�
+= a∆X
+2,2
+�
+and properties of mean,
+variance and MSE of X.
+4
+Critical values
+The exact critical values of ∆
+�
+2,2 based on 10,000 samples of diﬀerent sizes
+generated from an exponential distribution with rate parameter 1 at sig-
+niﬁcance level α = 0.10, α = 0.05 and α = 0.01 are given in Table 1,
+2 and 3 respectively.
+The critical values are obtained for sample sizes
+N = 5, 10, 20, 30, 40, 50, 100 with window sizes m ranging from 1 to 50. The
+next section deals with the simulation study through which the power of the
+test statistic is evaluated.
+Table 1. Critical values of |∆
+�
+2,2| statistics at signiﬁcance level α= 0.10
+
+S.K.Chaudhary and N.Gupta
+11
+m\N
+5
+10
+20
+30
+40
+50
+100
+1
+0.7174
+0.4347
+0.3197
+0.2808
+0.2359
+0.2087
+0.1503
+2
+0.5027
+0.1613
+0.1355
+0.1118
+0.0977
+0.0879
+0.0620
+3
+0.1411
+0.0962
+0.0842
+0.0761
+0.0684
+0.0491
+4
+0.1659
+0.0762
+0.0721
+0.0671
+0.0607
+0.0447
+5
+0.0660
+0.0632
+0.0611
+0.0563
+0.0423
+6
+0.0641
+0.0553
+0.0532
+0.0532
+0.0395
+7
+0.0691
+0.0509
+0.0487
+0.0493
+0.0393
+8
+0.0777
+0.0465
+0.0457
+0.0458
+0.0379
+9
+0.0925
+0.0453
+0.0424
+0.0426
+0.0368
+10
+0.0461
+0.0384
+0.0397
+0.0357
+14
+0.0697
+0.0380
+0.0309
+0.0323
+15
+0.0396
+0.0303
+0.0315
+19
+0.0570
+0.0341
+0.0279
+20
+0.0364
+0.0263
+24
+0.0510
+0.0228
+30
+0.0188
+35
+0.0188
+40
+0.0219
+45
+0.0283
+49
+0.0345
+Table 2. Critical values of |∆
+�
+2,2| statistics at signiﬁcance level α= 0.05
+
+12
+S.K.Chaudhary and N.Gupta
+m\N
+5
+10
+20
+30
+40
+50
+100
+1
+1.3223
+0.8269
+0.5832
+0.4767
+0.3779
+0.3409
+0.2232
+2
+0.6977
+0.2249
+0.1897
+0.1552
+0.1293
+0.1132
+0.0791
+3
+0.1772
+0.1257
+0.1095
+0.0974
+0.0873
+0.0600
+4
+0.2050
+0.0962
+0.0915
+0.0846
+0.0768
+0.0561
+5
+0.0820
+0.0781
+0.0767
+0.0705
+0.0526
+6
+0.0770
+0.0690
+0.0668
+0.0666
+0.0487
+7
+0.0829
+0.0617
+0.0604
+0.0611
+0.0478
+8
+0.0916
+0.0557
+0.0561
+0.0565
+0.0463
+9
+0.1075
+0.0546
+0.0507
+0.0519
+0.0449
+10
+0.0550
+0.0470
+0.0487
+0.0436
+14
+0.0809
+0.0449
+0.0371
+0.0389
+15
+0.0461
+0.0360
+0.0380
+19
+0.0655
+0.0404
+0.0332
+20
+0.0427
+0.0319
+24
+0.0581
+0.0272
+30
+0.0225
+35
+0.0221
+40
+0.0258
+45
+0.0331
+49
+0.0395
+Table 3. Critical values of |∆
+�
+2,2| statistics at signiﬁcance level α= 0.01
+
+S.K.Chaudhary and N.Gupta
+13
+m\N
+5
+10
+20
+30
+40
+50
+100
+1
+6.0144
+4.1581
+2.2252
+1.8855
+1.3925
+1.1696
+0.6743
+2
+1.3442
+0.4419
+0.3768
+0.3016
+0.2610
+0.2190
+0.1315
+3
+0.2843
+0.2203
+0.1915
+0.1666
+0.1402
+0.0882
+4
+0.3054
+0.1515
+0.1426
+0.1304
+0.1223
+0.0839
+5
+0.1204
+0.1229
+0.1191
+0.1053
+0.0771
+6
+0.1094
+0.0994
+0.1022
+0.0966
+0.0693
+7
+0.1176
+0.0888
+0.0897
+0.0873
+0.0705
+8
+0.1317
+0.0792
+0.0814
+0.0823
+0.0650
+9
+0.1441
+0.0727
+0.0731
+0.0761
+0.0638
+10
+0.0751
+0.0665
+0.0685
+0.0626
+14
+0.1049
+0.0590
+0.0498
+0.0530
+15
+0.0617
+0.0493
+0.0527
+19
+0.0839
+0.0522
+0.0458
+20
+0.0572
+0.0437
+24
+0.0731
+0.0375
+30
+0.0299
+35
+0.0293
+40
+0.0339
+45
+0.0424
+49
+0.0486
+5
+Power of test
+Table 4. Powers of ∆
+�
+2,2 statistics against alternative U(0, 1) at signiﬁcance level
+α = 0.10
+
+14
+S.K.Chaudhary and N.Gupta
+m\N
+5
+10
+20
+30
+40
+50
+100
+1
+0.9587
+0.1988
+0.1819
+0.2077
+0.2476
+0.2597
+0.4680
+2
+1.000
+0.8896
+0.5679
+0.5521
+0.5909
+0.6401
+0.8254
+3
+0.9932
+0.8149
+0.7164
+0.7293
+0.7485
+0.8937
+4
+1.000
+0.9269
+0.8365
+0.8095
+0.8080
+0.9196
+5
+0.9805
+0.9089
+0.8661
+0.8603
+0.9313
+6
+0.9972
+0.9558
+0.9199
+0.8977
+0.9378
+7
+0.9998
+0.9855
+0.9515
+0.9290
+0.9481
+8
+1.0000
+0.9961
+0.9768
+0.9523
+0.9609
+9
+1.0000
+0.9991
+0.9882
+0.9709
+0.9663
+10
+0.9997
+0.9966
+0.9866
+0.9705
+14
+1.0000
+1.0000
+0.9998
+0.9907
+15
+1.0000
+0.9999
+0.9921
+19
+1.0000
+1.0000
+0.9978
+20
+1.0000
+0.9993
+24
+1.0000
+0.9998
+25
+1.0000
+30
+1.0000
+35
+1.0000
+40
+1.0000
+45
+1.0000
+49
+1.0000
+Table 5. Powers of ∆
+�
+2,2 statistics against alternative U(0, 1) at signiﬁcance level
+α= 0.05
+
+S.K.Chaudhary and N.Gupta
+15
+m\N
+5
+10
+20
+30
+40
+50
+100
+1
+0.5524
+0.0629
+0.0545
+0.0609
+0.0742
+0.0774
+0.1579
+2
+1.000
+0.6353
+0.3067
+0.2882
+0.3485
+0.4247
+0.6890
+3
+0.9849
+0.6309
+0.5439
+0.5678
+0.5960
+0.8189
+4
+0.9999
+0.8607
+0.7166
+0.6899
+0.6964
+0.8536
+5
+0.9648
+0.8417
+0.7848
+0.7785
+0.8854
+6
+0.9947
+0.9226
+0.8662
+0.8390
+0.9036
+7
+0.9991
+0.9734
+0.9145
+0.8872
+0.9088
+8
+1.0000
+0.9912
+0.9603
+0.9226
+0.9368
+9
+1.0000
+0.9982
+0.9799
+0.9533
+0.9374
+10
+0.9996
+0.9926
+0.9791
+0.9484
+14
+1.0000
+1.0000
+0.9998
+0.9796
+15
+1.0000
+1.0000
+0.9854
+19
+1.0000
+1.0000
+0.9987
+20
+1.0000
+0.9988
+24
+1.0000
+1.0000
+25
+1.0000
+30
+1.0000
+35
+1.0000
+40
+1.0000
+45
+1.0000
+49
+1.0000
+Table 6. Powers of ∆
+�
+2,2 statistics against alternative U(0, 1) at signiﬁcance level
+α= 0.01
+
+16
+S.K.Chaudhary and N.Gupta
+m\N
+5
+10
+20
+30
+40
+50
+100
+1
+0.0719
+0.0084
+0.0076
+0.0115
+0.0119
+0.0086
+0.0108
+2
+0.9981
+0.0612
+0.0200
+0.0156
+0.0237
+0.0412
+0.2373
+3
+0.8347
+0.1888
+0.1431
+0.1793
+0.1556
+0.5524
+4
+0.9986
+0.4906
+0.2728
+0.2867
+0.3594
+0.6260
+5
+0.8247
+0.6058
+0.4169
+0.4377
+0.7117
+6
+0.9833
+0.7358
+0.6173
+0.5500
+0.7638
+7
+0.9979
+0.9125
+0.7548
+0.7145
+0.7896
+8
+1.0000
+0.9774
+0.8642
+0.7800
+0.8301
+9
+1.0000
+0.9936
+0.9299
+0.8670
+0.8293
+10
+0.9998
+0.9797
+0.9309
+0.8693
+14
+1.0000
+1.000
+0.9988
+0.9358
+15
+1.0000
+0.9992
+0.9615
+19
+1.0000
+1.0000
+0.9919
+20
+1.0000
+0.9952
+24
+1.0000
+0.9998
+25
+1.0000
+30
+1.0000
+35
+1.0000
+40
+1.0000
+45
+1.0000
+49
+1.0000
+Table 8. Size of ∆
+�
+2,2 for N = 20, 50, 100 and signiﬁcance level α = 0.05 for
+weibul distribution distribution.
+N
+m
+w(1, 1)
+N
+m
+w(1, 1)
+N
+m
+w(1, 1)
+1
+0.0291
+1
+0.0297
+1
+0.0296
+2
+0.0316
+2
+0.0276
+2
+0.0342
+3
+0.0358
+3
+0.0345
+6
+0.0371
+4
+0.0504
+5
+0.0420
+10
+0.0364
+5
+0.1025
+8
+0.0405
+15
+0.0450
+20
+6
+0.2724
+50
+10
+0.0452
+100
+17
+0.0501
+7
+0.5928
+15
+0.1197
+25
+0.0512
+8
+0.8650
+20
+0.6647
+30
+0.0731
+9
+0.9915
+24
+0.9707
+40
+0.4486
+Table 9. Proposed value of window size m for diﬀerent sample size N
+
+S.K.Chaudhary and N.Gupta
+17
+N
+m
+≤10
+3-5
+10-20
+6-8
+21-40
+11-14
+41-60
+15-18
+60-100
+20-22
+≥ 100
+25
+6
+Real data application
+In this section, we apply our test to detect the suitability of exponentiality
+on seven real-life data set. A graphical representation of good ﬁt models and
+the exponential distribution ﬁtted to the data sets 1,2,3 and 4 are presented
+using histogram and Q–Q plots in Jose and star (2022b) and Q-Q plots for
+data set 5 and data set 6 are given in Xiong et al. (2020). The exponential
+distribution is a good ﬁt for dataset 5, the Chen distribution is a good ﬁt for
+dataset 6 and the uniform distribution is a good ﬁt for dataset 7 (see Xiong
+et al. (2020)). Every test was conducted at a 5% nominal level, and 10,000
+replications were used for every simulation.
+Consider the seven datasets
+given below.
+Data set 1: 74, 57, 48, 29, 502, 12, 70, 21, 29, 386, 59, 27, 153, 26, 326.
+Dataset 1 is taken from Proschan (1963) and represents the times be-
+tween successive failures of air conditioning equipment in a Boeing 720 air-
+plane. The exponential distribution has been used to model this data set (see
+Shanker et al.(2015), Jose and Sathar (2022b)). For sample size is N = 15
+and window size is m = 3, the value of test statistics based on dataset 1 is
+2.0728 and the corresponding p-value is 0.9992. Our test also detects expo-
+nential distribution as a suitable model for this dataset.
+Data set 2: 12, 17, 7, 13, 5, 2, 12, 2, 6, 4, 5, 14, 6, 2, 4, 18, 4, 19, 5, 14,
+20, 8, 11, 26, 1, 3, 10, 18, 6, 10, 23, 7, 20, 4, 7, 6, 12, 10, 20, 3, 12, 3, 18, 18,
+14, 14, 8, 6, 22, 11, 8.
+Data set 2 consists of 51 observations that represent the average max-
+imum temperature (in degrees Celsius) for the 51 major US cities.
+The
+National Climatic Data Center (NCDC) of the USA produces the informa-
+tion, which is made available on the website https://www.ncdc.noaa.gov and
+the Lindley distribution has been used to model this data set (see Jose and
+Sathar (2022b), Thomas and Jose (2020a)). For sample size is N = 51 and
+window size is m = 25, the value of test statistics based on dataset 2 is 0.5268
+
+18
+S.K.Chaudhary and N.Gupta
+and the corresponding p-value is 0.0038. Our test suggests that exponential
+distribution does not ﬁt well for this dataset.
+Data set 3: 10.49, 8.8, 12.42, 4.58, 6.85, 4.58, 5., 4.75, 4.75, 12.25, 9.5,
+13.54, 10.42, 4.65, 9.88, 6.21, 8.6, 7.06, 7.96, 7.89, 9.7, 13.9, 12.65, 10., 12.65,
+12.07, 9.8, 13.54, 9.82, 13.54, 12.42, 12.73, 12.22, 12.25, 12.32, 8.75, 12., 17.5,
+11.88, 13.13, 13.56, 15.44, 13.22, 7.28, 11.7, 11.7, 11.6, 10.9, 11.84, 8., 10.2,
+5.77, 13.9, 4.58, 12.07, 15.44, 10.2, 11., 8.5, 10.99, 10.39, 9.9, 13.94, 15.21,
+13.56, 9., 20.47, 15.22, 11.5, 13.9, 13.22, 10.48, 15.48, 9.8, 12.21, 13.56, 7.04.
+Data set 3 is taken from Thomas and Jose (2020a). Jose and Sathar
+(2022b) also used this data set in testing exponentiality. Data set 3 com-
+prises of 77 observations recorded from geoelectrically derived parameters
+representing aquifer thickness and The two-parameter Weibull distribution
+is a good ﬁt for this data set (see Thomas and Jose (2020a), Jose and Sathar
+(2022b)). For sample size is N = 77 and window size is m = 30, the value
+of test statistics based on dataset 3 is 1.1914 and the corresponding p-value
+is 0.0051. Our test veriﬁes that exponential distribution does not ﬁt well for
+this dataset.
+Data set 4: 0.08, 2.09, 3.48, 4.87, 6.94, 8.66, 13.11, 23.63, 0.2, 2.23,
+3.52, 4.98, 6.97, 9.02, 13.29, 0.4, 2.26, 3.57, 5.06, 7.09, 9.22, 13.8, 25.74,
+0.5, 2.46, 3.64, 5.09, 7.26, 9.47, 14.24, 25.82, 0.51, 2.54, 3.7, 5.17, 7.28, 9.74,
+14.76, 6.31, 0.81, 2.62, 3.82, 5.32, 7.32, 10.06, 14.77, 32.15, 2.64, 3.88, 5.32,
+7.39, 10.34, 14.83, 34.26, 0.9, 2.69, 4.18, 5.34, 7.59, 10.66, 15.96, 36.66, 1.05,
+2.69, 4.23, 5.41, 7.62, 10.75, 16.62, 43.01, 1.19, 2.75, 4.26, 5.41, 7.63, 17.12,
+46.12, 1.26, 2.83, 4.33, 5.49, 7.66, 11.25, 17.14, 79.05, 1.35, 2.87, 5.62, 7.87,
+11.64, 17.36, 1.4, 3.02, 4.34, 5.71, 7.93, 11.79, 18.1, 1.46, 4.4, 5.85, 8.26,
+11.98, 19.13, 1.76, 3.25, 4.5, 6.25, 8.37, 12.02, 2.02, 3.31, 4.51, 6.54, 8.53,
+12.03, 20.28, 2.02, 3.36, 6.76, 12.07, 21.73, 2.07, 3.36, 6.93, 8.65, 12.63, 22.69.
+Dataset 4 is taken from Linhart and Zucchini (1986). This data set rep-
+resents the failure times of the air conditioning system of an airplane. The
+exponential distribution is a good ﬁt for this dataset (see Linhart and Zuc-
+chini (1986), Shanker et al.(2015), Jose and Sathar (2022b)). For sample
+size is N = 128 and window size is m = 9, the value of test statistics based
+on dataset 4 is 255.8024 and the corresponding p-value is 0.382. Our test
+veriﬁes that exponential distribution is a good ﬁt for this dataset.
+Data set 5: 5.1, 1.2, 1.3, 0.6, 0.5, 2.4, 0.5, 1.1, 8.0, 0.8, 0.4, 0.6, 0.9,
+0.4, 2.0, 0.5, 5.3, 3.2, 2.7, 2.9, 2.5, 2.3, 1.0, 0.2, 0.1, 0.1, 1.8, 0.9, 2.0, 4.0,
+6.8, 1.2, 0.4, 0.2.
+
+S.K.Chaudhary and N.Gupta
+19
+Data set 5 is taken from Bhaumik and Gibbons (2006). This dataset
+represents the vinyl chloride data obtained from clean-up gradient monitor-
+ing wells. This dataset has been ﬁtted very well by exponential distribution
+(see Xiong et al.(2020), Bhaumik and Gibbons (2006), Shanker et al.(2015)
+and Marange and Qin (2019)). For sample size is N = 34 and window size
+is m = 3, the value of test statistics based on dataset 5 is 1734.4354 and the
+corresponding p-value is 0.8335. Our test fails to reject the null hypothesis
+and therefore, the exponential distribution is a good ﬁt for this dataset.
+Data set 6: 0.014, 0.034, 0.059, 0.061, 0.069, 0.080, 0.123, 0.142, 0.165,
+0.210, 0.381, 0.464, 0.479, 0.556, 0.574, 0.839, 0.917, 0.969, 0.991, 1.064,
+1.088, 1.091, 1.174, 1.270, 1.275, 1.355, 1.397, 1.477, 1.578, 1.649, 1.702,
+1.893, 1.932, 2.001, 2.161, 2.292, 2.326, 2.337, 2.628, 2.785, 2.811, 2.886,
+2.993, 3.122, 3.248, 3.715, 3.790, 3.857, 3.912, 4.100.
+Data set 6 is taken from Lawless (2011) and it represents the number of
+thousands of cycles to failure for electrical appliances in a life test. It con-
+tains 50 observations. For sample size N = 50 and window size m = 20, the
+value of test statistics based on dataset 6 is 5.9071 and the corresponding
+p-value is 0.0. Our test rejects the null hypothesis even at the 1% level of
+signiﬁcance. This indicates that exponential distribution does not ﬁt this
+dataset. Chen distribution is a better ﬁt for this dataset than exponential
+distribution (see Xiong et al.(2020), Yousaf et al. (2019)).
+Data set 7: 0.0518, 0.0518, 0.1009, 0.1009, 0.1917, 0.1917, 0.1917,
+0.2336, 0.2336, 0.2336, 0.2733, 0.2733, 0.3467, 0.3805, 0.3805, 0.4126, 0.4431,
+0.4719, 0.4719, 0.4993, 0.6162, 0.6550, 0.6550, 0.7059, 0.7211, 0.7356, 0.7623,
+0.7863, 0.8178, 0.8810, 0.9337, 0.9404, 0.9732, 0.9858.
+Data set 7 is taken from Xiong et al. (2020) and uniform distribution is
+good-ﬁt for it. For sample size is N = 34 and window size is m = 5, the value
+of test statistics based on dataset 7 is 422.5549 and the corresponding p-value
+is 0.0001. Our test rejects the null hypothesis even at the 1% level of signif-
+icance. This indicates that exponential distribution does not ﬁt this dataset.
+See Table 11 for the value of test statistics and p-value for diﬀerent
+datasets based on the speciﬁc window size and sample size of each dataset.
+Table 11. Description of models ﬁtted
+
+20
+S.K.Chaudhary and N.Gupta
+Dataset
+N
+m
+∆
+�
+2,2
+p-value
+Dataset 1
+15
+3
+2.0728
+0.9992
+Dataset 2
+51
+25
+0.5268
+0.0038
+Dataset 3
+77
+30
+1.1914
+0.0051
+Dataset 4
+128
+9
+255.8024
+0.3820
+Dataset 5
+34
+3
+1734.4354
+0.8335
+Dataset 6
+50
+20
+5.9071
+0.0000
+Dataset 7
+34
+5
+422.5549
+0.0001
+When testing at a 5% level of signiﬁcance, a p-value of less than 0.05 indicates
+that the data does not have exponentiality, whereas a p-value of more than
+0.05 indicates that the data is exponential distribution as a suitable model.
+Table 11 indicates that the newly proposed test identiﬁes the exponentiality
+or non-exponentiality of the distribution of the random sample.
+The p-
+values show that datasets 2, 3, 6 and 7 do not have exponentiality in the
+distribution of the random sample at a 5% level of signiﬁcance.
+Similar
+to this, a moderate p-value implies that the distributions of datasets 1,
+4, and 5 are exponential.
+We were able to verify that the test statistic
+correctly identiﬁed the exponentiality in the random variable’s distribution
+as a consequence.
+7
+Conclusion
+In the current work, the extropy and an ordered random variable (upper k
+records) were utilized to characterize the exponential distribution. The test
+statistic for determining exponentiality was built using this characterisation
+result for the exponential distribution. . The simulation study is carried out
+using the Monte Carlo technique to ﬁnd the value of the estimator, critical
+value and power of the test. In the majority of cases, it is not the poorest.
+To demonstrate that the suggested test may be used in practice with conﬁ-
+dence, we also included seven examples from real life.
+Funding
+Santosh Kumar Chaudhary would like to thank the Council Of Scientiﬁc
+And Industrial Research (CSIR), Government of India (File Number 09/0081
+(14002)/2022-EMR-I) for ﬁnancial assistance.
+Conﬂict of interest
+The authors declare no conﬂict of interest.
+
+S.K.Chaudhary and N.Gupta
+21
+References
+[1] Arnold, B. C., Balakrishnan, N. and Nagaraja, H. N. (1998). Record.
+Johan Wiley and Sons, New York.
+[2] Arnold C., Balakrishnan N., and Nagaraja H. N. (2008). A ﬁrst course
+in order statistics, SIAM.
+[3] Park, S. (1999), ‘A Goodness-of-ﬁt Test for Normality Based on the
+Sample Entropy of Order Statistics’, Statistics and Probability Letters,
+44, 359–363.
+[4] Jose, J., and Sathar, E.I.A. (2022a), Symmetry being tested through si-
+multaneous application of upper and lower k-records in extropy, Journal
+of Statistical Computation and Simulation, 92 (4):830-846.
+[5] Jitto Jose, E. I. Abdul Sathar, Characterization of exponential distri-
+bution using extropy based on lower k-records and its application in
+testing exponentiality, Journal of Computational and Applied Mathe-
+matics, 402, 2022b, 113816.
+[6] Goﬀman, C., and Pedrick, G. (2017). A ﬁrst course in functional analysis
+(Vol. 319). American Mathematical Soc.
+[7] Guoxin Qiu and Kai Jia (2018) Extropy estimators with applications in
+testing uniformity, Journal of Nonparametric Statistics, 30:1, 182-196.
+[8] Jose, J., and Sathar, E.I.A. (2022a), Symmetry being tested through si-
+multaneous application of upper and lower k-records in extropy, Journal
+of Statistical Computation and Simulation, 92:4, 830-846.
+[9] Guoxin Qiu (2017), The extropy of order statistics and record values,
+Statistics and Probability Letters, 120, Pages 52-60.
+[10] Vasicek O. A test for normality based on sample entropy. J R Stat Soc
+Ser B Methodol. 1976;38:54–59.
+[11] Xiong, P., Zhuang, W., and Qiu, G. (2021), Testing symmetry based on
+the extropy of record values, Journal of Nonparametric Statistics, 33:1,
+134-155.
+[12] Xiong, P., Weiwei Zhuang and Guoxin Qiu (2020) Testing exponential-
+ity based on the extropy of record values, Journal of Applied Statistics,
+49:4, 782-802, DOI: 10.1080/02664763.2020.1840535.
+[13] R. Shanker, F. Hagos, S. Sujatha, On the modelling of lifetimes data
+using exponential and Lindley distributions, Biom. Biostat. Int. J. 2 (5)
+(2015) 1–9.
+
+22
+S.K.Chaudhary and N.Gupta
+[14] Proschan F. Theoretical explanation of observed decreasing failure rate.
+Technometrics. 1963;5(3):375–383.
+[15] P.Y. Thomas, J. Jose, A new bivariate distribution with Rayleigh and
+Lindley distributions as marginals, J. Stat. Theory Pract. 14 (2) (2020a)
+1–33, http://dx.doi.org/10.1007/s42519-020-00093-9.
+[16] P.Y. Thomas, J. Jose, On Weibull–Burr impounded bivariate dis-
+tribution,
+Japanese
+J.
+Stat.
+Data
+Sci.
+4
+(1)
+(2020b)
+73–105,
+http://dx.doi.org/10.1007/s42081-020-00085-w.
+[17] Linhart H, Zucchini W. Model Selection, John Wiley, New York, USA;
+1986.
+[18] D.K. Bhaumik and R.D. Gibbons, One-sided approximate prediction
+intervals for at least p of m observations from a gamma population at
+each of r locations, Technometrics 48 (2006), pp. 112–119.
+[19] C.S. Marange and Y. Qin, A moment-based empirical likelihood ratio
+test for exponentiality using the probability integral transformation, J.
+Appl. Stat. 46 (2019), pp. 2786–2803.
+[20] J.F. Lawless, Statistical Models and Methods for Lifetime Data, vol.
+362, Wiley, Hoboken, 2011.
+[21] F. Yousaf, S. Ali, and I. Shah, Statistical inference for the Chen dis-
+tribution based on upper record values, Ann. Data Sci. 6 (2019), pp.
+831–851.
+Appendix
+The following steps were used to determine the critical values and compute
+the power of our proposed test and that of other tests for symmetry at
+signiﬁcance level α = 0.10, α = 0.05, α = 0.01 :
+(1) we deﬁned a function to calculate the absolute value of ∆
+�
+2,2 .
+(2) Generate a sample of size N from the null distribution and compute the
+test statistics for the sample data;
+(3) Repeat Step 2 for 10,000 times and determine the 950th, 975th and 995th
+quantile respectively of the test statistics as the critical value;
+(4) Generate a sample of size N from an alternative distribution and check
+if the absolute value of the test statistic is greater than the critical value;
+(5) Repeat Step 4 for 10,000 times and the percentage of rejection is the
+power of the test.
+
+S.K.Chaudhary and N.Gupta
+23
+Nitin Gupta
+Department of Mathematics,
+Indian Institute of Technology Kharagpur
+Kharagpur-721302, INDIA
+E-mail: nitin.gupta@maths.iitkgp.ac.in
+Santosh Kumar Chaudhary
+Department of Mathematics,
+Indian Institute of Technology Kharagpur
+Kharagpur-721302, INDIA
+E-mail: skchaudhary1994@kgpian.iitkgp.ac.in
+
diff --git a/QtE0T4oBgHgl3EQf1QLb/content/tmp_files/load_file.txt b/QtE0T4oBgHgl3EQf1QLb/content/tmp_files/load_file.txt
new file mode 100644
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+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf,len=1316
+page_content='arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='02698v1  [stat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='AP]  6 Jan 2023  Testing exponentiality using extropy of upper  record values  Santosh Kumar Chaudhary* and Nitin Gupta**  Department of Mathematics, Indian Institute of Technology  Kharagpur, West Bengal 721302, India.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='  Abstract  We are giving one characterization result of exponential distribution using  extropy of nth upper k-record value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' We introduce test statistics based on  the proposed characterization result that will be used to test exponentiality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='  The critical value and power of the test have been calculated using monte  Carlo simulation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' The test is applied to seven real-life data sets to verify its  applicability in practice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='  Keyword: Exponential distribution, Extropy, Record values, Testing ex-  ponentiality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='  Mathematical Subject Classiﬁcation: 62B10, 62E10, 62G10, 62G30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='  1  Introduction  Let X1, X2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=', XN be a random sample of size N from a population with  unknown probability density function(pdf) f and cumulative distribution  function (cdf) F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' We consider X as a non-negative random variable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='  A  probability distribution is said to be exponential with parameter λ if  f(x) = λe−λx, x > 0, λ > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='  (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='1)  Here, we are interested in testing whether a distribution is exponential.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' That  is, H0 : X has exponential(λ) distribution against H1 : X does not have  exponential(λ) distribution .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='  Extropy of X is deﬁned by Lad et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' (2015) is  J(X) = −1  2  � ∞  0  f 2(x)dx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='  (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='2)  Corresponding author E-mail: skchaudhary1994@kgpian.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='iitkgp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='ac.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='in  ** E-mail: nitin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='gupta@maths.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='iitkgp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='ac.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='in  2  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='Chaudhary and N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='Gupta  The cumulative residual extropy (CRE) of X is deﬁned by Jahanshahi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='  (2020) is  ξJ(X) = −1  2  � ∞  0  ¯F 2  X(x)dx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='  (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='3)  The cumulative past extropy (CPE) of X is deﬁned as  ¯ξJ(X) = −1  2  � ∞  0  F 2  X(x)dx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='  (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='4)  Let X1, X2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' , XN, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' be a sequence of independent and identically dis-  tributed (iid) random variables from an absolutely continuous cdf F and pdf  f.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' Let Xr:N be rth order statistics for 0 ≤ r ≤ N which is rth smallest in the  sequence X1, X2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' , XN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' Sequence of upper record time U(k) is deﬁned as  U(1) = 1, U(k + 1) = min{j : j > U(k);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' Xj > U X  k }, k = 1, 2, 3, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' and the  kth upper record value Uk is deﬁned as Uk = XU(k).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' The pdf of kth upper  record value Uk is given as:  fUk(x) =  1  Γ(k)(− log ¯F(x))k−1f(x),  (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='5)  where ¯F(x) = 1 − F(x) is a survival function of X and Γ(k) = (k − 1)!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' is  a complete gamma function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' An analogous deﬁnition can be given to lower  k-record value (see Arnold et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='(1998))[1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' The pdf of kth lower record value  Lk is  fLk(x) =  1  Γ(k)(− log F(x))k−1f(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='  (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='6)  The pdf of the nth upper k-record value Un,k and the nth lower k-record  value Ln,k respectively are given by (see Arnold et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' (1998 [1], 2008 [2]) )  fUn,k(x) =  kn  Γ(n)(− log ¯F(x))n−1( ¯F(x))k−1fX(x),  (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='7)  and  fLn,k(x) =  kn  Γ(n)(− log FX(x))n−1(FX(x))k−1fX(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='  (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='8)  The cdf of Un,k and Ln,k, respectively, are  FUn,k(x) = 1 − ¯F k  X(x)  n−1  �  i=0  (−k log ¯FX(x))i  i!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='  ,  (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='9)  and  FLn,k(x) = F k  X(x)  n−1  �  i=0  (−k log FX(x))i  i!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='  (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='10)  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='Chaudhary and N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='Gupta  3  Xiong et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' (2020)[12] proposed test statistics based on the characteriza-  tion of exponential distribution using extropy of upper k-record value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' Jose  and Sathar (2022)[5] proposed test statistics based on the characterization  of exponential distribution using extropy of nth lower k-record value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' In  this paper, we present some more characterization of exponential distribu-  tion and introduce test statistics based on that characterization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='  Section  2 of this paper discusses some examples and theorems for the exponential  distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' In Section 3, we obtain test statistics for testing exponentiality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='  2  Characterization of exponential distribution  Let us discuss some examples before we proceed to the main result of this  section.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='  Example 1 When X is exponential random variable with parameter λ > 0,  and cdf FX(x) = 1 − e−λx, x > 0, then extropy of X,  J(X) = −1  2  � ∞  0  f 2(x)dx = −1  2  � ∞  0  λ2e−2λxdx = −λ  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='  Example 2 (Xiong et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' (2020)[12]) When X is exponential random vari-  able with parameter λ > 0, and cdf FX(x) = 1 − e−λx, x > 0, then extropy  of U X  k  is  J(U X  k ) = −λΓ(2k − 1)  22kΓ2(k)  = Γ(2k − 1)  22k−2Γ2(k)J(X)  Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='1 of Xiong et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' (2020)[12] tells that a non-negative random  variable X has an exponential distribution with a rate parameter λ > 0 if  and only if  J(U X  k ) = Γ(2k − 1)  22k−2Γ2(k)J(X), k = 1, 2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='  Also, Xiong et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' (2020)[12] proposed a goodness of ﬁt test for exponential-  ity based on the above characteristics and analysed the performance of the  proposed test statistics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='  Example 3 (Jose and Sathar (2022)[5]) When X is exponential random  variable with parameter λ > 0, and cdf FX(x) = 1 − e−λx, x > 0, then  4  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='Chaudhary and N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='Gupta  extropy of J(Ln,k) is  J(Ln,k) =−λkΓ(2n − 1)  22nΓ2(n)  ��  2k  2k − 1  �2n−1  − 1  �  =kJ(X)Γ(2n − 1)  22n−2Γ2(n)  ��  2k  2k − 1  �2n−1  − 1  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='  Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='1 of Jose and Sathar (2022)[5] proved that a non-negative random  variable X has an exponential distribution with a rate parameter λ > 0 if  and only if  J(Ln,k) = kJ(X)Γ(2n − 1)  22n−2Γ2(n)  ��  2k  2k − 1  �2n−1  − 1  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='  Also, Jose and Sathar (2022)[5] proposed a test for exponentiality based on  the above characteristics and analysed the performance of the proposed test  statistics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='  The following example is obtained as a particular case of Example 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='  Example 4 (Jose and Sathar (2022)[5]) When X is exponential random  variable with parameter λ > 0, and cdf FX(x) = 1 − e−λx, x > 0, then  extropy of J(LX  k ) is  J(LX  k ) =−λΓ(2k − 1)(22k−1 − 1)  22kΓ2(k)  =Γ(2k − 1)(22k−1 − 1)  22k−2Γ2(k)  J(X)  Example 5 When X is exponential random variable with parameter λ > 0,  and cdf FX(x) = 1 − e−λx, x > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' The extropy of Un,k is  J(Un,k) = −1  2  � ∞  0  f 2  Un,k(x)dx  = −1  2  � ∞  0  � kn  Γ(n)(− log ¯F(x))n−1( ¯F(x))k−1fX(x)  �2  dx  = −1  2  k2n  Γ2(n)  � ∞  0  �  (− log ¯F(x))2n−2( ¯F(x))2k−2f 2  X(x)  �  dx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='Chaudhary and N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='Gupta  5  Since X has exponential distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' Therefore putting ¯F(x) = e−λx, f(x) =  λe−λx and J(X) = −λ  4 , we have  J(Un,k) =−1  2  k2n  Γ2(n)  � ∞  0  (λx)2n−2(e−λx)2k−2λ2e−2λxdx  =−λkΓ(2n − 1)  22nΓ2(n)  =kΓ(2n − 1)  22n−2Γ2(n)J(X).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='  Example 6 When X is exponential random variable with parameter λ > 0,  and cdf FX(x) = 1−e−λx, x > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' The CRE of nth upper k-record value Un,k  is  ξJ(Un,k) =−1  2  � ∞  0  ¯F 2  Un,k(x)dx  =−1  2  � ∞  0  �  ¯F k(x)  n−1  �  i=0  �  −k log ¯F(x)  �i  i!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='  �2  dx  Since X has exponential distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' Therefore putting ¯F(x) = e−λx and  J(X) = −λ  4 , we get  ξJ(Un,k) = −1  2  � ∞  0  �  (e−λx)k  n−1  �  i=0  �  −k log e−λx�i  i!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='  �2  dx  = −1  2  n−1  �  i=0  n−1  �  j=0  (kλ)i+j  i!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='j!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='  � ∞  0  e−2kλxxi+jdx  = −1  4λk  n−1  �  i=0  n−1  �  j=0  (i + j)!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='  i!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='j!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='  �1  2  �i+j  =  1  16kJ(X)  n−1  �  j=0  n−1  �  i=0  (i + j)!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='  i!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='j!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='  �1  2  �i+j  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='  We state the following lemma from Goﬀman and Pedrick (2017) [6] which  helps us to establish a characterization result for the exponential distribu-  tion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='  Lemma 1 (Goﬀman and Pedrick (2017) [6]) A complete orthonormal sys-  tem for the space L2(0, +∞) is given by the sequence of Laguerre function  6  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='Chaudhary and N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='Gupta  φn(x) = e  −x  2 Ln(x)  n!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' , n ≥ 0, where Ln(x) is the Laguerre polynomial deﬁned  as the sum of coeﬃcients of e−x in the nth derivative of xne−x, that is  Ln(x) = ex dn  dxn (xne−x) = �n  i=0(−1)i�n  i  �  n(n−1) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' (i+1)xi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' The meaning of  the completeness of Laguerre functions in L2(0, +∞) is that if f ∈ L2(0, +∞)  and  � +∞  0  f(x)e− x  2 Ln(x)dx = 0 for all n ≥ 0, then f is zero almost every-  where.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='  Remark 1 Lemma 1 is also used to prove Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='7 in Qiu (2017) [9],  Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='1 in Xiong et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' (2020) [12] and Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='1 in Jose and Sathar  (2022) [5].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='  Theorem 1 A non-negative random variable X has an exponential distri-  bution with rate parameter λ > 0 if and only if  J(Un,k) = kΓ(2n − 1)  22n−2Γ2(n)J(X), k = 1, 2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='  Proof: Proof of necessity follows from Example 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' The proof of suﬃciency  is similar to the proof of Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='1 of Jose and Sathar (2022)[5] and we  present here.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' Suppose X is a non negative random variable such that  J(Un,k) = kΓ(2n − 1)  22n−2Γ2(n)J(X).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='  Using deﬁnition of extropy given in (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='2) and pdf of Un,k given in (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='7), we  have,  � ∞  0  �  log( ¯F(x))  �2n−2 ( ¯F(x))2k−2f 2(x)dx = −2J(X)Γ(2n − 1)  22n−2k2n−1  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='  Now, after substituting log( ¯F(x)) = −u, we get  � ∞  0  u2n−2(e−u)2k−1f( ¯F −1(e−u))du = −4J(X)Γ(2n − 1)  (2k)2n−1  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='1)  Using the result Γ(α)  kα =  � ∞  0 e−kuuα−1du, expression (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='1) reduces to  � ∞  0  e−2kuu2n−2{euf( ¯F −1(e−u)) + 4J(X)}du = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='2)  We can write the above equation as  � ∞  0  un−1e−u(2k+ 1  2){e2uf( ¯F −1(e−u)) + 4euJ(X)}e− u  2 Ln(u) = 0,  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='3)  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='Chaudhary and N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='Gupta  7  where Ln(u) is Lagurre polynomial deﬁned in lemma 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' Therefore,  un−1e−u(2k+ 1  2 ){e2uf( ¯F −1(e−u)) + 4euJ(X)} ∈ L2(0, +∞).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' Using the com-  pleteness property in lemma 1, we get,  e2uf( ¯F −1(e−u)) + 4euJ(X) = 0  that is, euf( ¯F −1(e−u)) + 4J(X) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='4)  If we take v = e−u then expression 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='4 reduces to  f( ¯F −1(v)) + 4vJ(X) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='5)  Further, substituting, t = ¯F −1(v), and using ¯F(0) = 1, we get  ¯F(t) = e4J(X)t, t > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='  Hence, random variable X has an exponential distribution with rate param-  eter −4J(X).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='  3  Test Statistics  We introduce a test statistics ∆n,k for testing exponentiality by using The-  orem 1 as given below  ∆n,k = J(Un,k) − kΓ(2n − 1)  22n−2Γ2(n)J(X)  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='1)  From Theorem 1, ∆n,k = 0 for all k = 1, 2, 3, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' if and only if X is ex-  ponential.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' Therefore, ∆n,k is suitable to consider test statistics in testing  the exponentiality of X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' For computation purposes, we choose n=2 and k=2  for further discussion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' One may choose another value for n and k, but the  procedure remains the same.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' Now, Test statistics is  ∆2,2 = J(U2,2) − J(X)  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='2)  An estimator of ∆2,2 is  ∆2,2  �  = J(U2,2)  �  − J(X)  �  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='3)  Remark 2 The test statistics Ek introduced by Xiong et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' (2020) [12] is a  particular case of our proposed test statistics ∆n,k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='  8  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='Chaudhary and N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='Gupta  Remark 3 Test statistics proposed by Xiong et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' (2020) [12] is  Ek = J(U X  k ) − Γ(2k − 1)  22k−2Γ2(k)J(X).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='  For simplicity of calculation, they choose k=2, We get E2 = J(U X  2 )− 1  2J(X)  but the estimator considered in Xiong et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' (2020) [12] for testing is E2  �  =  J(U X  2 )  �  − J(X)  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' The test statistics and estimator should be E2 = J(U X  2 ) −  1  2J(X) and E2  �  = J(U X  2 )  �  − 1  2J(X)  �  respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='  The Extropy of X can be expressed as  J(X) = −1  2  � ∞  0  f 2(x)dx = −1  2  � 1  0  � d  duF −1(u)  �−1  du  Qui and Jia (2018) [7] introduced the sample estimator of J(X) by J(X)  �  as:  J(X)  �  = −1  2N  N  �  i=1  cim/N  Xi+m:N − Xi−m:N  where X1:N, X2:N, X3:N, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' , XN:N are order statistics based on X1, X2, X3,  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' , XN, and  ci =  \uf8f1  \uf8f4  \uf8f2  \uf8f4  \uf8f3  1 + i−1  m  if 1 ≤ i ≤ m,  2  if m + 1 ≤ i ≤ N − m,  1 + N−i  m  if N − m + 1 ≤ i ≤ N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='  The window size m is positive integer smaller than N  2 , and if i − m < 1  then Xi−m:N = X1:N and if i + m > N then Xi+m:N = XN:N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='  Extropy of Un,k can be expressed as  J(Un,k) = −1  2  � ∞  0  f 2  Un,k(x)dx  = −k2n  2Γ2(n)  � ∞  0  �  (log ¯F(x))2n−2( ¯F(x))2k−2f 2  X(x)  �  dx  After Substituting u = F(x), we get  J(Un,k) = −k2n  2Γ2(n)  � 1  0  �  (log(1 − u))2n−2((1 − u))2k−2  � d  duF −1(u)  �−1�  du  J(U2,2) = − 8  � 1  0  �  (log(1 − u))2((1 − u))2  � d  duF −1(u)  �−1�  du  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='Chaudhary and N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='Gupta  9  Vasicek (1976), [10] developed a concept to ﬁnd an estimator, and in accor-  dance with that, an estimator of J(U2,2) will be produced by substituting the  empirical distribution function F  �  N for the distribution function F and using  the diﬀerence operator in place of a diﬀerential operator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' The derivative of  F −1(u) with respect to u, that is, dF −1(u)  du  will be estimated as  Xi+m:N − Xi−m:N  F  �  N(Xi+m:N) − F  �  N(Xi−m:N  = Xi+m:N − Xi−m:N  i+m  N  − i−m  N  = Xi+m:N − Xi−m:N  2m/N  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='  Analogous to Vasicek (1976) [10], Park (1999) [3], Xiong et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' (2020) [12],' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='  Jose and Sathar (2022) [5],' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' we write estimator of J(Un,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='k) and J(U2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='2),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' re-  spectively,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' as follows,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='  J(Un,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='k)  �  =  −k2n  2NΓ2(n)  N  �  i=1  �  (log(1 −  i  N + 1))2n−2((1 −  i  N + 1))2k−2  �  2m/N  Xi+m:N − Xi−m:N  ��  J(U2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='2)  �  =−8  N  N  �  i=1  �  (log(1 −  i  N + 1))2(1 −  i  N + 1)2  �  2m/N  Xi+m:N − Xi−m:N  ��  A reasonable estimator of ∆2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='2 is obtained as  ∆2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='2  �  = J(U2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='2)  �  − J(X)  �  = −8  N  N  �  i=1  �  (log(1 −  i  N + 1))2(1 −  i  N + 1)2  �  2m/N  Xi+m:N − Xi−m:N  ��  + 1  2N  N  �  i=1  cim/N  Xi+m:N − Xi−m:N  = − 1  2N  N  �  i=1  �  32  �  log(1 −  i  N + 1)  �2 �  1 −  i  N + 1  �2  − ci  �  m/N  Xi+m:N − Xi−m:N  The following Theorem says ∆  �  2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='2 is a consistent estimator of ∆2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='2 and  proof follows from lines of proof of Theorem 1 of Vasicek (1976) [10]  Theorem 2 Assume that X1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' X2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=', XN is a random sample of size N  taken from a population with pdf f and cdf F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' Also, let the variance of the  random variable be ﬁnite.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' Then ∆  �  2,2 converges in probability to ∆2,2, that is,  ∆  �  2,2 is consistent estimator of ∆2,2, as N −→ ∞, m −→ ∞ and m  N −→ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='  Note that the test statistics proposed by Park (1999) [3], Xiong et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='  (2020) [12], Xiong et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' (2021) [11], Jose and Sathar (2022a [8]) and Jose  and Sathar ( 2022b [5] ) are consistent due to the method given in Vasicek  (1976) [10].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='  10  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='Chaudhary and N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='Gupta  Theorem 3 Let X1, X2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=', XN be a sequence of iid random variables and  let Yi = aXi +b, a > 0, b ∈ R, i = 1, 2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=', N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' Denote the estimator for ∆2,2  based on Xi and Yi by ∆X  2,2  �  and ∆Y  2,2  �  , respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' Then  (i) E(∆Y  2,2)  �  = 1  aE(∆X  2,2)  �  (ii) Var(∆Y  2,2)  �  =  1  a2 V ar(∆X  2,2)  �  (iii) MSE(∆Y  2,2)  �  =  1  a3 MSE(∆X  2,2)  �  where E(X), V ar(X) and MSE(X) represent expectation, variance and  mean square error of random variable X, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='  Proof:  ∆Y  2,2  �  = − 1  2N  N  �  i=1  �  32  �  log(1 −  i  N + 1)  �2 �  1 −  i  N + 1  �2  − ci  �  m/N  Yi+m:N − Yi−m:N  = − 1  2N  N  �  i=1  �  32  �  log(1 −  i  N + 1)  �2 �  1 −  i  N + 1  �2  − ci  �  m/N  aXi+m:N − aXi−m:N  = 1  a∆X  2,2  �  Thus, proof is completed because of ∆Y  2,2  �  = a∆X  2,2  �  and properties of mean,  variance and MSE of X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='  4  Critical values  The exact critical values of ∆  �  2,2 based on 10,000 samples of diﬀerent sizes  generated from an exponential distribution with rate parameter 1 at sig-  niﬁcance level α = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='10, α = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='05 and α = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='01 are given in Table 1,  2 and 3 respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='  The critical values are obtained for sample sizes  N = 5, 10, 20, 30, 40, 50, 100 with window sizes m ranging from 1 to 50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' The  next section deals with the simulation study through which the power of the  test statistic is evaluated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='  Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' Critical values of |∆  �  2,2| statistics at signiﬁcance level α= 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='10  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='Chaudhary and N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='Gupta  11  m\\N  5  10  20  30  40  50  100  1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
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+page_content='4486  Table 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' Proposed value of window size m for diﬀerent sample size N  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='Chaudhary and N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='Gupta  17  N  m  ≤10  3-5  10-20  6-8  21-40  11-14  41-60  15-18  60-100  20-22  ≥ 100  25  6  Real data application  In this section, we apply our test to detect the suitability of exponentiality  on seven real-life data set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' A graphical representation of good ﬁt models and  the exponential distribution ﬁtted to the data sets 1,2,3 and 4 are presented  using histogram and Q–Q plots in Jose and star (2022b) and Q-Q plots for  data set 5 and data set 6 are given in Xiong et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' The exponential  distribution is a good ﬁt for dataset 5, the Chen distribution is a good ﬁt for  dataset 6 and the uniform distribution is a good ﬁt for dataset 7 (see Xiong  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' (2020)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' Every test was conducted at a 5% nominal level, and 10,000  replications were used for every simulation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='  Consider the seven datasets  given below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='  Data set 1: 74, 57, 48, 29, 502, 12, 70, 21, 29, 386, 59, 27, 153, 26, 326.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='  Dataset 1 is taken from Proschan (1963) and represents the times be-  tween successive failures of air conditioning equipment in a Boeing 720 air-  plane.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' The exponential distribution has been used to model this data set (see  Shanker et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' (2015), Jose and Sathar (2022b)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' For sample size is N = 15  and window size is m = 3, the value of test statistics based on dataset 1 is  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='0728 and the corresponding p-value is 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='9992.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' Our test also detects expo-  nential distribution as a suitable model for this dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='  Data set 2: 12, 17, 7, 13, 5, 2, 12, 2, 6, 4, 5, 14, 6, 2, 4, 18, 4, 19, 5, 14,  20, 8, 11, 26, 1, 3, 10, 18, 6, 10, 23, 7, 20, 4, 7, 6, 12, 10, 20, 3, 12, 3, 18, 18,  14, 14, 8, 6, 22, 11, 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='  Data set 2 consists of 51 observations that represent the average max-  imum temperature (in degrees Celsius) for the 51 major US cities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='  The  National Climatic Data Center (NCDC) of the USA produces the informa-  tion, which is made available on the website https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='ncdc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='noaa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='gov and  the Lindley distribution has been used to model this data set (see Jose and  Sathar (2022b), Thomas and Jose (2020a)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' For sample size is N = 51 and  window size is m = 25, the value of test statistics based on dataset 2 is 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='5268  18  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='Chaudhary and N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='Gupta  and the corresponding p-value is 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='0038.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' Our test suggests that exponential  distribution does not ﬁt well for this dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='  Data set 3: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='49, 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='8, 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
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+page_content='25, 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='5,  13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
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+page_content='  Data set 3 is taken from Thomas and Jose (2020a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' Jose and Sathar  (2022b) also used this data set in testing exponentiality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' Data set 3 com-  prises of 77 observations recorded from geoelectrically derived parameters  representing aquifer thickness and The two-parameter Weibull distribution  is a good ﬁt for this data set (see Thomas and Jose (2020a), Jose and Sathar  (2022b)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' For sample size is N = 77 and window size is m = 30, the value  of test statistics based on dataset 3 is 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
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+page_content=' Our test veriﬁes that exponential distribution does not ﬁt well for  this dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
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+page_content='65, 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='63, 22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='69.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='  Dataset 4 is taken from Linhart and Zucchini (1986).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' This data set rep-  resents the failure times of the air conditioning system of an airplane.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' The  exponential distribution is a good ﬁt for this dataset (see Linhart and Zuc-  chini (1986), Shanker et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' (2015), Jose and Sathar (2022b)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' For sample  size is N = 128 and window size is m = 9, the value of test statistics based  on dataset 4 is 255.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='8024 and the corresponding p-value is 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='382.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' Our test  veriﬁes that exponential distribution is a good ﬁt for this dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='  Data set 5: 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
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+page_content='1, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='1, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='8, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
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+page_content='0, 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='0,  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='8, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='2, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='4, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='Chaudhary and N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='Gupta  19  Data set 5 is taken from Bhaumik and Gibbons (2006).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' This dataset  represents the vinyl chloride data obtained from clean-up gradient monitor-  ing wells.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' This dataset has been ﬁtted very well by exponential distribution  (see Xiong et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' (2020), Bhaumik and Gibbons (2006), Shanker et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' (2015)  and Marange and Qin (2019)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' For sample size is N = 34 and window size  is m = 3, the value of test statistics based on dataset 5 is 1734.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='4354 and the  corresponding p-value is 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='8335.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' Our test fails to reject the null hypothesis  and therefore, the exponential distribution is a good ﬁt for this dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='  Data set 6: 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
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+page_content='100.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='  Data set 6 is taken from Lawless (2011) and it represents the number of  thousands of cycles to failure for electrical appliances in a life test.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' It con-  tains 50 observations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' For sample size N = 50 and window size m = 20, the  value of test statistics based on dataset 6 is 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='9071 and the corresponding  p-value is 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' Our test rejects the null hypothesis even at the 1% level of  signiﬁcance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' This indicates that exponential distribution does not ﬁt this  dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' Chen distribution is a better ﬁt for this dataset than exponential  distribution (see Xiong et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' (2020), Yousaf et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' (2019)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='  Data set 7: 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
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+page_content='8178, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='8810, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
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+page_content='9404, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='9732, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='9858.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='  Data set 7 is taken from Xiong et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' (2020) and uniform distribution is  good-ﬁt for it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' For sample size is N = 34 and window size is m = 5, the value  of test statistics based on dataset 7 is 422.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='5549 and the corresponding p-value  is 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='0001.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' Our test rejects the null hypothesis even at the 1% level of signif-  icance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' This indicates that exponential distribution does not ﬁt this dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='  See Table 11 for the value of test statistics and p-value for diﬀerent  datasets based on the speciﬁc window size and sample size of each dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='  Table 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' Description of models ﬁtted  20  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='Chaudhary and N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='Gupta  Dataset  N  m  ∆  �  2,2  p-value  Dataset 1  15  3  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='0728  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='9992  Dataset 2  51  25  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='5268  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='0038  Dataset 3  77  30  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='1914  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='0051  Dataset 4  128  9  255.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
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+page_content='3820  Dataset 5  34  3  1734.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
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+page_content='9071  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='0000  Dataset 7  34  5  422.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='5549  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='0001  When testing at a 5% level of signiﬁcance, a p-value of less than 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='05 indicates  that the data does not have exponentiality, whereas a p-value of more than  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='05 indicates that the data is exponential distribution as a suitable model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='  Table 11 indicates that the newly proposed test identiﬁes the exponentiality  or non-exponentiality of the distribution of the random sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='  The p-  values show that datasets 2, 3, 6 and 7 do not have exponentiality in the  distribution of the random sample at a 5% level of signiﬁcance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='  Similar  to this, a moderate p-value implies that the distributions of datasets 1,  4, and 5 are exponential.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='  We were able to verify that the test statistic  correctly identiﬁed the exponentiality in the random variable’s distribution  as a consequence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='  7  Conclusion  In the current work, the extropy and an ordered random variable (upper k  records) were utilized to characterize the exponential distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' The test  statistic for determining exponentiality was built using this characterisation  result for the exponential distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' The simulation study is carried out  using the Monte Carlo technique to ﬁnd the value of the estimator, critical  value and power of the test.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' In the majority of cases, it is not the poorest.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='  To demonstrate that the suggested test may be used in practice with conﬁ-  dence, we also included seven examples from real life.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='  Funding  Santosh Kumar Chaudhary would like to thank the Council Of Scientiﬁc  And Industrial Research (CSIR), Government of India (File Number 09/0081  (14002)/2022-EMR-I) for ﬁnancial assistance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='  Conﬂict of interest  The authors declare no conﬂict of interest.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='Chaudhary and N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='Gupta  21  References  [1] Arnold, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=', Balakrishnan, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' and Nagaraja, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' (1998).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' Record.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='  Johan Wiley and Sons, New York.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='  [2] Arnold C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=', Balakrishnan N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=', and Nagaraja H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' (2008).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' A ﬁrst course  in order statistics, SIAM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='  [3] Park, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' (1999), ‘A Goodness-of-ﬁt Test for Normality Based on the  Sample Entropy of Order Statistics’, Statistics and Probability Letters,  44, 359–363.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='  [4] Jose, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=', and Sathar, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' (2022a), Symmetry being tested through si-  multaneous application of upper and lower k-records in extropy, Journal  of Statistical Computation and Simulation, 92 (4):830-846.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='  [5] Jitto Jose, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' Abdul Sathar, Characterization of exponential distri-  bution using extropy based on lower k-records and its application in  testing exponentiality, Journal of Computational and Applied Mathe-  matics, 402, 2022b, 113816.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='  [6] Goﬀman, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=', and Pedrick, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' A ﬁrst course in functional analysis  (Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' 319).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' American Mathematical Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='  [7] Guoxin Qiu and Kai Jia (2018) Extropy estimators with applications in  testing uniformity, Journal of Nonparametric Statistics, 30:1, 182-196.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='  [8] Jose, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=', and Sathar, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' (2022a), Symmetry being tested through si-  multaneous application of upper and lower k-records in extropy, Journal  of Statistical Computation and Simulation, 92:4, 830-846.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='  [9] Guoxin Qiu (2017), The extropy of order statistics and record values,  Statistics and Probability Letters, 120, Pages 52-60.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='  [10] Vasicek O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' A test for normality based on sample entropy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' J R Stat Soc  Ser B Methodol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' 1976;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='38:54–59.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='  [11] Xiong, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=', Zhuang, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=', and Qiu, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' (2021), Testing symmetry based on  the extropy of record values, Journal of Nonparametric Statistics, 33:1,  134-155.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='  [12] Xiong, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=', Weiwei Zhuang and Guoxin Qiu (2020) Testing exponential-  ity based on the extropy of record values, Journal of Applied Statistics,  49:4, 782-802, DOI: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='1080/02664763.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='1840535.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='  [13] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' Shanker, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' Hagos, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' Sujatha, On the modelling of lifetimes data  using exponential and Lindley distributions, Biom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' Biostat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' Int.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' 2 (5)  (2015) 1–9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='  22  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='Chaudhary and N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='Gupta  [14] Proschan F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' Theoretical explanation of observed decreasing failure rate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='  Technometrics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' 1963;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='5(3):375–383.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='  [15] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' Thomas, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' Jose, A new bivariate distribution with Rayleigh and  Lindley distributions as marginals, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' Stat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' Theory Pract.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' 14 (2) (2020a)  1–33, http://dx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='1007/s42519-020-00093-9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='  [16] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' Thomas, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' Jose, On Weibull–Burr impounded bivariate dis-  tribution,  Japanese  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='  Stat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='  Data  Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='  4  (1)  (2020b)  73–105,  http://dx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='1007/s42081-020-00085-w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='  [17] Linhart H, Zucchini W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' Model Selection, John Wiley, New York, USA;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='  1986.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='  [18] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' Bhaumik and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' Gibbons, One-sided approximate prediction  intervals for at least p of m observations from a gamma population at  each of r locations, Technometrics 48 (2006), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' 112–119.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='  [19] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' Marange and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' Qin, A moment-based empirical likelihood ratio  test for exponentiality using the probability integral transformation, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='  Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' Stat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' 46 (2019), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' 2786–2803.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='  [20] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' Lawless, Statistical Models and Methods for Lifetime Data, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='  362, Wiley, Hoboken, 2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='  [21] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' Yousaf, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' Ali, and I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' Shah, Statistical inference for the Chen dis-  tribution based on upper record values, Ann.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' Data Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content=' 6 (2019), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='  831–851.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='  Appendix  The following steps were used to determine the critical values and compute  the power of our proposed test and that of other tests for symmetry at  signiﬁcance level α = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='10, α = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='05, α = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='01 :  (1) we deﬁned a function to calculate the absolute value of ∆  �  2,2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='  (2) Generate a sample of size N from the null distribution and compute the  test statistics for the sample data;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='  (3) Repeat Step 2 for 10,000 times and determine the 950th, 975th and 995th  quantile respectively of the test statistics as the critical value;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='  (4) Generate a sample of size N from an alternative distribution and check  if the absolute value of the test statistic is greater than the critical value;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='  (5) Repeat Step 4 for 10,000 times and the percentage of rejection is the  power of the test.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='Chaudhary and N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='Gupta  23  Nitin Gupta  Department of Mathematics,  Indian Institute of Technology Kharagpur  Kharagpur-721302, INDIA  E-mail: nitin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='gupta@maths.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='iitkgp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='ac.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='in  Santosh Kumar Chaudhary  Department of Mathematics,  Indian Institute of Technology Kharagpur  Kharagpur-721302, INDIA  E-mail: skchaudhary1994@kgpian.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='iitkgp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='ac.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
+page_content='in' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/QtE0T4oBgHgl3EQf1QLb/content/2301.02698v1.pdf'}
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+arXiv:2301.01316v1  [math.AT]  3 Jan 2023
+ON CYCLES AND MERGE TREES
+JULIAN BR¨UGGEMANN AND NICHOLAS A. SCOVILLE
+Abstract. In this paper, we extend the notion of a merge tree to that of a generalized
+merge tree, a merge tree that includes 1-dimensional cycle birth information.
+Given a
+discrete Morse function on a 1-dimensional regular CW complex, we construct the induced
+generalized merge tree. We give several notions of equivalence of discrete Morse functions
+based on the induced generalized merge tree and how these notions relate to one another.
+As a consequence, we obtain a complete solution to the inverse problem between discrete
+Morse functions on 1-dimensional regular CW complexes and generalized merge trees. After
+characterizing which generalized merge trees can be induced by a discrete Morse function
+on a simple graph, we give an algorithm based on the induced generalized merge tree of a
+discrete Morse function f : X → R that cancels the critical simplices of f and replaces it
+with an optimal discrete Morse function.
+Contents
+1.
+Introduction
+1
+2.
+Preliminaries on dMfs and Merge Trees
+2
+3.
+Inverse Problem for Multigraphs
+8
+4.
+Realization problem with simple graphs
+11
+5.
+How to ﬁnd cancellations with merge trees
+16
+References
+21
+1. Introduction
+Let X be a simplicial complex along with a sequence of subcomplexes ∅ = X0 ⊆ X1 ⊆
+· · · ⊆ Xn = X known as a ﬁltration. In the burgeoning ﬁeld of topological data analysis,
+a ﬁltration is often given by a sampling of points based on some increasing parameter.
+Geometrical and topological features of X are then estimated by studying the persistence
+of certain topological features [PRSZ20]. When the topological feature in question is the
+number of connected components, the persistence over the lifetime of the ﬁltration is given
+by birth and death information and is summarized in a barcode or persistence diagram
+[Oud15, CVJ22]. If one wishes to not only determine birth and death information from the
+ﬁltration but also how the components are evolving, i.e., which components are merging with
+which, one associates a merge tree tree to the ﬁltration. Because the merge tree carries with
+it this extra information, merge trees are a rich topic of study in both the theoretical and
+computational settings [CHM+22, Cur18, MBW13, GMO+, CCLL22].
+Date: January 5, 2023.
+2020 Mathematics Subject Classiﬁcation.
+(Primary) 57Q70; (Secondary) 05C90, 55N31.
+Key words and phrases. Discrete Morse Theory, merge trees.
+1
+
+2
+JULIAN BR¨UGGEMANN AND NICHOLAS A. SCOVILLE
+One way to induce a ﬁltration on X is with a discrete Morse function [For98, For02]. Such
+a function f induces a ﬁltration by considering subcomplexes associated to each critical value
+of f. The induced merge tree of a discrete Morse function on a tree, or 1-dimensional acyclic
+complex, was introduced in [JS22]. There the authors showed that a certain class of merge
+trees could be realized as the induced merge tree of a star graph. The authors went on to
+conjecture that any merge tree could be the induced merge tree of a certain discrete Morse
+function on a path. This conjecture was recently proved in [Br¨u22].
+The goal of this paper is to extend the theory of merge trees and discrete Morse theory to
+include cycles. More speciﬁcally, given any 1-dimensional regular CW complex (i.e. a graph
+with or without multiedges) equipped with a discrete Morse function, we deﬁne a generalized
+induced Morse labeled merge tree (Deﬁnition 2.6) associated to this discrete Morse function.
+The generalized induced Morse labeled merge tree keeps track of not only component birth,
+death, and merge information but also cycle birth information via a node with a single
+child. After deﬁning some basic properties, we introduce an equivalence relation on regular
+connected graphs called component-merge equivalence (cm-equivalence, Deﬁnition 2.10) and
+show that there is a one-to-one correspondence between the set of cm-equivalence classes
+of discrete Morse functions with only critical cells and the set of isomorphism classes of
+generalized Morse labeled merge tree in Theorem 3.1. In addition, we determine when a
+given generalized merge tree can be realized by an induced Morse function on a graph without
+multiedges. Unlike the case of merge trees, not all generalized merge trees can be realized.
+Theorem 4.1 gives a simple counting condition for when a generalized merge tree can be
+realized. The proof is constructive and builds oﬀ of the merge tree construction in [Br¨u22,
+Theorem 5.9]. Finally in Section 5, we give an algorithm on merge tree induced by a discrete
+Morse function in order to cancel critical cells of the discrete Morse function. The algorithm
+allows for some options depending on whether one wishes to preserve homeomorphism type
+of the graph or ﬁnd an optimal matching.
+We brieﬂy compare the algorithm to similar
+algorithms from the literature [LLT03a, RS20].
+2. Preliminaries on dMfs and Merge Trees
+We recall and introduce the necessary notions for this work. In this article, we use the
+term graph for ﬁnite abstract multigraphs without degenerate loops. That is, graphs in
+this work may have multiple edges between two given vertices, but they cannot have any
+degenerate loops, i.e., edges of the form (x, x). This notion of graph can be geometrically
+interpreted as one-dimensional regular CW complexes.
+On the other hand, we will use the term simple graph when we mean a graph in which there
+is at most one edge between two given vertices (degenerate loops are still not allowed). Simple
+graphs correspond to one-dimensional simplicial complexes.
+Since we consider graphs as
+geometrical objects, we also use geometrical terms like cells, simplices, and faces to describe
+them. For any graph X, we use v(X), e(X), and b1(X) to denote the number of vertices,
+edges, and cycles of X, respectively.
+We continue with one of the most central notions of the article, namely that of a discrete
+Morse function.
+Deﬁnition 2.1. Let X be a graph, not necessarily connected. A function f : X → R is
+called weakly increasing if f(v) ≤ f(e) whenever vertex v is a face of edge e. A discrete
+Morse function f : X → R is a weakly increasing function which is at most 2–1 and satisﬁes
+
+ON CYCLES AND MERGE TREES
+3
+the property that if f(v) = f(e), then v is incident with e. A cell s of X is critical if s is the
+unique preimage of f(s). Otherwise, s is called matched.
+For any a ∈ R, the sublevel subcomplex of X at a is Xa = {s ∈ X : f(s) ≤ a}. The
+connected component of s ∈ X is denoted X[s]. We use the notation Xa−ε to denote the
+sublevel subcomplex of X immediately preceding a, i.e., Xa−ε := {σ : f(σ) < a}.
+Remark 2.1. This deﬁnition of discrete Morse functions, due to B. Benedetti, is not equiv-
+alent to the more general deﬁnition originally given by Forman.
+Nonetheless, the given
+deﬁnition is generic in the sense that any discrete Morse function in the sense of Forman can
+be modiﬁed to fulﬁll the deﬁnition above without changing the induced acyclic matching.
+The deﬁnition stated above has the advantage that critical cells are distinguished by their
+critical values and at each level, at most either one critical cell or one pair of matched cells
+is added to the sublevel complex.
+Deﬁnition 2.2. A generalized merge tree T is a rooted chiral binary tree T such that each
+leaf has a sibling, and inner nodes without a sibling have the same chirality as their parent
+node. By convention, we say that the root always has chirality L. Furthermore, the root is
+never regarded as a leaf, even if it only has one child node.
+For nodes c of generalized merge trees we use the notation cl/cr for the left/right child
+node of c.
+Remark 2.2. Generalized merge trees may have nodes without siblings.
+The notion of
+chirality of only children does not really deserve the name chirality because there is only one
+total ordering on a set with one element. We impose the condition that an only child has
+the same chirality as its parent node for technical reasons. We need this convention so the
+constructions in Deﬁnition 2.7 and Deﬁnition 2.6 make part 2 of Theorem 3.1 work.
+Generalized merge trees generalize merge trees in the sense that that keep track of more
+information than merge trees do.
+Deﬁnition 2.3. Let T be a generalized merge tree. We call a total order ≤ on the nodes of
+T a Morse order if it fulﬁlls the following two properties for all generalized merge subtrees
+T ′ of T:
+(1) The restriction ≤|T ′ attains its maximum on the root p of T ′.
+(2) The minimum of ≤|T ′ has the same chirality as p.
+We call a generalized merge tree together with a Morse order (T, ≤) a generalized Morse
+ordered merge tree (gMo tree)
+Remark 2.3. Assuming property 2 of Deﬁnition 2.3 for every subtree T ′ with root p of T
+is equivalent to either of the following:
+• For any subtree T ′ with root p of T, the restriction ≤|T ′ attains its minimum on the
+subtree with root pl/pr if L/R is the chirality of the root p of T ′.
+• For any subtree T ′ with root p of T, all nodes on the shortest path between p and
+the minimum of ≤|T ′ have the same chirality as p.
+The equivalence can be proved by an inductive argument over all nodes of the shortest path
+between p and the minimum.
+Deﬁnition 2.4. We call a generalized merge tree (T, λ) with an injective map λ: T → R
+such that λ induces a Morse order on T a generalized Morse labeled merge tree (gMl tree).
+Any such map λ is called a Morse labeling on T.
+
+4
+JULIAN BR¨UGGEMANN AND NICHOLAS A. SCOVILLE
+Let (T, λ) and (T ′, λ′) be gMl trees. An order equivalence (ϕ, ψ): (T, λ) → (T ′, λ′) of gMl
+trees is a pair of maps consisting of an isomorphism of the underlying generalized merge
+trees ϕ: T → T ′ and a bijection ψ: R → R such that the restriction ψ|im(λ) : im(λ) → im(λ′)
+is order preserving.
+Proposition 2.1. Let gMoT be the set of generalized Morse ordered merge trees and let
+gMlT be the set of generalized Morse labeled merge trees. Then taking the Morse order
+induced by a Morse labeling and using a Morse order and the labels {0, 1, . . . , |V (T)| − 1} to
+induce a Morse labeling deﬁne inverse bijections
+iMl: gMoT/∼
+=
+gMlT/∼ : iMo
+where ∼ denotes order equivalence.
+Proof. The proof is completely analogous to [Br¨u22, Proposition 3.26].
+□
+Deﬁnition 2.5. Let (X, f) be a discrete Morse function on a graph. We call a critical edge
+σ ∈ X a closing edge if σ is part of a regular subdivision of S1 in X such that f(σ) is the
+maximum on said subdivision.
+We deﬁne C(X, f) := {c ∈ X|c is closing} to be the set of closing edges of (X, f) and
+( ¯X, ¯f) := (X \ C(X, f), f|X\C(X,f)) to be the spanning tree induced by f of X.
+Remark 2.4. In the previous deﬁnition, the subdivison of S1 that any closing edge σ must
+be part of does not need to be unique. Nonetheless, the removal of σ would lead to the
+reduction of the ﬁrst Betti number by one. Moreover, the notion of closing edges is well-
+deﬁned because the edge σ being closing implies that it is the unique maximal edge of all
+subdivisions of S1 in Xf(σ[σ].
+Furthermore, it is immediate that ( ¯X, ¯f) := (X \ C(X, f), f|X\C(X,f)) is a discrete Morse
+function on a tree.
+Deﬁnition 2.6 (Induced Morse Labeled Merge Tree). Let f : X → R be a discrete Morse
+function on a connected graph X. Let σ0 < σ1 < · · · < σn be the critical edges of (X, f)
+ordered by their values under f. The generalized Morse labeled merge tree induced by (X, f),
+denoted M(X, f) with labeling λf, is constructed inductively as follows:
+For the base case we construct a node M(σn) with label f(σn) and left chirality as root
+node. For any other critical edge σi between two 0-simplices v and w there are two cases:
+(1) The critical edge σi is closing ⇔ b1(Xf(σi) \ σi) = b1(Xf(σi)) − 1 ⇔ b0(Xf(σi) \ σi) =
+b0(Xf(σi)),
+(2) The critical edge σi is not closing ⇔ b1(Xf(σi) \ σi) = b1(Xf(σi)) ⇔ b0(Xf(σi) \ σi) =
+b0(Xf(σi)) + 1.
+Depending on the case at hand, we perform the following step for the construction of
+M(X, f):
+(1) We construct a child node c of M(σi) with label λ := max{f(σ)|σ ∈ Xf(σi)−ε, σcritical}
+and the same chirality as M(σi). The node c then corresponds to the edge of X la-
+beled λ.
+(2) We construct two child nodes cλv and cλw of M(σi). Deﬁne λv := max{f(σ)|σ ∈
+Xσi−ε[v], σ critical} and λw := max{f(σ)|σ ∈ Xσi−ε[w], σ critical}. Then label the
+new nodes λf(cλv) := λv and λf(cλw) := λw. If min{f(σ)|σ ∈ Xσi−ε[v]} < min{f(σ)|σ ∈
+
+ON CYCLES AND MERGE TREES
+5
+Xσi−ε[w]}, we assign cλv the same chirality (L or R) as cσi and give cλw the opposite
+chirality.
+Continue the induction over the rest of the critical edges of X.
+Remark 2.5. There is a one-to-one correspondence between vertices of X and leaves of
+M(X, f), non-closing edges of X and parents with two children of M(X, f), and closing
+edges (cycles) of X and parents with one child in M(X, f).
+Furthermore, the proof that the construction indeed produces a gMl tree is completely
+analogous to [Br¨u22, Proposition 2.20], respectively [JS22, Theorem 9].
+Lemma 2.1. Let (X, f) be a discrete Morse function on a graph and let M(X, f) be the
+induced generalized Morse labeled merge tree. For any simplex s ∈ X, the rooted subtree
+T(M(s)) of M(X, f) is induced by the connected component Xf(s)[s] of s in the sublevel com-
+plex of level f(s). Moreover, the rooted subtree T(M(s)) is isomorphic to M(Xf(s)[s], f|Xf(s)[s])
+as merge trees if and only if M(s) has chirality L. If M(s) has chirality R, then T(M(s)) is
+isomorphic to M(Xf(s)[s], f|Xf(s)[s]) as rooted binary trees but the chiralities of all nodes are
+opposite to the ones of their respective nodes in the other tree.
+Proof. We observe that by Deﬁnition 2.6 the label of M(s) is f(s) and the chirality of
+M(s) is decided by the minimum of f|Xf(s)[s] in comparison to the minimum of the connected
+component that Xf(s)[s] got divided from at level f(s). It follows inductively by construction
+that all nodes of the subtree T(M(s)) are induced by critical cells of Xf(s)[s] because they
+are constructed by removing critical edges of Xf(s)[s].
+The isomorphism as rooted binary trees is constructed by the same inductive argument.
+Since the chirality depends on the chirality of the respective parent node, said isomorphism
+is compatible with the chirality if and only if the root of the rooted subtree T(M(s)), namely
+M(s), has chirality L. This is true because the root of M(Xf(s)[s], f|Xf(s)[s]) by convention
+always has chirality L.
+□
+Deﬁnition 2.7. Let (T, λ) be a generalized Morse labeled merge tree. Let C(T) ⊂ V (T)
+be the set of nodes that have exactly one child node. We refer to the elements of C(T) as
+cycle nodes. We denote by ( ¯T, λ) the Morse labeled merge tree that is obtained from (T, λ)
+by removing the cycle nodes by connecting their parent nodes directly to their child nodes.
+We call ( ¯T, λ) the underlying Morse labeled merge tree of (T, λ).
+We obtain a discrete Morse function on a graph fλ: X → R from (T, λ) in two steps as
+follows: In a ﬁrst step, we construct the induced discrete Morse function on a path (P, fλ)
+as in [Br¨u22, Deﬁnition 3.21]. For the second step, for each node c of C(T) we add an edge
+parallel to the edge corresponding to c’s oldest descendant which has two children to P. We
+denote the graph obtained this way by X and extend the function fλ : P → R to X using
+the values of λ on the corresponding nodes. We denote the pair (P, fλ) by Φ(T, λ).
+Lemma 2.2. We have M( ¯X, f| ¯
+X) ∼= ¯
+M(X, f) as Morse labeled merge trees.
+Proof. The construction of the induced generalized merge tree induces a bijection M : X →
+V (M(X, f)). It follows immediately by construction that M bijectively maps closing edges
+to nodes of C(M(X, f)). Hence removing the closing edges from (X, f), that is, passing on
+to ( ¯X, f), precisely removes the nodes of C(M(X, f)), which corresponds to passing on to
+¯
+M(X, f). Hence, the statement holds because the values of f on non-closing edges are not
+changed.
+□
+
+6
+JULIAN BR¨UGGEMANN AND NICHOLAS A. SCOVILLE
+Deﬁnition 2.8. Let f : X → R be a dMf on a graph.
+For each non-empty connected
+component Xf
+c [v] of a sublevel complex Xf
+c we denote by Aut(Xf
+c [v]) the group of simplicial
+automorphisms of said connected component of said sublevel complex. Each a ∈ Aut(Xf
+c [v])
+can be extended by the identity to a set function that is a self-bijection X → X. The
+group �
+Aut(Xf
+c [v]) is deﬁned to be the group of said extensions of elements of Aut(Xf
+c [v])
+by the identity. We consider �
+Aut(Xf
+c [v]) as a subgroup of the group of all self-bijections of
+X. The total order on Cr(f) induced by f induces chains �
+Aut(Xf
+c0[v]) ⊂ �
+Aut(Xf
+c1[v]) ⊂ . . .
+of inclusions of subgroups.
+Moreover, we have inclusions �
+Aut(Xf
+ci[v]) ⊂ �
+Aut(Xf
+cj[v]) =
+�
+Aut(Xf
+cj[w]) ⊃ �
+Aut(Xf
+ci[w]) if v and w are in diﬀerent connected components of some sublevel
+complex Xf
+ci that merge together in some other sublevel complex Xf
+cj for j > i. We deﬁne the
+sublevel automorphism group of (X, f), denoted by Autsl(X, f), to be the subgroup generated
+by
+�
+c∈Cr(f),v∈X
+�
+Aut(Xf
+c [v]). We call the elements of Autsl(X, f) sublevel automorphisms.
+Note that an element a ∈ Autsl(X, f) is not necessarily an automorphism of X, but only a
+self-bijection of X that restricts to an automorphism on some connected component of some
+sublevel complex corresponding to a critical simplex.
+Deﬁnition 2.9. Let f : X → R and g : X → R be dMfs on a graph X. We call f and g
+sublevel-equivalent if they have the same critical values and isomorphic sublevel complexes.
+If additionally g = f ∗ a holds for a sublevel automorphism a ∈ Autsl(X, f) = Autsl(X, g),
+then we call f and g symmetry-equivalent. We call the map a a symmetry equivalence from
+f to g.
+We call two dMfs f : X → R and g : Y → R symmetry-equivalent if there is a simplicial
+isomorphism ϕ: X → Y such that f and g ◦ ϕ are symmetry-equivalent.
+Deﬁnition 2.10. Let (X, f) and (X′, f ′) be critical dMfs on connected graphs. A component-
+merge equivalence (cm equivalence) is a bijection ϕ: X → X′ such that at least one of the
+following cases holds:
+(1) ϕ is a symmetry equivalence.
+(2) ϕ fulﬁlls the following:
+• f ′ ◦ ϕ = f,
+• ϕ induces a bijection between the sets of connected components of sublevel
+complexes such that the restriction ϕ|Xa−ε[v] : Xa−ε[v] → X′
+a−ε[ϕ(v)] to each con-
+nected component is a cm equivalence, and
+• the edge σ ∈ X with f(σ) = a merges two connected components Xa−ε[v1]
+and Xa−ε[v2] in Xa[v1] = Xa[v2] if and only if the edge ϕ(σ) merges the corre-
+sponding two connected components X′
+a−ε[ϕ(v1)] and X′
+a−ε[ϕ(v2)] in X′
+a[ϕ(v1)] =
+X′
+a[ϕ(v2)]. Otherwise, if the edge σ ∈ X with f(σ) = a does not merge two
+connected components but rather closes a circle within a connected component
+Xa−ε[v], then and only then ϕ(σ) closes a circle within X′
+a−ε[ϕ(v)].
+If ϕ re-attaches the critical edge labeled a, we call ϕ non-trivial. Moreover, if ϕ re-
+attaches the critical edge of level a and acts as a symmetry equivalence everywhere
+else, we say that ϕ is of level a. If ϕ does not re-attach any critical edge, i.e., if ϕ is
+a symmetry equivalence, we call ϕ a trivial cm equivalence.
+Remark 2.6. Extending the notion of cm equivalences to dMfs with matched cells is a bit
+tedious. We would like to suggest getting rid of matched cells by identifying arbitrary dMfs
+
+ON CYCLES AND MERGE TREES
+7
+on graphs with critical dMfs on the corresponding graph that arises by collapsing matched
+cells beforehand but degenerate loops might arise in this process. Nonetheless, the newly
+created degenerate loops are critical by construction and the deﬁnition above works in this
+context.
+Example 2.1. Let f : X → R be the complex with discrete Morse function on the left and
+f ′: X′ → R be the complex with discrete Morse function on the right.
+7
+3
+2
+6
+4
+5
+8
+3
+6
+2
+4
+0
+1
+2
+4
+6
+7
+5
+8
+3
+3
+6
+2
+4
+0
+1
+Then a cm-equivalence of critical levels a = 7 is given by ϕ: X → X′ where ϕ(v) = v′
+whenever f(v) = f ′(v′) on vertices and ϕ(e) = e′ whenever f(e) = f ′(e′) on edges.
+Remark 2.7. It is clear from the case distinction made in Deﬁnition 2.10 that any cm
+equivalence ϕ: (X, f) → (X′, f ′) restricts to a bijection ϕ|C(X,f) : C(X, f) → C(X′, f ′).
+Lemma 2.3. Let f : X → R and f ′: X′ → R be cm-equivalent dMfs on multigraphs. Then
+M(X, f) ∼= M(X′, f ′) holds as generalized Morse labeled merge trees.
+Proof. Let ϕ be a cm equivalence ϕ: (X, f) → (X′, f ′). Since we work with a version of
+discrete Morse functions which are at most 2-1, at most one non-trivial cm equivalence of
+level a can occur for any level a because there is at most one critical edge labeled a in
+(X, f), (X′, f ′), respectively. Thus, we can decompose any cm equivalence into a sequence
+(ϕa)a of non-trivial cm equivalences of decreasing levels such that each ϕa only changes the
+attachment of the single edge σ with f(σ) = a and acts as a symmetry equivalence on the
+rest of graph and dMf. It suﬃces to consider a single level a because the statement then
+follows by induction from highest to lowest over all levels a.
+For such a non-trivial cm equivalence ϕa we consider the step of the construction of the
+induced Ml trees that considers the critical edge σ with f(σ) = a and the critical edge ϕ(σ).
+If σ is not closing, neither is ϕ(σ) by Remark 2.7 and the inductive step follows by [Br¨u22,
+Proposition 2.52]. In the case that σ is closing, so is ϕ(σ) and we inductively assume that
+ϕ induces an isomorphism of induced generalized Ml trees everywhere outside the subtree
+corresponding to the connected component of Xf
+a−ε that the edge σ with f(σ) = a is attached
+to. That is, on the rest of M(X, f) the map M(ϕ) is a bijection compatible with the chiral
+child relation onto M(X′, f ′) except possibly for the subtree of M(X′, f ′) which corresponds
+to the connected component of X′f′
+a−ε that the edge ϕ(σ) is attached to.
+Since the map ϕ is compatible with the dMfs and because it restricts to a cm equivalence
+Xf
+a−ε → X′f′
+a−ε, the dMf f attains the same minima and maxima on the two relevant con-
+nected component of Xf
+a−ε as f ′ does on its counterpart of X′f′
+a−ε via ϕ. Since Deﬁnition 2.6
+only considers which connected component the considered edge is attached to, it makes no
+diﬀerence for the isomorphism type of the induced Ml trees that in general σ is attached to
+
+8
+JULIAN BR¨UGGEMANN AND NICHOLAS A. SCOVILLE
+said connected component of Xf
+a−ε at vertices that do not correspond via ϕ to the ones ad-
+jacent to ϕ(σ) in X′f′
+a−ε. Thus, the construction of the induced generalized Ml tree produces
+nodes with the same chirality and label for both induced Ml trees in the steps that consider
+σ, ϕ(σ), respectively. By assumption, the restriction ϕXf
+a−ε : Xf
+a−ε → X′f′
+a−ε is a symmetry
+equivalence, so the isomorphism of Ml trees extends to the subtrees that correspond to the
+respective connected components.
+□
+3. Inverse Problem for Multigraphs
+In this section we want to describe the relationship between dMfs on graphs, generalized
+Ml trees, generalized Mo trees, and generalized merge trees:
+gMer
+DMF crit
+graphs
+gMoT
+gMlT
+iMl
+iMo
+M( , )
+Φ ◦ iMl◦ ≤sc
+Φ
+M( , )
+forget
+≤sc
+Figure 1. Relationships between dMfs and merge trees
+Theorem 3.1. Let DMF crit
+mult denote the set of cm-equivalence classes of discrete Morse
+functions with only critical cells on multigraphs. Let MlT denote the set of isomorphism
+classes of generalized Morse labeled merge trees. Then the induced discrete Morse function
+Φ, Deﬁnition 2.7, and the induced Morse labeled merge tree M( , ), Deﬁnition 2.6, deﬁne
+maps M( , ): DMF crit
+mult ↔ MlT : Φ that are inverse of each other in the sense that:
+(1) for any discrete Morse function (X, f) with only critical cells, the discrete Morse
+function Φ(M(X, f), λf) is cm-equivalent to (X, f), and
+(2) for any generalized Morse labeled merge tree (T, λ), we have M(ΦT, fλ) ∼= (T, λ).
+Proof.
+(1) Let (X, f) be a discrete Morse function with only critical cells on a graph X.
+We construct a cm equivalence ϕ(X, f) → Φ(M(X, f)) as follows: First we consider
+the spanning trees induced by (X, f) and (Φ(M(X, f)), fλf ) and show that they are
+cm equivalent. Then we deﬁne ϕ on the closing edges and prove that ϕ is a cm
+equivalence.
+By application of [Br¨u22, Theorem 5.6] we have a cm equivalence ˜ϕ: ( ¯X, ¯f) →
+(Φ(M( ¯X, ¯f)), ¯fλ ¯
+f). We extend ˜ϕ to a cm equivalence ϕ: (X, f) → Φ(M(X, f)) by
+mapping each closing edge σ ∈ X such that f(σ) = a to the unique edge σ′ ∈
+Φ(M(X, f)) with fλf (σ′) = a. The edge σ′ ∈ Φ(M(X, f)) is closing because a does
+not appear as a label on (M( ¯X, ¯f)), λ ¯f) ∼= ( ¯
+M(X, f), ¯λf) since a is the value of the
+closing critical edge σ ∈ X. Furthermore, the connected component of Xa−ε that σ
+is attached to corresponds to the subtree of M(X, f) that consists of all descendants
+of M(σ). By Deﬁnition 2.7, the edge σ′ is attached to the connected component of
+Φ(M(X, f)a−ε that corresponds to said subtree. It follows that ϕ is a cm equivalence.
+(2) Let (T, λ) be a generalized Morse labeled Merge tree. Let c0 < c1 < · · · < cn be the
+critical values of fλ and let σi ∈ ΦT such that fλ(σi) = ci. We recall that the induced
+merge tree M deﬁnes in particular a bijection between the critical cells of ΦT and
+
+ON CYCLES AND MERGE TREES
+9
+the nodes of M(ΦT, fλ). For any cell σ ∈ ΦT, we recall that we denote the node
+of M(ΦT, fλ) that corresponds to σ by M(σ). An isomorphism (ϕ, idR): (T, λ) →
+M(ΦT, fλ) is given by ϕ := M ◦ φ−1. It is immediate that ϕ is a bijection because M
+and φ are. Furthermore, ϕ is by construction compatible with the respective Morse
+labelings. It is only left to show that ϕ is compatible with the chiral child relation
+and the respective roots.
+Consider σn ∈ ΦT.
+For both trees, the cell σn corresponds to the root of the
+respective tree. In M(ΦT, fλ) this is the case because fλ attains its maximum on
+σn. In (T, λ) this holds because φ(σn) holds the maximal Morse label λ(φ(σn)) = cn.
+Thus, the map ϕ maps the root of (T, λ) to the root of M(ΦT, fλ).
+For each critical edge σi ∈ ΦT we have one of the two cases:
+a) σi is closing, or
+b) σi is not closing.
+For case b), the proof is identical to the proof of case (2) of [Br¨u22, Theorem 5.4].
+For case a), let σi be a closing critical edge. In this case, the compatibility with the
+chiral child relation follows directly by case 1. of Deﬁnition 2.6 and the property
+that only children of generalized merge trees need to have the same chirality as their
+parent node.
+□
+Corollary 3.1. Since the bijection from Theorem 3.1 is compatible with the Morse labels, it
+induces a bijection M( ,
+): DMF crit
+mult/≤ ↔ MlT/≤ : Φ where /≤ denotes dividing by order
+equivalence.
+Deﬁnition 3.1. Let ≤ and ≤′ be two Morse orders on a generalized merge tree T. We call
+≤ and ≤′ merge equivalent if
+(1) for each inner node a of T, the node a is the maximum of a subtree T ′ of T with
+respect to ≤ if and only if a is the maximum of T ′ with respect to ≤′, and
+(2) for each leaf a of T, the node a is the minimum of a subtree T ′ of T with respect to
+≤ if and only if a is the minimum of T ′ with respect to ≤′.
+A merge equivalence (T, ≤) → (T, ≤′) of Mo trees is a self-bijection ψ: V (T) ∼= V (T) such
+that ψ preserves conditions 1 and 2. A merge equivalence (T, ≤) → (T ′, ≤′) is a concatenation
+of an isomorphism ϕ: T → T ′ of underlying merge trees and a merge equivalence (T, ≤)
+ψ−→
+(T, ϕ∗ ≤′)
+ϕ−→ (T ′, ≤′).
+Proposition 3.1. Any two Morse orders ≤ and ≤′ on a generalized merge tree T are merge
+equivalent.
+Proof. The statement is proved inductively. Let a be the minimal leaf of a subtree T ′ of T
+with respect to ≤). Then a needs to be the minimal leaf of T ′ with respect to ≤′) because
+otherwise ≤′ would fail to be a Morseorder due to Remark 2.3. The statement for inner
+nodes follows similarly.
+□
+Corollary 3.2. Two generalized Mo trees have isomorphic underlying generalized merge
+trees if and only if they are merge equivalent.
+In particular, two (not generalized) Mo
+trees have isomorphic underlying (not generalized) merge trees if and only if they are merge
+equivalent.
+
+10
+JULIAN BR¨UGGEMANN AND NICHOLAS A. SCOVILLE
+For any generalized merge tree T, there are several ways to induce canonical Morse orders
+on T. We introduce the sublevel-connected Morse order (generalization of [Br¨u22, Deﬁnition
+4.1]) on any given generalized merge tree in the following:
+To deﬁne the sublevel-connected Morse order, we ﬁrst observe that every node a of T is
+uniquely determined by the shortest path from the root to a. We recall that the depth of T
+is the maximal length of any path in T that appears as the shortest path from the root to a
+leaf. Because T is chiral, we can identify such shortest paths with certain words:
+Deﬁnition 3.2. Let T be a generalized merge tree of depth n and let a be a node of T.
+The path word corresponding to a is a word a0a1 . . . an ∈ {L, R, }n+1 where
+denotes the
+empty letter. If a is of depth k, the letters a0 . . . ak are given by the chirality of the nodes
+belonging to the shortest path from the root to a. The letters ak+1 . . . an are then empty.
+Remark 3.1. Let a, b be nodes of a generalized merge tree T and let a0a1 . . . an be the
+path word corresponding to a and b0b1 . . . bn be the path word corresponding to b. Then
+the equation a0 = b0 = L always holds because we consider paths that begin at the root.
+Because a0 = b0 = L and because we consider ﬁnite trees, there is always a maximal k ∈ N
+such that ai = bi holds for all i ≤ k. Furthermore, the last non-empty letter of a path word
+is always the chirality of the considered node.
+Deﬁnition 3.3. Let T be a generalized merge tree. We deﬁne the sublevel-connected Morse
+order ≤sc on the nodes of T as follows:
+Let a, b be arbitrary nodes of T. Let a0a1 . . . an be the path word corresponding to a and
+b0b1 . . . bn the path word corresponding to b (see Deﬁnition 3.2). Furthermore, let k ∈ N be
+maximal such that ai = bi for all i ≤ k. If ak = bk = L/R we deﬁne a ≤sc b if and only if
+one of the following cases hold:
+a) ak+1 = L and bk+1 = R/ak+1 = R and bk+1 = L
+b) bk+1 =
+c) a = b
+Example 3.1. We depict the sublevel-connected Morse order in the following example:
+0
+4
+5
+6
+2
+1
+3
+7
+10
+12
+13
+16
+17
+18
+15
+19
+21
+22
+25
+26
+27
+30
+29
+31
+32
+8
+9
+11
+14
+20
+23
+24
+28
+
+ON CYCLES AND MERGE TREES
+11
+Proposition 3.2. The construction of the sublevel-connected Morse order and forgetting the
+Morse order deﬁnes a pair of inverse bijections
+≤sc : Mer/∼
+=
+gMoT/∼ : forget
+where ∼ denotes merge equivalence.
+Proof. The statement follows directly by Corollary 3.2.
+□
+To summarize our results of this section, we take a look at how Proposition 2.1, Theorem 3.1,
+and Proposition 3.2 turn the diﬀerent maps from Figure 1 into bijections by dividing out the
+needed notion of equivalence. If we do not divide out any equivalence relation, the map Φ is
+not even well-deﬁned. The maps M( , ), iMo, and forget are surjective, but not injective.
+The maps ≤sc and iMl are injective but not surjective.
+Identifying cm-equivalent dMfs makes Φ a well-deﬁned map and, moreover, a bijection
+which is inverse to M( , ): DMF crit
+graphs → gMlT by Theorem 3.1. Inverting order equiva-
+lences turns iMo and iMl into inverse bijections. Finally, inverting merge equivalences makes
+≤sc and forget inverse of each other. As a consequence, we have a complete description of the
+inverse problem for critical discrete Morse functions on multigraphs and their induced merge
+trees. The characterization for arbitrary discrete Morse functions on 1-dim regular CW com-
+plexes follows by collapsing matched cells and then applying a version of Theorem 3.1 that
+incorporates Remark 2.6. However, this procedure secretly makes use of a feature which
+might become problematic if one tries to generalize the result to higher dimensions: we are
+starting with regular CW complexes.
+Hence, the complex that arises by performing the
+simple collapses described by a Morse matching is not arbitrary but subject to being simple
+homotopy equivalent to a regular CW complex. It is a feature of dimension one that all 1-
+dimensional CW complexes are simple homotopy equivalent to a 1-dimensional regular CW
+complex. Hence, deﬁning cm-equivalences becomes more diﬃcult in a higher-dimensional
+setting, in particular, if one wants to work with non-critical discrete Morse functions. This
+would lead to the need to analyze which CW complexes are simple homotopy equivalent to
+regular CW complexes in order to know for which generality a notion of cm-equivalence is
+needed.
+4. Realization problem with simple graphs
+Let T be a generalized merge tree. Recall that C(T) = C denotes the set of all cycle nodes
+of T. For any c ∈ C, let cu denote the unique child of c. For any v ∈ T, let T(v) denote the
+subtree of T with root v and let ℓ(v) denote the number of leafs of T(v).
+Theorem 4.1. Let T be a generalized merge tree. Then there exists a simple graph X and
+discrete Morse function f : X → R such that M(X, f) = T if and only if for every c ∈ C(T),
+|C(T(cu))| < (ℓ(cu) − 2)(ℓ(cu) − 1)
+2
+.
+Furthermore, X can be made planar if and only if
+|C(T(cu))| < 2 · ℓ(cu) − 5.
+Proof. Suppose there exists a simple graph X and discrete Morse function f : X → R such
+that M(X, f) = T, and suppose by contradiction that there is a c ∈ C(T) with the property
+
+12
+JULIAN BR¨UGGEMANN AND NICHOLAS A. SCOVILLE
+that
+|C(T(cu))| ≥ (ℓ(cu) − 2)(ℓ(cu) − 1)
+2
+.
+By Lemma 2.1, the rooted subtree T(cu) is isomorphic as rooted binary trees to the induced
+Morse labeled merge tree of Xf(s)[s] where s is the simplex of X such that M(s) = cu. Letting
+v be the number of vertices in Xf(s)[s], e the number of edges in Xf(s)[s], and b1 the number
+of cycles in Xf(s)[s], we see that
+e
+=
+v − 1 + b1
+≥
+v − 1 + (v − 1)(v − 2)
+2
+=
+v − 1 + v(v − 1)
+2
++ 1 − v
+=
+v(v − 1)
+2
+which is the maximum number of edges any connected component can have. Hence it is
+impossible to add a cycle to this connected component so that
+|C(T(cu))| < (ℓ(cu) − 2)(ℓ(cu) − 1)
+2
+.
+for all c ∈ C. Now suppose further that X is planar, and suppose by contradiction that
+|C(T(cu))| ≥ 2 · ℓ(cu) − 5. Using the same notation as above, we have
+e
+=
+v − 1 + b1
+≥
+v − 1 + 2v − 5
+=
+3v − 6.
+But it is well known that a simple planar graph satisﬁes e ≤ 3v − 6 [Bic20, Theorem 5.9].
+Hence either Xf(s)[s] is not planar or maximal planar in the case of equality. In either case,
+another edge cannot be added to Xf(s)[s] without breaking planarity, and thus the result.
+For the other direction, given the generalized Merge tree T, construct the sublevel-
+connected Morse order ≤sc (Deﬁnition 3.3) on the nodes of T.
+Associate to this Morse
+order a Morse labeling λ: T → R such that a ≤sc b if and only if λ(a) ≤ λ(b). Apply
+the construction in Deﬁnition 2.7 to (T, λ) to obtain the underlying merge tree (T, λ). By
+[Br¨u22, Theorem 6.5], there is a path P and discrete Morse function f : P → R such that
+M(P, f) = (T, λ). We will inductively attach edges to P in one-to-one correspondence with
+cycle nodes of T. Each edge will be labeled with the same label as its corresponding cycle
+node.
+Induce on the cycle nodes of T with respect to the sublevel-connected Morse order c1 ≤sc
+c2 ≤sc · · ·. For the base case i = 1, write P = X1. We have by hypothesis that
+|C(T(c1u))| < (ℓ(c1u) − 2)(ℓ(c1u − 1)
+2
+.
+In addition, M(P, f) = (T, λ) so c1u = M(s1) for some simplex s1 ∈ P = X1. Applying the
+correspondence noted in Remark 2.5, this inequality means that
+b1(X1[s1])| < (v(X1[s1] − 2)(v(X1[s1] − 1)
+2
+.
+
+ON CYCLES AND MERGE TREES
+13
+By the computation in the forward direction, this implies that e(X1[s1]) < v(X1[s1])(v(X1)−1)
+2
+.
+Hence there are at least two vertices in X1[s1] not connected by an edge.
+A choice of
+vertex can be made by deﬁning a lexicographic ordering on a subset of ordered pairs of the
+vertex set of P where an ordered pair (v, u) satisﬁes f(v) < f(u) and (v, u) < (v′, u′) if
+f(v) < f(v′) or f(u) < f(u′) when f(v) = f(v′). Since all the vertices of P are given distinct
+values, < is a total order. Add an edge e1 incident with the vertices in the minimum pair
+over all available pairs to create X2 = X1 ∪ {e1} and extend f to f 1(e1) := λ(c1). Then
+M(X2, f 1) ≃ (T≤λ(c1), λ|T≤λ(c1)). The inductive step is identical to the base case.
+Now suppose that |C(T(cu))| < 2 · ℓ(cu) − 5 for all cycle nodes c ∈ T. By the forward
+direction, this is equivalent to e < 3v − 6 in the corresponding sublevel complex of X. The
+method of construction is analogous to the above construction and utilizes the fact that if a
+planar simple graph satisﬁes e < 3v − 6, then it is not maximal planar and hence an edge
+can be added while maintaining planarity [Bic20, Corollary 5.11].
+□
+Remark 4.1. While the choices made in the construction of the simple graph X in Theorem
+4.1 may be thought of as one canonical choice, the sublevel-connected Morse order is only one
+possible representative for the Morse order. Another just as natural (and shuﬄe equivalent)
+order would be the index Morse order [Br¨u22, Deﬁnition 3.3]. Furthermore, once a Morse
+order is picked, there are often several possible simple graphs with discrete Morse functions
+all related by cm equivalence that represent the given generalized merge tree.
+Example 4.1. To illustrate the construction in the planar case, consider the generalized
+merge tree T pictured below:
+We constructed the sublevel-connected Morse order and induced Morse labeling λ in
+Example 3.1.
+
+14
+JULIAN BR¨UGGEMANN AND NICHOLAS A. SCOVILLE
+0
+4
+5
+6
+2
+1
+3
+7
+10
+12
+13
+16
+17
+18
+15
+19
+21
+22
+25
+26
+27
+30
+29
+31
+32
+8
+9
+11
+14
+20
+23
+24
+28
+We then pass to the underlying merge tree T and restrict λ to T in order to apply [Br¨u22,
+Theorem 6.5] to obtain the index-ordered discrete Morse function on the graph below with
+induced merge tree T.
+10
+6
+7
+3
+13
+27
+26
+22
+18
+19
+32
+31
+0
+4
+5
+2
+1
+12
+25
+21
+16
+17
+15
+30
+29
+We induce on the cycle nodes ordered by their generalized Morse label. The ﬁrst cycle to
+be introduced is cycle node with label 8. This will be a cycle added to the graph
+6
+7
+3
+0
+4
+5
+2
+1
+to the component with the edge labeled 7.
+6
+7
+3
+8
+0
+4
+5
+2
+1
+We then add the cycle corresponding to the node labeled 9 to this same graph.
+6
+7
+3
+8
+9
+0
+4
+5
+2
+1
+Skipping to the cycle node labeled 23, we see that we need to add a cycle to the component
+with edge labeled 22:
+
+ON CYCLES AND MERGE TREES
+15
+10
+6
+7
+3
+13
+19
+22
+18
+8
+9
+11
+14
+20
+0
+4
+5
+2
+1
+12
+21
+16
+17
+15
+We add this edge
+10
+6
+7
+3
+13
+19
+22
+18
+8
+9
+11
+14
+20
+23
+0
+4
+5
+2
+1
+12
+21
+16
+17
+15
+and must add another cycle corresponding to cycle node labeled 24 to this same connected
+component.
+10
+6
+7
+3
+13
+19
+22
+18
+8
+9
+11
+14
+20
+23
+24
+0
+4
+5
+2
+1
+12
+21
+16
+17
+15
+Notice that this component is now a complete graph and that no more cycles can be added.
+The ﬁnal graph with discrete Morse function that induces the given generalized merge tree
+is
+10
+6
+7
+3
+13
+19
+27
+26
+32
+31
+22
+18
+8
+9
+11
+14
+20
+23
+24
+28
+0
+4
+5
+2
+1
+12
+21
+16
+17
+15
+30
+29
+
+16
+JULIAN BR¨UGGEMANN AND NICHOLAS A. SCOVILLE
+5. How to find cancellations with merge trees
+In this section, we present a way to ﬁnd cancellations of critical cells of dMfs with the help
+of the induced merge tree. The idea is to start with an arbitrary dMf that only has critical
+cells and to perform cancellations along the merge tree. It will turn out that depending
+on the chosen critical dMf, one sometimes has to decide whether one wants to keep the
+homeomorphism type of X or to produce an optimal dMf.
+Remark 5.1. In order to obtain an arbitrary dMf on a graph X that has only critical
+cells, one can simply choose any total order on the vertices and a total order on the edges.
+Then assign the values 0, . . . , |V (X)| − 1 to the vertices according to the chosen order and
+the numbers |V (X)|, . . . , |V (X)| + |E(X)| to the edges. This always produces an index-
+ordered dMf which is not necessary for the following algorithm. Perhaps more sophisticated
+approaches to ﬁnding a critical dMf might be useful, but for now we are satisﬁed with this
+simple one.
+Given a critical dMf f : X → R, the algorithm proceeds as follows:
+(1) Calculate the induced generalized Morse labeled merge tree M(X, f)).
+(2) Consider the leaves of M(X, f) in descending order with respect to their labels.
+Suppose we are considering the leaf c with the maximal label k such that c is critical.
+Let p be the youngest ancestor of c such that p is neither a cycle node nor matched.
+We have the following cases:
+a) The vertex M−1(c) is adjacent to the edge M−1(p).
+b) The vertex M−1(c) is not adjacent to the edge M−1(p) but there is a symmetry
+equivalence a of (X, f) such that a(M−1(c)) is adjacent to a(M−1(p)).
+c) The vertex M−1(c) is not adjacent to the edge M−1(p) and there is no symmetry
+equivalence as in case b).
+In case a) we match M−1(c) and M−1(p).This does not produce cycles because we
+explicitly exclude cycle nodes from the matching.
+In case b) we apply the symmetry equivalence a and then proceed as in case a). Since
+symmetry equivalences are only automorphisms of connected components of sublevel
+complexes, we do not alter the homeomorphism type of X in the process.
+In case c) we have to make a decision, we could
+i) simply skip c and leave M−1(c) critical,
+ii) apply a cm equivalence in order to make M−1(c) and M−1(p) adjacent, then
+proceed as in case a), or
+iii) observe that there is a unique gradient ﬂow line from M−1(c) to M−1(p) and
+cancel the two cells along this ﬂow line.
+If we choose possibility i), we might not obtain an optimal matching but we preserve
+the homeomorphism type of X. In case ii), we produce an optimal matching but may
+change the homeomorphism type of X. In case iii), we preserve the homeomorphism
+type of X and obtain an optimal matching but we change the order of the vertices
+induced by f.
+In the preceding algorithm, many claims are made, most of which are straightforward to
+prove. For example, the fact that the cases 2a), 2b), 2c)i), and 2c)ii) work as described
+follows immediately from the deﬁnition of the used equivalences. However in general it does
+not appear easy to decide whether case 2b) or 2c) holds. Nonetheless, case 2c)iii) is not so
+obvious, so we consider it in the following lemma:
+
+ON CYCLES AND MERGE TREES
+17
+Lemma 5.1. Let X be a graph, f : X → R a critical dMf, and M(X, f) the induced gener-
+alized Morse labeled merge tree. At any point of the cancellation algorithm, there is always
+a unique gradient ﬂow line from the vertex M−1(c) corresponding to the maximally labeled
+unmatched leaf c to the edge M−1(c) corresponding to its youngest unmatched ancestor p.
+Proof. If M−1(c) and M−1(p) are adjacent, there is nothing to prove. If M−1(c) and M−1(p)
+are not adjacent then there is no other non-closing critical edge in Xf(M−1(p)−ε)[M−1(c)] be-
+cause otherwise said other younger critical edge would induce a younger unmatched ancestor
+of c.
+Since M−1(c) is a critical vertex with no adjacent critical edge, all adjacent edges of
+M−1(c) are matched with their respective other vertex. This means that on all adjacent
+edges, there is a gradient ﬂow line pointing towards M−1(c). Following these gradient ﬂow
+lines backwards either leads to matched vertices that are adjacent only to the edge they
+are matched with, or to the unique critical edge of Xf(M−1(p)−ε)[M−1(c)]. One of the ﬂow
+lines eventually leads to M−1(p) because Xf(M−1(p)−ε)[M−1(c)] is connected.1 The ﬂow line
+is unique because closing edges remain critical, that is, because we only match cells along a
+subtree of X.
+□
+We apply the cancellation algorithm in the following example:
+Example 5.1. We consider the graph:
+We put some critical discrete Morse function on it and calculate the induced generalized
+merge tree:
+11
+9
+12
+15
+13
+14
+17
+16
+18
+19
+10
+6
+7
+8
+5
+3
+4
+1
+2
+0
+19
+18
+10
+17
+0
+2
+16
+15
+1
+14
+3
+13
+12
+4
+5
+11
+7
+9
+8
+6
+
+18
+JULIAN BR¨UGGEMANN AND NICHOLAS A. SCOVILLE
+We apply step 2a) as long as possible:
+11
+9
+12
+15
+13
+14
+17
+16
+18
+19
+10
+6
+7
+8
+5
+3
+4
+1
+2
+0
+19
+18
+10
+17
+0
+2
+16
+15
+1
+14
+3
+13
+12
+4
+5
+11
+7
+9
+8
+6
+Now is the ﬁrst time we run into case 2b)
+11
+9
+12
+15
+13
+14
+17
+16
+18
+19
+10
+6
+7
+8
+5
+3
+4
+1
+2
+0
+19
+18
+10
+17
+0
+2
+16
+15
+1
+14
+3
+13
+12
+4
+5
+11
+7
+9
+8
+6
+In this example, the cases 2a) and 2b) suﬃced.
+We consider the following example in order to see how quickly things can fail:
+Example 5.2. We consider the following dMf and its induced merge tree:
+2
+5
+1
+3
+4
+0
+10
+8
+9
+6
+7
+10
+7
+9
+8
+1
+3
+5
+0
+6
+4
+2
+
+ON CYCLES AND MERGE TREES
+19
+After twofold application of step 2a), we have the following:
+2
+5
+1
+3
+4
+0
+10
+8
+9
+6
+7
+10
+7
+9
+8
+1
+3
+5
+0
+6
+4
+2
+Now we have reached case 2c). We would need to have the vertex labeled 1 adjacent to the
+edge labeled 10. But this is not possible because all symmetry equivalences leave the vertex
+labeled 1 adjacent to the edge labeled 9 and no other edge. The three diﬀerent solutions
+result in the following:
+i)
+2
+5
+1
+3
+4
+0
+10
+8
+9
+6
+7
+ii)
+2
+5
+1
+3
+4
+0
+10
+8
+9
+6
+7
+iii)
+2
+5
+1
+3
+4
+0
+10
+8
+9
+6
+7
+Example 5.3. A sublevel symmetry of the last sublevel complex before the “merge tree al-
+gorithm” fails may not always be suﬃcient. Consider the graph with discrete Morse function
+given below.
+7
+9
+12
+10
+11
+8
+14
+13
+0
+1
+2
+3
+4
+5
+6
+14
+13
+12
+11
+10
+9
+8
+7
+6
+5
+4
+3
+2
+1
+0
+Proceeding as before, we obtain a matching on the graph until the algorithm speciﬁes to
+match the vertex labeled 1 with the edge labeled 13. Since these simplices are not incident,
+we need to ﬁnd a sublevel-symmetry of sublevel 12. However, the sublevel subcomplex X12
+
+20
+JULIAN BR¨UGGEMANN AND NICHOLAS A. SCOVILLE
+is given by
+which is well-known to have no non-trivial automorphisms.
+There is also no symmetry
+equivalence of a lower level than 12 that makes the vertex labeled 1 and the edge labeled 13
+adjacent. However, the three diﬀerent workarounds mentioned earlier result in the following:
+i)
+7
+9
+12
+10
+11
+8
+14
+13
+0
+1
+2
+3
+4
+5
+6
+ii)
+7
+9
+12
+10
+11
+8
+14 13
+0
+1
+2
+3
+4
+5
+6
+iii)
+7
+9
+12
+10
+11
+8
+14
+13
+0
+1
+2
+3
+4
+5
+6
+At the end of this section, we compare our algorithm for ﬁnding cancellations of criti-
+cal cells to similar algorithms from the literature. In [LLT03b] the authors introduce an
+algorithm to ﬁnd optimal discrete Morse functions on 2-dimensional manifolds which they
+generalize to higher dimensions and more general complexes in [LLT03a], even though losing
+the guarantee for optimality in the process. The main similarity to our approach is the use
+of an auxiliary tree structure, in our case the generalized merge tree, in the case of [LLT03a]
+a spanning hyperforest of a hypergraph associated to the Hasse diagram of a discrete Morse
+function.
+In [RS20], the authors provide an algorithm to ﬁnd optimal discrete Morse functions on
+trees. Said algorithm, combined with any standard algorithm to ﬁnd spanning trees, can
+easily be generalized to provide optimal discrete Morse functions on graphs with a prescribed
+critical vertex.
+The main feature of our new approach, compared to the pre-existing ones, seems to be
+that our algorithm allows to preserve certain properties of a given discrete Morse function.
+In certain cases, such a discrete Morse function might be given by an application and,
+therefore, might be worth preserving. We conjecture that, given a suitable version of higher
+merge trees, our algorithm can be generalized to higher dimensions. Since ﬁnding optimal
+Morse matchings is MAX–SNP hard, such a generalization might either fail to be optimal or
+be inconvenient to work with in practice. Nonetheless, we hope to ﬁnd interesting classes of
+examples in which such a generalized algorithm happens to be performative and informative.
+
+ON CYCLES AND MERGE TREES
+21
+References
+[Bic20]
+Allan Bickle. Fundamentals of graph theory, volume 43 of Pure and Applied Undergraduate Texts.
+American Mathematical Society, Providence, RI, [2020] ©2020. 12, 13
+[Br¨u22]
+Julian Br¨uggemann. On Merge Trees and Discrete Morse Functions on Paths and Trees. J Appl.
+and Comput. Topology, 11 2022. DOI: https://doi.org/10.1007/s41468-022-00101-w. 2, 4, 5, 7, 8,
+9, 10, 12, 13, 14
+[CCLL22]
+Robert Cardona, Justin Curry, Tung Lam, and Michael Lesnick. The universal ℓp-metric on merge
+trees. In 38th International Symposium on Computational Geometry, volume 224 of LIPIcs. Leib-
+niz Int. Proc. Inform., pages Art. No. 24, 20. Schloss Dagstuhl. Leibniz-Zent. Inform., Wadern,
+2022. 1
+[CHM+22] Justin Curry, Haibin Hang, Washington Mio, Tom Needham, and Osman Berat Okutan. Deco-
+rated merge trees for persistent topology. J. Appl. Comput. Topol., 6(3):371–428, 2022. 1
+[Cur18]
+Justin Curry. The ﬁber of the persistence map for functions on the interval. J. Appl. Comput.
+Topol., 2(3-4):301–321, 2018. 1
+[CVJ22]
+Gunnar Carlsson and Mikael Vejdemo-Johansson. Topological data analysis with applications.
+Cambridge University Press, Cambridge, 2022. 1
+[For98]
+Robin Forman. Morse theory for cell complexes. Adv. Math., 134(1):90–145, 1998. 2
+[For02]
+Robin Forman. A user’s guide to discrete Morse theory. S´em. Lothar. Combin., 48:Art. B48c, 35,
+2002. 2
+[GMO+]
+Ellen Gasparovic, Elizabeth Munch, Steve Oudot, Katharine Turner, Bei Wang, and Yusu Wang.
+Intrinsic interleaving distance for merge trees. trees, 38(37):32. 1
+[JS22]
+Benjamin Johnson and Nicholas A. Scoville. Merge trees in discrete Morse theory. Res. Math.
+Sci., 9:Paper No. 49, 07 2022. 2, 5
+[LLT03a]
+Thomas Lewiner, H´elio Lopes, and Geovan Tavares. Optimal discrete morse functions for 2-
+manifolds. Computational Geometry, 26(3):221–233, 2003. 2, 20
+[LLT03b]
+Thomas Lewiner, H´elio Lopes, and Geovan Tavares. Toward optimality in discrete morse theory.
+Experimental Mathematics, 12(3):271–285, 2003. 20
+[MBW13]
+Dmitriy Morozov, Kenes Beketayev, and Gunther Weber. Interleaving distance between merge
+trees. Discrete and Computational Geometry, 49(22-45):52, 2013. 1
+[Oud15]
+Steve Y. Oudot. Persistence theory: from quiver representations to data analysis, volume 209 of
+Mathematical Surveys and Monographs. American Mathematical Society, Providence, RI, 2015.
+1
+[PRSZ20]
+Leonid Polterovich, Daniel Rosen, Karina Samvelyan, and Jun Zhang. Topological persistence in
+geometry and analysis, volume 74 of University Lecture Series. American Mathematical Society,
+Providence, RI, [2020] ©2020. 1
+[RS20]
+Ian Rand and Nicholas A. Scoville. Discrete Morse functions, vector ﬁelds, and homological
+sequences on trees. Involve, 13(2):219–229, 2020. 2, 20
+(Julian Br¨uggemann) Max Planck Institute for Mathematics, Bonn, Germany
+Email address: brueggemann@mpim-bonn.mpg.de
+(Nicholas A. Scoville) Department of Mathematics and Computer Science, Ursinus College,
+Collegeville PA 19426
+Email address: nscoville@ursinus.edu
+
diff --git a/R9AzT4oBgHgl3EQfXPyv/content/tmp_files/load_file.txt b/R9AzT4oBgHgl3EQfXPyv/content/tmp_files/load_file.txt
new file mode 100644
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+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf,len=631
+page_content='arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='01316v1  [math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='AT]  3 Jan 2023  ON CYCLES AND MERGE TREES  JULIAN BR¨UGGEMANN AND NICHOLAS A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' SCOVILLE  Abstract.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' In this paper, we extend the notion of a merge tree to that of a generalized  merge tree, a merge tree that includes 1-dimensional cycle birth information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  Given a  discrete Morse function on a 1-dimensional regular CW complex, we construct the induced  generalized merge tree.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' We give several notions of equivalence of discrete Morse functions  based on the induced generalized merge tree and how these notions relate to one another.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  As a consequence, we obtain a complete solution to the inverse problem between discrete  Morse functions on 1-dimensional regular CW complexes and generalized merge trees.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' After  characterizing which generalized merge trees can be induced by a discrete Morse function  on a simple graph, we give an algorithm based on the induced generalized merge tree of a  discrete Morse function f : X → R that cancels the critical simplices of f and replaces it  with an optimal discrete Morse function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  Contents  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  Introduction  1  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  Preliminaries on dMfs and Merge Trees  2  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  Inverse Problem for Multigraphs  8  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  Realization problem with simple graphs  11  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  How to ﬁnd cancellations with merge trees  16  References  21  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' Introduction  Let X be a simplicial complex along with a sequence of subcomplexes ∅ = X0 ⊆ X1 ⊆  · · ⊆ Xn = X known as a ﬁltration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' In the burgeoning ﬁeld of topological data analysis,  a ﬁltration is often given by a sampling of points based on some increasing parameter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  Geometrical and topological features of X are then estimated by studying the persistence  of certain topological features [PRSZ20].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' When the topological feature in question is the  number of connected components, the persistence over the lifetime of the ﬁltration is given  by birth and death information and is summarized in a barcode or persistence diagram  [Oud15, CVJ22].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' If one wishes to not only determine birth and death information from the  ﬁltration but also how the components are evolving, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=', which components are merging with  which, one associates a merge tree tree to the ﬁltration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' Because the merge tree carries with  it this extra information, merge trees are a rich topic of study in both the theoretical and  computational settings [CHM+22, Cur18, MBW13, GMO+, CCLL22].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  Date: January 5, 2023.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  2020 Mathematics Subject Classiﬁcation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  (Primary) 57Q70;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' (Secondary) 05C90, 55N31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  Key words and phrases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' Discrete Morse Theory, merge trees.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  1  2  JULIAN BR¨UGGEMANN AND NICHOLAS A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' SCOVILLE  One way to induce a ﬁltration on X is with a discrete Morse function [For98, For02].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' Such  a function f induces a ﬁltration by considering subcomplexes associated to each critical value  of f.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' The induced merge tree of a discrete Morse function on a tree, or 1-dimensional acyclic  complex, was introduced in [JS22].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' There the authors showed that a certain class of merge  trees could be realized as the induced merge tree of a star graph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' The authors went on to  conjecture that any merge tree could be the induced merge tree of a certain discrete Morse  function on a path.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' This conjecture was recently proved in [Br¨u22].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  The goal of this paper is to extend the theory of merge trees and discrete Morse theory to  include cycles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' More speciﬁcally, given any 1-dimensional regular CW complex (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' a graph  with or without multiedges) equipped with a discrete Morse function, we deﬁne a generalized  induced Morse labeled merge tree (Deﬁnition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='6) associated to this discrete Morse function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  The generalized induced Morse labeled merge tree keeps track of not only component birth,  death, and merge information but also cycle birth information via a node with a single  child.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' After deﬁning some basic properties, we introduce an equivalence relation on regular  connected graphs called component-merge equivalence (cm-equivalence, Deﬁnition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='10) and  show that there is a one-to-one correspondence between the set of cm-equivalence classes  of discrete Morse functions with only critical cells and the set of isomorphism classes of  generalized Morse labeled merge tree in Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' In addition, we determine when a  given generalized merge tree can be realized by an induced Morse function on a graph without  multiedges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' Unlike the case of merge trees, not all generalized merge trees can be realized.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='1 gives a simple counting condition for when a generalized merge tree can be  realized.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' The proof is constructive and builds oﬀ of the merge tree construction in [Br¨u22,  Theorem 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='9].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' Finally in Section 5, we give an algorithm on merge tree induced by a discrete  Morse function in order to cancel critical cells of the discrete Morse function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' The algorithm  allows for some options depending on whether one wishes to preserve homeomorphism type  of the graph or ﬁnd an optimal matching.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  We brieﬂy compare the algorithm to similar  algorithms from the literature [LLT03a, RS20].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' Preliminaries on dMfs and Merge Trees  We recall and introduce the necessary notions for this work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' In this article, we use the  term graph for ﬁnite abstract multigraphs without degenerate loops.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' That is, graphs in  this work may have multiple edges between two given vertices, but they cannot have any  degenerate loops, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=', edges of the form (x, x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' This notion of graph can be geometrically  interpreted as one-dimensional regular CW complexes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  On the other hand, we will use the term simple graph when we mean a graph in which there  is at most one edge between two given vertices (degenerate loops are still not allowed).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' Simple  graphs correspond to one-dimensional simplicial complexes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  Since we consider graphs as  geometrical objects, we also use geometrical terms like cells, simplices, and faces to describe  them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' For any graph X, we use v(X), e(X), and b1(X) to denote the number of vertices,  edges, and cycles of X, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  We continue with one of the most central notions of the article, namely that of a discrete  Morse function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  Deﬁnition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' Let X be a graph, not necessarily connected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' A function f : X → R is  called weakly increasing if f(v) ≤ f(e) whenever vertex v is a face of edge e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' A discrete  Morse function f : X → R is a weakly increasing function which is at most 2–1 and satisﬁes  ON CYCLES AND MERGE TREES  3  the property that if f(v) = f(e), then v is incident with e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' A cell s of X is critical if s is the  unique preimage of f(s).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' Otherwise, s is called matched.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  For any a ∈ R, the sublevel subcomplex of X at a is Xa = {s ∈ X : f(s) ≤ a}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' The  connected component of s ∈ X is denoted X[s].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' We use the notation Xa−ε to denote the  sublevel subcomplex of X immediately preceding a, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=', Xa−ε := {σ : f(σ) < a}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  Remark 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' This deﬁnition of discrete Morse functions, due to B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' Benedetti, is not equiv-  alent to the more general deﬁnition originally given by Forman.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  Nonetheless, the given  deﬁnition is generic in the sense that any discrete Morse function in the sense of Forman can  be modiﬁed to fulﬁll the deﬁnition above without changing the induced acyclic matching.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  The deﬁnition stated above has the advantage that critical cells are distinguished by their  critical values and at each level, at most either one critical cell or one pair of matched cells  is added to the sublevel complex.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  Deﬁnition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' A generalized merge tree T is a rooted chiral binary tree T such that each  leaf has a sibling, and inner nodes without a sibling have the same chirality as their parent  node.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' By convention, we say that the root always has chirality L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' Furthermore, the root is  never regarded as a leaf, even if it only has one child node.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  For nodes c of generalized merge trees we use the notation cl/cr for the left/right child  node of c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  Remark 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' Generalized merge trees may have nodes without siblings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  The notion of  chirality of only children does not really deserve the name chirality because there is only one  total ordering on a set with one element.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' We impose the condition that an only child has  the same chirality as its parent node for technical reasons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' We need this convention so the  constructions in Deﬁnition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='7 and Deﬁnition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='6 make part 2 of Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='1 work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  Generalized merge trees generalize merge trees in the sense that that keep track of more  information than merge trees do.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  Deﬁnition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' Let T be a generalized merge tree.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' We call a total order ≤ on the nodes of  T a Morse order if it fulﬁlls the following two properties for all generalized merge subtrees  T ′ of T:  (1) The restriction ≤|T ′ attains its maximum on the root p of T ′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  (2) The minimum of ≤|T ′ has the same chirality as p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  We call a generalized merge tree together with a Morse order (T, ≤) a generalized Morse  ordered merge tree (gMo tree)  Remark 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' Assuming property 2 of Deﬁnition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='3 for every subtree T ′ with root p of T  is equivalent to either of the following:  For any subtree T ′ with root p of T, the restriction ≤|T ′ attains its minimum on the  subtree with root pl/pr if L/R is the chirality of the root p of T ′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  For any subtree T ′ with root p of T, all nodes on the shortest path between p and  the minimum of ≤|T ′ have the same chirality as p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  The equivalence can be proved by an inductive argument over all nodes of the shortest path  between p and the minimum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  Deﬁnition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' We call a generalized merge tree (T, λ) with an injective map λ: T → R  such that λ induces a Morse order on T a generalized Morse labeled merge tree (gMl tree).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  Any such map λ is called a Morse labeling on T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  4  JULIAN BR¨UGGEMANN AND NICHOLAS A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' SCOVILLE  Let (T, λ) and (T ′, λ′) be gMl trees.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' An order equivalence (ϕ, ψ): (T, λ) → (T ′, λ′) of gMl  trees is a pair of maps consisting of an isomorphism of the underlying generalized merge  trees ϕ: T → T ′ and a bijection ψ: R → R such that the restriction ψ|im(λ) : im(λ) → im(λ′)  is order preserving.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' Let gMoT be the set of generalized Morse ordered merge trees and let  gMlT be the set of generalized Morse labeled merge trees.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' Then taking the Morse order  induced by a Morse labeling and using a Morse order and the labels {0, 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' , |V (T)| − 1} to  induce a Morse labeling deﬁne inverse bijections  iMl: gMoT/∼  =  gMlT/∼ : iMo  where ∼ denotes order equivalence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' The proof is completely analogous to [Br¨u22, Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='26].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  □  Deﬁnition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' Let (X, f) be a discrete Morse function on a graph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' We call a critical edge  σ ∈ X a closing edge if σ is part of a regular subdivision of S1 in X such that f(σ) is the  maximum on said subdivision.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  We deﬁne C(X, f) := {c ∈ X|c is closing} to be the set of closing edges of (X, f) and  ( ¯X, ¯f) := (X \\ C(X, f), f|X\\C(X,f)) to be the spanning tree induced by f of X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  Remark 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' In the previous deﬁnition, the subdivison of S1 that any closing edge σ must  be part of does not need to be unique.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' Nonetheless, the removal of σ would lead to the  reduction of the ﬁrst Betti number by one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' Moreover, the notion of closing edges is well-  deﬁned because the edge σ being closing implies that it is the unique maximal edge of all  subdivisions of S1 in Xf(σ[σ].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  Furthermore, it is immediate that ( ¯X, ¯f) := (X \\ C(X, f), f|X\\C(X,f)) is a discrete Morse  function on a tree.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  Deﬁnition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='6 (Induced Morse Labeled Merge Tree).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' Let f : X → R be a discrete Morse  function on a connected graph X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' Let σ0 < σ1 < · · · < σn be the critical edges of (X, f)  ordered by their values under f.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' The generalized Morse labeled merge tree induced by (X, f),  denoted M(X, f) with labeling λf, is constructed inductively as follows:  For the base case we construct a node M(σn) with label f(σn) and left chirality as root  node.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' For any other critical edge σi between two 0-simplices v and w there are two cases:  (1) The critical edge σi is closing ⇔ b1(Xf(σi) \\ σi) = b1(Xf(σi)) − 1 ⇔ b0(Xf(σi) \\ σi) =  b0(Xf(σi)),  (2) The critical edge σi is not closing ⇔ b1(Xf(σi) \\ σi) = b1(Xf(σi)) ⇔ b0(Xf(σi) \\ σi) =  b0(Xf(σi)) + 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  Depending on the case at hand, we perform the following step for the construction of  M(X, f):  (1) We construct a child node c of M(σi) with label λ := max{f(σ)|σ ∈ Xf(σi)−ε, σcritical}  and the same chirality as M(σi).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' The node c then corresponds to the edge of X la-  beled λ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  (2) We construct two child nodes cλv and cλw of M(σi).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' Deﬁne λv := max{f(σ)|σ ∈  Xσi−ε[v], σ critical} and λw := max{f(σ)|σ ∈ Xσi−ε[w], σ critical}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' Then label the  new nodes λf(cλv) := λv and λf(cλw) := λw.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' If min{f(σ)|σ ∈ Xσi−ε[v]} < min{f(σ)|σ ∈  ON CYCLES AND MERGE TREES  5  Xσi−ε[w]}, we assign cλv the same chirality (L or R) as cσi and give cλw the opposite  chirality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  Continue the induction over the rest of the critical edges of X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  Remark 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' There is a one-to-one correspondence between vertices of X and leaves of  M(X, f), non-closing edges of X and parents with two children of M(X, f), and closing  edges (cycles) of X and parents with one child in M(X, f).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  Furthermore, the proof that the construction indeed produces a gMl tree is completely  analogous to [Br¨u22, Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='20], respectively [JS22, Theorem 9].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' Let (X, f) be a discrete Morse function on a graph and let M(X, f) be the  induced generalized Morse labeled merge tree.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' For any simplex s ∈ X, the rooted subtree  T(M(s)) of M(X, f) is induced by the connected component Xf(s)[s] of s in the sublevel com-  plex of level f(s).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' Moreover, the rooted subtree T(M(s)) is isomorphic to M(Xf(s)[s], f|Xf(s)[s])  as merge trees if and only if M(s) has chirality L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' If M(s) has chirality R, then T(M(s)) is  isomorphic to M(Xf(s)[s], f|Xf(s)[s]) as rooted binary trees but the chiralities of all nodes are  opposite to the ones of their respective nodes in the other tree.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' We observe that by Deﬁnition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='6 the label of M(s) is f(s) and the chirality of  M(s) is decided by the minimum of f|Xf(s)[s] in comparison to the minimum of the connected  component that Xf(s)[s] got divided from at level f(s).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' It follows inductively by construction  that all nodes of the subtree T(M(s)) are induced by critical cells of Xf(s)[s] because they  are constructed by removing critical edges of Xf(s)[s].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  The isomorphism as rooted binary trees is constructed by the same inductive argument.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  Since the chirality depends on the chirality of the respective parent node, said isomorphism  is compatible with the chirality if and only if the root of the rooted subtree T(M(s)), namely  M(s), has chirality L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' This is true because the root of M(Xf(s)[s], f|Xf(s)[s]) by convention  always has chirality L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  □  Deﬁnition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' Let (T, λ) be a generalized Morse labeled merge tree.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' Let C(T) ⊂ V (T)  be the set of nodes that have exactly one child node.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' We refer to the elements of C(T) as  cycle nodes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' We denote by ( ¯T, λ) the Morse labeled merge tree that is obtained from (T, λ)  by removing the cycle nodes by connecting their parent nodes directly to their child nodes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  We call ( ¯T, λ) the underlying Morse labeled merge tree of (T, λ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  We obtain a discrete Morse function on a graph fλ: X → R from (T, λ) in two steps as  follows: In a ﬁrst step, we construct the induced discrete Morse function on a path (P, fλ)  as in [Br¨u22, Deﬁnition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='21].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' For the second step, for each node c of C(T) we add an edge  parallel to the edge corresponding to c’s oldest descendant which has two children to P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' We  denote the graph obtained this way by X and extend the function fλ : P → R to X using  the values of λ on the corresponding nodes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' We denote the pair (P, fλ) by Φ(T, λ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' We have M( ¯X, f| ¯  X) ∼= ¯  M(X, f) as Morse labeled merge trees.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' The construction of the induced generalized merge tree induces a bijection M : X →  V (M(X, f)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' It follows immediately by construction that M bijectively maps closing edges  to nodes of C(M(X, f)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' Hence removing the closing edges from (X, f), that is, passing on  to ( ¯X, f), precisely removes the nodes of C(M(X, f)), which corresponds to passing on to  ¯  M(X, f).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' Hence, the statement holds because the values of f on non-closing edges are not  changed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  □  6  JULIAN BR¨UGGEMANN AND NICHOLAS A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' SCOVILLE  Deﬁnition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' Let f : X → R be a dMf on a graph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  For each non-empty connected  component Xf  c [v] of a sublevel complex Xf  c we denote by Aut(Xf  c [v]) the group of simplicial  automorphisms of said connected component of said sublevel complex.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' Each a ∈ Aut(Xf  c [v])  can be extended by the identity to a set function that is a self-bijection X → X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' The  group �  Aut(Xf  c [v]) is deﬁned to be the group of said extensions of elements of Aut(Xf  c [v])  by the identity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' We consider �  Aut(Xf  c [v]) as a subgroup of the group of all self-bijections of  X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' The total order on Cr(f) induced by f induces chains �  Aut(Xf  c0[v]) ⊂ �  Aut(Xf  c1[v]) ⊂ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  of inclusions of subgroups.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  Moreover, we have inclusions �  Aut(Xf  ci[v]) ⊂ �  Aut(Xf  cj[v]) =  �  Aut(Xf  cj[w]) ⊃ �  Aut(Xf  ci[w]) if v and w are in diﬀerent connected components of some sublevel  complex Xf  ci that merge together in some other sublevel complex Xf  cj for j > i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' We deﬁne the  sublevel automorphism group of (X, f), denoted by Autsl(X, f), to be the subgroup generated  by  �  c∈Cr(f),v∈X  �  Aut(Xf  c [v]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' We call the elements of Autsl(X, f) sublevel automorphisms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  Note that an element a ∈ Autsl(X, f) is not necessarily an automorphism of X, but only a  self-bijection of X that restricts to an automorphism on some connected component of some  sublevel complex corresponding to a critical simplex.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  Deﬁnition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' Let f : X → R and g : X → R be dMfs on a graph X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' We call f and g  sublevel-equivalent if they have the same critical values and isomorphic sublevel complexes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  If additionally g = f ∗ a holds for a sublevel automorphism a ∈ Autsl(X, f) = Autsl(X, g),  then we call f and g symmetry-equivalent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' We call the map a a symmetry equivalence from  f to g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  We call two dMfs f : X → R and g : Y → R symmetry-equivalent if there is a simplicial  isomorphism ϕ: X → Y such that f and g ◦ ϕ are symmetry-equivalent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  Deﬁnition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' Let (X, f) and (X′, f ′) be critical dMfs on connected graphs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' A component-  merge equivalence (cm equivalence) is a bijection ϕ: X → X′ such that at least one of the  following cases holds:  (1) ϕ is a symmetry equivalence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  (2) ϕ fulﬁlls the following:  f ′ ◦ ϕ = f,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  ϕ induces a bijection between the sets of connected components of sublevel  complexes such that the restriction ϕ|Xa−ε[v] : Xa−ε[v] → X′  a−ε[ϕ(v)] to each con-  nected component is a cm equivalence,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' and  the edge σ ∈ X with f(σ) = a merges two connected components Xa−ε[v1]  and Xa−ε[v2] in Xa[v1] = Xa[v2] if and only if the edge ϕ(σ) merges the corre-  sponding two connected components X′  a−ε[ϕ(v1)] and X′  a−ε[ϕ(v2)] in X′  a[ϕ(v1)] =  X′  a[ϕ(v2)].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' Otherwise, if the edge σ ∈ X with f(σ) = a does not merge two  connected components but rather closes a circle within a connected component  Xa−ε[v], then and only then ϕ(σ) closes a circle within X′  a−ε[ϕ(v)].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  If ϕ re-attaches the critical edge labeled a, we call ϕ non-trivial.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' Moreover, if ϕ re-  attaches the critical edge of level a and acts as a symmetry equivalence everywhere  else, we say that ϕ is of level a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' If ϕ does not re-attach any critical edge, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=', if ϕ is  a symmetry equivalence, we call ϕ a trivial cm equivalence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  Remark 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' Extending the notion of cm equivalences to dMfs with matched cells is a bit  tedious.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' We would like to suggest getting rid of matched cells by identifying arbitrary dMfs  ON CYCLES AND MERGE TREES  7  on graphs with critical dMfs on the corresponding graph that arises by collapsing matched  cells beforehand but degenerate loops might arise in this process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' Nonetheless, the newly  created degenerate loops are critical by construction and the deﬁnition above works in this  context.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  Example 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' Let f : X → R be the complex with discrete Morse function on the left and  f ′: X′ → R be the complex with discrete Morse function on the right.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  7  3  2  6  4  5  8  3  6  2  4  0  1  2  4  6  7  5  8  3  3  6  2  4  0  1  Then a cm-equivalence of critical levels a = 7 is given by ϕ: X → X′ where ϕ(v) = v′  whenever f(v) = f ′(v′) on vertices and ϕ(e) = e′ whenever f(e) = f ′(e′) on edges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  Remark 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' It is clear from the case distinction made in Deﬁnition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='10 that any cm  equivalence ϕ: (X, f) → (X′, f ′) restricts to a bijection ϕ|C(X,f) : C(X, f) → C(X′, f ′).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' Let f : X → R and f ′: X′ → R be cm-equivalent dMfs on multigraphs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' Then  M(X, f) ∼= M(X′, f ′) holds as generalized Morse labeled merge trees.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' Let ϕ be a cm equivalence ϕ: (X, f) → (X′, f ′).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' Since we work with a version of  discrete Morse functions which are at most 2-1, at most one non-trivial cm equivalence of  level a can occur for any level a because there is at most one critical edge labeled a in  (X, f), (X′, f ′), respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' Thus, we can decompose any cm equivalence into a sequence  (ϕa)a of non-trivial cm equivalences of decreasing levels such that each ϕa only changes the  attachment of the single edge σ with f(σ) = a and acts as a symmetry equivalence on the  rest of graph and dMf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' It suﬃces to consider a single level a because the statement then  follows by induction from highest to lowest over all levels a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  For such a non-trivial cm equivalence ϕa we consider the step of the construction of the  induced Ml trees that considers the critical edge σ with f(σ) = a and the critical edge ϕ(σ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  If σ is not closing, neither is ϕ(σ) by Remark 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='7 and the inductive step follows by [Br¨u22,  Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='52].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' In the case that σ is closing, so is ϕ(σ) and we inductively assume that  ϕ induces an isomorphism of induced generalized Ml trees everywhere outside the subtree  corresponding to the connected component of Xf  a−ε that the edge σ with f(σ) = a is attached  to.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' That is, on the rest of M(X, f) the map M(ϕ) is a bijection compatible with the chiral  child relation onto M(X′, f ′) except possibly for the subtree of M(X′, f ′) which corresponds  to the connected component of X′f′  a−ε that the edge ϕ(σ) is attached to.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  Since the map ϕ is compatible with the dMfs and because it restricts to a cm equivalence  Xf  a−ε → X′f′  a−ε, the dMf f attains the same minima and maxima on the two relevant con-  nected component of Xf  a−ε as f ′ does on its counterpart of X′f′  a−ε via ϕ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' Since Deﬁnition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='6  only considers which connected component the considered edge is attached to, it makes no  diﬀerence for the isomorphism type of the induced Ml trees that in general σ is attached to  8  JULIAN BR¨UGGEMANN AND NICHOLAS A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' SCOVILLE  said connected component of Xf  a−ε at vertices that do not correspond via ϕ to the ones ad-  jacent to ϕ(σ) in X′f′  a−ε.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' Thus, the construction of the induced generalized Ml tree produces  nodes with the same chirality and label for both induced Ml trees in the steps that consider  σ, ϕ(σ), respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' By assumption, the restriction ϕXf  a−ε : Xf  a−ε → X′f′  a−ε is a symmetry  equivalence, so the isomorphism of Ml trees extends to the subtrees that correspond to the  respective connected components.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  □  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' Inverse Problem for Multigraphs  In this section we want to describe the relationship between dMfs on graphs, generalized  Ml trees, generalized Mo trees, and generalized merge trees:  gMer  DMF crit  graphs  gMoT  gMlT  iMl  iMo  M( , )  Φ ◦ iMl◦ ≤sc  Φ  M( , )  forget  ≤sc  Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' Relationships between dMfs and merge trees  Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' Let DMF crit  mult denote the set of cm-equivalence classes of discrete Morse  functions with only critical cells on multigraphs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' Let MlT denote the set of isomorphism  classes of generalized Morse labeled merge trees.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' Then the induced discrete Morse function  Φ, Deﬁnition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='7, and the induced Morse labeled merge tree M( , ), Deﬁnition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='6, deﬁne  maps M( , ): DMF crit  mult ↔ MlT : Φ that are inverse of each other in the sense that:  (1) for any discrete Morse function (X, f) with only critical cells, the discrete Morse  function Φ(M(X, f), λf) is cm-equivalent to (X, f), and  (2) for any generalized Morse labeled merge tree (T, λ), we have M(ΦT, fλ) ∼= (T, λ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  (1) Let (X, f) be a discrete Morse function with only critical cells on a graph X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  We construct a cm equivalence ϕ(X, f) → Φ(M(X, f)) as follows: First we consider  the spanning trees induced by (X, f) and (Φ(M(X, f)), fλf ) and show that they are  cm equivalent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' Then we deﬁne ϕ on the closing edges and prove that ϕ is a cm  equivalence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  By application of [Br¨u22, Theorem 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='6] we have a cm equivalence ˜ϕ: ( ¯X, ¯f) →  (Φ(M( ¯X, ¯f)), ¯fλ ¯  f).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' We extend ˜ϕ to a cm equivalence ϕ: (X, f) → Φ(M(X, f)) by  mapping each closing edge σ ∈ X such that f(σ) = a to the unique edge σ′ ∈  Φ(M(X, f)) with fλf (σ′) = a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' The edge σ′ ∈ Φ(M(X, f)) is closing because a does  not appear as a label on (M( ¯X, ¯f)), λ ¯f) ∼= ( ¯  M(X, f), ¯λf) since a is the value of the  closing critical edge σ ∈ X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' Furthermore, the connected component of Xa−ε that σ  is attached to corresponds to the subtree of M(X, f) that consists of all descendants  of M(σ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' By Deﬁnition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='7, the edge σ′ is attached to the connected component of  Φ(M(X, f)a−ε that corresponds to said subtree.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' It follows that ϕ is a cm equivalence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  (2) Let (T, λ) be a generalized Morse labeled Merge tree.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' Let c0 < c1 < · · · < cn be the  critical values of fλ and let σi ∈ ΦT such that fλ(σi) = ci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' We recall that the induced  merge tree M deﬁnes in particular a bijection between the critical cells of ΦT and  ON CYCLES AND MERGE TREES  9  the nodes of M(ΦT, fλ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' For any cell σ ∈ ΦT, we recall that we denote the node  of M(ΦT, fλ) that corresponds to σ by M(σ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' An isomorphism (ϕ, idR): (T, λ) →  M(ΦT, fλ) is given by ϕ := M ◦ φ−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' It is immediate that ϕ is a bijection because M  and φ are.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' Furthermore, ϕ is by construction compatible with the respective Morse  labelings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' It is only left to show that ϕ is compatible with the chiral child relation  and the respective roots.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  Consider σn ∈ ΦT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  For both trees, the cell σn corresponds to the root of the  respective tree.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' In M(ΦT, fλ) this is the case because fλ attains its maximum on  σn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' In (T, λ) this holds because φ(σn) holds the maximal Morse label λ(φ(σn)) = cn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  Thus, the map ϕ maps the root of (T, λ) to the root of M(ΦT, fλ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  For each critical edge σi ∈ ΦT we have one of the two cases:  a) σi is closing, or  b) σi is not closing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  For case b), the proof is identical to the proof of case (2) of [Br¨u22, Theorem 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  For case a), let σi be a closing critical edge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' In this case, the compatibility with the  chiral child relation follows directly by case 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' of Deﬁnition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='6 and the property  that only children of generalized merge trees need to have the same chirality as their  parent node.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  □  Corollary 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' Since the bijection from Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='1 is compatible with the Morse labels, it  induces a bijection M( ,  ): DMF crit  mult/≤ ↔ MlT/≤ : Φ where /≤ denotes dividing by order  equivalence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  Deﬁnition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' Let ≤ and ≤′ be two Morse orders on a generalized merge tree T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' We call  ≤ and ≤′ merge equivalent if  (1) for each inner node a of T, the node a is the maximum of a subtree T ′ of T with  respect to ≤ if and only if a is the maximum of T ′ with respect to ≤′, and  (2) for each leaf a of T, the node a is the minimum of a subtree T ′ of T with respect to  ≤ if and only if a is the minimum of T ′ with respect to ≤′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  A merge equivalence (T, ≤) → (T, ≤′) of Mo trees is a self-bijection ψ: V (T) ∼= V (T) such  that ψ preserves conditions 1 and 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' A merge equivalence (T, ≤) → (T ′, ≤′) is a concatenation  of an isomorphism ϕ: T → T ′ of underlying merge trees and a merge equivalence (T, ≤)  ψ−→  (T, ϕ∗ ≤′)  ϕ−→ (T ′, ≤′).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' Any two Morse orders ≤ and ≤′ on a generalized merge tree T are merge  equivalent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' The statement is proved inductively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' Let a be the minimal leaf of a subtree T ′ of T  with respect to ≤).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' Then a needs to be the minimal leaf of T ′ with respect to ≤′) because  otherwise ≤′ would fail to be a Morseorder due to Remark 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' The statement for inner  nodes follows similarly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  □  Corollary 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' Two generalized Mo trees have isomorphic underlying generalized merge  trees if and only if they are merge equivalent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  In particular, two (not generalized) Mo  trees have isomorphic underlying (not generalized) merge trees if and only if they are merge  equivalent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  10  JULIAN BR¨UGGEMANN AND NICHOLAS A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' SCOVILLE  For any generalized merge tree T, there are several ways to induce canonical Morse orders  on T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' We introduce the sublevel-connected Morse order (generalization of [Br¨u22, Deﬁnition  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='1]) on any given generalized merge tree in the following:  To deﬁne the sublevel-connected Morse order, we ﬁrst observe that every node a of T is  uniquely determined by the shortest path from the root to a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' We recall that the depth of T  is the maximal length of any path in T that appears as the shortest path from the root to a  leaf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' Because T is chiral, we can identify such shortest paths with certain words:  Deﬁnition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' Let T be a generalized merge tree of depth n and let a be a node of T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  The path word corresponding to a is a word a0a1 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' an ∈ {L, R, }n+1 where  denotes the  empty letter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' If a is of depth k, the letters a0 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' ak are given by the chirality of the nodes  belonging to the shortest path from the root to a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' The letters ak+1 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' an are then empty.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  Remark 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' Let a, b be nodes of a generalized merge tree T and let a0a1 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' an be the  path word corresponding to a and b0b1 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' bn be the path word corresponding to b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' Then  the equation a0 = b0 = L always holds because we consider paths that begin at the root.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  Because a0 = b0 = L and because we consider ﬁnite trees, there is always a maximal k ∈ N  such that ai = bi holds for all i ≤ k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' Furthermore, the last non-empty letter of a path word  is always the chirality of the considered node.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  Deﬁnition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' Let T be a generalized merge tree.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' We deﬁne the sublevel-connected Morse  order ≤sc on the nodes of T as follows:  Let a, b be arbitrary nodes of T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' Let a0a1 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' an be the path word corresponding to a and  b0b1 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' bn the path word corresponding to b (see Deﬁnition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' Furthermore, let k ∈ N be  maximal such that ai = bi for all i ≤ k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' If ak = bk = L/R we deﬁne a ≤sc b if and only if  one of the following cases hold:  a) ak+1 = L and bk+1 = R/ak+1 = R and bk+1 = L  b) bk+1 =  c) a = b  Example 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' We depict the sublevel-connected Morse order in the following example:  0  4  5  6  2  1  3  7  10  12  13  16  17  18  15  19  21  22  25  26  27  30  29  31  32  8  9  11  14  20  23  24  28  ON CYCLES AND MERGE TREES  11  Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' The construction of the sublevel-connected Morse order and forgetting the  Morse order deﬁnes a pair of inverse bijections  ≤sc : Mer/∼  =  gMoT/∼ : forget  where ∼ denotes merge equivalence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' The statement follows directly by Corollary 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  □  To summarize our results of this section, we take a look at how Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='1, Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='1,  and Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='2 turn the diﬀerent maps from Figure 1 into bijections by dividing out the  needed notion of equivalence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' If we do not divide out any equivalence relation, the map Φ is  not even well-deﬁned.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' The maps M( , ), iMo, and forget are surjective, but not injective.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  The maps ≤sc and iMl are injective but not surjective.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  Identifying cm-equivalent dMfs makes Φ a well-deﬁned map and, moreover, a bijection  which is inverse to M( , ): DMF crit  graphs → gMlT by Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' Inverting order equiva-  lences turns iMo and iMl into inverse bijections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' Finally, inverting merge equivalences makes  ≤sc and forget inverse of each other.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' As a consequence, we have a complete description of the  inverse problem for critical discrete Morse functions on multigraphs and their induced merge  trees.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' The characterization for arbitrary discrete Morse functions on 1-dim regular CW com-  plexes follows by collapsing matched cells and then applying a version of Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='1 that  incorporates Remark 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' However, this procedure secretly makes use of a feature which  might become problematic if one tries to generalize the result to higher dimensions: we are  starting with regular CW complexes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  Hence, the complex that arises by performing the  simple collapses described by a Morse matching is not arbitrary but subject to being simple  homotopy equivalent to a regular CW complex.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' It is a feature of dimension one that all 1-  dimensional CW complexes are simple homotopy equivalent to a 1-dimensional regular CW  complex.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' Hence, deﬁning cm-equivalences becomes more diﬃcult in a higher-dimensional  setting, in particular, if one wants to work with non-critical discrete Morse functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' This  would lead to the need to analyze which CW complexes are simple homotopy equivalent to  regular CW complexes in order to know for which generality a notion of cm-equivalence is  needed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' Realization problem with simple graphs  Let T be a generalized merge tree.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' Recall that C(T) = C denotes the set of all cycle nodes  of T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' For any c ∈ C, let cu denote the unique child of c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' For any v ∈ T, let T(v) denote the  subtree of T with root v and let ℓ(v) denote the number of leafs of T(v).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' Let T be a generalized merge tree.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' Then there exists a simple graph X and  discrete Morse function f : X → R such that M(X, f) = T if and only if for every c ∈ C(T),  |C(T(cu))| < (ℓ(cu) − 2)(ℓ(cu) − 1)  2  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  Furthermore, X can be made planar if and only if  |C(T(cu))| < 2 · ℓ(cu) − 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' Suppose there exists a simple graph X and discrete Morse function f : X → R such  that M(X, f) = T, and suppose by contradiction that there is a c ∈ C(T) with the property  12  JULIAN BR¨UGGEMANN AND NICHOLAS A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' SCOVILLE  that  |C(T(cu))| ≥ (ℓ(cu) − 2)(ℓ(cu) − 1)  2  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  By Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='1, the rooted subtree T(cu) is isomorphic as rooted binary trees to the induced  Morse labeled merge tree of Xf(s)[s] where s is the simplex of X such that M(s) = cu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' Letting  v be the number of vertices in Xf(s)[s], e the number of edges in Xf(s)[s], and b1 the number  of cycles in Xf(s)[s], we see that  e  =  v − 1 + b1  ≥  v − 1 + (v − 1)(v − 2)  2  =  v − 1 + v(v − 1)  2  + 1 − v  =  v(v − 1)  2  which is the maximum number of edges any connected component can have.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' Hence it is  impossible to add a cycle to this connected component so that  |C(T(cu))| < (ℓ(cu) − 2)(ℓ(cu) − 1)  2  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  for all c ∈ C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' Now suppose further that X is planar, and suppose by contradiction that  |C(T(cu))| ≥ 2 · ℓ(cu) − 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' Using the same notation as above, we have  e  =  v − 1 + b1  ≥  v − 1 + 2v − 5  =  3v − 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  But it is well known that a simple planar graph satisﬁes e ≤ 3v − 6 [Bic20, Theorem 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='9].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  Hence either Xf(s)[s] is not planar or maximal planar in the case of equality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' In either case,  another edge cannot be added to Xf(s)[s] without breaking planarity, and thus the result.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  For the other direction, given the generalized Merge tree T, construct the sublevel-  connected Morse order ≤sc (Deﬁnition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='3) on the nodes of T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  Associate to this Morse  order a Morse labeling λ: T → R such that a ≤sc b if and only if λ(a) ≤ λ(b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' Apply  the construction in Deﬁnition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='7 to (T, λ) to obtain the underlying merge tree (T, λ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' By  [Br¨u22, Theorem 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='5], there is a path P and discrete Morse function f : P → R such that  M(P, f) = (T, λ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' We will inductively attach edges to P in one-to-one correspondence with  cycle nodes of T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' Each edge will be labeled with the same label as its corresponding cycle  node.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  Induce on the cycle nodes of T with respect to the sublevel-connected Morse order c1 ≤sc  c2 ≤sc · · ·.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' For the base case i = 1, write P = X1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' We have by hypothesis that  |C(T(c1u))| < (ℓ(c1u) − 2)(ℓ(c1u − 1)  2  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  In addition, M(P, f) = (T, λ) so c1u = M(s1) for some simplex s1 ∈ P = X1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' Applying the  correspondence noted in Remark 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='5, this inequality means that  b1(X1[s1])| < (v(X1[s1] − 2)(v(X1[s1] − 1)  2  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  ON CYCLES AND MERGE TREES  13  By the computation in the forward direction, this implies that e(X1[s1]) < v(X1[s1])(v(X1)−1)  2  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  Hence there are at least two vertices in X1[s1] not connected by an edge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  A choice of  vertex can be made by deﬁning a lexicographic ordering on a subset of ordered pairs of the  vertex set of P where an ordered pair (v, u) satisﬁes f(v) < f(u) and (v, u) < (v′, u′) if  f(v) < f(v′) or f(u) < f(u′) when f(v) = f(v′).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' Since all the vertices of P are given distinct  values, < is a total order.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' Add an edge e1 incident with the vertices in the minimum pair  over all available pairs to create X2 = X1 ∪ {e1} and extend f to f 1(e1) := λ(c1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' Then  M(X2, f 1) ≃ (T≤λ(c1), λ|T≤λ(c1)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' The inductive step is identical to the base case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  Now suppose that |C(T(cu))| < 2 · ℓ(cu) − 5 for all cycle nodes c ∈ T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' By the forward  direction, this is equivalent to e < 3v − 6 in the corresponding sublevel complex of X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' The  method of construction is analogous to the above construction and utilizes the fact that if a  planar simple graph satisﬁes e < 3v − 6, then it is not maximal planar and hence an edge  can be added while maintaining planarity [Bic20, Corollary 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  □  Remark 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' While the choices made in the construction of the simple graph X in Theorem  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='1 may be thought of as one canonical choice, the sublevel-connected Morse order is only one  possible representative for the Morse order.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' Another just as natural (and shuﬄe equivalent)  order would be the index Morse order [Br¨u22, Deﬁnition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' Furthermore, once a Morse  order is picked, there are often several possible simple graphs with discrete Morse functions  all related by cm equivalence that represent the given generalized merge tree.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  Example 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' To illustrate the construction in the planar case, consider the generalized  merge tree T pictured below:  We constructed the sublevel-connected Morse order and induced Morse labeling λ in  Example 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  14  JULIAN BR¨UGGEMANN AND NICHOLAS A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' SCOVILLE  0  4  5  6  2  1  3  7  10  12  13  16  17  18  15  19  21  22  25  26  27  30  29  31  32  8  9  11  14  20  23  24  28  We then pass to the underlying merge tree T and restrict λ to T in order to apply [Br¨u22,  Theorem 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='5] to obtain the index-ordered discrete Morse function on the graph below with  induced merge tree T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  10  6  7  3  13  27  26  22  18  19  32  31  0  4  5  2  1  12  25  21  16  17  15  30  29  We induce on the cycle nodes ordered by their generalized Morse label.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' The ﬁrst cycle to  be introduced is cycle node with label 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' This will be a cycle added to the graph  6  7  3  0  4  5  2  1  to the component with the edge labeled 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  6  7  3  8  0  4  5  2  1  We then add the cycle corresponding to the node labeled 9 to this same graph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  6  7  3  8  9  0  4  5  2  1  Skipping to the cycle node labeled 23, we see that we need to add a cycle to the component  with edge labeled 22:  ON CYCLES AND MERGE TREES  15  10  6  7  3  13  19  22  18  8  9  11  14  20  0  4  5  2  1  12  21  16  17  15  We add this edge  10  6  7  3  13  19  22  18  8  9  11  14  20  23  0  4  5  2  1  12  21  16  17  15  and must add another cycle corresponding to cycle node labeled 24 to this same connected  component.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  10  6  7  3  13  19  22  18  8  9  11  14  20  23  24  0  4  5  2  1  12  21  16  17  15  Notice that this component is now a complete graph and that no more cycles can be added.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  The ﬁnal graph with discrete Morse function that induces the given generalized merge tree  is  10  6  7  3  13  19  27  26  32  31  22  18  8  9  11  14  20  23  24  28  0  4  5  2  1  12  21  16  17  15  30  29  16  JULIAN BR¨UGGEMANN AND NICHOLAS A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' SCOVILLE  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' How to find cancellations with merge trees  In this section, we present a way to ﬁnd cancellations of critical cells of dMfs with the help  of the induced merge tree.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' The idea is to start with an arbitrary dMf that only has critical  cells and to perform cancellations along the merge tree.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' It will turn out that depending  on the chosen critical dMf, one sometimes has to decide whether one wants to keep the  homeomorphism type of X or to produce an optimal dMf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  Remark 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' In order to obtain an arbitrary dMf on a graph X that has only critical  cells, one can simply choose any total order on the vertices and a total order on the edges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  Then assign the values 0, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' , |V (X)| − 1 to the vertices according to the chosen order and  the numbers |V (X)|, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' , |V (X)| + |E(X)| to the edges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' This always produces an index-  ordered dMf which is not necessary for the following algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' Perhaps more sophisticated  approaches to ﬁnding a critical dMf might be useful, but for now we are satisﬁed with this  simple one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  Given a critical dMf f : X → R, the algorithm proceeds as follows:  (1) Calculate the induced generalized Morse labeled merge tree M(X, f)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  (2) Consider the leaves of M(X, f) in descending order with respect to their labels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  Suppose we are considering the leaf c with the maximal label k such that c is critical.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  Let p be the youngest ancestor of c such that p is neither a cycle node nor matched.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  We have the following cases:  a) The vertex M−1(c) is adjacent to the edge M−1(p).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  b) The vertex M−1(c) is not adjacent to the edge M−1(p) but there is a symmetry  equivalence a of (X, f) such that a(M−1(c)) is adjacent to a(M−1(p)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  c) The vertex M−1(c) is not adjacent to the edge M−1(p) and there is no symmetry  equivalence as in case b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  In case a) we match M−1(c) and M−1(p).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='This does not produce cycles because we  explicitly exclude cycle nodes from the matching.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  In case b) we apply the symmetry equivalence a and then proceed as in case a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' Since  symmetry equivalences are only automorphisms of connected components of sublevel  complexes, we do not alter the homeomorphism type of X in the process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  In case c) we have to make a decision, we could  i) simply skip c and leave M−1(c) critical,  ii) apply a cm equivalence in order to make M−1(c) and M−1(p) adjacent, then  proceed as in case a), or  iii) observe that there is a unique gradient ﬂow line from M−1(c) to M−1(p) and  cancel the two cells along this ﬂow line.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  If we choose possibility i), we might not obtain an optimal matching but we preserve  the homeomorphism type of X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' In case ii), we produce an optimal matching but may  change the homeomorphism type of X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' In case iii), we preserve the homeomorphism  type of X and obtain an optimal matching but we change the order of the vertices  induced by f.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  In the preceding algorithm, many claims are made, most of which are straightforward to  prove.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' For example, the fact that the cases 2a), 2b), 2c)i), and 2c)ii) work as described  follows immediately from the deﬁnition of the used equivalences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' However in general it does  not appear easy to decide whether case 2b) or 2c) holds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' Nonetheless, case 2c)iii) is not so  obvious, so we consider it in the following lemma:  ON CYCLES AND MERGE TREES  17  Lemma 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' Let X be a graph, f : X → R a critical dMf, and M(X, f) the induced gener-  alized Morse labeled merge tree.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' At any point of the cancellation algorithm, there is always  a unique gradient ﬂow line from the vertex M−1(c) corresponding to the maximally labeled  unmatched leaf c to the edge M−1(c) corresponding to its youngest unmatched ancestor p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' If M−1(c) and M−1(p) are adjacent, there is nothing to prove.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' If M−1(c) and M−1(p)  are not adjacent then there is no other non-closing critical edge in Xf(M−1(p)−ε)[M−1(c)] be-  cause otherwise said other younger critical edge would induce a younger unmatched ancestor  of c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  Since M−1(c) is a critical vertex with no adjacent critical edge, all adjacent edges of  M−1(c) are matched with their respective other vertex.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' This means that on all adjacent  edges, there is a gradient ﬂow line pointing towards M−1(c).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' Following these gradient ﬂow  lines backwards either leads to matched vertices that are adjacent only to the edge they  are matched with, or to the unique critical edge of Xf(M−1(p)−ε)[M−1(c)].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' One of the ﬂow  lines eventually leads to M−1(p) because Xf(M−1(p)−ε)[M−1(c)] is connected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='1 The ﬂow line  is unique because closing edges remain critical, that is, because we only match cells along a  subtree of X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  □  We apply the cancellation algorithm in the following example:  Example 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' We consider the graph:  We put some critical discrete Morse function on it and calculate the induced generalized  merge tree:  11  9  12  15  13  14  17  16  18  19  10  6  7  8  5  3  4  1  2  0  19  18  10  17  0  2  16  15  1  14  3  13  12  4  5  11  7  9  8  6  18  JULIAN BR¨UGGEMANN AND NICHOLAS A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' SCOVILLE  We apply step 2a) as long as possible:  11  9  12  15  13  14  17  16  18  19  10  6  7  8  5  3  4  1  2  0  19  18  10  17  0  2  16  15  1  14  3  13  12  4  5  11  7  9  8  6  Now is the ﬁrst time we run into case 2b)  11  9  12  15  13  14  17  16  18  19  10  6  7  8  5  3  4  1  2  0  19  18  10  17  0  2  16  15  1  14  3  13  12  4  5  11  7  9  8  6  In this example, the cases 2a) and 2b) suﬃced.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  We consider the following example in order to see how quickly things can fail:  Example 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' We consider the following dMf and its induced merge tree:  2  5  1  3  4  0  10  8  9  6  7  10  7  9  8  1  3  5  0  6  4  2  ON CYCLES AND MERGE TREES  19  After twofold application of step 2a), we have the following:  2  5  1  3  4  0  10  8  9  6  7  10  7  9  8  1  3  5  0  6  4  2  Now we have reached case 2c).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' We would need to have the vertex labeled 1 adjacent to the  edge labeled 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' But this is not possible because all symmetry equivalences leave the vertex  labeled 1 adjacent to the edge labeled 9 and no other edge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' The three diﬀerent solutions  result in the following:  i)  2  5  1  3  4  0  10  8  9  6  7  ii)  2  5  1  3  4  0  10  8  9  6  7  iii)  2  5  1  3  4  0  10  8  9  6  7  Example 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' A sublevel symmetry of the last sublevel complex before the “merge tree al-  gorithm” fails may not always be suﬃcient.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' Consider the graph with discrete Morse function  given below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  7  9  12  10  11  8  14  13  0  1  2  3  4  5  6  14  13  12  11  10  9  8  7  6  5  4  3  2  1  0  Proceeding as before, we obtain a matching on the graph until the algorithm speciﬁes to  match the vertex labeled 1 with the edge labeled 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' Since these simplices are not incident,  we need to ﬁnd a sublevel-symmetry of sublevel 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' However, the sublevel subcomplex X12  20  JULIAN BR¨UGGEMANN AND NICHOLAS A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' SCOVILLE  is given by  which is well-known to have no non-trivial automorphisms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  There is also no symmetry  equivalence of a lower level than 12 that makes the vertex labeled 1 and the edge labeled 13  adjacent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' However, the three diﬀerent workarounds mentioned earlier result in the following:  i)  7  9  12  10  11  8  14  13  0  1  2  3  4  5  6  ii)  7  9  12  10  11  8  14 13  0  1  2  3  4  5  6  iii)  7  9  12  10  11  8  14  13  0  1  2  3  4  5  6  At the end of this section, we compare our algorithm for ﬁnding cancellations of criti-  cal cells to similar algorithms from the literature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' In [LLT03b] the authors introduce an  algorithm to ﬁnd optimal discrete Morse functions on 2-dimensional manifolds which they  generalize to higher dimensions and more general complexes in [LLT03a], even though losing  the guarantee for optimality in the process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' The main similarity to our approach is the use  of an auxiliary tree structure, in our case the generalized merge tree, in the case of [LLT03a]  a spanning hyperforest of a hypergraph associated to the Hasse diagram of a discrete Morse  function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  In [RS20], the authors provide an algorithm to ﬁnd optimal discrete Morse functions on  trees.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' Said algorithm, combined with any standard algorithm to ﬁnd spanning trees, can  easily be generalized to provide optimal discrete Morse functions on graphs with a prescribed  critical vertex.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  The main feature of our new approach, compared to the pre-existing ones, seems to be  that our algorithm allows to preserve certain properties of a given discrete Morse function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  In certain cases, such a discrete Morse function might be given by an application and,  therefore, might be worth preserving.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' We conjecture that, given a suitable version of higher  merge trees, our algorithm can be generalized to higher dimensions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' Since ﬁnding optimal  Morse matchings is MAX–SNP hard, such a generalization might either fail to be optimal or  be inconvenient to work with in practice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' Nonetheless, we hope to ﬁnd interesting classes of  examples in which such a generalized algorithm happens to be performative and informative.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  ON CYCLES AND MERGE TREES  21  References  [Bic20]  Allan Bickle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' Fundamentals of graph theory, volume 43 of Pure and Applied Undergraduate Texts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  American Mathematical Society, Providence, RI, [2020] ©2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' 12, 13  [Br¨u22]  Julian Br¨uggemann.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' On Merge Trees and Discrete Morse Functions on Paths and Trees.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' J Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  and Comput.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' Topology, 11 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' DOI: https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='1007/s41468-022-00101-w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' 2, 4, 5, 7, 8,  9, 10, 12, 13, 14  [CCLL22]  Robert Cardona, Justin Curry, Tung Lam, and Michael Lesnick.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' The universal ℓp-metric on merge  trees.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' In 38th International Symposium on Computational Geometry, volume 224 of LIPIcs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' Leib-  niz Int.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' Inform.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=', pages Art.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' 24, 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' Schloss Dagstuhl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' Leibniz-Zent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' Inform.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=', Wadern,  2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' 1  [CHM+22] Justin Curry, Haibin Hang, Washington Mio, Tom Needham, and Osman Berat Okutan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' Deco-  rated merge trees for persistent topology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' Comput.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' Topol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=', 6(3):371–428, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' 1  [Cur18]  Justin Curry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' The ﬁber of the persistence map for functions on the interval.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' Comput.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  Topol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=', 2(3-4):301–321, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' 1  [CVJ22]  Gunnar Carlsson and Mikael Vejdemo-Johansson.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' Topological data analysis with applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  Cambridge University Press, Cambridge, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' 1  [For98]  Robin Forman.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' Morse theory for cell complexes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' Adv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=', 134(1):90–145, 1998.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' 2  [For02]  Robin Forman.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' A user’s guide to discrete Morse theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' S´em.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' Lothar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' Combin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=', 48:Art.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' B48c, 35,  2002.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' 2  [GMO+]  Ellen Gasparovic, Elizabeth Munch, Steve Oudot, Katharine Turner, Bei Wang, and Yusu Wang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  Intrinsic interleaving distance for merge trees.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' trees, 38(37):32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' 1  [JS22]  Benjamin Johnson and Nicholas A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' Scoville.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' Merge trees in discrete Morse theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' Res.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=', 9:Paper No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' 49, 07 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' 2, 5  [LLT03a]  Thomas Lewiner, H´elio Lopes, and Geovan Tavares.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' Optimal discrete morse functions for 2-  manifolds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' Computational Geometry, 26(3):221–233, 2003.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' 2, 20  [LLT03b]  Thomas Lewiner, H´elio Lopes, and Geovan Tavares.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' Toward optimality in discrete morse theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  Experimental Mathematics, 12(3):271–285, 2003.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' 20  [MBW13]  Dmitriy Morozov, Kenes Beketayev, and Gunther Weber.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' Interleaving distance between merge  trees.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' Discrete and Computational Geometry, 49(22-45):52, 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' 1  [Oud15]  Steve Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' Oudot.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' Persistence theory: from quiver representations to data analysis, volume 209 of  Mathematical Surveys and Monographs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' American Mathematical Society, Providence, RI, 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='  1  [PRSZ20]  Leonid Polterovich, Daniel Rosen, Karina Samvelyan, and Jun Zhang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' Topological persistence in  geometry and analysis, volume 74 of University Lecture Series.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' American Mathematical Society,  Providence, RI, [2020] ©2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' 1  [RS20]  Ian Rand and Nicholas A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' Scoville.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' Discrete Morse functions, vector ﬁelds, and homological  sequences on trees.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' Involve, 13(2):219–229, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' 2, 20  (Julian Br¨uggemann) Max Planck Institute for Mathematics, Bonn, Germany  Email address: brueggemann@mpim-bonn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='mpg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='de  (Nicholas A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content=' Scoville) Department of Mathematics and Computer Science, Ursinus College,  Collegeville PA 19426  Email address: nscoville@ursinus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
+page_content='edu' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9AzT4oBgHgl3EQfXPyv/content/2301.01316v1.pdf'}
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+1 
+VOLUME 4, 2016 
+ 
+ 
+ 
+ 
+ 
+Date of publication xxxx 00, 0000, date of current version xxxx 00, 0000. 
+Digital Object Identifier 10.1109/ACCESS.2023.DOI 
+ 
+ 
+ 
+Need of 6G for the Metaverse Realization 
+BARTLOMIEJ SINIARSKI1,CHAMITHA DE ALWIS2,7(Senior Member, IEEE),GOKUL 
+YENDURI3 (Student Member, IEEE),THIEN HUYNH-THE6(Member, 
+IEEE),GÜRKAN GÜR5(Senior Member, IEEE),THIPPA REDDY GADEKALLU3,4(Senior 
+Member, IEEE) and MADHUSANKA LIYANAGE1,8(Senior Member, IEEE) 
+1School of Computer Science, University College Dublin, Ireland 
+2School of Computer Science and Technology, University of Bedfordshire, United Kingdom 
+3School of Information Technology and Engineering, Vellore Institute of Technology, Vellore, Tamil Nadu, India 
+4Department of Electrical and Computer Engineering, Lebanese American University, Byblos, Lebanon 
+5ZHAW School of Engineering, Switzerland 
+6Department of Computer and Communication Engineering, Ho Chi Minh City University of Technology and Education, Vietnam 
+7Department of Electrical and Electronic Engineering, University of Sri Jayewardenepura, Sri Lanka 
+8Centre for Wireless Communications, University of Oulu, Finland 
+Corresponding author: Bartlomiej Siniarski (e-mail: bartlomiej.siniarski@ucd.ie). 
+ 
+ 
+ABSTRACT The concept of the Metaverse aims to bring a fully-fledged extended reality environment 
+to provide next generation applications and services. Development of the Metaverse is backed by many 
+technologies, including, 5G, artificial intelligence, edge computing and extended reality. The advent of 6G is 
+envisaged to mark a significant milestone in the development of the Metaverse, facilitating near-zero-latency, 
+a plethora of new services and upgraded real-world infrastructure. This paper establishes the advantages of 
+providing the Metaverse services over 6G along with an overview of the demanded technical requirements. 
+The paper provides an insight to the concepts of the Metaverse and the envisaged technical capabilities of 6G 
+mobile networks. Then, the technical aspects covering 6G for the development of the Metaverse, ranging 
+from validating digital assets, interoperability, and efficient user interaction in the Metaverse to related 
+security and privacy aspects are elaborated. Subsequently, the role of 6G technologies towards enabling 
+the Metaverse, including artificial intelligence, blockchain, open radio access networks, edge computing, 
+cloudification and internet of everything. The paper also presents 6G integration challenges and outlines 
+ongoing projects towards developing the Metaverse technologies to facilitate the Metaverse applications 
+and services. 
+ 
+INDEX TERMS Metaverse, 6G, AI, Blockchain, Edge Computing, Security, Privacy, vertical applications. 
+ 
+ 
+I. INTRODUCTION 
+The term ‘Metaverse’ has been coined to further facilitate 
+the digital transformation in every aspect of our physical 
+lives [1]. The Metaverse is a virtual world where you can 
+live a synchronous life through your avatar. The concept 
+is similar to an online game, however, instead of shooting 
+targets or driving cars, users will be engaged in real-life 
+activities. These activities could include attending meetings, 
+catching up with friends, attending music festivals, going 
+door to door selling digital collectables, or buying and selling 
+land, apartments or assets. Virtual interactive worlds or early 
+Metaverses have already been introduced primarily in video 
+games with releases such as Fortnite, Minecraft, Decentra- 
+land, Ifland. The list isn’t extensive and users are gravitating 
+toward other Metaverse ecosystems that are emerging today. 
+The Metaverse embraces a social interaction accelerated 
+through a virtual environment and driven by novel technolo- 
+gies such as Web 3.0, 5G, Artificial Intelligence (AI) and 
+Extended Reality (XR). The XR - which includes everything 
+from Virtual Reality (VR) to Mixed Reality (MR) to Aug- 
+mented Reality (AR) and haptics - have enormous poten- 
+tial to transform both industry and society. The widespread 
+adoption of XR was slowed down recently by a number 
+of issues including limited processing power, storage and 
+battery life of small head-mounted displays (HMDs). The 5G 
+made it possible to overcome some of these challenges by 
+offloading a portion of XR processing to the mobile network 
+edge. In addition to this, the 5G QoS framework makes 
+it possible to establish QoS flows that provide optimized 
+network treatment for specific traffic flows, in addition to 
+the default QoS flow used for mobile broadband (MBB). 
+Such additional QoS flows can be established either using 
+5GC QoS-exposure application programming interfaces to 
+communicate service requirements or by traffic detection 
+
+TEEEAcceSS2 
+VOLUME 4, 2016 
+Bartlomiej Siniarski et al.: Need 6G for the Metaverse Realization 
+ 
+ 
+ 
+together with pre-provisioned service requirements, such as 
+relying on standardized 5G QoS identifier characteristics. 
+Although the Metaverses have the potential to be transfor- 
+mational for both business and society, widespread adoption 
+has previously been hindered by issues such as heat gener- 
+ation and the limited processing power, storage, and battery 
+life of small form factor head-mounted devices. The time- 
+critical communication capabilities in 5G make it possible 
+to overcome only some of these challenges by offloading 
+XR processing to the mobile network edge. By evolving 
+the already existing 5G or B5G networks, mobile network 
+operators are in an excellent position to enable the real- 
+ization of the Metaverse on a large scale. The 6G aims to 
+achieve high spectrum and energy efficiency, low latency, 
+and massive connection due to the exponential growth of 
+the Internet of Things (IoT) devices. 6G will also effectively 
+link the physical, and digital worlds by providing seamless 
+and ubiquitous services such as extreme-scale environmen- 
+tal monitoring and control, virtual reality/virtual navigation, 
+telemedicine, digital sensing, and robotics. This will result in 
+a network that connects us to one another, to information, 
+to knowledge, and to purpose. As a result, 6G networks 
+will enhance the efficiency of technologies such as computer 
+vision, blockchain, AI, the IoT, robotics, and user interfaces 
+which are critical for the metaverse realization. In summary, 
+6G will enhance every feature of the 5G network that benefits 
+the user to improve areas such as smart cities, farming, manu- 
+facturing, and robots. 6G will provide enhanced productivity, 
+capabilities, and better user experiences. The main use of 6G 
+in the Metaverse is summarized below: 
+Near-zero-latency: In virtual interaction, 6G will contin- 
+uously provide users with a near-zero-latency sensory inter- 
+connection experience, such as the user’s virtual movement 
+in the Metaverse, virtual meetings, virtual paintings, and 
+other interactive, immersive holographic experiences. 
+New services: 6G is the main driver of multiple new 
+service models. For example, 6G communication technology 
+provides users with precise service models in autonomous 
+driving, industrial control, e-health, Internet robots, and au- 
+tonomous systems, bringing a more convenient lifestyle. 
+Upgraded real-world infrastructure available for use 
+in the Metaverses: 6G infrastructure mainly includes infor- 
+mation infrastructure, fusion infrastructure, and innovation 
+infrastructure. In particular, the 6G communication system 
+integrates infrastructure such as ground, UAV, and satellite 
+Internet. 6G also features high bandwidth, low latency, strong 
+reliability, and global coverage. 
+ 
+A. MOTIVATION 
+The main motivation of this paper is to realize if mobile 
+network operators can enable large-scale XR and at the same 
+time further development of Metaverses by introducing time- 
+critical communication capabilities in 6G networks. The 5G 
+networks already contribute to considerable improvement in 
+data rate, latency, and packet loss since the last network 
+generation (4G) and users already enjoy comfortable viewing 
+experiences. However, as the resolution of video increases 
+from 4K to 8K and 12K/24K for 3D video and the number 
+of worldwide users increases, the 5G network will not be 
+sufficient to support many use cases. Some of the main 
+cloud and network providers are defining the evolution of 
+the service experience into the fair-experience, comfortable 
+experience, and ideal-experience phases [2], where each has 
+its own network KPI requirement to be met. Table 1 sum- 
+marizes those KPI requirements based on different use cases 
+envisaged to be a part of future metaverses. In this work, we 
+aim to establish and explain the main advantages of providing 
+the Metaverse services over 6G and provide an overview of 
+the technical requirements. Furthermore, we aim to establish 
+what role will 6G play in the Metaverse operation and if the 
+envisaged architecture of 6G will be capable of supporting 
+the upcoming technology portrayed by the tech industry. 
+ 
+B. RELATED SURVEYS AND CONTRIBUTIONS 
+Our work is exclusively focused on the networking aspects 
+of the Metaverse and the role that 6G will play in the 
+Metaverse deployment. Though there are some Metaverse- 
+focused surveys we found it is lacking a comprehensive, and 
+detailed discussion on the role of B5G/6G technologies as 
+indicated by Table 2. The table also includes the limitations 
+of the related works in the context of technical challenges, 
+security and privacy, and research directions, which we have 
+already addressed in this paper. The surveys [3] and [4] inves- 
+tigate technical aspects and security threats comprehensively. 
+However, those papers are not focused on the future networks 
+and the role of 6G in the Metaverse specifically. The surveys 
+[5], [1] and [6] include an interesting view on the potential 
+use of the Metaverse in different domains and clearly define 
+network requirements. The limitations in [5], [1] and [6] 
+include the lack of coverage of future network aspects and 
+the discussion on the security and privacy issues is weak. 
+Surveys [7] and [8] discuss implementation challenges and 
+analyze the fusion of 6G-enabled edge with the Metaverse, 
+however, the security issues and research directions are only 
+partially covered. 
+Therefore, we contribute to addressing this gap in our work 
+on the comprehensive discussion on 6G for the Metaverse. 
+ 
+C. PAPER ORGANIZATION 
+The rest of this paper is organized as follows. Introduction 
+and discussion of the role of 6G networks in the Metaverse 
+are presented in Section I. Section II covers the expected 
+improvements from 5G to 6G and the impact it will have 
+on the Metaverses. Section III investigates the state-of-the- 
+art solutions provided by 6G for the Metaverse from tech- 
+nical perspective, followed by Section IV that discusses in 
+detail how different 6G technologies will help to achieve the 
+Metaverse aims. Section V identifies expected 6G challenges 
+that would have to be approached before the introduction of 
+Metaverses to wider community. Finally, Section VI provides 
+an overview of related research projects. 
+
+EEEAccessBartlomiej Siniarski et al.: Need 6G for the Metaverse Realization 
+3 
+VOLUME 4, 2016 
+ 
+ 
+IoE 
+ORAN 
+Cloudification 
+Artificial   Blockchain 
+Intelligence 
+Edge AI 
+THz Bands 
+Zero Touch Management 
+Network 
+1 Tbps 
+Data Rate 
+Multi Purpose 
+MURLLC 
+Service 
+The Metaverse 
+Deep Space 
+Smart Devices 
+Deep Sea 
+Smart 
+Healthcare 
+Smart Cities 
+ 
+TABLE 1. Network KPI requirements in different phases of cloud/ the Metaverse development 
+ 
+ 
+Type of interaction / use case 
+ 
+Network KPI requirement 
+Fair-experience 
+In the fair-experience phase, 
+most content is 4K, and the terminal 
+screen resolution is 2K to 4K. 
+Comfrotable-experience 
+In the comfortable-experience phase, 
+most content is 8K, the terminal 
+screen resolution is 4K to 8K 
+Ideal-experience 
+In the ideal-experience phase, 
+most content is 12K or 24K. 
+The terminal screen resolution is 8K to 16K. 
+ 
+Weak-interaction 
+Users select view and location, 
+but do not interact with entities 
+in the virtual environment. 
+For example IMAX, 360 video, 
+live broadcast, music, education. 
+ 
+Bitrate 
+≥ 40 Mbit/s (4K) 
+Full-view: ≥ 90 Mbit/s 
+FOV: ≥ 50 Mbit/s 
+Full-view: ≥ 290 Mbit/s (12K) 
+FO
+≥
+V
+1090 Mbit/s (24K) 
+: ≥ 155 Mbit/s (12K) 
+≥ 580 Mbit/s (24K) 
+ 
+Bandwidth requirement 
+≥ 60 Mbit/s (4K) 
+Full-view: ≥ 140 Mbit/s 
+FOV: ≥ 75 Mbit/s 
+Full-view: ≥ 440 Mbit/s (12K) 
+FO
+≥
+V
+1600 Mbit/s (24K) 
+: ≥ 230 Mbit/s (12K) 
+≥ 870 Mbit/s (24K) 
+Recommended network RTT 
+≤ 20ms 
+≤ 20ms 
+≤ 20ms 
+Packet loss requirement 
+≤ 9e-5 
+≤ 1.7e-5 
+≤ 1.7e-6 
+Strong-interaction 
+Users can interact with virtual 
+envirnomnets through interactive 
+devices. The virtual space displayed 
+needs to respond to interactions in 
+real time. For example gaming, 
+fitness, social networking, real estate, 
+engineering, healthcare, shopping. 
+Bitrate 
+≥ 40 Mbit/s 
+≥ 90 Mbit/s 
+≥ 360 Mbit/s (8K) 
+≥ 440 Mbit/s (16K) 
+Bandwidth requirement 
+≥ 80 Mbit/s 
+≥ 260 Mbit/s 
+≥ 1000 Mbit/s (8K) 
+≥ 1500 Mbit/s (16K) 
+Recommended network RTT 
+≤ 20 ms 
+≤ 15 ms 
+≤ 8 ms 
+Packet loss requirement 
+≤ 1e-5 
+≤ 1e-5 
+≤ 1e-6 
+ 
+II. 6G AND THE METAVERSE: PRELIMINARIES 
+The preliminary introduction to 6G and the Metaverse is 
+presented in this section, followed by the role of 6G in the 
+Metaverse. 
+ 
+A. PRELIMINARY TO 6G 
+Since the middle of 2019, commercial 5G mobile networks 
+have been standardized and deployed globally, with signif- 
+icant coverage in some countries. Numerous new applica- 
+tions and use cases are being developed, placing existing 
+networks’ capabilities to the test. The capacity of current 
+5G networks to handle the Internet of Everything (IoE), 
+holographic telepresence, collaborative robotics, and deep- 
+sea and space tourism is limited [9]. This has prompted 
+researchers to reconsider and work toward the development 
+of the next generation of mobile communications networks 
+called the sixth-generation of mobile networks 6G. Each time 
+mobile communication technology is upgraded and iterated, 
+its performance metrics improve by a factor of ten to hun- 
+dred times over the preceding generation [10]. Researchers 
+from all over the world propose AI/machine learning (ML), 
+quantum communication/quantum machine learning (QML), 
+blockchain, tera-hertz and millimetre wave communication, 
+tactile Internet, non-orthogonal multiple access (NOMA), 
+small cell communication, fog/edge computing, etc. as the 
+key technologies for the realisation of 6G communications. 
+6G aims to achieve high spectrum and energy efficiency, 
+low latency, and massive connection due to the exponential 
+growth of the IoT devices. 6G will make feasible intelli- 
+gent traffic, environmental monitoring and control, virtual 
+reality/virtual navigation, telemedicine, digital sensing, high 
+definition (HD), and full HD video transmission in connected 
+drones and robotics. 6G will also effectively link the physical, 
+and digital worlds. This will result in a network that connects 
+us to one another, to information, to knowledge, and to 
+purpose. 6G wireless networks operate in the terahertz band, 
+with a peak rate of 1T b/s and a network with ultra-reliable 
+and low-latency communication (URLLC) of less than 1 
+ms, considerably improving the overall quality of experience 
+(QoE) for consumers [11]. 6G has a high positioning accu- 
+racy of 1 m outdoors and 10 cm indoors [12] which also im- 
+proves positioning accuracy of deep-sea and space tourism. 
+6G utilises endogenous security technology to increase its 
+resistance to unknown security threats [13]. As a result, 6G 
+networks can enhance the efficiency of technologies such as 
+computer vision, blockchain, AI, the IoT, robotics, and user 
+interfaces [14]. The architecture of 6G is depicted in Fig. 1 
+ 
+ 
+FIGURE 1. 6G Architecture 
+ 
+To summarize, 6G will enhance every feature of the 5G 
+network that benefits the user. 6G will improve areas such 
+as smart cities, farming, manufacturing, and robots. 6G will 
+provide enhanced productivity, capabilities, and better user 
+experiences. Improved and expanded functionality is an in- 
+
+EEEAccess6G000Bartlomiej Siniarski et al.: Need 6G for the Metaverse Realization 
+4 
+VOLUME 4, 2016 
+ 
+ 
+Low Coverage: 
+Medium Coverage: 
+ 
+TABLE 2. Summary of Important Surveys on 6G and its role in the Metaverse 
+ 
+ 
+Ref 
+Technical 
+aspects 
+and 
+challenges 
+Security 
+and 
+privacy 
+issues 
+The role 
+of 6G in 
+Metaverse 
+Research 
+directions 
+(6G) 
+ 
+Remarks 
+ 
+Limitations 
+[5] 
+H 
+M 
+H 
+M 
+This paper aims to show the roadmap to the Meta- 
+verse in terms of communication and networking in 
+6G, including requirements (limited) and challenges 
+for 6G to realize the Metaverse, and discussing the 
+fundamental technologies to be integrated in 6G to 
+drive the implementation of the Metaverse. 
+The paper is missing some impor- 
+tant references and the requirements 
+are not discussed in detail except for 
+what is depicted in Fig. 2. 
+[3] 
+H 
+M 
+L 
+L 
+The paper investigates AI-based methods concerning 
+six technical aspects that have potentials for the Meta- 
+verse: natural language processing, machine vision, 
+blockchain, networking, digital twin, and neural inter- 
+face, and being potential for the Metaverse. 
+The discussion on attacks on AI 
+in the Metaverse is missing, subse- 
+quently the paper should discuss the 
+role of AI in future networks from 
+the security and privacy perspective. 
+[1] 
+H 
+M 
+L 
+M 
+The technology enablers are discussed in details in- 
+cluding latest state-of-the-art tools. The survey paper 
+includes an interesting discussion on user-centric fac- 
+tors. 
+The paper does not cover any as- 
+pects of future networks and how 
+those could play an important role in 
+creating Metaverses. 
+[4] 
+M 
+H 
+L 
+L 
+The security threats to the Metaverse are explained 
+comprehensively. The paper includes the countermea- 
+sures to those threats. From the security and privacy 
+perspective, it is a comprehensive survey. 
+The future networks enablers are not 
+discussed in this paper. The paper 
+provides good state-of-the-art sur- 
+vey, however it is lacking future di- 
+rections especially in the network- 
+ing aspect. 
+[6] 
+M 
+L 
+L 
+M 
+The paper provides an interesting view on the potential 
+use of the Metaverse in medical domain including a 
+proposed process of patient treatment using the Meta- 
+verse technology. 
+This paper does not cover any secu- 
+rity or privacy issues or the impor- 
+tance of future networks in design- 
+ing meta worlds. 
+[7] 
+H 
+M 
+L 
+M 
+This survey discusses how enablers of the Metaverse 
+can be implemented at a scale at mobile edge net- 
+works. The implementation challenges are also dis- 
+cussed in this survey. 
+The survey mentions the role of 
+B5G/6G, but it doesn’t cover how 
+6G will enable the Metaverse. 
+[8] 
+M 
+L 
+M 
+M 
+This survey analyzes the fusion of 6G-enabled edge 
+AI and the Metaverse, and introduces the features, ar- 
+chitecture, technologies, and applications of the Meta- 
+verse. 
+The paper only partially covers pri- 
+vacy and security issues. The 6G 
+requirements are discussed only to 
+certain level and the 6G enablers are 
+not covered in full. 
+Our 
+sur- 
+vey 
+H 
+M 
+H 
+H 
+In this paper we focus on 6G technology and how 
+it enables the deployment of Metaverses. We focus 
+heavily on specific requirements and cover each in 
+detail as supposed to provide the reader with general 
+overview. The security and privacy challenges are cov- 
+ered in depth despite it not being the main focus of this 
+paper. We clearly identify current research projects and 
+future research directions, which is something missing 
+in most survey papers that were investigated. 
+There is still space to discuss other 
+aspects once meteverses are ex- 
+plored in more depth, in particular 
+social aspects such as fairness, so- 
+cial acceptance, accountability, and 
+community ownership. 
+ 
+The paper did not consider this area or only very briefly discussed it through mentioning it in passing 
+The paper partially considers this area (leaves out vital aspects or discusses it in relation to other areas without a specific focus on it) 
+The paper considers this area in reasonable or high detail 
+ 
+evitability over successive generations. Even with 6G, this 
+will be the case. 6G will improve upon 5G by optimising 
+and lowering costs to increase adoption. Information man- 
+agement and consumption will be simplified with the advent 
+of 6G’s new human-machine interfaces. The touchscreen 
+interface of the future will instead be controlled by voice 
+instructions, gestures, or even brain signals. The comparison 
+of the features related to 5G and 6G are depicted in Table 3 
+ 
+B. PRELIMINARY TO THE METAVERSE 
+The Metaverse is a network of three-dimensional virtual 
+environments dedicated to social interaction. It is frequently 
+depicted in futurism and science fiction films. The worldwide 
+virtual environment will be made possible by the usage of 
+VR and AR devices [15]. The term "Metaverse" is not en- 
+tirely unfamiliar in the technological world. Neal Stephenson 
+coined the term "Metaverse" in 1992. His science fiction 
+novel Snow Crash envisioned an online universe in which 
+people may explore and escape the physical world using dig- 
+ital avatars [16]. Decades later, major technology firms like 
+Meta, Axie Infinity, The Sandbox, and Decentraland have 
+begun developing their versions of a futuristic Metaverse. 
+The overview of the enabling technologies, services, and 
+technical requirement is depicted in the Fig. 2 
+High Coverage: 
+
+EEEAccessBartlomiej Siniarski et al.: Need 6G for the Metaverse Realization 
+5 
+VOLUME 4, 2016 
+ 
+ 
+ 
+TABLE 3. The comparison of 5G and 6G Features 
+ 
+Features 
+5G 
+6G 
+Data Rate 
+1 Gbps to 20 Gbps. 
+1 Tbps. 
+Application 
+Types 
+Enhanced Mobile Broadband. 
+Ultra-Reliable Low Latency 
+Communications.Massive Ma- 
+chine Type Communications. 
+Massive 
+Broadband 
+Reliable Low. Latency 
+Communication. Massive- 
+URLLC. Human-Centric 
+Services.Multi-Purpose 
+Services. 
+Device Types 
+Smartphones,     Drones,     and 
+Sensors. 
+Sensors         &          DLT 
+devices,BCI 
+and 
+XR 
+equipment, 
+CRAS, 
+and 
+Smart implants. 
+Frequency Band 
+Sub 6 GHz and mm wave for 
+fixed access. 
+Sub 6 GHz mm wave for 
+mobile access exploration 
+of THz bands. Non-RF 
+bands. 
+Latency 
+5 ms 
+<1 ms 
+Architecture 
+Dense sub   6   GHz   smaller 
+BSs with umbrella macro BSs. 
+Mmwave small cells of about 
+100 meters. Cell free smart sur- 
+faces at high frequencies. 
+Cell free smart surfaces at 
+high frequencies. Tempo- 
+rary hotspots provided by 
+drone-mounted BSs. Trials 
+of tiny THz cells. 
+Spectral 
+and 
+Energy 
+Efficiency Gain 
+10 x in bps/Hz/m2. 
+1000 x in bps/Hz/m2. 
+Traffic Capacity 
+10 Mbps/m2. 
+1 to 10 Gbps/m2. 
+Reliability 
+10−5. 
+10−9. 
+Localization Pre- 
+cision 
+10cm. 
+1cm in 3D. 
+User Experience 
+50 Mbps. 
+10 Gbps. 
+Mobility 
+500 km/h 
+1000 km/h 
+Connection den- 
+sity 
+106 devices/km2 
+107 devices/km2 
+ 
+1) Enabling Technologies of the Metaverse 
+The immersive experience of the Metaverse will be enabled 
+by cutting-edge technologies such as blockchain, AR and 
+XR, AI, and the IoT. 
+• Blockchain: Blockchain technology enables decen- 
+tralised and transparent digital proofs of ownership, col- 
+lectibility, value transfer, governance, accessibility, and 
+interoperability in the Metaverse [17]. Blockchain also 
+enables individuals to exchange assets while working 
+and interacting in the Metaverse. 
+• Extended reality: XR enables the creation of 3D 
+computer-rendered virtual environments in the Meta- 
+verse. XR allows users to interact with these virtual 
+goods through head tracking devices or physical con- 
+trols [18]. As XR technology matures, it will be able to 
+broaden the Metaverse experience by including physical 
+simulations using XR equipment. Users will then have 
+the ability to sense, hear, and interact with people from 
+all around the world. 
+• Artificial intelligence: AI will allow users of the Meta- 
+verse to construct incredibly realistic avatars and have 
+multilingual accessibility. AI will help people make 
+better decisions in the Metaverse. A better human- 
+computer interface will also be provided by AI [19]. AI 
+can also help detect, prevent, and recover from cyber 
+attacks in the Metaverse. 
+• Internet of things: IoT will enable the Metaverse to map 
+data from real life and emerge it into virtual reality [20]. 
+The data provided from the IoT devices to the Metaverse 
+will help professionals to solve real-world problems. 
+The Metaverse with the help of IoT will support the 
+users to collect real-time data-driven decisions with 
+minimum need for training and computation. 
+• Edge Computing: Edge computing enables mobility and 
+the border-less Metaverse for the users [21]. Edge com- 
+puting improves the availability of data in the Metaverse 
+by bringing data closer to end consumers for retrieving 
+and storing data at remote data centre locations. Edge 
+computing will help data transferring with ultra-reduced 
+latency in the Metaverse which will help the users to 
+make quick and effective decisions. 
+ 
+ 
+Enabling Technologies 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+Security 
+Storage 
+Technical Requirements 
+ 
+ 
+ 
+ 
+FIGURE 2. Preliminary to the Metaverse 
+ 
+ 
+ 
+2) Applications of the Metaverse 
+The Metaverse has made its way into many sectors, 
+capturing the enthusiasm of entrepreneurs across the 
+world. The Metaverse will have a huge impact on ap- 
+plications like healthcare, real estate, manufacturing, 
+tourism, Entertainment, and shopping. 
+• Healthcare: Smart healthcare has contributed to resolv- 
+ing several healthcare difficulties, including linking pa- 
+tients to doctors situated throughout the world during 
+the COVID-19 epidemic. This prepared the door for 
+the application of the Metaverse in healthcare, which 
+is facilitated by medical IoT, VR, and AR [22]. The 
+Metaverse gives users control over how the virtual and 
+physical worlds interact. This enhances doctors’ abil- 
+ity to provide consistent and customised patient care. 
+Through the use of VR technology, the Metaverse can 
+aid in remote health monitoring, clinical data collec- 
+tion, and improved robotic surgery, while 3D immersive 
+technology will enable surgeons to practise through 
+Artificial Intelligence 
+Healthcare 
+Real Estate 
+Manufacturing 
+The metaverse 
+Tourism 
+Shopping 
+Privacy 
+Interoperability 
+Entertainment 
+Services 
+
+EEEAccess+%Bartlomiej Siniarski et al.: Need 6G for the Metaverse Realization 
+6 
+VOLUME 4, 2016 
+ 
+ 
+ 
+simulations that will raise their success rate in the real 
+world. 
+• Real Estate: The Metaverse allows organisations to es- 
+tablish retail and experience centres on its virtual land 
+[23]. Rather than downloading many applications, users 
+can access the Metaverse, which contains all currently 
+available applications. As a result, the value of virtual 
+land will increase. Property ownership in the Metaverse 
+is limitless, and owners are free to use their virtual 
+holdings. Digital property owners can make, run, lease, 
+and build billboards for advertising. 
+• Manufacturing: Manufacturers can create digital facto- 
+ries in the Metaverse to assist in organising production 
+and effective usage of machinery. This allows simula- 
+tion of human-machine interaction throughout the man- 
+ufacturing process [24]. As a result, firms can use virtual 
+production systems to train new employees and staff on 
+how to use them in the real world, which would boost 
+the manufacturing of products with a very low error rate. 
+The metaverse also allows mass personalization of the 
+product and allows the user to track the product from its 
+development to delivery, which will improve the trust of 
+the users in the organization. 
+• Tourism: The Metaverse has the potential to create the 
+most immersive experiences ever seen in the tourism 
+sector. The Metaverse allows hotel chains, tourism 
+boards, online travel agencies, and other businesses to 
+advertise their services [25]. Users can virtually visit 
+those locations and decide whether or not to visit them 
+in person. They can go through two distinct locations 
+without leaving their homes, comparing and evaluating 
+places through the use of 3D imagery. The Metaverse 
+will give users an experience that will be better than any 
+kind of communication that exists in the present day, 
+including video and audio interaction. 
+• Entertainment: The Metaverse will completely revo- 
+lutionise entertainment with its rich 3D environment 
+and avatars. Entertainment’s growth is highly linked 
+to the development of VR in the Metaverse. The 
+Metaverse-based entertainment, including movies and 
+video games, can be enjoyed in a virtual world that users 
+can access from the comfort and privacy of their home 
+[26]. It also allows users to attend virtual concerts and 
+sporting events from first-row seats or to ride virtual 
+roller coasters at theme parks. 
+• Shopping: Customer experiences in the Metaverse will 
+evolve constantly as a result of XR technologies, and 
+organisations selling products in metamalls will have 
+more creative freedom to express themselves and attract 
+customers than they do in traditional shopping. These 
+spaces will encompass much more than the basic ser- 
+vices seen on the majority of e-commerce sites today, 
+including user engagement, avatar customization, event 
+attendance, and skill acquisition [27]. Furthermore, the 
+products sold in the Metaverse will include both physi- 
+cal and virtual items. Consumers may feel and touch the 
+object with the use of sensors, which will completely 
+alter the traditional buying experience. Additionally, 
+customers can purchase things on the go while engaged 
+in real-world activities. 
+ 
+3) Technical Requirements of the Metaverse 
+Privacy, security, storage, and interoperability are the 
+important technical requirements of the Metaverse. 
+• Privacy: The Metaverse is a social platform that employs 
+interactive technology such as VR, AR, and AI that 
+requires sensitive user data. Since behavioral-learning 
+and recommender systems collect vast quantities of 
+personal information, they pose a threat to the pri- 
+vacy of the Metaverse users [28]. Therefore, the use 
+of such technologies poses a substantial risk to the 
+privacy of users’ data. The Metaverse must guarantee 
+privacy protection for such sensitive information, and 
+users must have complete control over their data, which 
+will increase their trust in the Metaverse. Even though 
+blockchain technology can help protect privacy in the 
+Metaverse, there are no specific rules designed for pri- 
+vacy protection in the Metaverse, which makes it a 
+critical requirement. 
+• Security: In the Metaverse, attackers and AI bots can 
+and will emerge from any location and at any time. 
+The Metaverse networks should have a high level of 
+security, and related protocols to incorporate continuous 
+awareness into these networks [5]. In addition to ex- 
+isting passwords, multi-factor authentication, enhanced 
+firewalls, and advanced threat detection technologies, 
+the Metaverse must be incorporated with higher trans- 
+parency and analysis to detect anomalies and uncover 
+malicious activities to maintain user security. Data must 
+be secured and safeguarded during transmission and 
+storage. To assure the security of the Metaverse in the 
+future, it is vital to draw on and build upon information 
+from the past. 
+• Storage: The Metaverse is a collection of technologies. 
+It is a huge concept which involves the simultaneous 
+integration of multiple technologies. The list includes 
+high-performance networks, sophisticated computing 
+and sensors, hardware, AR/VR, AI, 3D modelling, 
+blockchain, IoT, and many other technologies. The data 
+produced from these technologies and their related ap- 
+plication will be enormous [29]. The formation of the 
+Metaverse itself necessitates voluminous data storage. 
+Decentralised storage based on blockchain technology 
+can be used to store this massive amount of data. This 
+storage distributes data to numerous independent net- 
+work nodes using open-source applications and algo- 
+rithms. It also improves the privacy of data, the redun- 
+dancy of data backups, and the transparency of data in 
+the Metaverse. 
+• Interoperability: Interoperability across services, tech- 
+nology, and virtual worlds is a crucial aspect of the 
+
+EEEAccessBartlomiej Siniarski et al.: Need 6G for the Metaverse Realization 
+7 
+VOLUME 4, 2016 
+ 
+ 
+ 
+Metaverse [30]. A cross-chain protocol is an optimal ap- 
+proach for maintaining interoperability between diverse 
+Metaverse services, technologies, and configurations. 
+Among other protocols, this one permits the exchange 
+of assets like avatars, non-fungible tokens, and currency. 
+To make the Metaverse more interoperable, different 
+devices that use the same technology need to follow the 
+same rules and standards. 
+ 
+III. 6G FOR THE METAVERSE: TECHNICAL 
+PERSPECTIVE 
+This section investigates the state-of-the-art solutions pro- 
+vided by 6G for the Metaverse from the technical perspec- 
+tives, including validation of digital assets, cross-platform 
+integration, efficient support of AI, privacy and security, 
+high-speed data connection, content creation and storage, 
+user interactivity, low latency communication, and computer 
+vision. 
+ 
+A. 6G FOR VALIDATION OF DIGITAL ASSETS IN THE 
+METAVERSE 
+Non-fungible Token (NFT) is one of the key components of 
+a digital asset in the Metaverse. A visual asset, such as a 
+virtual building, can be represented by an NFT that can be 
+represented as a digital asset with unique data coding. When 
+a purchaser buys an NFT, a private digital key password 
+will be generated, that can certify that the purchaser owns a 
+particular digital asset. Through this private key, the owner 
+of the NFT can sell or transfer the digital asset to others 
+[31]. The blockchain associated with the specific Metaverse 
+will record the NFT for a digital asset in the Metaverse. 
+For instance, the Ethereum blockchain stores "Decentraland 
+Metaverse", which is highly popular. Ethereum records the 
+digital asset transactions of the NFT for Decentraland [32]. 
+Digital assets in the Metaverse can be created in the form 
+of NFTs by the users. These digital assets can be anything 
+ranging from virtual goods to digital art to virtual real estate, 
+which is minted into the NFTs that are securely stored on 
+the blockchain. The owners of these digital assets can see 
+these digital assets which are in the form of NFTs in the 
+form of crypto for purchasing other digital assets in the 
+Metaverse [33]. Content creators and artists can afford to 
+have an opportunity to monetize their assets uniquely due to 
+NFTs and blockchain. For instance, artists need not depend 
+on auction houses or galleries for selling their art. The artists 
+can sell their art directly to the customer in the form of an 
+NFT that allows them to keep the majority of the profits. The 
+artists can even receive royalties whenever their art is sold 
+to a new customer. Like art, the other digital assets also can 
+be traded through NFTs in the Metaverse [34]. The process 
+of creating NFTs and transferring them from one virtual 
+world to another requires a network that is highly reliable 
+and secure. 
+Digital assets in the Metaverse, represented by NFTs are 
+verified and tracked on the blockchain. Every NFT will have 
+a unique transaction hash that makes it non-replicable. All 
+the transactional data related to the NFTs are collected by the 
+blockchain and are stored in blocks, that forms a blockchain. 
+The information stored in the blockchain is stored forever 
+and can be viewed and verified by the public. Verification 
+of the digital assets in the Metaverse that has AR and other 
+MR technologies incorporated, needs significant amount of 
+bandwidth to create a more immersive experience add also 
+to reduce the load times. The validation and verification of 
+the digital assets in the blockchain incurs heavy computation 
+in the blockchain, which needs significant bandwidth so that 
+the users can see the results in near real-time, as depicted in 
+Fig. 4 . The transactions between the different entities in the 
+Metaverse are also powered by the consensus mechanism of 
+the blockchain, which requires huge amounts of data transfer 
+between nodes. This creates a requirement for a network that 
+is both transparent and capable of real-time communication. 
+These challenges faced during the creation, transfer, and 
+validation of digital assets in the Metaverse can be solved by 
+6G due to its low latency, reliability, transparency, and high- 
+speed connectivity [35]. 
+ 
+B. 6G FOR CROSS PLATFORM 
+INTEGRATION/INTEROPERABILITY IN THE METAVERSE 
+One of the hurdles in realizing the full potential of the 
+Metaverse is the lack of interoperability. Lack of interoper- 
+ability [36], [37] is a major hurdle in a mass adaption of 
+the Metaverse that makes the navigation of the users free 
+from one Metaverse application to the other challenging. The 
+Metaverse should mimic the interoperability that is experi- 
+enced in the physical world. For instance, in the real/physical 
+world, we can take physical assets/objects from one place 
+to another easily. The users in the Metaverse too should be 
+able to navigate seamlessly and freely to other Metaverses. 
+This is possible through interoperability that can form a 
+global interconnected Metaverse where various Metaverses 
+are integrated across the platforms as experienced in the real 
+world [38]. 
+Realization of interoperability in the Metaverse is a sig- 
+nificant challenge as heavy objects such as digital avatars, 
+3D holograms etc. have to be navigated across in feature- 
+rich Metaverse in near real-time. It requires a communication 
+infrastructure with high bandwidth and low latency. 6G net- 
+work with its high bandwidth and ultra-reliable low latency 
+communication infrastructure can solve the issue of seamless 
+communication in the Metaverse, as depicted in Fig. 5 . With 
+the help of supporting technologies like ORAN and ZSM, 
+the 6G network can be the common platform that provides 
+an interoperable infrastructure for multiple Metaverses. Net- 
+work slicing, software-defined networking, symbiotic radio, 
+and network function virtualization are the 6G techniques 
+that promote network interoperability and agility in the Meta- 
+verse. Intelligent collaboration between diverse wireless sig- 
+nals is supported by symbiotic radio. The SDN/NFV offers 
+open interfaces that facilitate interoperability between several 
+Metaverses and assist produce network slices for any vertical 
+application such as gaming and shopping over the common 
+
+EEEAccessBartlomiej Siniarski et al.: Need 6G for the Metaverse Realization 
+8 
+VOLUME 4, 2016 
+ 
+ 
+ 
+ 
+ 
+ 
+FIGURE 3. 6G for the Metaverse:Technical Perspective 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+FIGURE 4. 6G for Validation of Digital Assets in the Metaverse 
+ 
+ 
+ 
+ 
+ 
+physical infrastructure among different Metaverses [39]. 
+FIGURE 5. 6G for Cross Platform Integration/Interoperability in the Metaverse 
+ 
+ 
+C. 6G FOR EFFICIENT SUPPORT OF AI IN THE 
+METAVERSE 
+The Metaverse is a virtual world where the users will play 
+games, interact with each other and the 3D objects in the 
+virtual world, and build things in the virtual world. VR and 
+AR along with blockchain and AI are the key enabling tech- 
+nologies in realizing the Metaverse. The applications of AI in 
+IoE 
+ORAN 
+Cloudification 
+Artificial 
+Intelligence 
+Blockchain 
+Edge AI 
+THz Bands 
+Zero Touch Management 
+Network 
+1 Tbps 
+Data Rate 
+MURLLC 
+Multi Purpose 
+Service 
+The Metaverse 
+Deep Space 
+Smart Devices 
+Deep Sea 
+Smart 
+Healthcare 
+Smart Cities 
+ The Metaverse 
+ The Metaverse User 
+ The Metaverse User 
+Cryptocurrency 
+Transfer of Digital Asserts 
+Decentralization 
+Traceability 
+Blockchain 
+Transperncy 
+Security 
+Trust 
+Transfer of Digital Asserts 
+NFTs 
+Avatars 
+Digital Asserts 
+NFTs 
+ 
+ 
+The Metaverse 
+  Cross Platform Vendors   
+ Real-time Validation 
+ High Bandwidth   
+Low Latency 
+High Bandwidth 
+
+EEEAccess6G000NFTXOXamazon目Bartlomiej Siniarski et al.: Need 6G for the Metaverse Realization 
+9 
+VOLUME 4, 2016 
+ 
+ 
+ser 
+ 
+the Metaverse include speech processing, content analysis, 
+computer vision, etc [3]. These applications of AI can be 
+used to help build important components of the Metaverse 
+as discussed below: 
+Avatars: Avatars is one of the important and interesting 
+concepts of the Metaverse, where people in the physical 
+world will create a digital avatar in the virtual world. People 
+would like to get creative in the virtual world and they would 
+like to see themselves in a different way which may not 
+be possible in the physical world. They can change their 
+clothing, hairstyle, and body language, which is not their 
+regular norm in the real world. AI plays a major role in the 
+users designing their avatars in the virtual world. AI can be 
+used to analyze 3D scans or user images to create accurate, 
+realistic, and innovative avatars [40]. Some organizations 
+such as Ready Player Me are making use of AI to create 
+avatars for the Metaverse. 
+Digital Humans: In the Metaverse, 3D chatbots are 
+termed as digital humans. The digital humans respond and 
+react to the actions of humans in the virtual world. They are 
+usually non-playing characters that can be a character in a 
+game of virtual reality whose actions and responses depend 
+on a set of rules or automated scripts. They try to understand 
+what the users are communicating by listening and observing 
+them. Human-like interactions and conversations can hap- 
+pen in the Metaverse between humans and digital humans 
+through body language and speech recognition [41]. AI plays 
+a significant role in the successful implementation of digital 
+humans in the Metaverse. Some of the key functionalities 
+of digital humans like speech recognition, body language 
+identification, object detection, etc. can be realized through 
+AI [6]. 
+Language Processing: In the Metaverse users from across 
+the globe can communicate and interact easily without lan- 
+guage barriers. This is made possible with the help of AI. AI 
+can break the human language such as English into a format 
+that can be read by machines. The AI can then analyze the 
+sentences, and respond to the users in their language [42]. 
+From the above discussion, it is obvious that AI plays 
+a significant role in the realization of some of the key 
+features of the Metaverse. In the Metaverse, huge volumes 
+of heterogeneous big data will be generated at a very fast 
+rate. 6G, with its characteristics such as fast communication 
+infrastructure, and near real-time processing, can help in 
+processing/analyzing this big data to uncover the patterns 
+existing in the data that trains the AI/ML algorithms in near 
+real-time to make quick decisions/predictions through which 
+several components of the Metaverse can communicate eas- 
+ily. 
+ 
+D. 6G FOR HIGH SPEED DATA CONNECTION IN THE 
+METAVERSE 
+The wide adaption of AR and VR technologies is the key to 
+the transition to the Metaverse. It is expected that data usage 
+to be increased by 20 times to what is being used today due 
+to the revolution of the Metaverse by 2022. To realize the full 
+potential of the Metaverse with real-time experience of AR 
+and VR technologies, truly immersive 3D experiences. The 
+end-users should be able to access high-speed data connec- 
+tions that can deliver the data at speeds of approximately 1 
+Gbps [43]. Some of the key requirements that will be needed 
+to realize the true potential of the Metaverse are as follows: 
+• To create virtual reality worlds in real-time, high-speed 
+data connection is required. 
+• The communication infrastructure should high-speed 
+transmission in near real-time with very low latency, 
+typically, below 10 milliseconds. 
+• The existing 4K video resolution may not be sufficient 
+to convey the pixels for creating immersive worlds. 
+Higher-resolution videos have to be supported by the 
+data carriers. 
+• Next-generation video compression techniques that can 
+compress and decompress huge data files in the Meta- 
+verse in real time are the need of the hour. 
+The key features of 6G with high bandwidth and URLLC 
+[44] promise is a key enabling technology to realize the high 
+bandwidth requirement of the Metaverse. The use of Edge 
+AI-enabled 6G can also help applications and the Metaverse 
+devices address these issues. Edge AI is the combination of 
+edge computing and AI to run machine learning tasks directly 
+on connected edge devices. Edge AI computes and processes 
+data locally, which helps the Metaverse devices be efficient 
+and responsive in their communication. This also reduces the 
+amount of data sent from the Metaverse devices to the cloud, 
+thereby saving a huge amount of bandwidth. 
+ 
+E. 6G FOR EFFICIENT USER INTERACTION IN THE 
+METAVERSE 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+FIGURE 6. 6G for Efficient User Interaction in the Metaverse 
+ 
+The Metaverse enables the interaction between real-world 
+entities and virtual objects. It is a digital environment that in- 
+corporates social networking, real estate, online gaming, AR, 
+VR, and cryptocurrencies. In the Metaverse, with the help 
+of virtual objects, sounds, and other sensory input, AR tries 
+to enhance the user’s perception of the real world [5]. Each 
+time a user enters the Metaverse, the objects around them un- 
+dergo a dynamic transformation based on the requirements. 
+High Bandwidth 
+ 
+ 
+ 
+ 
+Ultra Reliable Low 
+Latency Communication 
+Interacting 
+with 
+existing 
+objects 
+Modifying  
+  
+      existing  
+   objects  
+UUser 
+Creation 
+of 
+new 
+objects 
+Realtime Data Processing 
+NFTs 
+BOTS 
+Avatars 
+The Metaverse 
+
+EEEAccess目1ms宁Bartlomiej Siniarski et al.: Need 6G for the Metaverse Realization 
+10 
+VOLUME 4, 2016 
+ 
+ 
+ 
+Everything in the Metaverse is constantly changing, which 
+indicates the dynamic nature of the Metaverse. Changes 
+to a physical object are mirrored in its virtual counterpart 
+in the Metaverse because of their digital twins, which are 
+linked to real-world objects. People can also change objects 
+by interacting with them. Instead of just looking at digital 
+objects in the Metaverse, users will be able to experience 
+a place and interact with them [45]. The creation of new 
+objects will require complex inputs and will demand high- 
+quality user interaction with the objects in the Metaverse. The 
+Metaverse poses three crucial challenges for effective user 
+interaction, as depicted in Fig. 6: 
+Interacting with existing objects: Users’ physical interac- 
+tions with these virtual worlds are an important consideration 
+[46]. For the Metaverse to persist, this is a fundamental 
+challenge that must be overcome. When the user is unable 
+to control the interaction, they will stop using it immediately. 
+When a user is completely immersed in a virtual world and 
+finds themselves unable to perform a task that they could do 
+in the real world, they become frustrated and annoyed. 
+Modifying existing objects: As technology gets better and 
+the real world keeps changing, the Metaverse objects will 
+need to be changed to make them seem more real [47]. 
+Realistic objects need more precise modelling algorithms, 
+just like real faces. Even in the Metaverse, where scenes and 
+avatars are always changing and interacting, objects have to 
+be changed all the time to reach this level of realism. 
+Creation of new virtual objects: The Metaverse is a vir- 
+tual 3D universe comprised of virtual 3D objects [48]. The 
+Metaverse requires the creation of immersive experiences 
+based on real-world artefacts to accomplish its objective of 
+combining the digital and physical worlds. In the Metaverse, 
+a lot of digital objects will need constant sensor inputs from 
+their physical counterparts to produce this realistic immersive 
+experience for the users. The Metaverse will also enable 
+its users to create virtual objects by providing them with 
+various tools and applications. As a result, it creates a huge 
+requirement for bandwidth, which is a challenge to achieve 
+with the present technology. From the above discussion, it is 
+obvious that efficient user interaction plays a significant role 
+in the creation, interaction, and modification of digital objects 
+in the Metaverse. This requires massive input from real-world 
+objects. 6G’s URLLC and real-time processing abilities will 
+aid in the building of a highly immersive 3D environment in 
+the Metaverse. 
+ 
+F. 6G FOR LOW LATENCY COMMUNICATION IN THE 
+METAVERSE 
+Low latency communication is the capability of the commu- 
+nication network to deliver large quantities of data with min- 
+imal delay and high accuracy. These networks are designed 
+to support operations that require access to rapidly changing 
+data in real-time. Advanced technologies like self-driving 
+cars, holographic telepresence, remote surgery, deep-sea and 
+space tourism, and other AR and VR innovations are becom- 
+ing part of the Metaverse [49]. For instance, we had been 
+accustomed to virtual communication using Zoom, Skype, 
+Microsoft Teams, and other platforms. Future developments 
+in VR and AR are well on their way to making an office 
+where people can talk to each other in a fully immersive way. 
+This integration of advanced technologies into the Metaverse 
+creates a huge demand for next-generation networks with 
+enhanced bandwidth and latency. 
+The present network infrastructure cannot provide the 
+bandwidth and latency required for the Metaverse and its 
+applications. The capacity of current 5G networks to handle 
+the IoE, holographic telepresence, collaborative robotics, and 
+deep-sea and space tourism is limited. These applications 
+require multiple terabytes of bandwidth as they depend on 
+real-time inputs from the real world. From the discussion, it 
+is clear that the Metaverse necessitates the highest network 
+positioning accuracy and multiple terabytes of bandwidth. 
+The 6G network, with its advancements like greater use of 
+the distributed radio access network (RAN) and the terahertz 
+(THz) spectrum to increase capacity and improve spectrum 
+sharing, will provide effective and low-latency communica- 
+tion required for the Metaverse [50]. 
+ 
+G. 6G FOR COMPUTER VISION IN THE METAVERSE 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+Vast Coverage and Transmission Rates 
+ 
+FIGURE 7. 6G for Computer Vision in the Metaverse 
+ 
+Computer vision is the study of how computers perceive 
+and interpret digital images and videos. Computer vision 
+encompasses all activities done by biological vision systems, 
+including seeing or sensing a visual signal, interpreting what 
+is being seen, and extracting complicated information in a 
+form usable by other processes [51]. Using sensors, comput- 
+Uninterrupted Network Service 
+Extended Reality 
+Virtual Reality 
+Augmented Reality   Mixed Reality 
+Healthcare Defense Construction Education Retail 
+Applications of XR in the Metaverse 
+Independent Frequency 
+Symmetric Speed 
+The Metaverse 
+
+EEEAccessAR+6GBartlomiej Siniarski et al.: Need 6G for the Metaverse Realization 
+11 
+VOLUME 4, 2016 
+ 
+ 
+ 
+ers, and machine learning algorithms, this multidisciplinary 
+field replicates and automates essential parts of human vision 
+systems. The objective behind computer vision is to develop 
+artificial intelligence systems that can see and understand 
+their surroundings. 
+In the Metaverse, computer vision plays an important role 
+in enabling humans to experience the virtual environment, 
+as depicted in Fig. 7. Through the use of digital avatars, 
+VR and computer vision provide a near-to-lifelike experience 
+in the Metaverse [52]. In order to connect to this virtual 
+world, the user needs to use XR devices, which are built 
+on the foundation of computer vision. XR applications rely 
+heavily on computer vision. Visual information in the form 
+of digital images or videos is often processed, analyzed, 
+and interpreted with the help of computer vision and visual 
+information. This helps people make effective decisions in 
+the Metaverse. As a result of computer vision, VR and AR 
+environments can be built that are more accurate, trustworthy, 
+and user-friendly than their real-world counterparts. Human 
+position tracking is a computer vision challenge that tries 
+to figure out where people are located in an environment 
+that is constantly changing. In the Metaverse, the healthcare, 
+military, construction, manufacturing, education, and retail 
+sectors will rely largely on computer vision. For example, 
+doctors can improve surgical processes and study data from 
+3D scans in real time using computer vision. The computer 
+vision will assist doctors in detecting, diagnosing, and treat- 
+ing potential diseases and enable them to examine patients 
+from anywhere in the world [53]. Computer vision in the 
+Metaverse will evolve at an accelerated rate, and even 5G 
+cannot compete with the rapidly evolving technological re- 
+quirements of the Metaverse’s computer vision capabilities. 
+The computer vision requires the continual collaboration 
+of heterogeneous devices to provide immersive experiences 
+for the users, which requires uninterrupted network service, 
+and should provide symmetric uploading and downloading 
+speeds for users to quickly upload all their content while 
+concurrently downloading the content of others. 6G supports 
+a higher number of device connections, which is very crucial 
+for computer vision in the Metaverse for delivering its fully 
+immersive services to customers [54]. The independent fre- 
+quency, higher data transmission rates, and large coverage 
+of 6G will enhance the QoS of computer vision in the 
+Metaverse. 
+ 
+H. 6G FOR HIGH TRANSACTION INTEGRATION/ 
+SCALABILITY 
+To date, the Metaverse implementations used a central- 
+ized cloud-based approach for avatar physics emulation and 
+graphical rendering. The centralized design is unfavourable 
+as it suffers from several drawbacks caused by the long 
+latency required for cloud access. Further deployments of 
+Metaverses will also bring scalability issues to the physical 
+layer due to the increased number of computing tasks mainly 
+generated by extremely demanding applications. The tradi- 
+tionally deployed centralized architectures are unlikely to 
+support a large number of Metaverses and their users, so the 
+introduction of de-centralized Metaverse systems including 
+frameworks and protocols is inevitable. There are several 
+approaches that can be taken, starting with leveraging Mobile 
+Edge Computing (MEC) technology. For example, [55] pro- 
+posed the blockchain-based MEC architecture, where base 
+stations allocate their computation and communication re- 
+sources for providing video streaming and the use of a series 
+of smart contracts enables a self-organized video transcoding 
+and delivery service without a centralized controller. Using 
+the MEC more efficiently will not fulfil the requirements 
+in full, so the decentralized architecture will have to further 
+distribute the communication and computational cost among 
+different nodes present in the virtual space. The concept of 
+de-centralizing the Metaverse applications was presented by 
+authors of Solipsis [56] - a system that allows the adaptive 
+streaming of 3D models including avatars, sites and objects 
+in a completely decentralized fashion. In general, to over- 
+come challenges related to a high number of transactions, 
+massive resource demands and scalability concerns a novel 
+framework should be proposed to address those emerging 
+challenges for the development of future Metaverses. In such 
+framework, the Metaverse Service Provider (MSP), which is 
+a service provider that offers applications or services such 
+as games, conferences or concerts should be able to get paid 
+for provided services and in addition to this, the MSP should 
+be allowed to negotiate with the Metaverse User (MU) to 
+use MUs computational resources in return for discounts 
+or rewards. The blockchain, which is provided by the MSP 
+can contain all interactions between the MSP and MU in 
+terms of transactions. The MetaChain [57] describes a similar 
+concept that could serve basis for future deployments. In this 
+particular proposal, the blockchain shards are used to allow 
+the MUs to contribute their computational resources to the 
+Metaverse application provided by the MSP. This is done in 
+exchange for digital assets such as tokens or service access. 
+With this approach, more users can be attracted to a particular 
+Metaverse. However, attracting users to contribute resources 
+is going to be particularly challenging. The reason is that 
+the service provider will not be able to directly allocate the 
+user resources to the shards. Sharding is so far one of the 
+most practical solutions to achieve a scale-out system where 
+the processing, storage, and computing can be conducted in 
+parallel. As such, the capacity and throughput being linearly 
+proportional to the number of participating nodes or the num- 
+ber of shards become possible, while preserving decentral- 
+ization and security. The consideration has to be taken when 
+creating shard-based systems as users (by human nature) will 
+aim to maximize their profits and concentrate resources on 
+the shards that pay more. Nevertheless, whichever form such 
+framework will take, a pay-per-share protocol is required 
+to off-load computational workload onto the Metaverse user 
+devices. 
+
+EEEAccessBartlomiej Siniarski et al.: Need 6G for the Metaverse Realization 
+12 
+VOLUME 4, 2016 
+ 
+ 
+  The Metaverse  
+  Continuous Integration          High Connectivity   
+ 
+I. 6G FOR SECURITY AND PRIVACY PROTECTION, 
+ELIMINATED CRIMINAL/HACKER ACTIVITIES, TRUST 
+AND ACCOUNTABILITY 
+ 
+ 
+  Network Analysis   
+  Artificial Intelligence  
+ 
+FIGURE 8. 6G for Security and Privacy Protection 
+ 
+Metaverses should offer their users an extraordinary im- 
+mersive experience in virtual environments, such as enter- 
+tainment games and smart cities, using its enabling tech- 
+nologies. The metaverse can track users’ physical actions 
+and physiological responses and may expose confidential 
+information about their habits and physiological nature to 
+third parties. If hackers get their hands on such sensitive in- 
+formation, it could lead to harassment and the theft of digital 
+assets, which could make users lose faith in the security and 
+privacy of the metaverse. These issues can be addressed by 
+utilizing privacy-protection technologies like "Private Copy" 
+and "Clone Cloud", as depicted in Fig. 8. The creation 
+of private copies and clone clouds is dependent on high 
+connectivity and continuous integration with the metaverse 
+environment. The edge intelligence facilitated by 6G can 
+support the needs of these technologies in the metaverse. The 
+use of a blockchain-based digital twin wireless network and 
+an edge computing federated learning architecture can further 
+enhance the users’ privacy and data security [8]. Together 
+with 6G, AI can optimize connectivity while also enabling 
+traffic prediction and improving security in the metaverse. To 
+avoid information breaches, physical layer communication 
+may use a machine learning-based antenna design. Machine 
+learning and quantum encryption can also be used to protect 
+the security of communication devices in the metaverse. The 
+metaverse’s security may be increased by using early warning 
+systems and AI-enabled 6G to identify network anomalies. 
+The use of distributed and federated AI in a 6G network also 
+eliminates the necessity for data sharing across the metaverse 
+devices, which preserves the privacy of the users. 
+ 
+IV. ROLE OF 6G TECHNOLOGIES FOR THE METAVERSE 
+6G will play a key role in the Metaverse operation since 
+such an environment requires pervasive connectivity for full- 
+fledged and omnipresent Metaverse immersion. Essentially, 
+very-high bitrates and ultra-low delay are crucial for a sat- 
+isfactory Metaverse experience. An important factor on this 
+performance is the smart management of connectivity re- 
+sources/services, scalable infrastructure and very low latency 
+communications. Therefore, Edge AI and cloud infrastruc- 
+ture are necessary for efficient and performant handling of 
+relevant use cases in the Metaverse. Edge AI is an impor- 
+tant enabler since it facilitates AI-driven optimized network 
+management and minimizes delay with distributed and close- 
+to-the-user computing paradigms. This technology will be 
+compounded with the AI native design of 6G which will 
+be embedded for numerous functions ranging from physi- 
+cal layer control to service management. Furthermore, the 
+required flexibility and scalability for network and service 
+environment requires moving towards cloud-native technolo- 
+gies which can also form telco clouds for more efficient and 
+scalable Metaverse infrastructure in the backend. 
+In the cyber-physical domain, another aspect of the Meta- 
+verse regarding 6G will IoE and robotics play a key role. 
+Additionally, 6G will have the essential toolbox to enable 
+AR/VR, which is critical since the Metaverse will be the 
+main vessel for AR/VR experience. An appropriate immer- 
+sive experience in the Metaverse will be possible with those 
+technologies enabled by 6G communication and computa- 
+tion functions. As a transversal technology similar to AI, 
+blockchain can also help the distributed and open nature of 
+the Metaverse and enable the transferability of digital assets 
+which will be an important capability for the Metaverse use 
+cases. A depiction of these technologies and their roles is 
+provided in Fig. 9 and the summary of all related works is 
+presented in Table 4. 
+ 
+A. AI 
+1) Introduction 
+Based on the combination of many advanced technologies, 
+the Metaverse should be built to convey a groundbreaking 
+immersive experience to users, in which AI has played a vital 
+role in the foundation and development of the Metaverse re- 
+garding numerous aspects, including core services and appli- 
+cations. Besides the responsibility of ensuring the reliability 
+of the Metaverse’s infrastructure, AI can help developers in 
+designing and building a smarter and more beautiful virtual 
+world and further allows users to acquire hyperreal creation 
+using built-in tools. In 6G systems, numerous challenging 
+tasks and applications can be solved and enabled by advanced 
+ML algorithms with different learning mechanisms (i.e., su- 
+pervised learning, unsupervised learning, and reinforcement 
+learning) to achieve high performance and low latency. Espe- 
+cially, DL with the advantage of effectively learning complex 
+patterns from practical large and messy datasets will be the 
+key technology to polish many aspects of the Metaverse, 
+from the intelligence of AI agents and virtual assistants 
+(a.k.a., chatbots) to the visual quality of 3D worlds [58]. 
+Indeed, the presence of AI in the Metaverse can be realized in 
+the interactions between a user (represented by an avatar) and 
+other objects (e.g., non-player characters) by automatically 
+analyzing sensory data for multiple tasks, such as speech 
+recognition and understanding, facial expression analysis, 
+body movement tracking, and gesture recognition. Besides, 
+  Private Copy 
+Cloud Clone   
+  Privacy Protection Technologies  
+  Quantum Security  
+  Quantum computing   
+  Data Privacy   
+  Federated Learning   
+USER 
+
+EEEAccessMETA6GBartlomiej Siniarski et al.: Need 6G for the Metaverse Realization 
+13 
+VOLUME 4, 2016 
+ 
+ 
+ 
+ 
+ 
+ 
+FIGURE 9. 6G key technologies and their roles for the Metaverse. 
+ 
+ 
+AI can be applied to preserve users’ identity and their digital 
+assets from cyberattacks, especially in the scenario in which 
+the Metaverse is built with a cross-chain bridge. 
+ 
+2) How 6G AI can help, on which features 
+In the Metaverse, natural language processing (NLP) plays 
+an important role to deploy intelligent virtual assistants (in- 
+cluding chatbot) [59], which helps the Metaverse compre- 
+hensively understand what users are typing and talking, from 
+simple sentences to complicated and long conversations, over 
+unlimited, to smooth user interaction accordingly. Empow- 
+ered by AI with ML and DL algorithms, chatbots can imme- 
+diately respond to the users and adapt to an environment with 
+reinforcement learning to consolidate operation and improve 
+the performance of an overall virtual assistant system [60]. 
+In the NLP domain, language modelling aims to predict 
+linguistic components in sentences and paragraphs by min- 
+ing syntactic and semantic relations of words and phrases, 
+which is commonly developed for machine translation and 
+text recommendation. Several advanced language modelling 
+methods have exploited DL with RNN, LSTM, and CNN 
+architectures to improve the overall system efficiency and 
+addressed many fundamental tasks [61], such as identify- 
+ing long-term dependency in long sentences in complicated 
+scenarios, recognizing hyphenated words, misspelt words, 
+suffixes, and prefixes. Especially, language modelling should 
+be taken into consideration with different popular languages, 
+such as English, Chinese, Spanish, and French [62], [63] 
+ 
+to attract as many as possible users from over the world 
+to join the Metaverse. Some advanced structures in deep 
+networks, such as bidirectional LSTM, bidirectional gated 
+recurrent unit (GRU), and channel-wise attention connection, 
+have been leveraged to deal with some challenging prob- 
+lems, such as sentiment analysis, question type classification, 
+and answer identification with multiple sentences [64], [65], 
+which accordingly improved readability, interpretation, and 
+rationality of virtual assistant agents. Some other specific AI- 
+based NLP tasks (e.g., context retrieval, semantic notation, 
+and named entity recognition) can be considered to uplift 
+text-based and speech-based user interactive experiences in 
+the Metaverse. 
+Commercial headset devices with VR/XR technology have 
+been designed to bring 3D viewing experiences to users, 
+including high video quality (i.e., high resolution and high 
+frame rate) and wonderful wearing comfort thanks to the ad- 
+vancement of AI. In [66], an eye fixation prediction method 
+was introduced for gaze-based applications (e.g., video ren- 
+dering and content visualization), in which a DL framework 
+with hierarchical CNN architectures was exploited to process 
+different data types, including VR images, gaze data and 
+head data collected by wearable sensors. Some recent works 
+have studied advanced ML and DL algorithms to precisely 
+identify periodic behaviours of VR gear’s user (e.g., gaming 
+controllers and head-mounted display) for automatic identity 
+authentication and health issues detection [67]. Some deep 
+networks with CNN architectures have been designed to 
+Body 
+Area 
+Networks 
+Hyper- 
+connectivity 
+Nano-scale 
+IoE 
+Networks 
+Explainable 
+AI 
+Edge 
+Computing / 
+Sensing and 
+Mapping 
+Immersive 
+Data Security 
+and Privacy 
+Latency 
+Edge 
+Edge AI 
+minimization devices 
+Context 
+Awareness 
+Intelligence AI-driven Smart edge 
+Privacy 
+services 
+Elastic 
+Metaverse 
+services 
+Federation 
+Efﬁciency 
+Cloudiﬁcation 
+Ultra-scalable 
+Consolidation 
+Privacy 
+preservation Interoperabilty 
+Data 
+storage 
+compute- 
+storage 
+METAVERSE 
+Blockchain 
+Virtual 
+economy 
+(trading, 
+NFTs, ...) 
+Intelligent 
+Radio 
+Improved 
+QoS/QoE 
+Spectrum 
+ﬂexibility 
+Open RAN 
+Data 
+acquisition 
+Asset and 
+identity 
+protection 
+Virtual and 
+AI agents 
+Connectivity 
+ﬂexibility 
+NLP 
+AI 
+Performance 
+optimizations 
+Infrastructure 
+reliability 
+Computer 
+vision 
+
+EEEAccess8
+-RANBartlomiej Siniarski et al.: Need 6G for the Metaverse Realization 
+14 
+VOLUME 4, 2016 
+ 
+ 
+ 
+ 
+ 
+FIGURE 10. The roles of AI for the development and advancement of the Metaverse. 
+ 
+ 
+assess the quality of images/videos (e.g., color saturation, 
+brightness, resolution, and frame rate) displayed on the 
+screen of VR devices, and then automatically adjust screen 
+settings to optimize the visualization based on video contents 
+and user conditions [68]. 
+Along with the VR/XR technologies, computer vision is 
+one of the most important sectors to build a beautiful virtual 
+world in the Metaverse and enable it to be more intelligent 
+from the user’s viewpoint with the adoption of AI, especially 
+DL in a few years [69]–[71]. Many sophisticated CNN 
+architectures have been designed for different fundamen- 
+tal image processing and computer vision tasks, such as 
+object detection, semantic segmentation, and scene under- 
+standing [72], [73]. For instance, atrous convolution was 
+introduced by DeepLab [74] for semantic segmentation to 
+capture more meaningful features by enlarging the receptive 
+field of kernels to enhance the learning efficiency of a deep 
+network while obtaining a small network size. Static and 
+dynamic objects can be detected and located in the virtual 
+worlds accurately by several recently advanced DL models 
+to provide useful information to users and be synthetized 
+for higher-level tasks like scene understanding and detailed 
+captioning. Some image/video quality distortion problems, 
+such as blurring, noise, and frame corruption, can be ad- 
+dressed effectively by AI technology to guarantee the high- 
+class visual perception of a user when experiencing the Meta- 
+verse [75]. In addition, the activities, including single actions 
+and interactions, of users and non-player characters in the 
+Metaverse can be automatically detected and recognized by 
+AI-powered human pose estimation and action recognition 
+methods [76]. Some convolutional networks have exploited 
+cutting-edge layer structures, such as dense connection, skip 
+connection, and attention connection, to estimate complex 
+ 
+human poses and classify grouped activities while handling 
+other challenges like varying viewpoints, object occlusion, 
+and complicated actions in practice. For example, generative 
+statistic models and hybrid LSTM-CNN architectures are 
+suggested in [77] to precisely examine pose transition in 
+the spatiotemporal domain, thus increasing the accuracy of 
+action recognition and activity classification. 
+To preserve the Metaverse from different cyberattacks, 
+especially protect users’ digital goods and cryptocurrency 
+assets, many advanced ML algorithms and DL models can 
+be deployed in multiple layers (e.g., network and services 
+layers) of the Metaverse’s platform for intrusion detec- 
+tion [78]–[80], in which various malicious attacks can be 
+automatically and accurately detected and classified to im- 
+mediately provide an efficient security solution. In [81], a 
+holistic security method with sufficient assurability and ex- 
+plainability was proposed to quickly and sequentially detect 
+abnormalities and time-dependent abnormal events in IoT 
+systems and software-defined networks, in which zero-bias 
+neural networks are transformed into performance-assured 
+binary abnormality detectors to increase detection accuracy 
+while presenting the lowest latency based on false alarm 
+constraints. In the effort to exploit DL denoising autoencoder 
+(DAE) for many fusion security problems, many variants 
+of DAE, including stacked autoencoder, stacked sparse au- 
+toencoder, stacked noise autoencoder, stacked contractive 
+autoencoder, deep belief network, were benchmarked in for 
+performance comparison with different practical intrusion 
+detection datasets [82]. Reinforcement learning (RL) with 
+the capability of learning environmental factors to adapt 
+learnable parameters was also exploited to deal with different 
+types of cyberattacks (such as malware, denial-of-service at- 
+tack, and man-in-the-middle attack) [83]. In addition, privacy 
+Understand and respond to user to 
+enhance text-base and speech-based 
+user interactive experiences 
+Improve viewing experience of high 
+video/image quality with VR/XR 
+devices 
+Multi-language modeling 
+Eye ﬁxation estimation 
+Semantic analysis 
+Smart 
+Assistance 
+Quality 
+Experience 
+Video/image quality enhancement 
+Question type classiﬁcation 
+Adaptive content-based visualization 
+ 
+Answer identiﬁcation 
+VR gear's user behavior prediction 
+Ai for the 
+Metaverse 
+Create a 3D virtual world with beautiful 
+outlook and intelligent environment 
+Attractive 
+3D World 
+Security 
+Protect user digital goods and 
+cryptocurrency assets from different 
+cyber-attacks 
+Object detection 
+Intrusion detection 
+Semantic segmentation 
+Malware and denial-of-service 
+ 
+Image restoration and registration 
+Man-in-the-middle attack detection 
+Video analysis and scene 
+Privacy preservation 
+understanding 
+Enhance intelligence of AI 
+agents in real-time strategy 
+and ﬁghting games 
+Increase the 
+performance of 3D 
+rendering 
+AI-based data security 
+Computer vision for 3D world 
+development 
+Analyze mental state 
+with brain-computer 
+interaction 
+AI-aided VR/XR 
+NLP for intelligent virtual assistant 
+Improve performance  of 
+data transmission in URLLC 
+with intelligent MEC 
+
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+ 
+preservation in the Metaverse should be uplifted comprehen- 
+sively with the help of AI to ensure that there are no leakable 
+risks and threats to users’ big data in the virtual world. 
+For instance, a privacy-aware and asynchronous DL-based 
+method was introduced in [84] to maintain the confidentiality 
+of data among different collaborative data collection sites. 
+In [85], an optimal centralized privacy-preserving aggregate 
+mobility data release mechanism was proposed to minimize 
+the data and information leakage, in which deep RL models 
+and the Asynchronous Advantage Actor-Critic algorithms are 
+combined to optimize the privacy-preserving method. The 
+above-mentioned privacy-preserving DL-based methods can 
+be recommended for the Metaverse to combat information 
+leakage threats and adversary attack effectively. 
+ 
+3) Summary 
+In the Metaverse, AI has presented a plentiful foundation and 
+development in numerous aspects and helped to construct 
+a more beautiful virtual world with intelligent and secured 
+services, thus bringing a wonderful experience to users. Sev- 
+eral advanced ML algorithms and DL architectures have been 
+deployed to take care of the comfortableness of VR users, 
+and the interaction between users with virtual assistants, and 
+automatically provide useful information about the virtual 
+worlds to users. Besides some popular domains like NLP 
+and computer vision, AI has great potential for deployment 
+in other sectors: protecting users’ digital assets from hackers, 
+early detecting intrusions for data security and privacy preser- 
+vation, improving the performance of URLLC with intelli- 
+gent MEC, enhancing the intelligence of AI agents in real- 
+time strategy and fighting games, and analyzing mental state 
+with the brain-computer interface as illustrated in Fig. 10. 
+Although some advanced ML and DL models can conduct 
+a high performance in many detection and classification 
+tasks, they represent black boxes that lack the capability of 
+explainability and interpretability. Therefore, there remains 
+room for AI research and development in the Metaverse. 
+ 
+B. BLOCKCHAIN 
+1) Introduction 
+In the Metaverse, data privacy and virtual asset (e.g., cryp- 
+tocurrency and NFT) security of users should be guaranteed 
+as the top priority. In this context, blockchain technology 
+represents a promising solution with many unique features 
+at once, for example, decentralization, transparency, and 
+immutability. Fundamentally, blockchain is an innovative 
+technology that permanently records transactions in a decen- 
+tralized and public database so-called a ledger [86]. Although 
+all transactions are transparent (i.e., being available to check 
+by anyone), the decentralized recording system of blockchain 
+is very difficult to fool or control. Some blockchains like 
+Ethereum and Solana are programmable through smart con- 
+tracts with different consensus mechanisms, such as proof- 
+of-work and proof-of-stake, which can meet high-security re- 
+quirements of e-commerce platforms and enable the revolu- 
+tion of the digital ecosystem in the Metaverse, especially sup- 
+porting virtual asset payment and trading activities. A smart 
+contract on the blockchain could be used to establish the 
+ownership of any digital object, such as artwork and music, 
+over NFT specialized by unique and nonreplaceable (i.e., no 
+one else can claim the ownership of that digital product on the 
+blockchain even if they have a copy version on computers). 
+The role of blockchain in the Metaverse relies on ensuring 
+data privacy and security, enabling seamless and secured 
+data sharing, data interoperability and integrity with some 
+common applications and services, such as decentralized 
+finance and NFT market [87]. Besides that, blockchain allows 
+digital goods to be tradable safely in a virtual world and 
+enables the connection of physical objects to the Metaverse 
+over NFTs. Notably, if two virtual worlds are interoperable, 
+the blockchain has to authenticate the proof of ownership 
+of digital goods in both virtual worlds. Indeed, blockchain 
+bridges the real world and the virtual world besides playing 
+as the gateway for users to access the Metaverse. 
+ 
+2) How 6G BC can help, on which features 
+Data acquisition is one of the most fundamental processes 
+to build the virtual world in the Metaverse, which collects 
+big data from different modalities. Notably, the sensitive 
+data collected from users to train AI models for several 
+special modules (such as decision-making of virtual assistant, 
+recommendation system, digital product development, and 
+automated market maker) in the Metaverse should be secure. 
+For secure and large-scale environment data acquisition, the 
+work in [88] proposed a blockchain-based system which is 
+specialized by one valuation layer to assess the quality of 
+acquired data, one consensus layer to encourage and incen- 
+tivize high-quality data acquisition, and one ledger layer to 
+record transactions and qualified environmental data. In [89], 
+a blockchain-based efficient data collection and secure data 
+sharing mechanism was introduced for reliable industrial 
+IoT systems. This mechanism has exploited the Ethereum 
+blockchain to maximize the amount of acquired data and 
+the deep reinforcement learning algorithm to obtain highly 
+secure and reliable shared data. To guarantee the users’ 
+privacy in crowdsourcing systems, Li et al. [90] designed 
+a blockchain-based decentralized framework for data collec- 
+tion and sharing. There were three standard smart contracts 
+on blockchain executed for the whole process of data acquisi- 
+tion to achieve such crowdsourcing information as task post- 
+ing, receiving, and assignment. The proposed method was 
+implemented and verified on an Ethereum test network with 
+real-world data, which demonstrated usability, feasibility, 
+and scalability to be suitable for distributed crowdsourcing 
+systems. Although blockchain technology can ensure highly 
+secure and reliable data supplied to the Metaverse, its draw- 
+back is low latency due to the complicated and distributed 
+nature of processing transactions with smart contracts and 
+consensus mechanisms like PoW. Besides, the high transac- 
+tion fee is also a realistic barrier for a low-income user to 
+experience the Metaverse. 
+In a large-scale Metaverse platform, data storage should 
+
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+ 
+ 
+ 
+ 
+FIGURE 11. The roles of blockchain for ensuring the security and privacy of data acquisition, data sharing, data storage, and data interoperability in the Metaverse. 
+ 
+ 
+be taken into consideration seriously because of the high 
+velocity, big volume, and complicated variety of big data 
+from a plentiful number of applications and services de- 
+ployed in virtual worldds [91]. There exist many underlying 
+risks, such as leakage, tampering, and loss if the Metaverse 
+is built on a platform with centralized storage systems. Some 
+sensitive data like biometric login data of the user (e.g., face 
+and touch identification on iPhone) can become the target of 
+cyberattacks to steal virtual assets. To overcome the above- 
+mentioned issues of centralized systems, the work in [92] 
+proposed a large-scale secured IoT data storage scheme by 
+exploiting blockchain miners to manipulate IoT data stored 
+in distributed hash tables (DHTs). In the blockchain sys- 
+tem, a certificateless cryptography scheme was applied to 
+reduce redundancy in traditional public key infrastructure 
+and authenticate IoT devices, where the generated public key 
+pairs are broadcasted to all devices with verification done by 
+the blockchain miners. In [93], the time-series data in the 
+Metaverse was stored in a locality-aware auditable decen- 
+tralized storage ecosystem that was designed and managed 
+thanks to the advancement of blockchain technology. Some 
+data storage systems with recovery functionality have been 
+developed to effectively address multiple problems, such as 
+low integrity, high cost, and easy tempering. Liang et al. [94] 
+introduced a secure blockchain-based data storage scheme, 
+wherein the incoming data packets are verified with smart 
+contract and consensus mechanism, and then checked to early 
+detect any threats before being stored on a decentralized 
+ 
+system. Notably, when distortion occurs to the stored data, 
+multiple nodes in the blockchain network can repair it suc- 
+cessfully. 
+As the mixture of numerous digital realms, the Metaverse 
+demands manipulating and processing the big data that is 
+acquired from incompatible infrastructures for different pur- 
+poses, in which the standardizations of data for different 
+applications and services in the virtual worlds are dissimilar. 
+This reveals a serious concern about data interoperability 
+when expanding the Metaverse with an interconnection ca- 
+pability among different virtual worlds. To ensure the inter- 
+operability between different virtual worlds in the Metaverse, 
+building a cross-chain protocol or an inter-blockchain bridge 
+becomes a promising solution in many specific domains like 
+healthcare and e-commerce [95]–[97]. A blockchain bridge is 
+a protocol connecting two economically and technologically 
+separate blockchains (such as Bitcoin, Ethereum, Avalanche, 
+Solana and Polygon) for interactions and acts like a phys- 
+ical bridge linking the ecosystems of one blockchain with 
+another. As a result, blockchain bridges enable what is called 
+interoperability means that digital assets and data hosted in 
+Metaverses built on different chains can interact with each 
+other [98]. Besides, blockchain bridges allow users to access 
+new protocols on other chains and encourage collaboration 
+between developers from different blockchains, thus promot- 
+ing a virtual economy in the Metaverse. A novel blockchain 
+framework, namely BiiMED, was introduced in [95]to uplift 
+the data interoperability and integrity in electronic health 
+Data privacy preservation 
+Data interoperability 
+Data storage 
+Data acquisitio 
+ BLOCKCHAIN 
+Should have cheap transaction fee 
+for low-income Metaverse users 
+Encourage high-quality data 
+acquisition and sharing with 
+incentive 
+For secure aanndd lsahrgaer-inscgale 
+environment data acquisition 
+Dn aatnadaschqaurisinitgion 
+Veriﬁed with smart contract and consensus 
+mechanism 
+Reducing redundancy with 
+certiﬁcateless cryptography scheme 
+For secure storage of high velocity, 
+big volume, and complicated variety 
+of Metaverse big data 
+Cross-chain interactive decentralized 
+access model 
+Blockchain bridge for different chains 
+interacting with each other 
+Data interoperability between 
+different virtual worlds in the 
+Metaverse 
+For dealing with dissimilar data 
+acquired from incompatible 
+infrastructures 
+Blockchain-based identiﬁcation and 
+authentication 
+Blockchain-based crowdsourcing 
+for privacy preservation in mobile 
+environments. 
+For dealing with privacy issues in 
+ﬁnancial ecosystem having DEXs 
+and DeFi 
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+records (EHR) sharing systems. The proposed framework 
+facilitated the medical data on EHR systems between dif- 
+ferent medical providers and healthcare institutions with a 
+decentralized trusted third-party audior for interoperation 
+validation. Some recent cross-chain protocols [99], [100] 
+have been introduced to interconnect multiple blockchains 
+for secure data utilization and management while obtain- 
+ing full interoperability. In [99], a cross-chain interactive 
+decentralized access model was designed with a gateway 
+to reading the information on multiple chains and route 
+cross-chain transactions, and a notary network with an inter- 
+planetary file system and BigchainDB to verify and confirm 
+each transaction based on a voting mechanism. Such kinds 
+of cross-chain protocols allow users to easily buy, sell, and 
+trade virtual assets among different digital worlds with- 
+out any intermediate tools, and consequently encourage the 
+adoption of the Metaverse. Along with interoperability, data 
+integrity has also received much attention in the Metaverse, 
+in which blockchain technology was considered to verify 
+and protect data integrity in decentralized cloud computing 
+systems [101], [102]. 
+In the Metaverse, a user can freely interact and trade virtual 
+goods (including cryptocurrency and other virtual assets like 
+NFT) with a virtual assistant and other users via decen- 
+tralized exchanges (DEXs) integrated into the Metaverse to 
+promote the development of decentralized finance (DeFi). As 
+an ecosystem of financial applications built on blockchain 
+networks, DeFi enables easy access to financial services, 
+facilitates traditional financial systems, and has a modular 
+framework with interoperability with public blockchains. 
+Recently, GameFi, a fusion of words game and finance, refers 
+to play-to-earn blockchain-based games with economic in- 
+centives to players, which is being developed and integrated 
+in the Metaverse. A GameFi ecosystem uses cryptocurrency, 
+NFTs, and blockchain technology to create a virtual gaming 
+environment, where various GameFi ecosystems built on 
+different chains can be involved in the Metaverse owning 
+to chain bridges. In this context, it arises many privacy 
+issues (e.g., the leakage of user identity and other personal 
+information that can be stolen for illegal purposes) can be ef- 
+fectively handled by blockchain technology with immutabil- 
+ity [103]. In a blockchain-powered Metaverse, third-party 
+intermediaries are not permitted to manipulate the data of 
+other parties. In [104], a blockchain-enabled crowdsourcing 
+approach was proposed to deal with privacy preservation in 
+mobile environments, where users can access the Metaverse 
+using mobile devices. In secure 5G and 6G communica- 
+tion networks [105], blockchain was exploited to minimize 
+privacy breaches by completely integrating authentication 
+mechanisms with blockchain-based identification systems. 
+ 
+3) Summary 
+With the distinctive features of decentralization, immutabil- 
+ity, and transparency, blockchain technology has promoted 
+the development and advancement of the Metaverse, where 
+it has played an important role in any Metaverse platforms 
+with some great contributions in terms of many technical 
+aspects, including data acquisition, data storage, data in- 
+teroperability, and privacy preservation. Besides ensuring 
+the privacy of sensitive information and security in trading 
+activities (e.g., buy/sell cryptocurrency, NFTs, and other 
+virtual assets), blockchain has shown great achievement to 
+revolutionize user’s immersive experience, boosting the eco- 
+nomic growth, and attracting new users to the Metaverse 
+via numerous blockchain-aided applications and services 
+supplied in the virtual worlds. However, it remains several 
+challenging issues to concurrently attain security, scalabil- 
+ity, and decentralization when the Metaverse must serve a 
+huge number of users and a rapidly increasing number of 
+transactions to process. Consequently, many research topics 
+to optimize blockchain for the Metaverse should be con- 
+tinuously exploited in the future, such as consensus algo- 
+rithms, blockchain interoperability, smart contract, and net- 
+work management. 
+ 
+C. EDGE COMPUTING AND EDGE AI 
+1) Introduction 
+The Metaverse is envisaged to map and simulate all our 
+daily life activities in cyberspace at a huge scale while 
+enriching such mapping with an immersive and interactive 
+user experience. Cyber-physical and digital twin applications 
+will also be integrated with the Metaverse application to 
+offer realistic cyber representations of the physical world. 
+In the ICT infrastructure, there will be the Metaverse engine 
+which performs computations required to run virtual universe 
+simulations carrying out computationally heavy tasks such as 
+collision detection in the virtual universe and computation 
+of 3D physics, and also other aspects of virtual universe 
+that demand high computational power [106]. The Metaverse 
+is striving to connect billions of users and create a shared 
+world where virtual and reality merge [8]. Therefore, users 
+interact in the physical-virtual world with the characteristics 
+of diversification of information, identities, and modes un- 
+der the requirements of ultra-low latency, massive resource 
+demands, interoperability between applications, and security 
+and privacy issues [107]. 
+The promised Metaverse operation will require extremely 
+low latency with highly elastic and omnipresent compute and 
+storage resources. The latency and processing challenge for 
+the Metaverse is in line with what is expected with 6G edge 
+computing realization: For the Metaverse extended-reality 
+computations to be offloaded, the entire process must be 
+shortened so that input from the user device, a network trip, 
+processing by the service, a return network trip and drawing 
+the output on the user device fits in the 20ms time taken by a 
+single network trip today [108]. Cloud-based processing for 
+Metaverse operation can be unfavourable as it suffers from 
+several drawbacks caused by the long latency required for 
+cloud access, such as low-quality visualization in XR. 6G 
+enables real-time, ubiquitous, and ultra-reliable communica- 
+tions for massive Metaverse devices with support for device 
+mobility, which can reach 1020 Gbps [109]. To this end, Fog 
+
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+Computing [110] and Mobile Edge Computing [111] have 
+been proven effective to tackle the issues faced by cloud- 
+based systems, by moving the computational heavy load near 
+the end-user and distribute it among edge devices; such ap- 
+proach can significantly reduce the latency and optimize the 
+system performance. Furthermore, there is the cost-benefit: 
+such an approach it would drive down the cost of XR devices 
+and allow mass adoption. Verizon has estimated that any 
+more than 20ms of motion-to-photon (total stack) latency 
+causes many users to become nauseated; for comparison, 
+well-built wireline broadband networks today typically have 
+20ms of network latency alone, and typical LTE latencies 
+are 3x higher. Therefore, edge computing is an important 
+technology. For instance, Zhang et al. [112] introduced the 
+MEC into the Metaverse to improve the quality of users’ 
+experience. Xu et al. [7] discussed the potentials of AI, Edge 
+computing and blockchain for ubiquitous, seamless access 
+to the Metaverse. Similarly, Lim et al. [113] present the 
+infrastructural architecture required for the Metaverse with 
+a special focus on the convergence of edge intelligence and 
+the infrastructure layer of the Metaverse. 
+6G-enabled edge intelligence opens up a new era of 
+Internet of Everything and makes it possible to intercon- 
+nect people-devices-cloud anytime, anywhere. In this con- 
+text, industry, and academia have developed a new learn- 
+ing paradigm, Edge Artificial Intelligence (Edge AI) [114], 
+which allows AI models to be deployed on devices and 
+perform real-time data processing and model inference. 6G 
+mobile communication technology provides edge AI with 
+lower latency, more stable network connection, and more 
+secure network architecture. Edge AI with 6G is expected 
+to be applied to solve problems such as high bandwidth 
+and high connection density in the Metaverse. However, the 
+Metaverse still faces many challenges, such as users’ privacy, 
+network latency, and resource allocation issues. Moreover, 
+the Metaverse places higher demands on the current edge AI 
+architecture. As mentioned above, 6G edge intelligence has 
+the advantages of low latency, computing offload, and high 
+performance [115]. Overall, the application of 6G-oriented 
+edge intelligence has the benefits of balanced data storage, 
+efficient data transmission and high reliability. 
+ 
+2) How 6G EC and Edge AI can help the Metaverse 
+As noted above, a high-speed and low-latency network con- 
+nection and ubiquitous access to services is an important 
+foundations for improving the user experience in Metaverse. 
+Otherwise, issues such as visual jitter or delay and other 
+undesirable phenomena might lead to the subpar perfor- 
+mance of Metaverse. In that regard, to reduce network la- 
+tency, an incentive mechanism framework for VR services 
+was proposed in [116], which uses perceived quality as a 
+criterion for measuring immersive experience and effectively 
+evaluates the immersive experience in the Metaverse. [117] 
+presents a novel MEC-based mobile VR delivery framework 
+that is able to cache parts of the field of views (FOVs) in 
+advance and compute certain post-processing procedures on 
+demand at the mobile VR device. Jiang et al. [118] found that 
+coded distributed computing (CDC) can improve the latency 
+problem in the Metaverse and proposed a CDC and dual 
+blockchain distributed collaborative computing framework. 
+However, the computing, communication, and storage 
+shortage will seriously affect the user’s immersive experi- 
+ence. For the resource allocation problem, a new blockchain- 
+based framework called Metachain was proposed in [87] 
+which uses Stackelberg game theory analysis to propose an 
+incentive mechanism, i.e., users obtain corresponding re- 
+wards by providing resources to blockchain shards. Based on 
+the intelligent 6G edge network, a machine learning frame- 
+work was proposed in [119] for decentralized learning and 
+coordination of edge nodes to improve resource allocation 
+strategies. 
+For Edge AI and its applications in 6G, there are various 
+challenges which are investigated by the research commu- 
+nity. Edge AI paradigm and its applications still have the 
+following issues that need to be optimized [8]: 
+– High Latency: Since edge AI generally involves thou- 
+sands of remote devices and needs to transmit and process 
+massive amounts of data [120], [121], the high latency issue 
+in the current network environment has always been one of 
+the bottlenecks hindering the wide application of edge AI 
+[122], [123]. 
+– Fragile Stability: In edge AI, the training of large- 
+scale models often requires powerful computing power and 
+stable network connections, especially the training of large 
+language models [124]. However, the current network en- 
+vironment is only suitable for the training of small-scale 
+models [125]. This is due to the fragility of the network 
+connection leads to the failure of large-scale model training. 
+– Low Security: The current network architecture no 
+longer meets the security needs of thousands of remote de- 
+vices connecting to cloud servers today [120]. Furthermore, 
+the openness of the network further challenges the security 
+of the current network architecture. 
+These issues are expected to be exacerbated with the 
+utilization of Edge AI in 6G for the Metaverse applications. 
+For instance, in [8], Chang et al. propose a self-balancing 
+federated learning-based Metaverse framework to address the 
+statistical heterogeneity faced by edge-cloud architectures. 
+Besides, in [126], Lu et al. proposed a blockchain-based digi- 
+tal twin wireless network (DTWN) edge computing federated 
+learning framework to solve the problem of user privacy data 
+security. 
+ 
+3) Summary 
+The integration of edge computing and realization of edge AI 
+in 6G will provide various capabilities as well as challenges 
+for the Metaverse. The key benefit is related to latency min- 
+imization needed for superb Metaverse user experience and 
+pervasive services. Similarly, the inherent Edge AI support 
+in 6G will also serve the Metaverse for smart edge services 
+leading to better Metaverse services and device simplicity 
+and flexibility. However, the potential benefits of 6G edge 
+
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+technologies should be supported with relevant research for 
+improving on the aspects such as smart resource allocation, 
+security, and privacy-preserving AI techniques. 
+ 
+D. 6G OPEN RAN 
+1) Introduction 
+Radio Access Network (RAN) is a very important component 
+of a mobile communication system that can link individual 
+devices like mobile phones or terminals to other parts of 
+the network using cellular radio. RAN coordinates the re- 
+source management in the cellular network across the radio 
+sites. RAN can send the signal from a mobile device that 
+is connected wirelessly to the core/backbone network to 
+several endpoints in the wireless network, thereby, enabling 
+the signal to travel along with the traffic generated from other 
+networks. A RAN will typically comprise of base stations, 
+that can transmit and receive signals to and from mobile 
+devices in the network. The signals are then digitized in 
+the RAN-based station and are connected to the network. 
+RAN contains radio units (RU), distributed units (DU), a 
+centralised unit (CU), and the RAN Intelligent Controller 
+(RIC) for the creation of an effective mobile communication 
+system. RAN is very important for meeting the low latency 
+and high-speed internet connectivity requirements of real- 
+time applications [127]. 
+RAN requires manual intervention if any network issues 
+arise in software or connecting devices. Pointing out the 
+cause and the origin of these issues in the network by the 
+mitigation experts is difficult as RAN is black-box in nature. 
+The process involved in the mitigation of these network 
+issues requires significant cost and time, subsequently affect- 
+ing the overall quality of the network. This necessitates the 
+creation of open, intelligent, virtualised, and fully automated 
+interoperable RAN for the next generation 6G networks 
+[128]. Open RAN (ORAN) is one such technology that 
+integrates AI to optimize radio resources and also automates 
+the management and operations of infrastructure. 6G ORAN 
+integrated with AI can be used to implement Self-Organizing 
+Networks (SON) and Radio Resource Management (RRM) 
+solutions that improve network coverage, capacity, handover, 
+and interference. They could also be used to increase the 
+spectral efficiency of massive MIMO systems by optimising 
+their performance. AI/ML can also enhance the user expe- 
+rience through VoLTE/video quality optimization, terminal 
+anomalies detection, and other Quality of Service/Quality of 
+Experience (QoS/QoE)-based use cases [129]. The use of 
+ORAN gives mobile network operators (MNOs) the flexibil- 
+ity to provide 6G connectivity in a cost-effective, secure, and 
+energy-efficient way. The openness of ORAN also enables 
+the MNOs a unique ability where all the vendors can share 
+the RAN functionalities [130]. As a result, it avoids vendor 
+lock-in by replacing vendor-proprietary interfaces with a 
+fully disaggregated RAN based on open standards. 
+2) How 6G Open RaN can help the Metaverse 
+The users navigate in the Metaverse frequently with the 
+help of technologies such as AI, XR, digital twins, IoT, 
+etc. As a consequence, the Metaverse demands continuous 
+connectivity with sensors, hardware devices, and many other 
+peripherals for providing high-quality and immersive ser- 
+vices to the user. Any disruption in the network connectivity 
+of these devices will cause the users extreme discomfort and 
+make them feel that the surroundings are out of their control 
+[131]. The standards for the Metaverse are substantially more 
+demanding than those for the vast majority of internet appli- 
+cations in the present day. The current capacity of MNOs to 
+handle the network requirements of devices connected to the 
+Metaverse is rather questionable. This presents a challenge 
+in the adaptation of the Metaverse. To solve these issues 
+ORAN in 6G is a potential solution.ORAN in 6G with its 
+AI, automation, and fully disaggregated open standards will 
+enable the Metaverse to be cost-effective, secure, and energy- 
+efficient way. 
+Let us consider the application of the Metaverse in the 
+healthcare domain. The Metaverse allows healthcare profes- 
+sionals to have better interactions with patients who are in 
+different demographic locations, such as viewing a three- 
+dimensional model of the human body while discussing di- 
+agnoses and treatments. This would allow doctors to simulate 
+the effect of a proposed treatment on a patient’s body before 
+its application, creating a more personal and informative 
+experience than is currently possible with two-dimensional 
+images displayed on a screen. VR, AR, and MR technologies 
+are currently being used for medical training and surgical 
+procedures, These enabling technologies of the Metaverse 
+demand reliable connectivity. If any failure of software or 
+hardware occurs in the network at the time of medical inter- 
+vention it will lead to serious catastrophic situations. ORAN 
+in 6G enables devices to relay on multiple MNO, so, this will 
+ensure the medical devices connected to the Metaverse with 
+much reliable connectivity. The remote medical surgeries 
+supported by the Metaverse require real-time insights. The 
+network supporting these devices must be faster in recovering 
+from the related issue and failures. The ORAN in 6G will 
+provide the Metaverse with zero-touch network and service 
+management capabilities which will automatically resolve 
+the raised issues related to the network faster than the tra- 
+ditional RAN. The vital monitoring devices connected to the 
+Metaverse require a latency-free and cost-efficient network. 
+These devices connected to the Metaverse will be greatly 
+benefited by ORAN service management and orchestration 
+platform in 6G. ORAN service management and orchestra- 
+tion platform in 6G is an intelligent automation platform 
+that applies automation reduces the complexity of networks, 
+improves network performance, and enhances the customer 
+experience in the Metaverse which minimizes ORAN opera- 
+tional costs, as depicted in Fig. 12. 
+In the Metaverse, the possibilities of what can be created 
+and purchased are nearly limitless. Users can purchase avatar 
+skins, hairstyles, clothing, and accessories, as well as virtual 
+
+EEEAccessBartlomiej Siniarski et al.: Need 6G for the Metaverse Realization 
+20 
+VOLUME 4, 2016 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+FIGURE 12. The role of 6G Open RAN for the development and advancement of the Metaverse. 
+ 
+ 
+land and property. Cryptocurrency and digital wallets will 
+play a role in the Metaverse payments. Blockchain-based 
+cryptocurrencies in the Metaverse or a crypto wallet are 
+required to store and transport digital assets purchased in 
+the Metaverse as well as between the virtual worlds. Digital 
+wallets will be an alternative payment method that enables 
+users to purchase digital goods securely. Thus the number 
+of transactions occurring in the Metaverse will be limitless. 
+Any breach or a critical update to the network will interrupt 
+or halt these transactions and may affect the QoS/QoE of 
+the customer in the Metaverse. ORAN in 6G will be less 
+dependent on hardware which will reduce the risk associated 
+with automated upgrades or isolated security breaches. The 
+enhanced modularity available with open interfaces makes 
+it easier for operators to serve the Metaverse towards a 
+continuous integration/continuous delivery of services. Every 
+trade or purchase that occurs in the Metaverse is recorded as a 
+transaction, which results in huge network traffic because the 
+data is to be stored in multiple peers. ORAN in 6G helps the 
+Metaverse in better traffic management and also determines 
+where to send traffic across the network. ORAN in 6G and 
+AI enables the Metaverse to predict network conditions, such 
+as congestion, so the controller can find an optimal path to 
+send traffic over. This provides the users of the Metaverse 
+with valuable insights about the network. 
+ 
+3) Summary 
+ORAN in 6G with features like openness, better security, 
+enhanced resource sharing, improved traffic management, 
+and zero-touch network and services management provides 
+the Metaverse with a network that is faster, reliable, cost- 
+effective, automated, and intelligent. This is will help the 
+Metaverse applications and services to be real-time. ORAN 
+in 6G will help the users in the Metaverse with high-quality 
+immersive experiences. The issues related to network soft- 
+ware updates or threats will not affect the transactions in the 
+Metaverse as ORAN in 6G is secured and depends less on 
+hardware compared to the traditional RAN. ORAN in 6G 
+allows AI to easily analyze the network and provide valuable 
+insights for the Metaverse to persist. Though ORAN in 6G 
+provides better network capabilities to the Metaverse it still 
+faces challenges related to widespread adoption, technical 
+ 
+support difficulties, system integration problems, and secu- 
+rity risks. 
+ 
+E. 6G CLOUDIFICATION AND CLOUD NATIVE 
+TECHNOLOGIES 
+1) Introduction 
+A key aspect of 6G networks will be the cloud-native design 
+of the overall ecosystem. With the actual realization of the 
+Metaverse, the cloud, infrastructure, and telecom companies 
+will have to provide a fully immersive Metaverse experience 
+challenging servers with a 100x harder compute task than an 
+AAA game server hosting Fortnite today, and telecom access 
+networks facing 24x more traffic in a decade [108]. To ad- 
+dress these compute-storage requirements, the State-of-the- 
+art Metaverse architectures rely on a cloud-based approach 
+for core Metaverse functions such as avatar physics emula- 
+tion and graphics rendering computation. Specifically, XR 
+places extraordinary demands on networks with native cloud 
+design of 6G networks, on-board computation capability to 
+eliminate external computing device dependency can still be 
+delivered on simpler, lighter, and cheaper end-user devices if 
+computationally intensive tasks can be offloaded to a cloud 
+computing instance. 
+The Metaverse leads to a clear need for cloud computing, 
+considering the amount of storage and processing required 
+to support a virtual reality universe: compute, storage and 
+network loads [132]. As more performance and details will 
+be demanded, remote cloud-based computers will become a 
+necessary cost-effective way to solve that problem. The cloud 
+computing technologies will be heavily exploited in two di- 
+mensions: First, by the Metaverse providers themselves built 
+whether with private data centres or managed services. Due 
+to their advantages, these compute- and graphics-intensive 
+systems will be built on public cloud providers. Another 
+option is to provide on-demand access compute and storage 
+using pay-as-you-go models which can be done by public 
+cloud providers with points of presence distributed globally. 
+However, there is also the latency dimension: navigating the 
+Metaverse smoothly through VR technology depends mainly 
+on the network latency. As VR technologies are delay- 
+sensitive and required very short latency, communicates with 
+the Metaverse servers plays a pivotal role that leads to telco 
+Faster Data Transmission 
+Open 
+Midhaul 
+ Reliable Network 
+vCU 
+OpenRU 
+Fronthaul 
+Cost-Effective Network 
+ 
+ Automated Network Recovery 
+IP 
+RIC 
+RU 
+IP 
+Virtualized 
+Packet 
+Core 
+ Intelligent Network Management 
+vDU 
+The Metaverse 
+ORAN 
+Backhaul 
+RoE 
+eCPRI 
+
+EEEAccessAiBartlomiej Siniarski et al.: Need 6G for the Metaverse Realization 
+21 
+VOLUME 4, 2016 
+ 
+ 
+ 
+clouds where this concept is embedded in the telco network 
+itself. 
+For example, the validation of Non-Fungible Token 
+(NTF) trading transactions requires tremendous computa- 
+tional power. This challenge is also valid for other Metaverse 
+applications such as data processing of digital twin appli- 
+cations or AI-enabled services like storytelling and recom- 
+mendation services that empower the virtual universe sim- 
+ulation [106]. Current state-of-the-art Metaverse implemen- 
+tations perform the computational on the cloud, which may 
+limit the simulation capacity, and increase access latency. 
+Moreover, there are several independent and fragmented 
+Metaverses that rely on different hardware and software tech- 
+nologies. Since the service providers would like to exploit 
+the advantages of controlling users’ Metaverse data in their 
+servers, we may end up with isolated Metaverses rather 
+than a universal Metaverse. Additionally, due to capacity 
+limitations, the number of users that can access each re- 
+gion may be limited by the cloud service provider’s local 
+computational and communication capacity. Such limitations 
+defeat the purpose of a virtual world, which is supposed to 
+accommodate avatars as much as the real-world location can 
+physically accommodate people. 
+Mobility support is also crucial since Metaverse will be a 
+pervasive experience. Cloud can also help there as proposed 
+by [106]. In this context, they propose a distributed archi- 
+tecture that can achieve a universal Metaverse, and solves 
+the computational bottleneck. The advantage of layered ar- 
+chitecture is twofold. Firstly, the users control their data, 
+which enables organizations to access a universal Metaverse, 
+rather than multiple separated Meta- verses. Secondly, the 
+computational bottleneck is resolved by distributing the com- 
+putational cost of heavy tasks. 
+ 
+2) How 6G cloudification can help the Metaverse 
+The real-time interactive nature and high demands on data 
+storage, streaming rates, and the processing power of Meta- 
+verse applications will accelerate the merging of the cloud 
+into the network, leading to highly distributed tightly- 
+integrated compute- and data- intensive networks becoming 
+universal compute platforms for next-generation digital expe- 
+riences [133]. For instance, Google Stadia [134] and Nvidia 
+GeForce Now [135] instead offload such rendering tasks to a 
+remote compute cloud—allowing the highest level of quality 
+on weaker devices such as smartphones. less latency- and 
+loss-tolerant (to provide satisfying responsiveness to inputs). 
+To an even greater extent than AAA video games, VR and 
+MR are highly computationally intensive. 
+ 
+3) Summary 
+Cloud computing technologies and their adoption by telecom 
+operators as telco clouds and cloud-native design in 6G have 
+important implications for the Metaverse. First, they allow 
+elastic Metaverse services which can be dynamically de- 
+ployed and provisioned. Moreover, the Metaverse is expected 
+to be a federated entity where different service providers, 
+applications and users are present. Cloud computing enables 
+such an environment where different Metaverse apps can 
+easily reside together and integrate. Moreover, efficiency 
+gains via consolidation and infrastructure sharing is possible. 
+6G clouds can support ultra-scalable compute storage for 
+spatiotemporal changes in the Metaverse services. However, 
+the trade-off between latency and cloud centralization is an 
+important research topic [133]. 
+ 
+F. 6G IOE 
+1) Introduction 
+The growth of IoT applications results in increasing the num- 
+ber of IoT devices, which is expected to grow up to 24 billion 
+by 2030 [136]. Furthermore, the total IoT market will also 
+grow up to USD 1.5 trillion in 2030. The dawn of Internet of 
+Everything (IoE) is envisaged to expand the IoT paradigm to 
+weave a hyper-connected network of not only things but also 
+data, people, and processes [137]. Therefore, IoE is expected 
+to integrate “Everything" for connecting, identifying, mon- 
+itoring, and making intelligent decisions towards realizing 
+new applications and services. IoE will connect many ecosys- 
+tems involving heterogeneous sensors, actuators, user equip- 
+ment, data types, services, and applications [138]. Numerous 
+heterogeneous sensors in IoE can obtain data related to var- 
+ious parameters ranging from location, speed, acceleration, 
+temperature, ambient light, humidity and air pressure to bio- 
+signals. This sensory information is paramount for the func- 
+tionality of the Metaverse as real-world information provides 
+inputs to form and update the virtual space and allow interac- 
+tions between the real world and the virtual world. Further- 
+more, Human-Computer Interaction (HCI) can provide more 
+flexible ways to access the Metaverse through human sensing 
+(e.g. gesture recognition) [5]. Numerous cameras can capture 
+video sequences from multiple angles to recognize human 
+activities through advanced AI-enabled computer vision al- 
+gorithms. In addition, the captured audio-visual information 
+can be used to predict human emotions with the aid of smart 
+wearables. These smart wearables can also capture data that 
+are useful to obtain health metrics, such as heart rate, oxygen 
+saturation level, body temperature, and electrocardiogram 
+(ECG). 6G provides the ubiquitous, uninterruptible, ultra- 
+high reliable/available and massive low-latency communi- 
+cation demanded by IoE [5], [137]. In addition, the edge- 
+6G capabilities of 6G can process massive amounts of data 
+collected from IoE devices to provide meaningful informa- 
+tion for 6G applications and services. The integration of 6G 
+and IoE will have the potential to enable many services, 
+including the internet of medical things, smart healthcare, 
+robotics, industry 5.0, smart grids, smart cities, and body area 
+networks [137]. The superior connectivity offered through 
+6G with features such as, near real-time connectivity, extreme 
+data rates, access to powerful computing resources at the 
+network edge, and massive machine-type communication 
+under strict delay constraints between heterogeneous sensory 
+devices will facilitate the smooth operation of the Metaverse 
+services and applications [139], [140]. 
+
+EEEAccessBartlomiej Siniarski et al.: Need 6G for the Metaverse Realization 
+22 
+VOLUME 4, 2016 
+ 
+ 
+ 
+2) How 6G IOE can help the Metaverse 
+6G IoE plays an important role towards enabling the Meta- 
+verse by supporting an extremely large number of users, 
+sensors, and devices to connect and communicate seamlessly 
+with extremely high data rates, ultra-low delays, and jit- 
+ters [137]. In addition, the data obtained through heteroge- 
+neous IoE devices can be processed using AI and ML through 
+powerful Multi-access Edge Computing (MEC) resources in 
+envisaged 6G networks. 
+For instance, [141] discusses the expansion of IoE and how 
+a multitude of sensors will enable the Extended Reality (XR) 
+applications in the Metaverse. This work also explores the 
+convergence of AI, MEC, Robots, and Distributed Ledger 
+Technologies, such as blockchain, towards expanding the 
+horizons of IoT towards IoE and beyond to provide a beyond 
+smartphone experience. The proposed multisensory archi- 
+tecture is capable of integrating ubiquitous and pervasive 
+computing towards enhancing human perception through ad- 
+vanced XR experiences. This is performed by utilizing wear- 
+ables and nearby network resources in the 6G era. Hence, 
+the dawn and the evolution of IoE will facilitate cross-reality 
+environments, such as the Metaverse that can fuse real and 
+virtual worlds with networked humans, avatars, and robots. 
+In addition, 6G IoE enables “wireless sensing" to sense 
+the behavior of surrounding humans and the environment [5]. 
+The functionality of IoT is expanded from simply network- 
+ing a large number of devices towards sensing the wire- 
+less network. Various wireless signals including Wireless 
+Fidelity (WiFi), Zigbee, Bluetooth, and Radio-Frequency 
+IDentification (RFID) are used as sensing mediums through 
+analyzing the signal variation (e.g. signal blocking, signal 
+reflection, and signal scattering) caused by surrounding hu- 
+mans and objects [142]. These variations may change signal 
+properties, such as phase, frequency and amplitude, which 
+can be inferred through parameters including Received Sig- 
+nal Strength (RSS), Channel State Information (CSI), and 
+Doppler shift. Together with signal preprocessing techniques, 
+such as filtering and de-noising to minimize the effect of 
+signal interference and noise, changes in the environment can 
+be recognized by identifying distinguishable unique features 
+owing to ML models. The accuracy of such predictions can 
+be enhanced through the widespread of mmWave and MIMO 
+technologies. In addition, an Integrated Sensing and Commu- 
+nication (ISAC) system, where communication systems and 
+IoE hardware are jointly designed can improve the accuracy 
+of wireless sensing while enhancing spectrum efficiency and 
+minimizing hardware implementation cost [143]. However, 
+modelling such systems, providing real-time access to pow- 
+erful computational resources for data processing through 
+advanced AI and ML schemes, and providing real-time ultra- 
+low latency communication with seamless coverage requires 
+beyond 5G network capabilities that are expected to be 
+facilitated by emerging 6G networks. 
+Ubiquitous and Pervasive Computing 
+Seamless Communication 
+AI and ML 
+XR 
+ 
+6G IoE 
+ 
+Metaverse 
+ 
+Blockchain 
+Wireless Sensing 
+Multisensory Inputs 
+Integrated Sensing and Communication 
+ 
+FIGURE 13. 6G IoE for the Metaverse 
+ 
+ 
+3) Summary 
+The evolution of IoT towards IoE with the dawn of 6G 
+provides seamless connectivity, extreme data rates, ultra-low 
+latency and ultra-high reliable/available communication, and 
+real-time access to powerful Edge-AI-enabled computational 
+resources to facilitate the Metaverse applications. 6G IoE 
+also facilitates advanced wireless sensing with mmWave and 
+MIMO technologies. The development of ISAC harnessing 
+extreme communication capabilities and Edge-AI processing 
+of 6G networks can further improve the capabilities of 6G 
+IoE that would enable emerging the Metaverse applications. 
+6G IoE features that enable the Metaverse applications are 
+illustrated in Fig. 13. 
+ 
+G. OTHER 6G TECHNOLOGIES 
+1) Extended Reality 
+Extended Reality (XR) combines Virtual Reality (VR), Aug- 
+mented Reality (AR) and Mixed Reality (MR) to blur the 
+border between physical and virtual worlds with wear- 
+ables supporting human-machine interactions with real and 
+computer-generated environments [137]. 6G is capable of 
+facilitating the massive low-latency, extremely low latency 
+and extremely high data rate demanded by XR applications. 
+Together with Edge-AI capabilities, 6G can facilitate the 
+seamless 3C (computing, caching and communication) ser- 
+vices for XR applications. Many sensors are used for the 
+data collection on user location, orientation and movements. 
+XR enables telepresence towards facilitating various aspects 
+of human life, such as work, education, shopping, health- 
+care, tourism, and entertainment [144]. For instance, [145] 
+explores how XR impacts six dimensions of workload, as 
+defined by NASA Task Load Index (NASA-TLX), namely, 
+mental demand, physical demand, temporal demand, per- 
+formance, effort, and frustration, and the overall workload 
+in the retail sector. The results of the study indicate that 
+albeit VR alone did not have a significant impact on the 
+various dimensions of workload, XR had a significant impact 
+on performing shopping-related tasks. In addition, [146] 
+
+EEEAccess1Bartlomiej Siniarski et al.: Need 6G for the Metaverse Realization 
+23 
+VOLUME 4, 2016 
+ 
+ 
+ 
+presents how users can actively engage with 3D content 
+to stimulate healthy behaviour using XR in the Metaverse. 
+This work discusses how XR can be effectively used in the 
+Metaverse to address long-term health issues and challenges. 
+Accordingly, XR can be identified as an important enabler to 
+provide services efficiently using the Metaverse. However, 
+challenges, such as limitations in physical and cognitive 
+resources, lack of experience with VR environments, and dif- 
+ficulties in using existing XR devices for prolonged periods, 
+need to be addressed towards utilizing XR for the Metaverse 
+applications in future 6G networks. 
+ 
+2) Digital Twins 
+The Metaverse applications demand next-generation net- 
+works to facilitate the high processing capabilities demanded 
+by the Metaverse applications. These can be provided 
+through the edge-AI capabilities of emerging 6G networks. 
+Digital Twins (DT) can be an important enabler of the 
+cloud-native network paradigm, which can efficiently support 
+the Metaverse [147]. DTs act as a digital representation of 
+humans and things in cyberspace. Cybertwins can provide 
+a multitude of services for the Metaverse, including, acting 
+as a communication assistant, logging network behavior, and 
+own digital assets, in a flexible, scalable, secure and reliable 
+manner. 6G IoE can play a key role towards facilitating 
+DTs. In [148], the authors discuss how to utilize a cloud 
+network operating system that can work distributively in 
+a real-time multi-agent platform to allocate 3C resources, 
+which are considered to be integral components of envisaged 
+6G networks [137]. In addition, the Metaverse applications 
+demand 6G networks to support intelligent and fully au- 
+tonomous operation. In response [149] proposes a Digital 
+Twin Edge Network (DITEN). DITEN is able to combine 
+Multi-access Edge Computing (MEC) together with DT to 
+improve the network throughput, enhance network security, 
+and reduce the cost of 3C services. DITEN continuously 
+monitors the network status for DT modelling, updating 
+and deployment and performs tasks such as routing and 
+resource management efficiently to enable applications such 
+as the Metaverse. However, there are several open issues 
+and challenges, including high-precision DT modelling, DT 
+migration for mobility and ensuring security and privacy. 
+ 
+3) Space-Air-Ground Integrated Network (SAGIN) 
+Global sensing and seamless connectivity are paramount 
+to providing uninterrupted access to the Metaverse appli- 
+cations through 6G networks. However, ground networks 
+alone are not capable of providing ubiquitous connectivity 
+to the Metaverse applications in a reliable and cost-efficient 
+fashion [149]. This is even evident in mountain areas and 
+in disastrous situations. As a solution, Non-Terrestrial Net- 
+works (NTN) Towards 3D Networking are proposed with 
+6G networks [137]. NTN provides 3D network coverage 
+and backhauling through integrating Unmanned Aerial Ve- 
+hicles (UAVs), satellites, balloons and High Altitude Plat- 
+form (HAP) stations [150].3D networking expands the NTN 
+paradigm through incorporating space, underground, and un- 
+derwater communication [151]. For instance, project 3GPP 
+TR 38.811 intends to support non-terrestrial networks by 
+considering the architecture and channel models across 
+satellite, air access, and terrestrial cellular networks [137]. 
+In addition, multi-dimensional networks named Space-Air- 
+Ground Integrated Network (SAGIN) envisage to deeply 
+integrate of space nodes (e.g. satellites), air nodes (e.g. UAVs, 
+drones, air balloons), and terrestrial network nodes (e.g. 
+5G and beyond network nodes) towards providing seamless 
+connectivity [5]. However, the seamless inter-operation and 
+resource management among multiple types of networks 
+require unified access methods and network standards to- 
+wards facilitating seamless connectivity for the Metaverse 
+applications. 
+ 
+V. 6G INTEGRATION CHALLENGES 
+In this section, we present the challenges raised by lim- 
+ited backwards compatibility with existing devices, lack of 
+standards, accountability, resilience & privacy preservation, 
+energy inefficiency, and radio design & carrier bandwidths 
+while integrating 6G with the Metaverse. 
+ 
+A. LIMITED BACKWARDS COMPATIBILITY WITH 
+EXISTING DEVICES 
+1) Introduction to issues 
+Effective communication in the Metaverse requires compati- 
+bility with previous-generation networks such as 4G and 5G. 
+Despite that, some Metaverse applications can operate on 
+existing network capabilities devices due to the deployment 
+of 6G these devices become worthless. 
+ 
+2) Possible solutions 
+A potential solution to address this issue is the backward 
+compatibility of the 6G network with existing devices that 
+enables the addition of high-capacity communication in the 
+Metaverse and also delivers faster data rates for applications 
+requiring real-time processing and integration. The 6G net- 
+works should support the features of the previous generations 
+of communications like the 5G network for some time, 
+enabling progressive migration of the Metaverse devices and 
+lowering the overall cost of 6G and the Metaverse integration. 
+In order to evaluate backward compatibility, mobile operators 
+need to consider how the 5G and 6G core networks are 
+connected and work on the 3GPP standard accordingly. 
+ 
+B. LACK OF STANDARDS 
+1) Introduction to issues 
+There is a concern among users about the Metaverse’s po- 
+tential legal consequences. If a problem arises, there is no 
+agreed-upon policy framework or set of standards for the 
+integration of 6G with the Metaverse. Any problem with the 
+integration of these technologies will affect the trust and the 
+capabilities of the 6G networks and the Metaverse. 
+
+EEEAccessBartlomiej Siniarski et al.: Need 6G for the Metaverse Realization 
+24 
+VOLUME 4, 2016 
+ 
+ 
+ 
+TABLE 4. Summary of related works 
+ 
+6G for the Metaverse - technical perspective 
+Ref. 
+Validation 
+of digital 
+assets 
+Cross platform 
+integration and 
+interoperability 
+Efficient 
+support 
+of AI 
+High speed 
+data 
+connection 
+Low 
+Latency 
+Communication 
+Computer 
+Vision 
+High 
+transaction 
+integration 
+Security 
+and 
+privacy 
+7 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+x 
+30-34 
+x 
+ 
+ 
+ 
+ 
+x 
+ 
+ 
+35-38 
+ 
+x 
+ 
+ 
+ 
+ 
+ 
+x 
+39-41 
+ 
+ 
+x 
+ 
+ 
+ 
+ 
+ 
+42-47 
+ 
+ 
+ 
+x 
+x 
+x 
+ 
+ 
+48-49 
+ 
+ 
+ 
+x 
+x 
+x 
+ 
+ 
+50-53 
+ 
+ 
+x 
+ 
+ 
+x 
+ 
+ 
+54-56 
+ 
+ 
+ 
+ 
+ 
+ 
+x 
+ 
+The role of 6G technologies for the Metaverse 
+Ref. 
+AI 
+Blockchain 
+Edge 
+OpenRAN 
+Cloud 
+IoE/IoT 
+XR 
+Digital 
+Twin 
+57-84 
+x 
+ 
+ 
+ 
+ 
+ 
+x 
+ 
+85-104 
+ 
+x 
+x 
+ 
+ 
+ 
+ 
+ 
+105-125 
+x 
+ 
+x 
+x 
+x 
+ 
+ 
+ 
+126-130 
+ 
+ 
+ 
+x 
+ 
+ 
+ 
+ 
+131-134 
+ 
+ 
+ 
+ 
+x 
+ 
+ 
+ 
+135-142 
+ 
+ 
+x 
+ 
+x 
+x 
+x 
+ 
+2, 143-148 
+x 
+x 
+x 
+ 
+x 
+x 
+x 
+x 
+ 
+2) Possible solutions 
+These challenges may be resolved by establishing a forum 
+involving service providers, researchers, and legal counsel to 
+develop standards and policy frameworks that address con- 
+cerns about user ethics, safety, and privacy while integrating 
+6G with the Metaverse. The users should be provided with 
+complete control and transparency of their data transmit- 
+ted over 6G networks, which ensures their privacy in the 
+Metaverse. As a consequence, this will raise the bar for the 
+6G communication networks and the Metaverse, which will 
+increase trust among the users. For example, though ORAN 
+is not yet fully functional it has an alliance focusing on the 
+integration issues of multiple service providers which will 
+enhance the bandwidth availability and security of the overall 
+networks. 
+ 
+C. ACCOUNTABILITY, RESILIENCE AND PRIVACY 
+PRESERVATION 
+1) Introduction to issues 
+The functionalities across 6G integrated Metaverse will be 
+mostly automated based on the decisions made by AI. Any 
+misclassification made by these decisions that cannot be 
+traced because of the black box nature of AI will have a direct 
+effect on the accountability of the 6G integrated Metaverse. 
+ 
+2) Possible solutions 
+Explainable AI (XAI) is a promising solution for this issue 
+which allows us to understand the misclassification issues 
+and improve trust in the decisions made in the 6G inte- 
+grated Metaverse. The usage of xAI will aid in pinpointing 
+the problem’s cause, assist the Metaverse’s administrators 
+in understanding the issue, and motivate them to prevent 
+a recurrence - this enhances the transparency of auditing 
+of issues related to the 6G integrated Metaverse. Addition- 
+ally, existing and newly proposed AI algorithms need to 
+be analysed considering their accountability, resilience and 
+privacy preservation capabilities within the context of future 
+networks. 
+ 
+D. ENERGY INEFFICIENCY 
+1) Introduction to issues 
+The integration of processing, communication, sensing, and 
+control capabilities inside a 6G network enables a seamless 
+transition between the virtual and physical worlds, conse- 
+quently contributing to the realisation of the Metaverse. 
+To support the requirements of the Metaverse, the cellular 
+capacity should be increased on top of the existing network 
+infrastructure. This will require 6G to deploy more micro- 
+scopic and even micro-cells in the network. This increases 
+technological and network complexity and will further strain 
+the energy efficiency and sustainability of the Metaverse. 
+ 
+2) Possible solutions 
+The integration of AI with 6G will address the issues of 
+energy efficiency and network complexity, opening the door 
+to a sustainable Metaverse ecosystem. The use of Zero touch 
+network & Service Management (ZSM) in 6G provides an 
+intelligent network for the Metaverse by enabling effective 
+data access and cross-domain data exposure by permitting 
+operational data to be maintained apart from the management 
+applications. This will also improve the reliability of commu- 
+nication in the Metaverse. 
+ 
+E. RADIO DESIGN AND CARRIER BANDWIDTHS 
+
+EEEAccessBartlomiej Siniarski et al.: Need 6G for the Metaverse Realization 
+25 
+VOLUME 4, 2016 
+ 
+ 
+ 
+1) Introduction to issues 
+One of the main goals of 6G is to achieve Tb/s data rates, 
+which requires large bandwidths (10-100 GHz spectrum for 
+THz bands), which requires an aggregation of a large number 
+of carriers to create larger bandwidth. Designing radios that 
+work at sub-THz bands present a significant challenge to the 
+industry and research due to the complexity of associated 
+RF circuits. Finding the right balance in terms of transceiver 
+efficiency, power generation, heat dissipation and the cost 
+is critical for the successful adoption of radios to sub-THz 
+bands. 
+ 
+2) Possible solutions 
+6G should provide more bandwidth and lower latency to 
+improve the overall connectivity of the Metaverse. On 6G 
+networks, there should be a 10 to 100-fold reduction in 
+latency and an increase in bandwidth capacity for the users 
+of the Metaverse to have the best immersive experiences. 
+Every piece of networking hardware must have its material, 
+component manufacture, and antenna architecture modified. 
+To comply with the 6G standard, base station operations 
+must change. 6G should depend on tightly focused, packaged 
+radio signals rather than "omnidirectional" radio channels. 
+Moreover, tightly focused radio signals use less energy, have 
+high transceiver efficiency, less heat dissipation and less cost. 
+ 
+VI. 6G METAVERSE PROJECTS 
+This section provides an overview of research projects and 
+developments that are already underway towards realizing 
+the Metaverse by harnessing the extreme network capabilities 
+of envisioned B5G and 6G mobile networks. 
+ 
+A. META 
+Meta, formerly known as Facebook, is presently working on 
+combining social media with VR and AR towards realizing 
+the Metaverse for users to work, play and interact with other 
+users online [152]. This is possible due to the extreme mobile 
+broadband capabilities, near zero latency, extreme reliability 
+and availability, and network intelligence of emerging mobile 
+networks. Users can join the Metaverse using VR head- 
+sets. The envisaged applications will range from connecting 
+people, education, training, healthcare and the workplace to 
+gaming. For instance, education technologies are expected 
+to broaden their horizons from platforms to passively absorb 
+information to learn by doing and experiencing through 3D 
+immersion. In addition, Meta is working on building the 
+Metaverse responsibly ensuring a safe, secure, and transpar- 
+ent operation. Meta has also launched the Meta Immersive 
+Learning Academy and Research Fund to collaborate in 
+building a solid and interoperable Metaverse platform. In 
+addition, their Spark AR platform enables the creation and 
+sharing of AR experiences through their apps and devices. 
+Furthermore, Meta is working on building economic oppor- 
+tunities in the Metaverse to maintain and thrive in a digital 
+economy in the future. 
+B. VR HIVE 
+VR Hive [153] aims to transform e-learning through VR 
+from the comfort of home or workplace. This project aims to 
+design and develop a fully immersive learning platform over 
+6G mobile networks to feature the Metaverse that can be used 
+to provide education, training, holographic telepresence, and 
+real-time communication. These features will be provided 
+through the extreme network capabilities of emerging 6G 
+networks, such as, near real-time ultra-reliable communica- 
+tion with ultra-low latency and edge intelligence. Relevant 
+infrastructure and network-aware immersive and adaptive en- 
+vironments will be developed to facilitate education through 
+the range of products offered through VR Hive. 
+ 
+C. 6G LIFE 
+6G Life [154] aims to facilitate the envisaged digital transfor- 
+mation where 6G mobile networks will play a significant role 
+in this revolution. The project not only aims to develop the 
+digital infrastructure and high-performance computing plat- 
+forms but also concentrates on political and social issues that 
+are required to realize future 6G applications. Realizing 6G 
+applications will require diverse communication capabilities 
+including human-machine interaction in virtual worlds, such 
+as the Metaverse. The project aims to provide innovative so- 
+lutions in the areas of scalable communication, flexible soft- 
+ware concepts, and adaptive hardware platforms. The four 
+key aspects considered by the project are latency, resilience, 
+security and sustainability. The research work, including both 
+basic and applied research, is mainly performed considering 
+Industry 4.0/5.0, and intelligent healthcare applications. 
+ 
+D. DECENTRALAND 
+Decentraland [155] is a decentralized virtual world where 
+users can create objects, trade and interact with others in a 
+virtual world. This also allows users to control policies on the 
+operation of the virtual world. Decentraland operates as a De- 
+centralized Autonomous Organization (DAO), where it owns 
+smart contracts and assets on virtual land and estate contracts, 
+wearables and other devices, and the marketplace to trade vir- 
+tual assets. These developments can be realized through the 
+capabilities of emerging 6G mobile networks, where extreme 
+mobile connectivity will facilitate seamless connectivity to 
+the virtual world. Furthermore, blockchain operation and 
+smart contract execution will be enabled through the edge 
+computing capabilities of the 6G networks. 
+Similar projects, such as Sandbox [156], Axie Infin- 
+ity [157], and Illuvium [158] also envisage harnessing the 
+capabilities of blockchain and emerging mobile networks 
+towards realizing the Metaverse. 
+ 
+E. LUXEMBOURG METAVERSE 
+The Luxembourg Metaverse [159] project aims to build a 
+digital twin of an area of Luxembourg City. These digital 
+twins can be explored by the public and the industry to 
+provide multiple working opportunities. Luxemburg 5G-6G 
+network digital twin aims to enable seamless and highly 
+
+EEEAccessBartlomiej Siniarski et al.: Need 6G for the Metaverse Realization 
+26 
+VOLUME 4, 2016 
+ 
+ 
+ 
+TABLE 5. 6G Metaverse Projects 
+ 
+Project 
+Objective 
+6G Technologies 
+AI 
+Blockchain 
+Edge 
+OpenRAN 
+Cloud 
+IoE 
+XR 
+Digital Twin 
+Meta 
+Combine social media with VR and AR to 
+facilitate work, play and other interactions 
+among users online 
+✓ 
+✓ 
+✓ 
+✓ 
+✓ 
+ 
+✓ 
+✓ 
+VR Hive 
+Transform e-learning through VR to be ac- 
+cessed at home or workplace 
+✓  
+ 
+ 
+✓ 
+ 
+✓ 
+ 
+6G Life 
+Facilitate the digital transformation towards 
+6G with human machine collaboration 
+✓  
+✓ 
+✓ 
+✓ 
+✓ 
+✓ 
+✓ 
+Decentraland 
+Create a virtual world for users to create 
+objects, trade and interact with users 
+✓ 
+✓ 
+✓ 
+ 
+✓ 
+✓ 
+✓ 
+✓ 
+Luxembourg 
+Metaverse 
+Build a digital twin of an area of Luxem- 
+bourg city 
+✓  
+ 
+ 
+✓ 
+✓ 
+✓ 
+✓ 
+ 
+capable network connectivity to facilitate real-time services 
+banking on emerging communication networks, such as be- 
+yond 5G and 6G. This project will also raise awareness of the 
+advantages and applications of the Metaverse to the public 
+and the industry. Furthermore, the project expects to optimise 
+and secure the Metaverse deployments while integrating the 
+latest developments of networks in a cost-effective and cost- 
+efficient manner. 
+The 6G technological directions explored by the 6G meta- 
+verse projects presented in this section are tabulated in TA- 
+BLE 5. 
+ 
+VII. CONCLUSION 
+This paper presents the role of 6G towards realizing the 
+Metaverse applications and services. The paper presents the 
+role of 6G technologies in the immersive, smart, scalable and 
+secure realization of the Metaverse. Furthermore, the paper 
+presents how various 6G capabilities play a key role towards 
+the realization of the Metaverse, including the role of 6G 
+for, cross-platform integration, efficient support for AI, high- 
+speed data connectivity, efficient user interaction, low latency 
+communication, computer vision, high transaction integra- 
+tion, and security and privacy protection. Consequently, the 
+integration challenges of 6G with the Metaverse are elab- 
+orated while providing several research directions towards 
+realizing the Metaverse owing to the capabilities of future 
+6G networks. 
+ 
+REFERENCES 
+[1] L.-H. Lee, T. Braud, P. Zhou, L. Wang, D. Xu, Z. Lin, A. Kumar, 
+C. Bermejo, and P. Hui, “All one needs to know about metaverse: A 
+complete survey on technological singularity, virtual ecosystem, and 
+research agenda,” arXiv preprint arXiv:2110.05352, 2021. 
+[2] “Cloud vr network solution white paper.” 
+[3] T. Huynh-The, Q.-V. Pham, X.-Q. Pham, T. T. Nguyen, Z. Han, and D.-S. 
+Kim, “Artificial intelligence for the metaverse: A survey,” arXiv preprint 
+arXiv:2202.10336, 2022. 
+[4] Y. Wang, Z. Su, N. Zhang, R. Xing, D. Liu, T. H. Luan, and X. Shen, 
+“A survey on metaverse: Fundamentals, security, and privacy,” IEEE 
+Communications Surveys & Tutorials, pp. 1–1, 2022. 
+[5] F. Tang, X. Chen, M. Zhao, and N. Kato, “The roadmap of com- 
+munication and networking in 6g for the metaverse,” IEEE Wireless 
+Communications, 2022. 
+[6] M. A. I. Mozumder, M. M. Sheeraz, A. Athar, S. Aich, and H.-C. Kim, 
+“Overview: technology roadmap of the future trend of metaverse based 
+on iot, blockchain, ai technique, and medical domain metaverse activity,” 
+in 2022 24th International Conference on Advanced Communication 
+Technology (ICACT), pp. 256–261, IEEE, 2022. 
+[7] M. Xu, W. C. Ng, W. Y. B. Lim, J. Kang, Z. Xiong, D. Niyato, Q. Yang, 
+X. Sherman Shen, and C. Miao, “A Full Dive into Realizing the Edge- 
+enabled Metaverse: Visions, Enabling Technologies,and Challenges,” 
+arXiv e-prints, p. arXiv:2203.05471, Mar. 2022. 
+[8] L. Chang, Z. Zhang, P. Li, S. Xi, W. Guo, Y. Shen, Z. Xiong, 
+J. Kang, D. Niyato, X. Qiao, et al., “6g-enabled edge ai for metaverse: 
+Challenges, methods, and future research directions,” arXiv preprint 
+arXiv:2204.06192, 2022. 
+[9] C. D. Alwis, A. Kalla, Q.-V. Pham, P. Kumar, K. Dev, W.-J. Hwang, 
+and M. Liyanage, “Survey on 6g frontiers: Trends, applications, require- 
+ments, technologies and future research,” IEEE Open Journal of the 
+Communications Society, vol. 2, pp. 836–886, 2021. 
+[10] T. S. Rappaport, Y. Xing, O. Kanhere, S. Ju, A. Madanayake, S. Mandal, 
+A. Alkhateeb, and G. C. Trichopoulos, “Wireless communications and 
+applications above 100 ghz: Opportunities and challenges for 6g and 
+beyond,” IEEE access, vol. 7, pp. 78729–78757, 2019. 
+[11] A. Salh, L. Audah, N. S. M. Shah, A. Alhammadi, Q. Abdullah, Y. H. 
+Kim, S. A. Al-Gailani, S. A. Hamzah, B. A. F. Esmail, and A. A. 
+Almohammedi, “A survey on deep learning for ultra-reliable and low- 
+latency communications challenges on 6g wireless systems,” IEEE Ac- 
+cess, vol. 9, pp. 55098–55131, 2021. 
+[12] X. Shen, W. Liao, and Q. Yin, “A novel wireless resource management 
+for the 6g-enabled high-density internet of things,” IEEE Wireless Com- 
+munications, vol. 29, no. 1, pp. 32–39, 2022. 
+[13] Y. Chen, W. Liu, Z. Niu, Z. Feng, Q. Hu, and T. Jiang, “Pervasive 
+intelligent endogenous 6g wireless systems: Prospects, theories and 
+key technologies,” Digital communications and networks, vol. 6, no. 3, 
+pp. 312–320, 2020. 
+[14] X. Shen, W. Liao, and Q. Yin, “A novel wireless resource management 
+for the 6g-enabled high-density internet of things,” IEEE Wireless Com- 
+munications, vol. 29, no. 1, pp. 32–39, 2022. 
+[15] S. Kraus, D. K. Kanbach, P. M. Krysta, M. M. Steinhoff, and N. Tomini, 
+“Facebook and the creation of the metaverse: radical business model 
+innovation or incremental transformation?,” International Journal of En- 
+trepreneurial Behavior & Research, 2022. 
+[16] S. Hollensen, P. Kotler, and M. O. Opresnik, “Metaverse–the new mar- 
+keting universe,” Journal of Business Strategy, 2022. 
+[17] H. R. Hasan and K. Salah, “Proof of delivery of digital assets using 
+blockchain and smart contracts,” IEEE Access, vol. 6, pp. 65439–65448, 
+2018. 
+[18] Å. Fast-Berglund, L. Gong, and D. Li, “Testing and validating extended 
+reality (xr) technologies in manufacturing,” Procedia Manufacturing, 
+vol. 25, pp. 31–38, 2018. 
+[19] A. Siyaev and G.-S. Jo, “Neuro-symbolic speech understanding in air- 
+craft maintenance metaverse,” IEEE Access, vol. 9, pp. 154484–154499, 
+2021. 
+[20] T. Zhang, L. Gao, C. He, M. Zhang, B. Krishnamachari, and A. S. 
+Avestimehr, “Federated learning for the internet of things: Applications, 
+challenges, and opportunities,” IEEE Internet of Things Magazine, vol. 5, 
+no. 1, pp. 24–29, 2022. 
+[21] Y. Lu, X. Huang, K. Zhang, S. Maharjan, and Y. Zhang, 
+“Communication-efficient federated learning for digital twin edge 
+networks in industrial iot,” IEEE Transactions on Industrial Informatics, 
+vol. 17, no. 8, pp. 5709–5718, 2020. 
+
+EEEAccessBartlomiej Siniarski et al.: Need 6G for the Metaverse Realization 
+27 
+VOLUME 4, 2016 
+ 
+ 
+ 
+[22] I. Skalidis, O. Muller, and S. Fournier, “Cardioverse: The cardiovascular 
+medicine in the era of metaverse,” Trends in Cardiovascular Medicine, 
+2022. 
+[23] Surfing the Metaverse’s Real Estate Boom. 
+[24] A. Beniiche, S. Rostami, and M. Maier, “Society 5.0: Internet as if people 
+mattered,” IEEE Wireless Communications, 2022. 
+[25] D. Gursoy, S. Malodia, and A. Dhir, “The metaverse in the hospitality 
+and tourism industry: An overview of current trends and future research 
+directions,” Journal of Hospitality Marketing & Management, pp. 1–8, 
+2022. 
+[26] D. Shin, “The actualization of meta affordances: Conceptualizing af- 
+fordance actualization in the metaverse games,” Computers in Human 
+Behavior, vol. 133, p. 107292, 2022. 
+[27] I. A. Ilyina, E. A. Eltikova, K. A. Uvarova, and S. D. Chelysheva, 
+“Metaverse-death to offline communication or empowerment of inter- 
+action?,” in 2022 Communication Strategies in Digital Society Seminar 
+(ComSDS), pp. 117–119, IEEE, 2022. 
+[28] B. Falchuk, S. Loeb, and R. Neff, “The social metaverse: Battle for 
+privacy,” IEEE Technology and Society Magazine, vol. 37, no. 2, pp. 52– 
+61, 2018. 
+[29] T. R. Gadekallu, T. Huynh-The, W. Wang, G. Yenduri, P. Ranaweera, 
+Q.-V. Pham, D. B. da Costa, and M. Liyanage, “Blockchain for the 
+metaverse: A review,” arXiv preprint arXiv:2203.09738, 2022. 
+[30] J. Kim, “Advertising in the metaverse: Research agenda,” Journal of 
+Interactive Advertising, vol. 21, no. 3, pp. 141–144, 2021. 
+[31] M. Nadini, L. Alessandretti, F. Di Giacinto, M. Martino, L. M. Aiello, 
+and A. Baronchelli, “Mapping the nft revolution: market trends, trade 
+networks, and visual features,” Scientific reports, vol. 11, no. 1, pp. 1–11, 
+2021. 
+[32] H. Ko, B. Son, Y. Lee, H. Jang, and J. Lee, “The economic value of 
+nft: Evidence from a portfolio analysis using mean–variance framework,” 
+Finance Research Letters, vol. 47, p. 102784, 2022. 
+[33] A. Park, J. Kietzmann, L. Pitt, and A. Dabirian, “The evolution of nonfun- 
+gible tokens: Complexity and novelty of nft use-cases,” IT Professional, 
+vol. 24, no. 1, pp. 9–14, 2022. 
+[34] D. Vidal-Tomás, “The new crypto niche: Nfts, play-to-earn, and meta- 
+verse tokens,” Finance Research Letters, p. 102742, 2022. 
+[35] C. Hackl, D. Lueth, and T. Di Bartolo, Navigating the Metaverse: A 
+Guide to Limitless Possibilities in a Web 3.0 World. John Wiley & Sons, 
+2022. 
+[36] E. Lee, Y.-D. Seo, S.-R. Oh, and Y.-G. Kim, “A survey on standards for 
+interoperability and security in the internet of things,” IEEE Communi- 
+cations Surveys & Tutorials, vol. 23, no. 2, pp. 1020–1047, 2021. 
+[37] A. Hazra, M. Adhikari, T. Amgoth, and S. N. Srirama, “A comprehen- 
+sive survey on interoperability for iiot: taxonomy, standards, and future 
+directions,” ACM Computing Surveys (CSUR), vol. 55, no. 1, pp. 1–35, 
+2021. 
+[38] M. Sparkes, “What is a metaverse,” 2021. 
+[39] S. A. Khan, I. Shayea, M. Ergen, and H. Mohamad, “Handover man- 
+agement over dual connectivity in 5g technology with future ultra-dense 
+mobile heterogeneous networks: A review,” Engineering Science and 
+Technology, an International Journal, p. 101172, 2022. 
+[40] S. Mystakidis, “Metaverse,” Encyclopedia, vol. 2, no. 1, pp. 486–497, 
+2022. 
+[41] M. Campbell and M. Jovanovic, “Digital self: The next evolution of the 
+digital human,” Computer, vol. 55, no. 04, pp. 82–86, 2022. 
+[42] B. K. Wiederhold, “Ready (or not) player one: initial musings on the 
+metaverse,” 2022. 
+[43] H. Duan, J. Li, S. Fan, Z. Lin, X. Wu, and W. Cai, “Metaverse for social 
+good: A university campus prototype,” in Proceedings of the 29th ACM 
+International Conference on Multimedia, pp. 153–161, 2021. 
+[44] M. Inomata, W. Yamada, N. Kuno, M. Sasaki, K. Kitao, M. Nakamura, 
+H. Ishikawa, and Y. Oda, “Terahertz propagation characteristics for 6g 
+mobile communication systems,” in 2021 15th European Conference on 
+Antennas and Propagation (EuCAP), pp. 1–5, IEEE, 2021. 
+[45] D.-I. D. Han, Y. Bergs, and N. Moorhouse, “Virtual reality consumer 
+experience escapes: preparing for the metaverse,” Virtual Reality, pp. 1– 
+16, 2022. 
+[46] C. Girvan, “What is a virtual world? definition and classification,” Educa- 
+tional Technology Research and Development, vol. 66, no. 5, pp. 1087– 
+1100, 2018. 
+[47] D. M. Markowitz, R. Laha, B. P. Perone, R. D. Pea, and J. N. Bailenson, 
+“Immersive virtual reality field trips facilitate learning about climate 
+change,” Frontiers in psychology, vol. 9, p. 2364, 2018. 
+[48] D. Mendes, F. M. Caputo, A. Giachetti, A. Ferreira, and J. Jorge, “A 
+survey on 3d virtual object manipulation: From the desktop to immersive 
+virtual environments,” in Computer graphics forum, vol. 38, pp. 21–45, 
+Wiley Online Library, 2019. 
+[49] R. Suzuki, A. Karim, T. Xia, H. Hedayati, and N. Marquardt, “Augmented 
+reality and robotics: A survey and taxonomy for ar-enhanced human- 
+robot interaction and robotic interfaces,” in CHI Conference on Human 
+Factors in Computing Systems, pp. 1–33, 2022. 
+[50] M. Adhikari and A. Hazra, “6g-enabled ultra-reliable low-latency com- 
+munication in edge networks,” IEEE Communications Standards Maga- 
+zine, vol. 6, no. 1, pp. 67–74, 2022. 
+[51] M.-H. Guo, T.-X. Xu, J.-J. Liu, Z.-N. Liu, P.-T. Jiang, T.-J. Mu, S.-H. 
+Zhang, R. R. Martin, M.-M. Cheng, and S.-M. Hu, “Attention mecha- 
+nisms in computer vision: A survey,” Computational Visual Media, pp. 1– 
+38, 2022. 
+[52] T. Braud, C. B. Fernández, and P. Hui, “Scaling-up ar: University campus 
+as a physical-digital metaverse,” in 2022 IEEE Conference on Virtual Re- 
+ality and 3D User Interfaces Abstracts and Workshops (VRW), pp. 169– 
+175, IEEE, 2022. 
+[53] H. Kumar et al., “Epidemiological mucormycosis treatment and diagno- 
+sis challenges using the adaptive properties of computer vision techniques 
+based approach: a review,” Multimedia Tools and Applications, pp. 1–29, 
+2022. 
+[54] C. Yeh, G. Do Jo, Y.-J. Ko, and H. K. Chung, “Perspectives on 6g wireless 
+communications,” ICT Express, 2022. 
+[55] Y. Liu, F. R. Yu, X. Li, H. Ji, and V. C. Leung, “Decentralized resource 
+allocation for video transcoding and delivery in blockchain-based system 
+with mobile edge computing,” IEEE Transactions on Vehicular Technol- 
+ogy, vol. 68, no. 11, pp. 11169–11185, 2019. 
+[56] D. Frey, J. Royan, R. Piegay, A.-M. Kermarrec, E. Anceaume, and 
+F. Le Fessant, “Solipsis: A decentralized architecture for virtual envi- 
+ronments,” in 1st International Workshop on Massively Multiuser Virtual 
+Environments, 2008. 
+[57] C. Nguyen, D. Hoang, D. Nguyen, and E. Dutkiewicz, “Metachain: a 
+novel blockchain-based framework for metaverse applications. arxiv,” 
+arXiv preprint arXiv:2201.00759, 2021. 
+[58] T. Huynh-The, Q.-V. Pham, X.-Q. Pham, T. T. Nguyen, Z. Han, and D.-S. 
+Kim, “Artificial intelligence for the metaverse: A survey,” arXiv preprint 
+arXiv:2202.10336, 2022. 
+[59] A. Fuad and M. Al-Yahya, “Recent developments in arabic conversa- 
+tional ai: A literature review,” IEEE Access, vol. 10, pp. 23842–23859, 
+2022. 
+[60] P.-S. Chiu, J.-W. Chang, M.-C. Lee, C.-H. Chen, and D.-S. Lee, “En- 
+abling intelligent environment by the design of emotionally aware virtual 
+assistant: A case of smart campus,” IEEE Access, vol. 8, pp. 62032– 
+62041, 2020. 
+[61] F. Cui, Q. Cui, and Y. Song, “A survey on learning-based approaches for 
+modeling and classification of human–machine dialog systems,” IEEE 
+Transactions on Neural Networks and Learning Systems, vol. 32, no. 4, 
+pp. 1418–1432, 2021. 
+[62] I. Giorgi, B. Golosio, M. Esposito, A. Cangelosi, and G. L. Masala, 
+“Modeling multiple language learning in a developmental cognitive 
+architecture,” IEEE Transactions on Cognitive and Developmental Sys- 
+tems, vol. 13, no. 4, pp. 922–933, 2021. 
+[63] D. W. Otter, J. R. Medina, and J. K. Kalita, “A survey of the usages of 
+deep learning for natural language processing,” IEEE Transactions on 
+Neural Networks and Learning Systems, vol. 32, no. 2, pp. 604–624, 
+2021. 
+[64] G. Xu, Y. Meng, X. Qiu, Z. Yu, and X. Wu, “Sentiment analysis of 
+comment texts based on bilstm,” IEEE Access, vol. 7, pp. 51522–51532, 
+2019. 
+[65] Y. Cheng, L. Yao, G. Xiang, G. Zhang, T. Tang, and L. Zhong, “Text sen- 
+timent orientation analysis based on multi-channel cnn and bidirectional 
+gru with attention mechanism,” IEEE Access, vol. 8, pp. 134964–134975, 
+2020. 
+[66] Z. Hu, A. Bulling, S. Li, and G. Wang, “Fixationnet: Forecasting eye 
+fixations in task-oriented virtual environments,” IEEE Transactions on 
+Visualization and Computer Graphics, vol. 27, pp. 2681–2690, Mar. 
+2021. 
+[67] R. Miller, N. K. Banerjee, and S. Banerjee, “Combining real-world 
+constraints on user behavior with deep neural networks for virtual reality 
+(vr) biometrics,” in 2022 IEEE Conference on Virtual Reality and 3D 
+User Interfaces (VR), (Christchurch, New Zealand), pp. 409–418, 2022. 
+
+EEEAccessBartlomiej Siniarski et al.: Need 6G for the Metaverse Realization 
+28 
+VOLUME 4, 2016 
+ 
+ 
+ 
+[68] Y. Jin, M. Chen, T. Goodall, A. Patney, and A. C. Bovik, “Subjective and 
+objective quality assessment of 2d and 3d foveated video compression 
+in virtual reality,” IEEE Transactions on Image Processing, vol. 30, 
+pp. 5905–5919, Jun. 2021. 
+[69] T. Huynh-The, C.-H. Hua, N. A. Tu, T. Hur, J. Bang, D. Kim, M. B. 
+Amin, B. H. Kang, H. Seung, S.-Y. Shin, et al., “Hierarchical topic 
+modeling with pose-transition feature for action recognition using 3d 
+skeleton data,” Information Sciences, vol. 444, pp. 20–35, May 2018. 
+[70] T. Huynh-The, C.-H. Hua, N. A. Tu, and D.-S. Kim, “Learning 3d 
+spatiotemporal gait feature by convolutional network for person identi- 
+fication,” Neurocomputing, vol. 397, pp. 192–202, Jul. 2020. 
+[71] T. Huynh-The, C.-H. Hua, and D.-S. Kim, “Encoding pose features 
+to images with data augmentation for 3-d action recognition,” IEEE 
+Transactions on Industrial Informatics, vol. 16, pp. 3100–3111, May 
+2020. 
+[72] C.-H. Hua, T. Huynh-The, and S. Lee, “Convolutional networks with 
+bracket-style decoder for semantic scene segmentation,” in Proc. 2018 
+IEEE International Conference on Systems, Man, and Cybernetics 
+(SMC), (Miyazaki, Japan), pp. 2980–2985, IEEE, 2018. 
+[73] C.-H. Hua, T. Huynh-The, S.-H. Bae, and S. Lee, “Cross-attentional 
+bracket-shaped convolutional network for semantic image segmentation,” 
+Information Sciences, vol. 539, pp. 277–294, Oct. 2020. 
+[74] L.-C. Chen, G. Papandreou, I. Kokkinos, K. Murphy, and A. L. Yuille, 
+“Deeplab: Semantic image segmentation with deep convolutional nets, 
+atrous convolution, and fully connected crfs,” IEEE Transactions on 
+Pattern Analysis and Machine Intelligence, vol. 40, pp. 834–848, Apr. 
+2018. 
+[75] J. Kim, H. Zeng, D. Ghadiyaram, S. Lee, L. Zhang, and A. C. Bovik, 
+“Deep convolutional neural models for picture-quality prediction: Chal- 
+lenges and solutions to data-driven image quality assessment,” IEEE 
+Signal Processing Magazine, vol. 34, pp. 130–141, Nov. 2017. 
+[76] R. Ranjan, V. M. Patel, and R. Chellappa, “Hyperface: A deep multi-task 
+learning framework for face detection, landmark localization, pose esti- 
+mation, and gender recognition,” IEEE Transactions on Pattern Analysis 
+and Machine Intelligence, vol. 41, pp. 121–135, Dec. 2019. 
+[77] X. Wang, L. Gao, J. Song, and H. Shen, “Beyond frame-level cnn: 
+Saliency-aware 3-d cnn with lstm for video action recognition,” IEEE 
+Signal Processing Letters, vol. 24, pp. 510–514, Sep. 2017. 
+[78] Y. Xin, L. Kong, Z. Liu, Y. Chen, Y. Li, H. Zhu, M. Gao, H. Hou, and 
+C. Wang, “Machine learning and deep learning methods for cybersecu- 
+rity,” IEEE Access, vol. 6, pp. 35365–35381, 2018. 
+[79] R. Vinayakumar, M. Alazab, K. P. Soman, P. Poornachandran, A. Al- 
+Nemrat, and S. Venkatraman, “Deep learning approach for intelligent 
+intrusion detection system,” IEEE Access, vol. 7, pp. 41525–41550, 
+2019. 
+[80] A. Jamalipour and S. Murali, “A taxonomy of machine-learning-based 
+intrusion detection systems for the internet of things: A survey,” IEEE 
+Internet of Things Journal, vol. 9, no. 12, pp. 9444–9466, 2022. 
+[81] Y. Liu, J. Wang, J. Li, S. Niu, L. Wu, and H. Song, “Zero-bias deep- 
+learning-enabled quickest abnormal event detection in iot,” IEEE Internet 
+of Things Journal, vol. 9, pp. 11385–11395, Jul. 2022. 
+[82] Z. Lv, L. Qiao, J. Li, and H. Song, “Deep-learning-enabled security 
+issues in the internet of things,” IEEE Internet of Things Journal, vol. 8, 
+pp. 9531–9538, Jun. 2021. 
+[83] A. Uprety and D. B. Rawat, “Reinforcement learning for iot security: 
+A comprehensive survey,” IEEE Internet of Things Journal, vol. 8, 
+pp. 8693–8706, Jun. 2021. 
+[84] X. Liu, H. Li, G. Xu, S. Liu, Z. Liu, and R. Lu, “Padl: Privacy-aware and 
+asynchronous deep learning for iot applications,” IEEE Internet of Things 
+Journal, vol. 7, pp. 6955–6969, Aug. 2020. 
+[85] W. Zhang, B. Jiang, M. Li, and X. Lin, “Privacy-preserving aggregate 
+mobility data release: An information-theoretic deep reinforcement learn- 
+ing approach,” IEEE Transactions on Information Forensics and Security, 
+vol. 17, pp. 849–864, 2022. 
+[86] N. Deepa, Q.-V. Pham, D. C. Nguyen, S. Bhattacharya, B. Prabadevi, 
+T. R. Gadekallu, P. K. R. Maddikunta, F. Fang, and P. N. Pathirana, “A 
+survey on blockchain for big data: Approaches, opportunities, and future 
+directions,” Future Generation Computer Systems, vol. 131, pp. 209–226, 
+Jun. 2022. 
+[87] C. T. Nguyen, D. T. Hoang, D. N. Nguyen, and E. Dutkiewicz, 
+“Metachain: A novel blockchain-based framework for metaverse appli- 
+cations,” arXiv preprint arXiv:2201.00759, 2022. 
+[88] K. Cheng, S. Quan, and J. Yan, “A blockchain-based crowdsourcing 
+system for large scale environmental data acquisition,” in 2021 IEEE 24th 
+International Conference on Computer Supported Cooperative Work in 
+Design (CSCWD), (Dailan, China), pp. 855–860, May 2021. 
+[89] C. H. Liu, Q. Lin, and S. Wen, “Blockchain-enabled data collection 
+and sharing for industrial iot with deep reinforcement learning,” IEEE 
+Transactions on Industrial Informatics, vol. 15, pp. 3516–3526, Jun. 
+2019. 
+[90] M. Li, J. Weng, A. Yang, W. Lu, Y. Zhang, L. Hou, J.-N. Liu, Y. Xiang, 
+and R. H. Deng, “Crowdbc: A blockchain-based decentralized framework 
+for crowdsourcing,” IEEE Transactions on Parallel and Distributed Sys- 
+tems, vol. 30, pp. 1251–1266, Jun. 2019. 
+[91] U. Bodkhe, S. Tanwar, K. Parekh, P. Khanpara, S. Tyagi, N. Kumar, and 
+M. Alazab, “Blockchain for industry 4.0: A comprehensive review,” IEEE 
+Access, vol. 8, pp. 79764–79800, 2020. 
+[92] R. Li, T. Song, B. Mei, H. Li, X. Cheng, and L. Sun, “Blockchain 
+for large-scale internet of things data storage and protection,” IEEE 
+Transactions on Services Computing, vol. 12, pp. 762–771, Sept.-Oct. 
+2019. 
+[93] H. Shafagh, L. Burkhalter, A. Hithnawi, and S. Duquennoy, “Towards 
+blockchain-based auditable storage and sharing of iot data,” in Proceed- 
+ings of the 2017 on Cloud Computing Security Workshop, (Dallas, Texas, 
+USA), p. 45–50, Nov. 2017. 
+[94] W. Liang, Y. Fan, K.-C. Li, D. Zhang, and J.-L. Gaudiot, “Secure data 
+storage and recovery in industrial blockchain network environments,” 
+IEEE Transactions on Industrial Informatics, vol. 16, pp. 6543–6552, 
+Oct. 2020. 
+[95] R. Jabbar, N. Fetais, M. Krichen, and K. Barkaoui, “Blockchain tech- 
+nology for healthcare: Enhancing shared electronic health record inter- 
+operability and integrity,” in 2020 IEEE International Conference on 
+Informatics, IoT, and Enabling Technologies (ICIoT), (Doha, Qatar), 
+pp. 310–317, Feb. 2020. 
+[96] W. J. Gordon and C. Catalini, “Blockchain technology for healthcare: Fa- 
+cilitating the transition to patient-driven interoperability,” Computational 
+and Structural Biotechnology Journal, vol. 16, pp. 224–230, Jul. 2018. 
+[97] X. Liu, S. X. Sun, and G. Huang, “Decentralized services computing 
+paradigm for blockchain-based data governance: Programmability, inter- 
+operability, and intelligence,” IEEE Transactions on Services Computing, 
+vol. 13, pp. 343–355, Mar.-Apr. 2020. 
+[98] S. Schulte, M. Sigwart, P. Frauenthaler, and M. Borkowski, “Towards 
+blockchain interoperability,” in Proc. International Conference on Busi- 
+ness Process Management, (Vienna, Austria), pp. 3–10, Springer, 2019. 
+[99] Y. Jiang, C. Wang, Y. Wang, and L. Gao, “A cross-chain solution to 
+integrating multiple blockchains for iot data management,” Sensors, 
+vol. 19, May 2019. 
+[100] 
+B. Pillai, K. Biswas, and V. Muthukkumarasamy, “Cross-chain inter- 
+operability among blockchain-based systems using transactions,” The 
+Knowledge Engineering Review, vol. 35, p. e23, Jun. 2020. 
+[101] 
+P. Wei, D. Wang, Y. Zhao, S. K. S. Tyagi, and N. Kumar, “Blockchain 
+data-based cloud data integrity protection mechanism,” Future Genera- 
+tion Computer Systems, vol. 102, pp. 902–911, Jan. 2020. 
+[102] 
+Y.-J. Chen, L.-C. Wang, and S. Wang, “Stochastic blockchain for iot 
+data integrity,” IEEE Transactions on Network Science and Engineering, 
+vol. 7, pp. 373–384, Jan.-March 2020. 
+[103] 
+Q. Feng, D. He, S. Zeadally, M. K. Khan, and N. Kumar, “A survey 
+on privacy protection in blockchain system,” Journal of Network and 
+Computer Applications, vol. 126, pp. 45–58, Jan. 2019. 
+[104] 
+X. Xu, Q. Liu, X. Zhang, J. Zhang, L. Qi, and W. Dou, “A blockchain- 
+powered crowdsourcing method with privacy preservation in mobile en- 
+vironment,” IEEE Transactions on Computational Social Systems, vol. 6, 
+pp. 1407–1419, Dec. 2019. 
+[105] 
+Y. Wu, H.-N. Dai, H. Wang, and K.-K. R. Choo, “Blockchain-based 
+privacy preservation for 5g-enabled drone communications,” IEEE Net- 
+work, vol. 35, pp. 50–56, Jan./Feb. 2021. 
+[106] 
+S. Dhelim, T. Kechadi, L. Chen, N. Aung, H. Ning, and L. Atzori, 
+“Edge-enabled metaverse: The convergence of metaverse and mobile 
+edge computing,” arXiv preprint arXiv:2205.02764, 2022. 
+[107] 
+J. D. N. Dionisio, W. G. B. III, and R. Gilbert, “3d virtual worlds and the 
+metaverse: Current status and future possibilities,” ACM Comput. Surv., 
+vol. 45, jul 2013. 
+[108] 
+Credit Suisse, “Metaverse: A guide to the next-gen internet,” 2022. 
+Accessed on 27.08.2022. 
+[109] 
+A. Bujari, O. Gaggi, M. Luglio, C. E. Palazzi, G. Quadrio, C. Roseti, and 
+F. Zampognaro, “Addressing the bandwidth demand of immersive appli- 
+cations through nfv in a 5g network,” Mobile Networks and Applications, 
+vol. 25, no. 3, pp. 1114–1121, 2020. 
+
+EEEAccessBartlomiej Siniarski et al.: Need 6G for the Metaverse Realization 
+29 
+VOLUME 4, 2016 
+ 
+ 
+ 
+[110] P. Hu, S. Dhelim, H. Ning, and T. Qiu, “Survey on fog computing: 
+architecture, key technologies, applications and open issues,” Journal of 
+Network and Computer Applications, vol. 98, pp. 27–42, 2017. 
+[111] A. Naouri, H. Wu, N. A. Nouri, S. Dhelim, and H. Ning, “A novel 
+framework for mobile-edge computing by optimizing task offloading,” 
+IEEE Internet of Things Journal, vol. 8, no. 16, pp. 13065–13076, 2021. 
+[112] W. Zhang, J. Chen, Y. Zhang, and D. Raychaudhuri, “Towards efficient 
+edge cloud augmentation for virtual reality mmogs,” in Proceedings of 
+the Second ACM/IEEE Symposium on Edge Computing, SEC ’17, (New 
+York, NY, USA), Association for Computing Machinery, 2017. 
+[113] W. Y. B. Lim, Z. Xiong, D. Niyato, X. Cao, C. Miao, S. Sun, and Q. Yang, 
+“Realizing the Metaverse with Edge Intelligence: A Match Made in 
+Heaven,” arXiv e-prints, p. arXiv:2201.01634, Jan. 2022. 
+[114] K. B. Letaief, Y. Shi, J. Lu, and J. Lu, “Edge artificial intelligence for 
+6g: Vision, enabling technologies, and applications,” IEEE Journal on 
+Selected Areas in Communications, vol. 40, no. 1, pp. 5–36, 2022. 
+[115] Z. Wang, J. Qiu, Y. Zhou, Y. Shi, L. Fu, W. Chen, and K. B. Letaief, 
+“Federated learning via intelligent reflecting surface,” IEEE Transactions 
+on Wireless Communications, vol. 21, no. 2, pp. 808–822, 2022. 
+[116] M. Xu, D. Niyato, J. Kang, Z. Xiong, C. Miao, and D. I. Kim, “Wireless 
+edge-empowered metaverse: A learning-based incentive mechanism for 
+virtual reality,” in ICC 2022-IEEE International Conference on Commu- 
+nications, pp. 5220–5225, IEEE, 2022. 
+[117] Y. Sun, Z. Chen, M. Tao, and H. Liu, “Communications, caching, and 
+computing for mobile virtual reality: Modeling and tradeoff,” IEEE 
+Transactions on Communications, vol. 67, no. 11, pp. 7573–7586, 2019. 
+[118] Y. Jiang, J. Kang, D. Niyato, X. Ge, Z. Xiong, C. Miao, Xuemin, and 
+Shen, “Reliable Distributed Computing for Metaverse: A Hierarchical 
+Game-Theoretic Approach,” arXiv e-prints, p. arXiv:2111.10548, Nov. 
+2021. 
+[119] X. Huang, K. Zhang, F. Wu, and S. Leng, “Collaborative machine learn- 
+ing for energy-efficient edge networks in 6g,” IEEE Network, vol. 35, 
+no. 6, pp. 12–19, 2021. 
+[120] X. Wang, Y. Han, C. Wang, Q. Zhao, X. Chen, and M. Chen, “In-edge ai: 
+Intelligentizing mobile edge computing, caching and communication by 
+federated learning,” IEEE Network, vol. 33, no. 5, pp. 156–165, 2019. 
+[121] W. Y. B. Lim, N. C. Luong, D. T. Hoang, Y. Jiao, Y.-C. Liang, Q. Yang, 
+D. Niyato, and C. Miao, “Federated learning in mobile edge networks: 
+A comprehensive survey,” IEEE Communications Surveys & Tutorials, 
+vol. 22, no. 3, pp. 2031–2063, 2020. 
+[122] X. Wang, Y. Han, V. C. M. Leung, D. Niyato, X. Yan, and X. Chen, 
+“Convergence of edge computing and deep learning: A comprehensive 
+survey,” IEEE Communications Surveys & Tutorials, vol. 22, no. 2, 
+pp. 869–904, 2020. 
+[123] Y. Liu, Y. Zhu, and J. J. Yu, “Resource-constrained federated edge learn- 
+ing with heterogeneous data: Formulation and analysis,” IEEE Transac- 
+tions on Network Science and Engineering, vol. 9, no. 5, pp. 3166–3178, 
+2022. 
+[124] T. Mikolov, A. Deoras, D. Povey, L. Burget, and J. Cˇ ernocký, “Strategies 
+for training large scale neural network language models,” in 2011 IEEE 
+Workshop on Automatic Speech Recognition & Understanding, pp. 196– 
+201, 2011. 
+[125] Z. Li, S. Zhuang, S. Guo, D. Zhuo, H. Zhang, D. Song, and I. Stoica, “Ter- 
+apipe: Token-level pipeline parallelism for training large-scale language 
+models,” in International Conference on Machine Learning, pp. 6543– 
+6552, PMLR, 2021. 
+[126] Y. Lu, X. Huang, K. Zhang, S. Maharjan, and Y. Zhang, “Low-latency 
+federated learning and blockchain for edge association in digital twin 
+empowered 6g networks,” IEEE Transactions on Industrial Informatics, 
+vol. 17, no. 7, pp. 5098–5107, 2021. 
+[127] N.-N. Dao, Q.-V. Pham, N. H. Tu, T. T. Thanh, V. N. Q. Bao, D. S. 
+Lakew, and S. Cho, “Survey on aerial radio access networks: Toward a 
+comprehensive 6g access infrastructure,” IEEE Communications Surveys 
+& Tutorials, vol. 23, no. 2, pp. 1193–1225, 2021. 
+[128] “Europe urged to act now to build open ran ecosystem.” Accessed on 
+24.08.2022. 
+[129] “Openran begins work on ai/ml.” Accessed on 24.08.2022. 
+[130] A. S. Abdalla, P. S. Upadhyaya, V. K. Shah, and V. Marojevic, “Toward 
+next generation open radio access networks–what o-ran can and cannot 
+do!,” IEEE Network, 2022. 
+[131] F. Tang, X. Chen, M. Zhao, and N. Kato, “The roadmap of com- 
+munication and networking in 6g for the metaverse,” IEEE Wireless 
+Communications, pp. 1–15, 2022. 
+[132] D. Linthicum, “Cloud computing and the metaverse,” 2022. Accessed on 
+27.07.2022. 
+[133] Y. Cai, J. Llorca, A. M. Tulino, and A. F. Molisch, “Compute-and data-
+intensive networks: The key to the metaverse,” arXiv preprint 
+arXiv:2204.02001, 2022. 
+[134] Google, “Google Stadia.” Accessed on 27.08.2022. 
+[135] Nvidia, “Nvidia GeForce Now.” Accessed on 25.08.2022. 
+[136] “Global IoT Market will Grow to 24.1 Billion Devices in 2030, Gener- 
+ating $1.5 Trillion Annual Revenue.” Transforma Insights research, May, 
+2020. [Accessed on 09.06.2022]. 
+[137] C. De Alwis, A. Kalla, Q.-V. Pham, P. Kumar, K. Dev, W.-J. Hwang, 
+and M. Liyanage, “Survey on 6g frontiers: Trends, applications, require- 
+ments, technologies and future research,” IEEE Open Journal of the 
+Communications Society, vol. 2, pp. 836–886, 2021. 
+[138] N. Janbi, I. Katib, A. Albeshri, and R. Mehmood, “Distributed artificial 
+intelligence-as-a-service (daiaas) for smarter ioe and 6g environments,” 
+Sensors, vol. 20, no. 20, p. 5796, 2020. 
+[139] S. K. Jagatheesaperumal, K. Ahmad, A. Al-Fuqaha, and J. Qadir, “Ad- 
+vancing education through extended reality and internet of everything 
+enabled metaverses: Applications, challenges, and open issues,” arXiv 
+preprint arXiv:2207.01512, 2022. 
+[140] S. Nayak and R. Patgiri, “6g communication: Envisioning the key issues 
+and challenges,” arXiv preprint arXiv:2004.04024, 2020. 
+[141] M. Maier, A. Ebrahimzadeh, S. Rostami, and A. Beniiche, “The internet 
+of no things: Making the internet disappear and" see the invisible",” IEEE 
+Communications Magazine, vol. 58, no. 11, pp. 76–82, 2020. 
+[142] J. Liu, H. Liu, Y. Chen, Y. Wang, and C. Wang, “Wireless sensing for 
+human activity: A survey,” IEEE Communications Surveys & Tutorials, 
+vol. 22, no. 3, pp. 1629–1645, 2019. 
+[143] Y. Cui, F. Liu, X. Jing, and J. Mu, “Integrating sensing and communi- 
+cations for ubiquitous iot: Applications, trends, and challenges,” IEEE 
+Network, vol. 35, no. 5, pp. 158–167, 2021. 
+[144] Y. Siriwardhana, P. Porambage, M. Liyanage, and M. Ylianttila, “A 
+survey on mobile augmented reality with 5g mobile edge computing: ar- 
+chitectures, applications, and technical aspects,” IEEE Communications 
+Surveys & Tutorials, vol. 23, no. 2, pp. 1160–1192, 2021. 
+[145] N. Xi, J. Chen, F. Gama, M. Riar, and J. Hamari, “The challenges of 
+entering the metaverse: An experiment on the effect of extended reality 
+on workload,” Information Systems Frontiers, pp. 1–22, 2022. 
+[146] A. Plechatá, G. Makransky, and R. Böhm, “Can extended reality in the 
+metaverse revolutionise health communication?,” NPJ digital medicine, 
+vol. 5, no. 1, pp. 1–4, 2022. 
+[147] Q. Yu, M. Wang, H. Zhou, J. Ni, J. Chen, and S. Céspedes, “Guest 
+editorial special issue on cybertwin-driven 6g: Architectures, methods, 
+and applications,” IEEE Internet of Things Journal, vol. 8, no. 22, 
+pp. 16191–16194, 2021. 
+[148] Q. Yu, J. Ren, Y. Fu, Y. Li, and W. Zhang, “Cybertwin: An origin of 
+next generation network architecture,” IEEE Wireless Communications, 
+vol. 26, no. 6, pp. 111–117, 2019. 
+[149] F. Tang, X. Chen, T. K. Rodrigues, M. Zhao, and N. Kato, “Survey on 
+digital twin edge networks (diten) towards 6g,” IEEE Open Journal of the 
+Communications Society, 2022. 
+[150] W. Saad, M. Bennis, and M. Chen, “A vision of 6g wireless systems: 
+Applications, trends, technologies, and open research problems,” IEEE 
+network, vol. 34, no. 3, pp. 134–142, 2019. 
+[151] M. Z. Chowdhury, M. Shahjalal, S. Ahmed, and Y. M. Jang, “6g wire- 
+less communication systems: Applications, requirements, technologies, 
+challenges, and research directions,” IEEE Open Journal of the Commu- 
+nications Society, vol. 1, pp. 957–975, 2020. 
+[152] “Meta.” Accessed on 27.07.2022. 
+[153] “Vr hive.” Accessed on 27.07.2022. 
+[154] “6g-life.” Accessed on 27.07.2022. 
+[155] “Decentralland.” Accessed on 27.07.2022. 
+[156] “Sandbox.” Accessed on 27.07.2022. 
+[157] “Axie infinity.” Accessed on 27.07.2022. 
+[158] “Illuvium.” Accessed on 27.07.2022. 
+[159] “Luxembourg metaverse.” Accessed on 27.07.2022. 
+
+EEEAccessBartlomiej Siniarski et al.: Need 6G for the Metaverse Realization 
+30 
+VOLUME 4, 2016 
+ 
+ 
+ 
+BARTLOMIEJ SINIARSKI is currently a post 
+doctoral researcher and a project manager for 
+the EU H2020 SPATIAL project at University 
+College Dublin. He completed his undergraduate 
+studies in Computer Science at University College 
+Dublin (Ireland) and University of New South 
+Wales (Australia). He was awarded with a doctoral 
+degree in 2018. He has a particular interest and 
+experience in the design of the IoT networks and 
+in particular collecting, storing and analysing data 
+gathered from intelligent sensors. Furthermore, he was actively involved in 
+MSCA-ITN-ETN, ICT-52-2020 and H2020-SU-DS-2020 projects which are 
+focused on solving problems in the area of network security, performance 
+and management in 5G and B5G networks. 
+THIEN HUYNH-THE received the B.S. degree in 
+Electronics and Telecommunication Engineering 
+and the M.Sc. degree in Electronics Engineering 
+from Ho Chi Minh City University of Technol- 
+ogy and Education, Vietnam, in 2011 and 2013, 
+respectively, and the Ph.D. degree in Computer 
+Science and Engineering from Kyung Hee Uni- 
+versity (KHU), South Korea, in 2018. He was a 
+recipient of the Superior Thesis Prize awarded by 
+KHU. From March 2018 to August 2018, he was 
+a Postdoctoral Researcher with Ubiquitous Computing Laboratory, KHU. 
+From September 2018 to May 2022, he was a Postdoctoral Researcher 
+with the ICT Convergence Research Center, Kumoh National Institute of 
+Technology, South Korea. He is currently a Lecturer in Department of 
+Computer and Communication Engineering, Ho Chi Minh City University 
+of Technology and Education (HCMUTE), Vietnam. He was a recipient of 
+Golden Globe Award 2020 for Vietnamese Young Scientist by Central Ho 
+Chi Minh Communist Youth Union associated with Ministry of Science and 
+Technology. His current research interests include digital image processing, 
+radio signal processing, computer vision, wireless communications, IoT 
+applications, machine learning, and deep learning. 
+ 
+ 
+ 
+ 
+CHAMITHA DE ALWIS (Senior Member, IEEE) 
+is a Lecturer, Researcher and Consultant in Cy- 
+bersecurity. Presently he works as a Lecturer in 
+Cybersecurity in the School of Computer Sci- 
+ence and Technology, University of Bedfordshire, 
+United Kingdom. He is the founder Head of the 
+Department of Electrical and Electronic Engineer- 
+ing, University of Sri Jayewardenepura, Sri Lanka, 
+where he also served as a Senior Lecturer. He 
+received the B.Sc. (First Class Hons.) in Electronic 
+and Telecommunication Engineering from University of Moratuwa, Sri 
+Lanka, in 2009, and the Ph.D. in Electronic Engineering from University 
+of Surrey, United Kingdom, in 2014. He has over 13 years of experience 
+in the academia and the industry. He has published over 30 research arti- 
+cles and serves as guest editor/reviewer/TPC member for reputed journals 
+and conferences. He was awarded several competitive research grants and 
+actively contributes to various research projects related to network security, 
+5G/6G, and blockchain. He also provides consultancy services for ICT and 
+cybersecurity related projects and activities. 
+ 
+ 
+GÜRKAN GÜR (Senior Member, IEEE) is a se- 
+nior lecturer at Zurich University of Applied Sci- 
+ences (ZHAW) – Institute of Applied Information 
+Technology (InIT) in Winterthur, Switzerland. He 
+received his B.S. degree in electrical engineering 
+in 2001 and Ph.D. degree in computer engineer- 
+ing in 2013 from Bogazici University in Istan- 
+bul, Turkey. His research interests include Future 
+Internet, 5G and Beyond networks, information 
+security, and information-centric networking. He 
+has two patents (one in US, one in TR) and published more than 80 
+academic works. Currently, he is involved in EU H2020 RIA – INSPIRE- 
+5Gplus project. He is a senior member of IEEE and a member of ACM. 
+His research interests include Future Internet, information security, next- 
+generation wireless networks and ICN. 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+GOKUL YENDURI received his Master’s degree 
+(M.Tech., IT) from Vellore Institute of Technology 
+in the year 2013. Currently, he is a senior research 
+fellow at the DIVERSASIA project, co-funded by 
+the Erasmus+ programme of the European Union. 
+His areas of interest are machine learning and 
+predictive analysis, software engineering, assistive 
+technologies, and the metaverse. He has worked as 
+an assistant professor in the past. He attended sev- 
+eral national and international conferences, work- 
+shops, and guest lectures and published papers in peer-reviewed international 
+journals. He is also acting as a reviewer for many prestigious peer-reviewed 
+international journals. 
+THIPPA REDDY GADEKALLU is currently 
+working as an Associate Professor in the School 
+of Information Technology and Engineering, Vel- 
+lore Institute of Technology, Vellore, Tamil Nadu, 
+India. He obtained his Bachelors in Computer 
+Science and Engineering from Nagarjuna Univer- 
+sity, India, in the year 2003, Masters in Computer 
+Science and Engineering from Anna University, 
+Chennai, Tamil Nadu, India in the year 2011 and 
+his Ph.D in Vellore Institute of Technology, Vel- 
+lore, Tamil Nadu, India in the year 2017. He has more than 14 years 
+of experience in teaching. He has more than 150 international/national 
+publications in reputed journals and conferences. Currently, his areas of 
+research include Machine Learning, Internet of Things, Deep Neural Net- 
+works, Blockchain, Computer Vision. He is an editor in several publishers 
+like Springer, Hindawi, Plosone, Scientific Reports (Nature), Wiley. He also 
+acted as a guest editor in several reputed publishers like IEEE, Elsevier, 
+Springer, Hindawi, MDPI. He is recently recognized as one among the top 
+2% scientists in the world as per the survey conducted by Elsevier in the year 
+2021, 2022. 
+
+EEEAccessBartlomiej Siniarski et al.: Need 6G for the Metaverse Realization 
+31 
+VOLUME 4, 2016 
+ 
+ 
+ 
+MADHUSANKA LIYANAGE (Senior Member, 
+IEEE) is an Assistant Professor/Ad Astra Fellow 
+and Director of Graduate Research at the School 
+of Computer Science, University College Dublin, 
+Ireland. He is also acting as a Docent/Adjunct Pro- 
+fessor at the Center for Wireless Communications, 
+University of Oulu, Finland, and Honorary Ad- 
+junct Professor at the Department of Electrical and 
+Information Engineering, University of Ruhuna, 
+Sri Lanka. He received his Doctor of Technology 
+degree in communication engineering from the University of Oulu, Oulu, 
+Finland, in 2016. From 2011 to 2012, he worked as a Research Scientist 
+at the I3S Laboratory and Inria, Sophia Antipolis, France. He was also 
+a recipient of the prestigious Marie Skłodowska-Curie Actions Individual 
+Fellowship and Government of Ireland Postdoctoral Fellowship during 
+2018-2020. During 2015-2018, he has been a Visiting Research Fellow at 
+the CSIRO, Australia, the Infolabs21, Lancaster University, U.K., Computer 
+Science and Engineering, The University of New South Wales, Australia, 
+School of IT, University of Sydney, Australia, LIP6, Sorbonne University, 
+France and Computer Science and Engineering, The University of Oxford, 
+U.K. He is also a senior member of IEEE. In 2020, he received the "2020 
+IEEE ComSoc Outstanding Young Researcher" award by IEEE ComSoc 
+EMEA. In 2021, he was ranked among the World’s Top 2% Scientists (2020) 
+in the List prepared by Elsevier BV, Stanford University, USA. Also, he was 
+awarded an Irish Research Council (IRC) Research Ally Prize as part of 
+the IRC Researcher of the Year 2021 awards for the positive impact he has 
+made as a supervisor. Dr. Liyanage’s research interests are 5G/6G, SDN, 
+IoT, Blockchain, MEC, mobile, and virtual network security. More info: 
+www.madhusanka.com 
+ 
+
+EEEAccess
\ No newline at end of file
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+page_content=' Switzerland 6Department of Computer and Communication Engineering,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Ho Chi Minh City University of Technology and Education,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Vietnam 7Department of Electrical and Electronic Engineering,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' University of Sri Jayewardenepura,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Sri Lanka 8Centre for Wireless Communications,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' University of Oulu,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Finland Corresponding author: Bartlomiej Siniarski (e-mail: bartlomiej.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='siniarski@ucd.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='ie).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='  ABSTRACT The concept of the Metaverse aims to bring a fully-fledged extended reality environment to provide next generation applications and services.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Development of the Metaverse is backed by many technologies, including, 5G, artificial intelligence, edge computing and extended reality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' The advent of 6G is envisaged to mark a significant milestone in the development of the Metaverse, facilitating near-zero-latency, a plethora of new services and upgraded real-world infrastructure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' This paper establishes the advantages of providing the Metaverse services over 6G along with an overview of the demanded technical requirements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' The paper provides an insight to the concepts of the Metaverse and the envisaged technical capabilities of 6G mobile networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Then, the technical aspects covering 6G for the development of the Metaverse, ranging from validating digital assets, interoperability, and efficient user interaction in the Metaverse to related security and privacy aspects are elaborated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Subsequently, the role of 6G technologies towards enabling the Metaverse, including artificial intelligence, blockchain, open radio access networks, edge computing, cloudification and internet of everything.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' The paper also presents 6G integration challenges and outlines ongoing projects towards developing the Metaverse technologies to facilitate the Metaverse applications and services.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='  INDEX TERMS Metaverse, 6G, AI, Blockchain, Edge Computing, Security, Privacy, vertical applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='  I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' INTRODUCTION The term ‘Metaverse’ has been coined to further facilitate the digital transformation in every aspect of our physical lives [1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' The Metaverse is a virtual world where you can live a synchronous life through your avatar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' The concept is similar to an online game, however, instead of shooting targets or driving cars, users will be engaged in real-life activities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' These activities could include attending meetings, catching up with friends, attending music festivals, going door to door selling digital collectables, or buying and selling land, apartments or assets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Virtual interactive worlds or early Metaverses have already been introduced primarily in video games with releases such as Fortnite, Minecraft, Decentra- land, Ifland.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' The list isn’t extensive and users are gravitating toward other Metaverse ecosystems that are emerging today.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' The Metaverse embraces a social interaction accelerated through a virtual environment and driven by novel technolo- gies such as Web 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='0, 5G, Artificial Intelligence (AI) and Extended Reality (XR).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' The XR - which includes everything from Virtual Reality (VR) to Mixed Reality (MR) to Aug- mented Reality (AR) and haptics - have enormous poten- tial to transform both industry and society.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' The widespread adoption of XR was slowed down recently by a number of issues including limited processing power, storage and battery life of small head-mounted displays (HMDs).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='  The 5G made it possible to overcome some of these challenges by offloading a portion of XR processing to the mobile network edge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' In addition to this, the 5G QoS framework makes it possible to establish QoS flows that provide optimized network treatment for specific traffic flows, in addition to the default QoS flow used for mobile broadband (MBB).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Such additional QoS flows can be established either using 5GC QoS-exposure application programming interfaces to communicate service requirements or by traffic detection  TEEEAcceSS2 VOLUME 4, 2016 Bartlomiej Siniarski et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' : Need 6G for the Metaverse Realization  together with pre-provisioned service requirements, such as relying on standardized 5G QoS identifier characteristics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Although the Metaverses have the potential to be transfor- mational for both business and society, widespread adoption has previously been hindered by issues such as heat gener- ation and the limited processing power, storage, and battery life of small form factor head-mounted devices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' The time- critical communication capabilities in 5G make it possible to overcome only some of these challenges by offloading XR processing to the mobile network edge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' By evolving the already existing 5G or B5G networks, mobile network operators are in an excellent position to enable the real- ization of the Metaverse on a large scale.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' The 6G aims to achieve high spectrum and energy efficiency, low latency, and massive connection due to the exponential growth of the Internet of Things (IoT) devices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 6G will also effectively link the physical, and digital worlds by providing seamless and ubiquitous services such as extreme-scale environmen- tal monitoring and control, virtual reality/virtual navigation, telemedicine, digital sensing, and robotics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' This will result in a network that connects us to one another, to information, to knowledge, and to purpose.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' As a result, 6G networks will enhance the efficiency of technologies such as computer vision, blockchain, AI, the IoT, robotics, and user interfaces which are critical for the metaverse realization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='  In summary, 6G will enhance every feature of the 5G network that benefits the user to improve areas such as smart cities, farming, manu- facturing, and robots.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 6G will provide enhanced productivity, capabilities, and better user experiences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' The main use of 6G in the Metaverse is summarized below: Near-zero-latency: In virtual interaction, 6G will contin- uously provide users with a near-zero-latency sensory inter- connection experience, such as the user’s virtual movement in the Metaverse, virtual meetings, virtual paintings, and other interactive, immersive holographic experiences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' New services: 6G is the main driver of multiple new service models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' For example, 6G communication technology provides users with precise service models in autonomous driving, industrial control, e-health, Internet robots, and au- tonomous systems, bringing a more convenient lifestyle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Upgraded real-world infrastructure available for use in the Metaverses: 6G infrastructure mainly includes infor- mation infrastructure, fusion infrastructure, and innovation infrastructure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' In particular, the 6G communication system integrates infrastructure such as ground, UAV, and satellite Internet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 6G also features high bandwidth, low latency, strong reliability, and global coverage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' MOTIVATION The main motivation of this paper is to realize if mobile network operators can enable large-scale XR and at the same time further development of Metaverses by introducing time- critical communication capabilities in 6G networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' The 5G networks already contribute to considerable improvement in data rate, latency, and packet loss since the last network generation (4G) and users already enjoy comfortable viewing experiences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' However, as the resolution of video increases from 4K to 8K and 12K/24K for 3D video and the number of worldwide users increases, the 5G network will not be sufficient to support many use cases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Some of the main cloud and network providers are defining the evolution of the service experience into the fair-experience, comfortable experience, and ideal-experience phases [2], where each has its own network KPI requirement to be met.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Table 1 sum- marizes those KPI requirements based on different use cases envisaged to be a part of future metaverses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' In this work, we aim to establish and explain the main advantages of providing the Metaverse services over 6G and provide an overview of the technical requirements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Furthermore, we aim to establish what role will 6G play in the Metaverse operation and if the envisaged architecture of 6G will be capable of supporting the upcoming technology portrayed by the tech industry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' RELATED SURVEYS AND CONTRIBUTIONS Our work is exclusively focused on the networking aspects of the Metaverse and the role that 6G will play in the Metaverse deployment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Though there are some Metaverse- focused surveys we found it is lacking a comprehensive, and detailed discussion on the role of B5G/6G technologies as indicated by Table 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' The table also includes the limitations of the related works in the context of technical challenges, security and privacy, and research directions, which we have already addressed in this paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' The surveys [3] and [4] inves- tigate technical aspects and security threats comprehensively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' However, those papers are not focused on the future networks and the role of 6G in the Metaverse specifically.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' The surveys [5], [1] and [6] include an interesting view on the potential use of the Metaverse in different domains and clearly define network requirements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' The limitations in [5], [1] and [6] include the lack of coverage of future network aspects and the discussion on the security and privacy issues is weak.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Surveys [7] and [8] discuss implementation challenges and analyze the fusion of 6G-enabled edge with the Metaverse, however, the security issues and research directions are only partially covered.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Therefore, we contribute to addressing this gap in our work on the comprehensive discussion on 6G for the Metaverse.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' PAPER ORGANIZATION The rest of this paper is organized as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Introduction and discussion of the role of 6G networks in the Metaverse are presented in Section I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Section II covers the expected improvements from 5G to 6G and the impact it will have on the Metaverses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Section III investigates the state-of-the- art solutions provided by 6G for the Metaverse from tech- nical perspective, followed by Section IV that discusses in detail how different 6G technologies will help to achieve the Metaverse aims.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Section V identifies expected 6G challenges that would have to be approached before the introduction of Metaverses to wider community.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Finally, Section VI provides an overview of related research projects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='  EEEAccessBartlomiej Siniarski et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' : Need 6G for the Metaverse Realization 3 VOLUME 4, 2016  IoE  ORAN  Cloudification  Artificial   Blockchain  Intelligence  Edge AI  THz Bands  Zero Touch Management  Network  1 Tbps  Data Rate  Multi Purpose  MURLLC  Service  The Metaverse  Deep Space  Smart Devices  Deep Sea  Smart  Healthcare  Smart Cities  TABLE 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Network KPI requirements in different phases of cloud/ the Metaverse development  Type of interaction / use case  Network KPI requirement Fair-experience In the fair-experience phase, most content is 4K, and the terminal screen resolution is 2K to 4K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Comfrotable-experience In the comfortable-experience phase, most content is 8K, the terminal screen resolution is 4K to 8K Ideal-experience In the ideal-experience phase, most content is 12K or 24K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' The terminal screen resolution is 8K to 16K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='  Weak-interaction Users select view and location, but do not interact with entities in the virtual environment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' For example IMAX, 360 video, live broadcast, music, education.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='  Bitrate ≥ 40 Mbit/s (4K) Full-view: ≥ 90 Mbit/s FOV: ≥ 50 Mbit/s Full-view: ≥ 290 Mbit/s (12K) FO ≥ V 1090 Mbit/s (24K) : ≥ 155 Mbit/s (12K) ≥ 580 Mbit/s (24K)  Bandwidth requirement ≥ 60 Mbit/s (4K) Full-view: ≥ 140 Mbit/s FOV: ≥ 75 Mbit/s Full-view: ≥ 440 Mbit/s (12K) FO ≥ V 1600 Mbit/s (24K) : ≥ 230 Mbit/s (12K) ≥ 870 Mbit/s (24K) Recommended network RTT ≤ 20ms ≤ 20ms ≤ 20ms Packet loss requirement ≤ 9e-5 ≤ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='7e-5 ≤ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='7e-6 Strong-interaction Users can interact with virtual envirnomnets through interactive devices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' The virtual space displayed needs to respond to interactions in real time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' For example gaming, fitness, social networking, real estate, engineering, healthcare, shopping.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Bitrate ≥ 40 Mbit/s ≥ 90 Mbit/s ≥ 360 Mbit/s (8K) ≥ 440 Mbit/s (16K) Bandwidth requirement ≥ 80 Mbit/s ≥ 260 Mbit/s ≥ 1000 Mbit/s (8K) ≥ 1500 Mbit/s (16K) Recommended network RTT ≤ 20 ms ≤ 15 ms ≤ 8 ms Packet loss requirement ≤ 1e-5 ≤ 1e-5 ≤ 1e-6  II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 6G AND THE METAVERSE: PRELIMINARIES The preliminary introduction to 6G and the Metaverse is presented in this section, followed by the role of 6G in the Metaverse.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' PRELIMINARY TO 6G Since the middle of 2019, commercial 5G mobile networks have been standardized and deployed globally, with signif- icant coverage in some countries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Numerous new applica- tions and use cases are being developed, placing existing networks’ capabilities to the test.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' The capacity of current 5G networks to handle the Internet of Everything (IoE), holographic telepresence, collaborative robotics, and deep- sea and space tourism is limited [9].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' This has prompted researchers to reconsider and work toward the development of the next generation of mobile communications networks called the sixth-generation of mobile networks 6G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Each time mobile communication technology is upgraded and iterated, its performance metrics improve by a factor of ten to hun- dred times over the preceding generation [10].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Researchers from all over the world propose AI/machine learning (ML), quantum communication/quantum machine learning (QML), blockchain, tera-hertz and millimetre wave communication, tactile Internet, non-orthogonal multiple access (NOMA), small cell communication, fog/edge computing, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' as the key technologies for the realisation of 6G communications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 6G aims to achieve high spectrum and energy efficiency, low latency, and massive connection due to the exponential growth of the IoT devices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='  6G will make feasible intelli- gent traffic, environmental monitoring and control, virtual reality/virtual navigation, telemedicine, digital sensing, high definition (HD), and full HD video transmission in connected drones and robotics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 6G will also effectively link the physical, and digital worlds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' This will result in a network that connects us to one another, to information, to knowledge, and to purpose.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 6G wireless networks operate in the terahertz band, with a peak rate of 1T b/s and a network with ultra-reliable and low-latency communication (URLLC) of less than 1 ms, considerably improving the overall quality of experience (QoE) for consumers [11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 6G has a high positioning accu- racy of 1 m outdoors and 10 cm indoors [12] which also im- proves positioning accuracy of deep-sea and space tourism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 6G utilises endogenous security technology to increase its resistance to unknown security threats [13].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' As a result, 6G networks can enhance the efficiency of technologies such as computer vision, blockchain, AI, the IoT, robotics, and user interfaces [14].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' The architecture of 6G is depicted in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 1  FIGURE 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 6G Architecture  To summarize, 6G will enhance every feature of the 5G network that benefits the user.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 6G will improve areas such as smart cities, farming, manufacturing, and robots.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 6G will provide enhanced productivity, capabilities, and better user experiences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Improved and expanded functionality is an in-  EEEAccess6G000Bartlomiej Siniarski et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' : Need 6G for the Metaverse Realization 4 VOLUME 4, 2016  Low Coverage:  Medium Coverage:  TABLE 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Summary of Important Surveys on 6G and its role in the Metaverse  Ref  Technical  aspects  and  challenges  Security  and  privacy  issues  The role  of 6G in  Metaverse  Research  directions  (6G)  Remarks  Limitations [5] H M H M This paper aims to show the roadmap to the Meta- verse in terms of communication and networking in 6G,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' including requirements (limited) and challenges for 6G to realize the Metaverse,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' and discussing the fundamental technologies to be integrated in 6G to drive the implementation of the Metaverse.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' The paper is missing some impor- tant references and the requirements are not discussed in detail except for what is depicted in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' [3] H M L L The paper investigates AI-based methods concerning six technical aspects that have potentials for the Meta- verse: natural language processing, machine vision, blockchain, networking, digital twin, and neural inter- face, and being potential for the Metaverse.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' The discussion on attacks on AI in the Metaverse is missing, subse- quently the paper should discuss the role of AI in future networks from the security and privacy perspective.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' [1] H M L M The technology enablers are discussed in details in- cluding latest state-of-the-art tools.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' The survey paper includes an interesting discussion on user-centric fac- tors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' The paper does not cover any as- pects of future networks and how those could play an important role in creating Metaverses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' [4] M H L L The security threats to the Metaverse are explained comprehensively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' The paper includes the countermea- sures to those threats.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' From the security and privacy perspective, it is a comprehensive survey.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' The future networks enablers are not discussed in this paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='  The paper provides good state-of-the-art sur- vey, however it is lacking future di- rections especially in the network- ing aspect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' [6] M L L M The paper provides an interesting view on the potential use of the Metaverse in medical domain including a proposed process of patient treatment using the Meta- verse technology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' This paper does not cover any secu- rity or privacy issues or the impor- tance of future networks in design- ing meta worlds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' [7] H M L M This survey discusses how enablers of the Metaverse can be implemented at a scale at mobile edge net- works.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' The implementation challenges are also dis- cussed in this survey.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' The survey mentions the role of B5G/6G, but it doesn’t cover how 6G will enable the Metaverse.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' [8] M L M M This survey analyzes the fusion of 6G-enabled edge AI and the Metaverse, and introduces the features, ar- chitecture, technologies, and applications of the Meta- verse.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' The paper only partially covers pri- vacy and security issues.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' The 6G requirements are discussed only to certain level and the 6G enablers are not covered in full.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Our sur- vey H M H H In this paper we focus on 6G technology and how it enables the deployment of Metaverses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' We focus heavily on specific requirements and cover each in detail as supposed to provide the reader with general overview.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' The security and privacy challenges are cov- ered in depth despite it not being the main focus of this paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='  We clearly identify current research projects and future research directions, which is something missing in most survey papers that were investigated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' There is still space to discuss other aspects once meteverses are ex- plored in more depth, in particular social aspects such as fairness, so- cial acceptance, accountability, and community ownership.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='  The paper did not consider this area or only very briefly discussed it through mentioning it in passing The paper partially considers this area (leaves out vital aspects or discusses it in relation to other areas without a specific focus on it) The paper considers this area in reasonable or high detail  evitability over successive generations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Even with 6G, this will be the case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 6G will improve upon 5G by optimising and lowering costs to increase adoption.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Information man- agement and consumption will be simplified with the advent of 6G’s new human-machine interfaces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' The touchscreen interface of the future will instead be controlled by voice instructions, gestures, or even brain signals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' The comparison of the features related to 5G and 6G are depicted in Table 3  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' PRELIMINARY TO THE METAVERSE The Metaverse is a network of three-dimensional virtual environments dedicated to social interaction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' It is frequently depicted in futurism and science fiction films.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' The worldwide virtual environment will be made possible by the usage of VR and AR devices [15].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' The term "Metaverse" is not en- tirely unfamiliar in the technological world.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Neal Stephenson coined the term "Metaverse" in 1992.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' His science fiction novel Snow Crash envisioned an online universe in which people may explore and escape the physical world using dig- ital avatars [16].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Decades later, major technology firms like Meta, Axie Infinity, The Sandbox, and Decentraland have begun developing their versions of a futuristic Metaverse.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' The overview of the enabling technologies, services, and technical requirement is depicted in the Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 2 High Coverage:  EEEAccessBartlomiej Siniarski et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' : Need 6G for the Metaverse Realization 5 VOLUME 4, 2016  TABLE 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' The comparison of 5G and 6G Features  Features 5G 6G Data Rate 1 Gbps to 20 Gbps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 1 Tbps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Application Types Enhanced Mobile Broadband.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Ultra-Reliable Low Latency Communications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='Massive Ma- chine Type Communications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Massive Broadband Reliable Low.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Latency Communication.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Massive- URLLC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Human-Centric Services.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='Multi-Purpose Services.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Device Types Smartphones,     Drones,     and Sensors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Sensors         &          DLT devices,BCI and XR equipment, CRAS, and Smart implants.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Frequency Band Sub 6 GHz and mm wave for fixed access.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Sub 6 GHz mm wave for mobile access exploration of THz bands.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Non-RF bands.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Latency 5 ms <1 ms Architecture Dense sub   6   GHz   smaller BSs with umbrella macro BSs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Mmwave small cells of about 100 meters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Cell free smart sur- faces at high frequencies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Cell free smart surfaces at high frequencies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Tempo- rary hotspots provided by drone-mounted BSs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Trials of tiny THz cells.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Spectral and Energy Efficiency Gain 10 x in bps/Hz/m2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 1000 x in bps/Hz/m2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Traffic Capacity 10 Mbps/m2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 1 to 10 Gbps/m2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Reliability 10−5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 10−9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Localization Pre- cision 10cm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 1cm in 3D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' User Experience 50 Mbps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 10 Gbps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Mobility 500 km/h 1000 km/h Connection den- sity 106 devices/km2 107 devices/km2  1) Enabling Technologies of the Metaverse The immersive experience of the Metaverse will be enabled by cutting-edge technologies such as blockchain, AR and XR, AI, and the IoT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' • Blockchain: Blockchain technology enables decen- tralised and transparent digital proofs of ownership, col- lectibility, value transfer, governance, accessibility, and interoperability in the Metaverse [17].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Blockchain also enables individuals to exchange assets while working and interacting in the Metaverse.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' • Extended reality: XR enables the creation of 3D computer-rendered virtual environments in the Meta- verse.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' XR allows users to interact with these virtual goods through head tracking devices or physical con- trols [18].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' As XR technology matures, it will be able to broaden the Metaverse experience by including physical simulations using XR equipment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Users will then have the ability to sense, hear, and interact with people from all around the world.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' • Artificial intelligence: AI will allow users of the Meta- verse to construct incredibly realistic avatars and have multilingual accessibility.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' AI will help people make better decisions in the Metaverse.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' A better human- computer interface will also be provided by AI [19].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' AI can also help detect, prevent, and recover from cyber attacks in the Metaverse.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' • Internet of things: IoT will enable the Metaverse to map data from real life and emerge it into virtual reality [20].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='  The data provided from the IoT devices to the Metaverse will help professionals to solve real-world problems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' The Metaverse with the help of IoT will support the users to collect real-time data-driven decisions with minimum need for training and computation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' • Edge Computing: Edge computing enables mobility and the border-less Metaverse for the users [21].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Edge com- puting improves the availability of data in the Metaverse by bringing data closer to end consumers for retrieving and storing data at remote data centre locations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Edge computing will help data transferring with ultra-reduced latency in the Metaverse which will help the users to make quick and effective decisions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='  Enabling Technologies  Security  Storage  Technical Requirements  FIGURE 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Preliminary to the Metaverse  2) Applications of the Metaverse The Metaverse has made its way into many sectors, capturing the enthusiasm of entrepreneurs across the world.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' The Metaverse will have a huge impact on ap- plications like healthcare, real estate, manufacturing, tourism, Entertainment, and shopping.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' • Healthcare: Smart healthcare has contributed to resolv- ing several healthcare difficulties, including linking pa- tients to doctors situated throughout the world during the COVID-19 epidemic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' This prepared the door for the application of the Metaverse in healthcare, which is facilitated by medical IoT, VR, and AR [22].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' The Metaverse gives users control over how the virtual and physical worlds interact.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' This enhances doctors’ abil- ity to provide consistent and customised patient care.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Through the use of VR technology, the Metaverse can aid in remote health monitoring, clinical data collec- tion, and improved robotic surgery, while 3D immersive technology will enable surgeons to practise through Artificial Intelligence Healthcare Real Estate Manufacturing The metaverse Tourism Shopping Privacy Interoperability Entertainment Services  EEEAccess+%Bartlomiej Siniarski et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' : Need 6G for the Metaverse Realization 6 VOLUME 4, 2016  simulations that will raise their success rate in the real world.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' • Real Estate: The Metaverse allows organisations to es- tablish retail and experience centres on its virtual land [23].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Rather than downloading many applications, users can access the Metaverse, which contains all currently available applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' As a result, the value of virtual land will increase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Property ownership in the Metaverse is limitless, and owners are free to use their virtual holdings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Digital property owners can make, run, lease, and build billboards for advertising.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' • Manufacturing: Manufacturers can create digital facto- ries in the Metaverse to assist in organising production and effective usage of machinery.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' This allows simula- tion of human-machine interaction throughout the man- ufacturing process [24].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' As a result, firms can use virtual production systems to train new employees and staff on how to use them in the real world, which would boost the manufacturing of products with a very low error rate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' The metaverse also allows mass personalization of the product and allows the user to track the product from its development to delivery, which will improve the trust of the users in the organization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' • Tourism: The Metaverse has the potential to create the most immersive experiences ever seen in the tourism sector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' The Metaverse allows hotel chains, tourism boards, online travel agencies, and other businesses to advertise their services [25].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='  Users can virtually visit those locations and decide whether or not to visit them in person.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' They can go through two distinct locations without leaving their homes, comparing and evaluating places through the use of 3D imagery.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' The Metaverse will give users an experience that will be better than any kind of communication that exists in the present day, including video and audio interaction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' • Entertainment: The Metaverse will completely revo- lutionise entertainment with its rich 3D environment and avatars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Entertainment’s growth is highly linked to the development of VR in the Metaverse.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' The Metaverse-based entertainment, including movies and video games, can be enjoyed in a virtual world that users can access from the comfort and privacy of their home [26].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' It also allows users to attend virtual concerts and sporting events from first-row seats or to ride virtual roller coasters at theme parks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' • Shopping: Customer experiences in the Metaverse will evolve constantly as a result of XR technologies, and organisations selling products in metamalls will have more creative freedom to express themselves and attract customers than they do in traditional shopping.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' These spaces will encompass much more than the basic ser- vices seen on the majority of e-commerce sites today, including user engagement, avatar customization, event attendance, and skill acquisition [27].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Furthermore, the products sold in the Metaverse will include both physi- cal and virtual items.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='  Consumers may feel and touch the object with the use of sensors, which will completely alter the traditional buying experience.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Additionally, customers can purchase things on the go while engaged in real-world activities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='  3) Technical Requirements of the Metaverse Privacy, security, storage, and interoperability are the important technical requirements of the Metaverse.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' • Privacy: The Metaverse is a social platform that employs interactive technology such as VR, AR, and AI that requires sensitive user data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Since behavioral-learning and recommender systems collect vast quantities of personal information, they pose a threat to the pri- vacy of the Metaverse users [28].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Therefore, the use of such technologies poses a substantial risk to the privacy of users’ data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' The Metaverse must guarantee privacy protection for such sensitive information, and users must have complete control over their data, which will increase their trust in the Metaverse.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Even though blockchain technology can help protect privacy in the Metaverse, there are no specific rules designed for pri- vacy protection in the Metaverse, which makes it a critical requirement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' • Security: In the Metaverse, attackers and AI bots can and will emerge from any location and at any time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' The Metaverse networks should have a high level of security, and related protocols to incorporate continuous awareness into these networks [5].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' In addition to ex- isting passwords, multi-factor authentication, enhanced firewalls, and advanced threat detection technologies, the Metaverse must be incorporated with higher trans- parency and analysis to detect anomalies and uncover malicious activities to maintain user security.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='  Data must be secured and safeguarded during transmission and storage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' To assure the security of the Metaverse in the future, it is vital to draw on and build upon information from the past.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' • Storage: The Metaverse is a collection of technologies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' It is a huge concept which involves the simultaneous integration of multiple technologies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' The list includes high-performance networks, sophisticated computing and sensors, hardware, AR/VR, AI, 3D modelling, blockchain, IoT, and many other technologies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' The data produced from these technologies and their related ap- plication will be enormous [29].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' The formation of the Metaverse itself necessitates voluminous data storage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Decentralised storage based on blockchain technology can be used to store this massive amount of data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' This storage distributes data to numerous independent net- work nodes using open-source applications and algo- rithms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' It also improves the privacy of data, the redun- dancy of data backups, and the transparency of data in the Metaverse.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' • Interoperability: Interoperability across services, tech- nology, and virtual worlds is a crucial aspect of the  EEEAccessBartlomiej Siniarski et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' : Need 6G for the Metaverse Realization 7 VOLUME 4, 2016  Metaverse [30].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' A cross-chain protocol is an optimal ap- proach for maintaining interoperability between diverse Metaverse services, technologies, and configurations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Among other protocols, this one permits the exchange of assets like avatars, non-fungible tokens, and currency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' To make the Metaverse more interoperable, different devices that use the same technology need to follow the same rules and standards.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='  III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 6G FOR THE METAVERSE: TECHNICAL PERSPECTIVE This section investigates the state-of-the-art solutions pro- vided by 6G for the Metaverse from the technical perspec- tives, including validation of digital assets, cross-platform integration, efficient support of AI, privacy and security, high-speed data connection, content creation and storage, user interactivity, low latency communication, and computer vision.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 6G FOR VALIDATION OF DIGITAL ASSETS IN THE METAVERSE Non-fungible Token (NFT) is one of the key components of a digital asset in the Metaverse.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' A visual asset, such as a virtual building, can be represented by an NFT that can be represented as a digital asset with unique data coding.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' When a purchaser buys an NFT, a private digital key password will be generated, that can certify that the purchaser owns a particular digital asset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Through this private key, the owner of the NFT can sell or transfer the digital asset to others [31].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' The blockchain associated with the specific Metaverse will record the NFT for a digital asset in the Metaverse.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' For instance, the Ethereum blockchain stores "Decentraland Metaverse", which is highly popular.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Ethereum records the digital asset transactions of the NFT for Decentraland [32].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Digital assets in the Metaverse can be created in the form of NFTs by the users.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' These digital assets can be anything ranging from virtual goods to digital art to virtual real estate, which is minted into the NFTs that are securely stored on the blockchain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' The owners of these digital assets can see these digital assets which are in the form of NFTs in the form of crypto for purchasing other digital assets in the Metaverse [33].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Content creators and artists can afford to have an opportunity to monetize their assets uniquely due to NFTs and blockchain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' For instance, artists need not depend on auction houses or galleries for selling their art.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='  The artists can sell their art directly to the customer in the form of an NFT that allows them to keep the majority of the profits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' The artists can even receive royalties whenever their art is sold to a new customer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Like art, the other digital assets also can be traded through NFTs in the Metaverse [34].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' The process of creating NFTs and transferring them from one virtual world to another requires a network that is highly reliable and secure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Digital assets in the Metaverse, represented by NFTs are verified and tracked on the blockchain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Every NFT will have a unique transaction hash that makes it non-replicable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' All the transactional data related to the NFTs are collected by the blockchain and are stored in blocks, that forms a blockchain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' The information stored in the blockchain is stored forever and can be viewed and verified by the public.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Verification of the digital assets in the Metaverse that has AR and other MR technologies incorporated, needs significant amount of bandwidth to create a more immersive experience add also to reduce the load times.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' The validation and verification of the digital assets in the blockchain incurs heavy computation in the blockchain, which needs significant bandwidth so that the users can see the results in near real-time, as depicted in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 4 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' The transactions between the different entities in the Metaverse are also powered by the consensus mechanism of the blockchain, which requires huge amounts of data transfer between nodes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='  This creates a requirement for a network that is both transparent and capable of real-time communication.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' These challenges faced during the creation, transfer, and validation of digital assets in the Metaverse can be solved by 6G due to its low latency, reliability, transparency, and high- speed connectivity [35].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 6G FOR CROSS PLATFORM INTEGRATION/INTEROPERABILITY IN THE METAVERSE One of the hurdles in realizing the full potential of the Metaverse is the lack of interoperability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Lack of interoper- ability [36], [37] is a major hurdle in a mass adaption of the Metaverse that makes the navigation of the users free from one Metaverse application to the other challenging.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' The Metaverse should mimic the interoperability that is experi- enced in the physical world.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' For instance, in the real/physical world, we can take physical assets/objects from one place to another easily.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' The users in the Metaverse too should be able to navigate seamlessly and freely to other Metaverses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' This is possible through interoperability that can form a global interconnected Metaverse where various Metaverses are integrated across the platforms as experienced in the real world [38].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Realization of interoperability in the Metaverse is a sig- nificant challenge as heavy objects such as digital avatars, 3D holograms etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' have to be navigated across in feature- rich Metaverse in near real-time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' It requires a communication infrastructure with high bandwidth and low latency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 6G net- work with its high bandwidth and ultra-reliable low latency communication infrastructure can solve the issue of seamless communication in the Metaverse, as depicted in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 5 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='  With the help of supporting technologies like ORAN and ZSM, the 6G network can be the common platform that provides an interoperable infrastructure for multiple Metaverses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Net- work slicing, software-defined networking, symbiotic radio, and network function virtualization are the 6G techniques that promote network interoperability and agility in the Meta- verse.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Intelligent collaboration between diverse wireless sig- nals is supported by symbiotic radio.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' The SDN/NFV offers open interfaces that facilitate interoperability between several Metaverses and assist produce network slices for any vertical application such as gaming and shopping over the common  EEEAccessBartlomiej Siniarski et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' : Need 6G for the Metaverse Realization 8 VOLUME 4, 2016  FIGURE 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 6G for the Metaverse:Technical Perspective  FIGURE 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 6G for Validation of Digital Assets in the Metaverse  physical infrastructure among different Metaverses [39].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' FIGURE 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 6G for Cross Platform Integration/Interoperability in the Metaverse  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 6G FOR EFFICIENT SUPPORT OF AI IN THE METAVERSE The Metaverse is a virtual world where the users will play games, interact with each other and the 3D objects in the virtual world, and build things in the virtual world.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' VR and AR along with blockchain and AI are the key enabling tech- nologies in realizing the Metaverse.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' The applications of AI in IoE ORAN Cloudification Artificial Intelligence Blockchain Edge AI THz Bands Zero Touch Management Network 1 Tbps Data Rate MURLLC Multi Purpose Service The Metaverse Deep Space Smart Devices Deep Sea Smart Healthcare Smart Cities The Metaverse The Metaverse User The Metaverse User Cryptocurrency Transfer of Digital Asserts Decentralization Traceability Blockchain Transperncy Security Trust Transfer of Digital Asserts NFTs Avatars Digital Asserts NFTs  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='The Metaverse  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='Cross Platform Vendors  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='Real time Validation  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='High Bandwidth  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='Low Latency  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='High Bandwidth  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='EEEAccess6G000NFTXOXamazon目Bartlomiej Siniarski et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' : Need 6G for the Metaverse Realization 9 VOLUME 4, 2016  ser  the Metaverse include speech processing, content analysis, computer vision, etc [3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' These applications of AI can be used to help build important components of the Metaverse as discussed below: Avatars: Avatars is one of the important and interesting concepts of the Metaverse, where people in the physical world will create a digital avatar in the virtual world.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' People would like to get creative in the virtual world and they would like to see themselves in a different way which may not be possible in the physical world.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' They can change their clothing, hairstyle, and body language, which is not their regular norm in the real world.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' AI plays a major role in the users designing their avatars in the virtual world.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' AI can be used to analyze 3D scans or user images to create accurate, realistic, and innovative avatars [40].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Some organizations such as Ready Player Me are making use of AI to create avatars for the Metaverse.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Digital Humans: In the Metaverse, 3D chatbots are termed as digital humans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' The digital humans respond and react to the actions of humans in the virtual world.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' They are usually non-playing characters that can be a character in a game of virtual reality whose actions and responses depend on a set of rules or automated scripts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' They try to understand what the users are communicating by listening and observing them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='  Human-like interactions and conversations can hap- pen in the Metaverse between humans and digital humans through body language and speech recognition [41].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' AI plays a significant role in the successful implementation of digital humans in the Metaverse.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Some of the key functionalities of digital humans like speech recognition, body language identification, object detection, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' can be realized through AI [6].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Language Processing: In the Metaverse users from across the globe can communicate and interact easily without lan- guage barriers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' This is made possible with the help of AI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' AI can break the human language such as English into a format that can be read by machines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' The AI can then analyze the sentences, and respond to the users in their language [42].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' From the above discussion, it is obvious that AI plays a significant role in the realization of some of the key features of the Metaverse.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' In the Metaverse, huge volumes of heterogeneous big data will be generated at a very fast rate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 6G, with its characteristics such as fast communication infrastructure, and near real-time processing, can help in processing/analyzing this big data to uncover the patterns existing in the data that trains the AI/ML algorithms in near real-time to make quick decisions/predictions through which several components of the Metaverse can communicate eas- ily.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 6G FOR HIGH SPEED DATA CONNECTION IN THE METAVERSE The wide adaption of AR and VR technologies is the key to the transition to the Metaverse.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' It is expected that data usage to be increased by 20 times to what is being used today due to the revolution of the Metaverse by 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' To realize the full potential of the Metaverse with real-time experience of AR and VR technologies, truly immersive 3D experiences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' The end-users should be able to access high-speed data connec- tions that can deliver the data at speeds of approximately 1 Gbps [43].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Some of the key requirements that will be needed to realize the true potential of the Metaverse are as follows: • To create virtual reality worlds in real-time, high-speed data connection is required.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' • The communication infrastructure should high-speed transmission in near real-time with very low latency, typically, below 10 milliseconds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' • The existing 4K video resolution may not be sufficient to convey the pixels for creating immersive worlds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Higher-resolution videos have to be supported by the data carriers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' • Next-generation video compression techniques that can compress and decompress huge data files in the Meta- verse in real time are the need of the hour.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' The key features of 6G with high bandwidth and URLLC [44] promise is a key enabling technology to realize the high bandwidth requirement of the Metaverse.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' The use of Edge AI-enabled 6G can also help applications and the Metaverse devices address these issues.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='  Edge AI is the combination of edge computing and AI to run machine learning tasks directly on connected edge devices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Edge AI computes and processes data locally, which helps the Metaverse devices be efficient and responsive in their communication.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' This also reduces the amount of data sent from the Metaverse devices to the cloud, thereby saving a huge amount of bandwidth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='  E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 6G FOR EFFICIENT USER INTERACTION IN THE METAVERSE  FIGURE 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 6G for Efficient User Interaction in the Metaverse  The Metaverse enables the interaction between real-world entities and virtual objects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' It is a digital environment that in- corporates social networking, real estate, online gaming, AR, VR, and cryptocurrencies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' In the Metaverse, with the help of virtual objects, sounds, and other sensory input, AR tries to enhance the user’s perception of the real world [5].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Each time a user enters the Metaverse, the objects around them un- dergo a dynamic transformation based on the requirements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' High Bandwidth  Ultra Reliable Low  Latency Communication  Interacting  with  existing  objects  Modifying  existing  objects  UUser  Creation  of  new  objects  Realtime Data Processing  NFTs  BOTS  Avatars  The Metaverse  EEEAccess目1ms宁Bartlomiej Siniarski et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' : Need 6G for the Metaverse Realization 10 VOLUME 4, 2016  Everything in the Metaverse is constantly changing, which indicates the dynamic nature of the Metaverse.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Changes to a physical object are mirrored in its virtual counterpart in the Metaverse because of their digital twins, which are linked to real-world objects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' People can also change objects by interacting with them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Instead of just looking at digital objects in the Metaverse, users will be able to experience a place and interact with them [45].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' The creation of new objects will require complex inputs and will demand high- quality user interaction with the objects in the Metaverse.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' The Metaverse poses three crucial challenges for effective user interaction, as depicted in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 6: Interacting with existing objects: Users’ physical interac- tions with these virtual worlds are an important consideration [46].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' For the Metaverse to persist, this is a fundamental challenge that must be overcome.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' When the user is unable to control the interaction, they will stop using it immediately.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' When a user is completely immersed in a virtual world and finds themselves unable to perform a task that they could do in the real world, they become frustrated and annoyed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Modifying existing objects: As technology gets better and the real world keeps changing, the Metaverse objects will need to be changed to make them seem more real [47].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Realistic objects need more precise modelling algorithms, just like real faces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='  Even in the Metaverse, where scenes and avatars are always changing and interacting, objects have to be changed all the time to reach this level of realism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Creation of new virtual objects: The Metaverse is a vir- tual 3D universe comprised of virtual 3D objects [48].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' The Metaverse requires the creation of immersive experiences based on real-world artefacts to accomplish its objective of combining the digital and physical worlds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' In the Metaverse, a lot of digital objects will need constant sensor inputs from their physical counterparts to produce this realistic immersive experience for the users.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' The Metaverse will also enable its users to create virtual objects by providing them with various tools and applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' As a result, it creates a huge requirement for bandwidth, which is a challenge to achieve with the present technology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' From the above discussion, it is obvious that efficient user interaction plays a significant role in the creation, interaction, and modification of digital objects in the Metaverse.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' This requires massive input from real-world objects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 6G’s URLLC and real-time processing abilities will aid in the building of a highly immersive 3D environment in the Metaverse.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='  F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 6G FOR LOW LATENCY COMMUNICATION IN THE METAVERSE Low latency communication is the capability of the commu- nication network to deliver large quantities of data with min- imal delay and high accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' These networks are designed to support operations that require access to rapidly changing data in real-time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Advanced technologies like self-driving cars, holographic telepresence, remote surgery, deep-sea and space tourism, and other AR and VR innovations are becom- ing part of the Metaverse [49].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' For instance, we had been accustomed to virtual communication using Zoom, Skype, Microsoft Teams, and other platforms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Future developments in VR and AR are well on their way to making an office where people can talk to each other in a fully immersive way.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' This integration of advanced technologies into the Metaverse creates a huge demand for next-generation networks with enhanced bandwidth and latency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' The present network infrastructure cannot provide the bandwidth and latency required for the Metaverse and its applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' The capacity of current 5G networks to handle the IoE, holographic telepresence, collaborative robotics, and deep-sea and space tourism is limited.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' These applications require multiple terabytes of bandwidth as they depend on real-time inputs from the real world.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' From the discussion, it is clear that the Metaverse necessitates the highest network positioning accuracy and multiple terabytes of bandwidth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='  The 6G network, with its advancements like greater use of the distributed radio access network (RAN) and the terahertz (THz) spectrum to increase capacity and improve spectrum sharing, will provide effective and low-latency communica- tion required for the Metaverse [50].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='  G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 6G FOR COMPUTER VISION IN THE METAVERSE  Vast Coverage and Transmission Rates  FIGURE 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 6G for Computer Vision in the Metaverse  Computer vision is the study of how computers perceive and interpret digital images and videos.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Computer vision encompasses all activities done by biological vision systems, including seeing or sensing a visual signal, interpreting what is being seen, and extracting complicated information in a form usable by other processes [51].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Using sensors, comput- Uninterrupted Network Service Extended Reality Virtual Reality Augmented Reality   Mixed Reality Healthcare Defense Construction Education Retail Applications of XR in the Metaverse Independent Frequency Symmetric Speed The Metaverse  EEEAccessAR+6GBartlomiej Siniarski et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' : Need 6G for the Metaverse Realization 11 VOLUME 4, 2016  ers, and machine learning algorithms, this multidisciplinary field replicates and automates essential parts of human vision systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' The objective behind computer vision is to develop artificial intelligence systems that can see and understand their surroundings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' In the Metaverse, computer vision plays an important role in enabling humans to experience the virtual environment, as depicted in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Through the use of digital avatars, VR and computer vision provide a near-to-lifelike experience in the Metaverse [52].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' In order to connect to this virtual world, the user needs to use XR devices, which are built on the foundation of computer vision.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' XR applications rely heavily on computer vision.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Visual information in the form of digital images or videos is often processed, analyzed, and interpreted with the help of computer vision and visual information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' This helps people make effective decisions in the Metaverse.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' As a result of computer vision, VR and AR environments can be built that are more accurate, trustworthy, and user-friendly than their real-world counterparts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Human position tracking is a computer vision challenge that tries to figure out where people are located in an environment that is constantly changing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' In the Metaverse, the healthcare, military, construction, manufacturing, education, and retail sectors will rely largely on computer vision.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' For example, doctors can improve surgical processes and study data from 3D scans in real time using computer vision.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='  The computer vision will assist doctors in detecting, diagnosing, and treat- ing potential diseases and enable them to examine patients from anywhere in the world [53].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Computer vision in the Metaverse will evolve at an accelerated rate, and even 5G cannot compete with the rapidly evolving technological re- quirements of the Metaverse’s computer vision capabilities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' The computer vision requires the continual collaboration of heterogeneous devices to provide immersive experiences for the users, which requires uninterrupted network service, and should provide symmetric uploading and downloading speeds for users to quickly upload all their content while concurrently downloading the content of others.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 6G supports a higher number of device connections, which is very crucial for computer vision in the Metaverse for delivering its fully immersive services to customers [54].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' The independent fre- quency, higher data transmission rates, and large coverage of 6G will enhance the QoS of computer vision in the Metaverse.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='  H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 6G FOR HIGH TRANSACTION INTEGRATION/ SCALABILITY To date, the Metaverse implementations used a central- ized cloud-based approach for avatar physics emulation and graphical rendering.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' The centralized design is unfavourable as it suffers from several drawbacks caused by the long latency required for cloud access.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Further deployments of Metaverses will also bring scalability issues to the physical layer due to the increased number of computing tasks mainly generated by extremely demanding applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' The tradi- tionally deployed centralized architectures are unlikely to support a large number of Metaverses and their users, so the introduction of de-centralized Metaverse systems including frameworks and protocols is inevitable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' There are several approaches that can be taken, starting with leveraging Mobile Edge Computing (MEC) technology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' For example, [55] pro- posed the blockchain-based MEC architecture, where base stations allocate their computation and communication re- sources for providing video streaming and the use of a series of smart contracts enables a self-organized video transcoding and delivery service without a centralized controller.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Using the MEC more efficiently will not fulfil the requirements in full, so the decentralized architecture will have to further distribute the communication and computational cost among different nodes present in the virtual space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='  The concept of de-centralizing the Metaverse applications was presented by authors of Solipsis [56] - a system that allows the adaptive streaming of 3D models including avatars, sites and objects in a completely decentralized fashion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' In general, to over- come challenges related to a high number of transactions, massive resource demands and scalability concerns a novel framework should be proposed to address those emerging challenges for the development of future Metaverses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' In such framework, the Metaverse Service Provider (MSP), which is a service provider that offers applications or services such as games, conferences or concerts should be able to get paid for provided services and in addition to this, the MSP should be allowed to negotiate with the Metaverse User (MU) to use MUs computational resources in return for discounts or rewards.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' The blockchain, which is provided by the MSP can contain all interactions between the MSP and MU in terms of transactions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' The MetaChain [57] describes a similar concept that could serve basis for future deployments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' In this particular proposal, the blockchain shards are used to allow the MUs to contribute their computational resources to the Metaverse application provided by the MSP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' This is done in exchange for digital assets such as tokens or service access.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' With this approach, more users can be attracted to a particular Metaverse.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' However, attracting users to contribute resources is going to be particularly challenging.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='  The reason is that the service provider will not be able to directly allocate the user resources to the shards.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Sharding is so far one of the most practical solutions to achieve a scale-out system where the processing, storage, and computing can be conducted in parallel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' As such, the capacity and throughput being linearly proportional to the number of participating nodes or the num- ber of shards become possible, while preserving decentral- ization and security.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' The consideration has to be taken when creating shard-based systems as users (by human nature) will aim to maximize their profits and concentrate resources on the shards that pay more.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Nevertheless, whichever form such framework will take, a pay-per-share protocol is required to off-load computational workload onto the Metaverse user devices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='  EEEAccessBartlomiej Siniarski et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' : Need 6G for the Metaverse Realization 12 VOLUME 4, 2016  The Metaverse Continuous Integration          High Connectivity  I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 6G FOR SECURITY AND PRIVACY PROTECTION, ELIMINATED CRIMINAL/HACKER ACTIVITIES, TRUST AND ACCOUNTABILITY  Network Analysis  Artificial Intelligence  FIGURE 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 6G for Security and Privacy Protection  Metaverses should offer their users an extraordinary im- mersive experience in virtual environments, such as enter- tainment games and smart cities, using its enabling tech- nologies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' The metaverse can track users’ physical actions and physiological responses and may expose confidential information about their habits and physiological nature to third parties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' If hackers get their hands on such sensitive in- formation, it could lead to harassment and the theft of digital assets, which could make users lose faith in the security and privacy of the metaverse.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' These issues can be addressed by utilizing privacy-protection technologies like "Private Copy" and "Clone Cloud", as depicted in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' The creation of private copies and clone clouds is dependent on high connectivity and continuous integration with the metaverse environment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' The edge intelligence facilitated by 6G can support the needs of these technologies in the metaverse.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' The use of a blockchain-based digital twin wireless network and an edge computing federated learning architecture can further enhance the users’ privacy and data security [8].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Together with 6G, AI can optimize connectivity while also enabling traffic prediction and improving security in the metaverse.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' To avoid information breaches, physical layer communication may use a machine learning-based antenna design.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Machine learning and quantum encryption can also be used to protect the security of communication devices in the metaverse.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='  The metaverse’s security may be increased by using early warning systems and AI-enabled 6G to identify network anomalies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' The use of distributed and federated AI in a 6G network also eliminates the necessity for data sharing across the metaverse devices, which preserves the privacy of the users.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='  IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' ROLE OF 6G TECHNOLOGIES FOR THE METAVERSE 6G will play a key role in the Metaverse operation since such an environment requires pervasive connectivity for full- fledged and omnipresent Metaverse immersion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Essentially, very-high bitrates and ultra-low delay are crucial for a sat- isfactory Metaverse experience.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' An important factor on this performance is the smart management of connectivity re- sources/services, scalable infrastructure and very low latency communications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Therefore, Edge AI and cloud infrastruc- ture are necessary for efficient and performant handling of relevant use cases in the Metaverse.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Edge AI is an impor- tant enabler since it facilitates AI-driven optimized network management and minimizes delay with distributed and close- to-the-user computing paradigms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' This technology will be compounded with the AI native design of 6G which will be embedded for numerous functions ranging from physi- cal layer control to service management.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Furthermore, the required flexibility and scalability for network and service environment requires moving towards cloud-native technolo- gies which can also form telco clouds for more efficient and scalable Metaverse infrastructure in the backend.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' In the cyber-physical domain, another aspect of the Meta- verse regarding 6G will IoE and robotics play a key role.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Additionally, 6G will have the essential toolbox to enable AR/VR, which is critical since the Metaverse will be the main vessel for AR/VR experience.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='  An appropriate immer- sive experience in the Metaverse will be possible with those technologies enabled by 6G communication and computa- tion functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' As a transversal technology similar to AI, blockchain can also help the distributed and open nature of the Metaverse and enable the transferability of digital assets which will be an important capability for the Metaverse use cases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' A depiction of these technologies and their roles is provided in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 9 and the summary of all related works is presented in Table 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' AI 1) Introduction Based on the combination of many advanced technologies, the Metaverse should be built to convey a groundbreaking immersive experience to users, in which AI has played a vital role in the foundation and development of the Metaverse re- garding numerous aspects, including core services and appli- cations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Besides the responsibility of ensuring the reliability of the Metaverse’s infrastructure, AI can help developers in designing and building a smarter and more beautiful virtual world and further allows users to acquire hyperreal creation using built-in tools.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' In 6G systems, numerous challenging tasks and applications can be solved and enabled by advanced ML algorithms with different learning mechanisms (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=', su- pervised learning, unsupervised learning, and reinforcement learning) to achieve high performance and low latency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Espe- cially, DL with the advantage of effectively learning complex patterns from practical large and messy datasets will be the key technology to polish many aspects of the Metaverse, from the intelligence of AI agents and virtual assistants (a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=', chatbots) to the visual quality of 3D worlds [58].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='  Indeed, the presence of AI in the Metaverse can be realized in the interactions between a user (represented by an avatar) and other objects (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=', non-player characters) by automatically analyzing sensory data for multiple tasks, such as speech recognition and understanding, facial expression analysis, body movement tracking, and gesture recognition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Besides, Private Copy Cloud Clone Privacy Protection Technologies Quantum Security Quantum computing Data Privacy Federated Learning USER  EEEAccessMETA6GBartlomiej Siniarski et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' : Need 6G for the Metaverse Realization 13 VOLUME 4, 2016  FIGURE 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 6G key technologies and their roles for the Metaverse.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='  AI can be applied to preserve users’ identity and their digital assets from cyberattacks, especially in the scenario in which the Metaverse is built with a cross-chain bridge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='  2) How 6G AI can help, on which features In the Metaverse, natural language processing (NLP) plays an important role to deploy intelligent virtual assistants (in- cluding chatbot) [59], which helps the Metaverse compre- hensively understand what users are typing and talking, from simple sentences to complicated and long conversations, over unlimited, to smooth user interaction accordingly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Empow- ered by AI with ML and DL algorithms, chatbots can imme- diately respond to the users and adapt to an environment with reinforcement learning to consolidate operation and improve the performance of an overall virtual assistant system [60].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' In the NLP domain, language modelling aims to predict linguistic components in sentences and paragraphs by min- ing syntactic and semantic relations of words and phrases, which is commonly developed for machine translation and text recommendation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Several advanced language modelling methods have exploited DL with RNN, LSTM, and CNN architectures to improve the overall system efficiency and addressed many fundamental tasks [61], such as identify- ing long-term dependency in long sentences in complicated scenarios, recognizing hyphenated words, misspelt words, suffixes, and prefixes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Especially, language modelling should be taken into consideration with different popular languages, such as English, Chinese, Spanish, and French [62], [63]  to attract as many as possible users from over the world to join the Metaverse.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Some advanced structures in deep networks, such as bidirectional LSTM, bidirectional gated recurrent unit (GRU), and channel-wise attention connection, have been leveraged to deal with some challenging prob- lems, such as sentiment analysis, question type classification, and answer identification with multiple sentences [64], [65], which accordingly improved readability, interpretation, and rationality of virtual assistant agents.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Some other specific AI- based NLP tasks (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=', context retrieval, semantic notation, and named entity recognition) can be considered to uplift text-based and speech-based user interactive experiences in the Metaverse.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Commercial headset devices with VR/XR technology have been designed to bring 3D viewing experiences to users, including high video quality (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=', high resolution and high frame rate) and wonderful wearing comfort thanks to the ad- vancement of AI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' In [66], an eye fixation prediction method was introduced for gaze-based applications (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=', video ren- dering and content visualization), in which a DL framework with hierarchical CNN architectures was exploited to process different data types, including VR images, gaze data and head data collected by wearable sensors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='  Some recent works have studied advanced ML and DL algorithms to precisely identify periodic behaviours of VR gear’s user (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=', gaming controllers and head-mounted display) for automatic identity authentication and health issues detection [67].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
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+page_content='Edge ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='Edge ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='AI ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='minimization ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='devices ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='Context ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='Awareness ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='Intelligence ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='AI-driven ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='Smart ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='edge ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='Privacy ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='services ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='Elastic ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='Metaverse ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='services ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='Federation ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='Efﬁciency ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='Cloudiﬁcation ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='Ultra-scalable ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='Consolidation ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='Privacy ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='preservation ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='Interoperabilty ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='Data ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='storage ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='compute- ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='storage ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='METAVERSE ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='Blockchain ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='Virtual ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='economy ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='(trading,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' NFTs,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=') Intelligent Radio Improved QoS/QoE Spectrum ﬂexibility Open RAN Data acquisition Asset and identity protection Virtual and AI agents Connectivity ﬂexibility NLP AI Performance optimizations Infrastructure reliability Computer vision  EEEAccess8 -RANBartlomiej Siniarski et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' : Need 6G for the Metaverse Realization 14 VOLUME 4, 2016  FIGURE 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' The roles of AI for the development and advancement of the Metaverse.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='  assess the quality of images/videos (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=', color saturation, brightness, resolution, and frame rate) displayed on the screen of VR devices, and then automatically adjust screen settings to optimize the visualization based on video contents and user conditions [68].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Along with the VR/XR technologies, computer vision is one of the most important sectors to build a beautiful virtual world in the Metaverse and enable it to be more intelligent from the user’s viewpoint with the adoption of AI, especially DL in a few years [69]–[71].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Many sophisticated CNN architectures have been designed for different fundamen- tal image processing and computer vision tasks, such as object detection, semantic segmentation, and scene under- standing [72], [73].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' For instance, atrous convolution was introduced by DeepLab [74] for semantic segmentation to capture more meaningful features by enlarging the receptive field of kernels to enhance the learning efficiency of a deep network while obtaining a small network size.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Static and dynamic objects can be detected and located in the virtual worlds accurately by several recently advanced DL models to provide useful information to users and be synthetized for higher-level tasks like scene understanding and detailed captioning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='  Some image/video quality distortion problems, such as blurring, noise, and frame corruption, can be ad- dressed effectively by AI technology to guarantee the high- class visual perception of a user when experiencing the Meta- verse [75].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' In addition, the activities, including single actions and interactions, of users and non-player characters in the Metaverse can be automatically detected and recognized by AI-powered human pose estimation and action recognition methods [76].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Some convolutional networks have exploited cutting-edge layer structures, such as dense connection, skip connection, and attention connection, to estimate complex  human poses and classify grouped activities while handling other challenges like varying viewpoints, object occlusion, and complicated actions in practice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' For example, generative statistic models and hybrid LSTM-CNN architectures are suggested in [77] to precisely examine pose transition in the spatiotemporal domain, thus increasing the accuracy of action recognition and activity classification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' To preserve the Metaverse from different cyberattacks, especially protect users’ digital goods and cryptocurrency assets, many advanced ML algorithms and DL models can be deployed in multiple layers (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=', network and services layers) of the Metaverse’s platform for intrusion detec- tion [78]–[80], in which various malicious attacks can be automatically and accurately detected and classified to im- mediately provide an efficient security solution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' In [81], a holistic security method with sufficient assurability and ex- plainability was proposed to quickly and sequentially detect abnormalities and time-dependent abnormal events in IoT systems and software-defined networks, in which zero-bias neural networks are transformed into performance-assured binary abnormality detectors to increase detection accuracy while presenting the lowest latency based on false alarm constraints.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='  In the effort to exploit DL denoising autoencoder (DAE) for many fusion security problems, many variants of DAE, including stacked autoencoder, stacked sparse au- toencoder, stacked noise autoencoder, stacked contractive autoencoder, deep belief network, were benchmarked in for performance comparison with different practical intrusion detection datasets [82].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Reinforcement learning (RL) with the capability of learning environmental factors to adapt learnable parameters was also exploited to deal with different types of cyberattacks (such as malware, denial-of-service at- tack, and man-in-the-middle attack) [83].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' In addition,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' privacy Understand and respond to user to enhance text-base and speech-based user interactive experiences Improve viewing experience of high video/image quality with VR/XR devices Multi-language modeling Eye ﬁxation estimation Semantic analysis Smart Assistance Quality Experience Video/image quality enhancement Question type classiﬁcation Adaptive content-based visualization  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content="Answer identiﬁcation VR gear's user behavior prediction Ai for the Metaverse Create a 3D virtual world with beautiful outlook and intelligent environment Attractive 3D World Security Protect user digital goods and cryptocurrency assets from different cyber-attacks Object detection Intrusion detection Semantic segmentation Malware and denial-of-service  " metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='Image restoration and registration Man-in-the-middle attack detection Video analysis and scene Privacy preservation understanding Enhance intelligence of AI agents in real-time strategy and ﬁghting games Increase the performance of 3D rendering AI-based data security Computer vision for 3D world development Analyze mental state with brain-computer interaction AI-aided VR/XR NLP for intelligent virtual assistant Improve performance  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='of data transmission in URLLC with intelligent MEC  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='EEEAccessBartlomiej Siniarski et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' : Need 6G for the Metaverse Realization 15 VOLUME 4, 2016  preservation in the Metaverse should be uplifted comprehen- sively with the help of AI to ensure that there are no leakable risks and threats to users’ big data in the virtual world.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' For instance, a privacy-aware and asynchronous DL-based method was introduced in [84] to maintain the confidentiality of data among different collaborative data collection sites.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' In [85], an optimal centralized privacy-preserving aggregate mobility data release mechanism was proposed to minimize the data and information leakage, in which deep RL models and the Asynchronous Advantage Actor-Critic algorithms are combined to optimize the privacy-preserving method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' The above-mentioned privacy-preserving DL-based methods can be recommended for the Metaverse to combat information leakage threats and adversary attack effectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='  3) Summary In the Metaverse, AI has presented a plentiful foundation and development in numerous aspects and helped to construct a more beautiful virtual world with intelligent and secured services, thus bringing a wonderful experience to users.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Sev- eral advanced ML algorithms and DL architectures have been deployed to take care of the comfortableness of VR users, and the interaction between users with virtual assistants, and automatically provide useful information about the virtual worlds to users.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Besides some popular domains like NLP and computer vision, AI has great potential for deployment in other sectors: protecting users’ digital assets from hackers, early detecting intrusions for data security and privacy preser- vation, improving the performance of URLLC with intelli- gent MEC, enhancing the intelligence of AI agents in real- time strategy and fighting games, and analyzing mental state with the brain-computer interface as illustrated in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Although some advanced ML and DL models can conduct a high performance in many detection and classification tasks, they represent black boxes that lack the capability of explainability and interpretability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Therefore, there remains room for AI research and development in the Metaverse.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' BLOCKCHAIN 1) Introduction In the Metaverse, data privacy and virtual asset (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=', cryp- tocurrency and NFT) security of users should be guaranteed as the top priority.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' In this context, blockchain technology represents a promising solution with many unique features at once, for example, decentralization, transparency, and immutability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Fundamentally, blockchain is an innovative technology that permanently records transactions in a decen- tralized and public database so-called a ledger [86].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Although all transactions are transparent (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=', being available to check by anyone), the decentralized recording system of blockchain is very difficult to fool or control.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Some blockchains like Ethereum and Solana are programmable through smart con- tracts with different consensus mechanisms, such as proof- of-work and proof-of-stake, which can meet high-security re- quirements of e-commerce platforms and enable the revolu- tion of the digital ecosystem in the Metaverse, especially sup- porting virtual asset payment and trading activities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' A smart contract on the blockchain could be used to establish the ownership of any digital object, such as artwork and music, over NFT specialized by unique and nonreplaceable (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=', no one else can claim the ownership of that digital product on the blockchain even if they have a copy version on computers).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='  The role of blockchain in the Metaverse relies on ensuring data privacy and security, enabling seamless and secured data sharing, data interoperability and integrity with some common applications and services, such as decentralized finance and NFT market [87].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Besides that, blockchain allows digital goods to be tradable safely in a virtual world and enables the connection of physical objects to the Metaverse over NFTs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Notably, if two virtual worlds are interoperable, the blockchain has to authenticate the proof of ownership of digital goods in both virtual worlds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Indeed, blockchain bridges the real world and the virtual world besides playing as the gateway for users to access the Metaverse.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='  2) How 6G BC can help, on which features Data acquisition is one of the most fundamental processes to build the virtual world in the Metaverse, which collects big data from different modalities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Notably, the sensitive data collected from users to train AI models for several special modules (such as decision-making of virtual assistant, recommendation system, digital product development, and automated market maker) in the Metaverse should be secure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' For secure and large-scale environment data acquisition, the work in [88] proposed a blockchain-based system which is specialized by one valuation layer to assess the quality of acquired data, one consensus layer to encourage and incen- tivize high-quality data acquisition, and one ledger layer to record transactions and qualified environmental data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' In [89], a blockchain-based efficient data collection and secure data sharing mechanism was introduced for reliable industrial IoT systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' This mechanism has exploited the Ethereum blockchain to maximize the amount of acquired data and the deep reinforcement learning algorithm to obtain highly secure and reliable shared data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' To guarantee the users’ privacy in crowdsourcing systems, Li et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' [90] designed a blockchain-based decentralized framework for data collec- tion and sharing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' There were three standard smart contracts on blockchain executed for the whole process of data acquisi- tion to achieve such crowdsourcing information as task post- ing, receiving, and assignment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='  The proposed method was implemented and verified on an Ethereum test network with real-world data, which demonstrated usability, feasibility, and scalability to be suitable for distributed crowdsourcing systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Although blockchain technology can ensure highly secure and reliable data supplied to the Metaverse, its draw- back is low latency due to the complicated and distributed nature of processing transactions with smart contracts and consensus mechanisms like PoW.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Besides, the high transac- tion fee is also a realistic barrier for a low-income user to experience the Metaverse.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' In a large-scale Metaverse platform, data storage should  EEEAccessBartlomiej Siniarski et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' : Need 6G for the Metaverse Realization 16 VOLUME 4, 2016  FIGURE 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' The roles of blockchain for ensuring the security and privacy of data acquisition, data sharing, data storage, and data interoperability in the Metaverse.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='  be taken into consideration seriously because of the high velocity, big volume, and complicated variety of big data from a plentiful number of applications and services de- ployed in virtual worldds [91].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' There exist many underlying risks, such as leakage, tampering, and loss if the Metaverse is built on a platform with centralized storage systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Some sensitive data like biometric login data of the user (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=', face and touch identification on iPhone) can become the target of cyberattacks to steal virtual assets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' To overcome the above- mentioned issues of centralized systems, the work in [92] proposed a large-scale secured IoT data storage scheme by exploiting blockchain miners to manipulate IoT data stored in distributed hash tables (DHTs).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' In the blockchain sys- tem, a certificateless cryptography scheme was applied to reduce redundancy in traditional public key infrastructure and authenticate IoT devices, where the generated public key pairs are broadcasted to all devices with verification done by the blockchain miners.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' In [93], the time-series data in the Metaverse was stored in a locality-aware auditable decen- tralized storage ecosystem that was designed and managed thanks to the advancement of blockchain technology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Some data storage systems with recovery functionality have been developed to effectively address multiple problems, such as low integrity, high cost, and easy tempering.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Liang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='  [94] introduced a secure blockchain-based data storage scheme, wherein the incoming data packets are verified with smart contract and consensus mechanism, and then checked to early detect any threats before being stored on a decentralized  system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Notably, when distortion occurs to the stored data, multiple nodes in the blockchain network can repair it suc- cessfully.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' As the mixture of numerous digital realms, the Metaverse demands manipulating and processing the big data that is acquired from incompatible infrastructures for different pur- poses, in which the standardizations of data for different applications and services in the virtual worlds are dissimilar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' This reveals a serious concern about data interoperability when expanding the Metaverse with an interconnection ca- pability among different virtual worlds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' To ensure the inter- operability between different virtual worlds in the Metaverse, building a cross-chain protocol or an inter-blockchain bridge becomes a promising solution in many specific domains like healthcare and e-commerce [95]–[97].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' A blockchain bridge is a protocol connecting two economically and technologically separate blockchains (such as Bitcoin, Ethereum, Avalanche, Solana and Polygon) for interactions and acts like a phys- ical bridge linking the ecosystems of one blockchain with another.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' As a result, blockchain bridges enable what is called interoperability means that digital assets and data hosted in Metaverses built on different chains can interact with each other [98].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Besides, blockchain bridges allow users to access new protocols on other chains and encourage collaboration between developers from different blockchains, thus promot- ing a virtual economy in the Metaverse.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
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+page_content=' and complicated variety of Metaverse big data Cross-chain interactive decentralized access model Blockchain bridge for different chains interacting with each other Data interoperability between different virtual worlds in the Metaverse For dealing with dissimilar data acquired from incompatible infrastructures Blockchain-based identiﬁcation and authentication Blockchain-based crowdsourcing for privacy preservation in mobile environments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' For dealing with privacy issues in ﬁnancial ecosystem having DEXs and DeFi  EEEAccessBartlomiej Siniarski et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' : Need 6G for the Metaverse Realization 17 VOLUME 4, 2016  records (EHR) sharing systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' The proposed framework facilitated the medical data on EHR systems between dif- ferent medical providers and healthcare institutions with a decentralized trusted third-party audior for interoperation validation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Some recent cross-chain protocols [99], [100] have been introduced to interconnect multiple blockchains for secure data utilization and management while obtain- ing full interoperability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' In [99], a cross-chain interactive decentralized access model was designed with a gateway to reading the information on multiple chains and route cross-chain transactions, and a notary network with an inter- planetary file system and BigchainDB to verify and confirm each transaction based on a voting mechanism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Such kinds of cross-chain protocols allow users to easily buy, sell, and trade virtual assets among different digital worlds with- out any intermediate tools, and consequently encourage the adoption of the Metaverse.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Along with interoperability, data integrity has also received much attention in the Metaverse, in which blockchain technology was considered to verify and protect data integrity in decentralized cloud computing systems [101], [102].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' In the Metaverse, a user can freely interact and trade virtual goods (including cryptocurrency and other virtual assets like NFT) with a virtual assistant and other users via decen- tralized exchanges (DEXs) integrated into the Metaverse to promote the development of decentralized finance (DeFi).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='  As an ecosystem of financial applications built on blockchain networks, DeFi enables easy access to financial services, facilitates traditional financial systems, and has a modular framework with interoperability with public blockchains.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Recently, GameFi, a fusion of words game and finance, refers to play-to-earn blockchain-based games with economic in- centives to players, which is being developed and integrated in the Metaverse.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' A GameFi ecosystem uses cryptocurrency, NFTs, and blockchain technology to create a virtual gaming environment, where various GameFi ecosystems built on different chains can be involved in the Metaverse owning to chain bridges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' In this context, it arises many privacy issues (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=', the leakage of user identity and other personal information that can be stolen for illegal purposes) can be ef- fectively handled by blockchain technology with immutabil- ity [103].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' In a blockchain-powered Metaverse, third-party intermediaries are not permitted to manipulate the data of other parties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' In [104], a blockchain-enabled crowdsourcing approach was proposed to deal with privacy preservation in mobile environments, where users can access the Metaverse using mobile devices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' In secure 5G and 6G communica- tion networks [105], blockchain was exploited to minimize privacy breaches by completely integrating authentication mechanisms with blockchain-based identification systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='  3) Summary With the distinctive features of decentralization, immutabil- ity, and transparency, blockchain technology has promoted the development and advancement of the Metaverse, where it has played an important role in any Metaverse platforms with some great contributions in terms of many technical aspects, including data acquisition, data storage, data in- teroperability, and privacy preservation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Besides ensuring the privacy of sensitive information and security in trading activities (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=', buy/sell cryptocurrency, NFTs, and other virtual assets), blockchain has shown great achievement to revolutionize user’s immersive experience, boosting the eco- nomic growth, and attracting new users to the Metaverse via numerous blockchain-aided applications and services supplied in the virtual worlds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' However, it remains several challenging issues to concurrently attain security, scalabil- ity, and decentralization when the Metaverse must serve a huge number of users and a rapidly increasing number of transactions to process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Consequently, many research topics to optimize blockchain for the Metaverse should be con- tinuously exploited in the future, such as consensus algo- rithms, blockchain interoperability, smart contract, and net- work management.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' EDGE COMPUTING AND EDGE AI 1) Introduction The Metaverse is envisaged to map and simulate all our daily life activities in cyberspace at a huge scale while enriching such mapping with an immersive and interactive user experience.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Cyber-physical and digital twin applications will also be integrated with the Metaverse application to offer realistic cyber representations of the physical world.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' In the ICT infrastructure, there will be the Metaverse engine which performs computations required to run virtual universe simulations carrying out computationally heavy tasks such as collision detection in the virtual universe and computation of 3D physics, and also other aspects of virtual universe that demand high computational power [106].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' The Metaverse is striving to connect billions of users and create a shared world where virtual and reality merge [8].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Therefore, users interact in the physical-virtual world with the characteristics of diversification of information, identities, and modes un- der the requirements of ultra-low latency, massive resource demands, interoperability between applications, and security and privacy issues [107].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' The promised Metaverse operation will require extremely low latency with highly elastic and omnipresent compute and storage resources.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='  The latency and processing challenge for the Metaverse is in line with what is expected with 6G edge computing realization: For the Metaverse extended-reality computations to be offloaded, the entire process must be shortened so that input from the user device, a network trip, processing by the service, a return network trip and drawing the output on the user device fits in the 20ms time taken by a single network trip today [108].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Cloud-based processing for Metaverse operation can be unfavourable as it suffers from several drawbacks caused by the long latency required for cloud access, such as low-quality visualization in XR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 6G enables real-time, ubiquitous, and ultra-reliable communica- tions for massive Metaverse devices with support for device mobility, which can reach 1020 Gbps [109].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' To this end, Fog  EEEAccessBartlomiej Siniarski et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' : Need 6G for the Metaverse Realization 18 VOLUME 4, 2016  Computing [110] and Mobile Edge Computing [111] have been proven effective to tackle the issues faced by cloud- based systems, by moving the computational heavy load near the end-user and distribute it among edge devices;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' such ap- proach can significantly reduce the latency and optimize the system performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Furthermore, there is the cost-benefit: such an approach it would drive down the cost of XR devices and allow mass adoption.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Verizon has estimated that any more than 20ms of motion-to-photon (total stack) latency causes many users to become nauseated;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' for comparison, well-built wireline broadband networks today typically have 20ms of network latency alone, and typical LTE latencies are 3x higher.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Therefore, edge computing is an important technology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' For instance, Zhang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' [112] introduced the MEC into the Metaverse to improve the quality of users’ experience.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Xu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' [7] discussed the potentials of AI, Edge computing and blockchain for ubiquitous, seamless access to the Metaverse.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Similarly, Lim et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' [113] present the infrastructural architecture required for the Metaverse with a special focus on the convergence of edge intelligence and the infrastructure layer of the Metaverse.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 6G-enabled edge intelligence opens up a new era of Internet of Everything and makes it possible to intercon- nect people-devices-cloud anytime, anywhere.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='  In this con- text, industry, and academia have developed a new learn- ing paradigm, Edge Artificial Intelligence (Edge AI) [114], which allows AI models to be deployed on devices and perform real-time data processing and model inference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 6G mobile communication technology provides edge AI with lower latency, more stable network connection, and more secure network architecture.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Edge AI with 6G is expected to be applied to solve problems such as high bandwidth and high connection density in the Metaverse.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' However, the Metaverse still faces many challenges, such as users’ privacy, network latency, and resource allocation issues.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Moreover, the Metaverse places higher demands on the current edge AI architecture.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' As mentioned above, 6G edge intelligence has the advantages of low latency, computing offload, and high performance [115].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Overall, the application of 6G-oriented edge intelligence has the benefits of balanced data storage, efficient data transmission and high reliability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='  2) How 6G EC and Edge AI can help the Metaverse As noted above, a high-speed and low-latency network con- nection and ubiquitous access to services is an important foundations for improving the user experience in Metaverse.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Otherwise, issues such as visual jitter or delay and other undesirable phenomena might lead to the subpar perfor- mance of Metaverse.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' In that regard, to reduce network la- tency, an incentive mechanism framework for VR services was proposed in [116], which uses perceived quality as a criterion for measuring immersive experience and effectively evaluates the immersive experience in the Metaverse.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' [117] presents a novel MEC-based mobile VR delivery framework that is able to cache parts of the field of views (FOVs) in advance and compute certain post-processing procedures on demand at the mobile VR device.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Jiang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' [118] found that coded distributed computing (CDC) can improve the latency problem in the Metaverse and proposed a CDC and dual blockchain distributed collaborative computing framework.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' However, the computing, communication, and storage shortage will seriously affect the user’s immersive experi- ence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' For the resource allocation problem, a new blockchain- based framework called Metachain was proposed in [87] which uses Stackelberg game theory analysis to propose an incentive mechanism, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=', users obtain corresponding re- wards by providing resources to blockchain shards.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='  Based on the intelligent 6G edge network, a machine learning frame- work was proposed in [119] for decentralized learning and coordination of edge nodes to improve resource allocation strategies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' For Edge AI and its applications in 6G, there are various challenges which are investigated by the research commu- nity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Edge AI paradigm and its applications still have the following issues that need to be optimized [8]: – High Latency: Since edge AI generally involves thou- sands of remote devices and needs to transmit and process massive amounts of data [120], [121], the high latency issue in the current network environment has always been one of the bottlenecks hindering the wide application of edge AI [122], [123].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' – Fragile Stability: In edge AI, the training of large- scale models often requires powerful computing power and stable network connections, especially the training of large language models [124].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' However, the current network en- vironment is only suitable for the training of small-scale models [125].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' This is due to the fragility of the network connection leads to the failure of large-scale model training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' – Low Security: The current network architecture no longer meets the security needs of thousands of remote de- vices connecting to cloud servers today [120].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Furthermore, the openness of the network further challenges the security of the current network architecture.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='  These issues are expected to be exacerbated with the utilization of Edge AI in 6G for the Metaverse applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' For instance, in [8], Chang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' propose a self-balancing federated learning-based Metaverse framework to address the statistical heterogeneity faced by edge-cloud architectures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Besides, in [126], Lu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' proposed a blockchain-based digi- tal twin wireless network (DTWN) edge computing federated learning framework to solve the problem of user privacy data security.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='  3) Summary The integration of edge computing and realization of edge AI in 6G will provide various capabilities as well as challenges for the Metaverse.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' The key benefit is related to latency min- imization needed for superb Metaverse user experience and pervasive services.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Similarly, the inherent Edge AI support in 6G will also serve the Metaverse for smart edge services leading to better Metaverse services and device simplicity and flexibility.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' However, the potential benefits of 6G edge  EEEAccessBartlomiej Siniarski et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' : Need 6G for the Metaverse Realization 19 VOLUME 4, 2016  technologies should be supported with relevant research for improving on the aspects such as smart resource allocation, security, and privacy-preserving AI techniques.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 6G OPEN RAN 1) Introduction Radio Access Network (RAN) is a very important component of a mobile communication system that can link individual devices like mobile phones or terminals to other parts of the network using cellular radio.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' RAN coordinates the re- source management in the cellular network across the radio sites.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' RAN can send the signal from a mobile device that is connected wirelessly to the core/backbone network to several endpoints in the wireless network, thereby, enabling the signal to travel along with the traffic generated from other networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' A RAN will typically comprise of base stations, that can transmit and receive signals to and from mobile devices in the network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' The signals are then digitized in the RAN-based station and are connected to the network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' RAN contains radio units (RU), distributed units (DU), a centralised unit (CU), and the RAN Intelligent Controller (RIC) for the creation of an effective mobile communication system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' RAN is very important for meeting the low latency and high-speed internet connectivity requirements of real- time applications [127].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' RAN requires manual intervention if any network issues arise in software or connecting devices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Pointing out the cause and the origin of these issues in the network by the mitigation experts is difficult as RAN is black-box in nature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' The process involved in the mitigation of these network issues requires significant cost and time, subsequently affect- ing the overall quality of the network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='  This necessitates the creation of open, intelligent, virtualised, and fully automated interoperable RAN for the next generation 6G networks [128].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Open RAN (ORAN) is one such technology that integrates AI to optimize radio resources and also automates the management and operations of infrastructure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 6G ORAN integrated with AI can be used to implement Self-Organizing Networks (SON) and Radio Resource Management (RRM) solutions that improve network coverage, capacity, handover, and interference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' They could also be used to increase the spectral efficiency of massive MIMO systems by optimising their performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' AI/ML can also enhance the user expe- rience through VoLTE/video quality optimization, terminal anomalies detection, and other Quality of Service/Quality of Experience (QoS/QoE)-based use cases [129].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' The use of ORAN gives mobile network operators (MNOs) the flexibil- ity to provide 6G connectivity in a cost-effective, secure, and energy-efficient way.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' The openness of ORAN also enables the MNOs a unique ability where all the vendors can share the RAN functionalities [130].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' As a result, it avoids vendor lock-in by replacing vendor-proprietary interfaces with a fully disaggregated RAN based on open standards.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 2) How 6G Open RaN can help the Metaverse The users navigate in the Metaverse frequently with the help of technologies such as AI, XR, digital twins, IoT, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='  As a consequence, the Metaverse demands continuous connectivity with sensors, hardware devices, and many other peripherals for providing high-quality and immersive ser- vices to the user.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Any disruption in the network connectivity of these devices will cause the users extreme discomfort and make them feel that the surroundings are out of their control [131].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' The standards for the Metaverse are substantially more demanding than those for the vast majority of internet appli- cations in the present day.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' The current capacity of MNOs to handle the network requirements of devices connected to the Metaverse is rather questionable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' This presents a challenge in the adaptation of the Metaverse.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' To solve these issues ORAN in 6G is a potential solution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='ORAN in 6G with its AI, automation, and fully disaggregated open standards will enable the Metaverse to be cost-effective, secure, and energy- efficient way.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Let us consider the application of the Metaverse in the healthcare domain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' The Metaverse allows healthcare profes- sionals to have better interactions with patients who are in different demographic locations, such as viewing a three- dimensional model of the human body while discussing di- agnoses and treatments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' This would allow doctors to simulate the effect of a proposed treatment on a patient’s body before its application, creating a more personal and informative experience than is currently possible with two-dimensional images displayed on a screen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='  VR, AR, and MR technologies are currently being used for medical training and surgical procedures, These enabling technologies of the Metaverse demand reliable connectivity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' If any failure of software or hardware occurs in the network at the time of medical inter- vention it will lead to serious catastrophic situations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' ORAN in 6G enables devices to relay on multiple MNO, so, this will ensure the medical devices connected to the Metaverse with much reliable connectivity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' The remote medical surgeries supported by the Metaverse require real-time insights.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' The network supporting these devices must be faster in recovering from the related issue and failures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' The ORAN in 6G will provide the Metaverse with zero-touch network and service management capabilities which will automatically resolve the raised issues related to the network faster than the tra- ditional RAN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' The vital monitoring devices connected to the Metaverse require a latency-free and cost-efficient network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' These devices connected to the Metaverse will be greatly benefited by ORAN service management and orchestration platform in 6G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' ORAN service management and orchestra- tion platform in 6G is an intelligent automation platform that applies automation reduces the complexity of networks, improves network performance, and enhances the customer experience in the Metaverse which minimizes ORAN opera- tional costs, as depicted in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='  In the Metaverse, the possibilities of what can be created and purchased are nearly limitless.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Users can purchase avatar skins, hairstyles, clothing, and accessories, as well as virtual  EEEAccessBartlomiej Siniarski et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' : Need 6G for the Metaverse Realization 20 VOLUME 4, 2016  FIGURE 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' The role of 6G Open RAN for the development and advancement of the Metaverse.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='  land and property.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Cryptocurrency and digital wallets will play a role in the Metaverse payments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Blockchain-based cryptocurrencies in the Metaverse or a crypto wallet are required to store and transport digital assets purchased in the Metaverse as well as between the virtual worlds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Digital wallets will be an alternative payment method that enables users to purchase digital goods securely.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Thus the number of transactions occurring in the Metaverse will be limitless.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Any breach or a critical update to the network will interrupt or halt these transactions and may affect the QoS/QoE of the customer in the Metaverse.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' ORAN in 6G will be less dependent on hardware which will reduce the risk associated with automated upgrades or isolated security breaches.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' The enhanced modularity available with open interfaces makes it easier for operators to serve the Metaverse towards a continuous integration/continuous delivery of services.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Every trade or purchase that occurs in the Metaverse is recorded as a transaction, which results in huge network traffic because the data is to be stored in multiple peers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' ORAN in 6G helps the Metaverse in better traffic management and also determines where to send traffic across the network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' ORAN in 6G and AI enables the Metaverse to predict network conditions, such as congestion, so the controller can find an optimal path to send traffic over.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' This provides the users of the Metaverse with valuable insights about the network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='  3) Summary ORAN in 6G with features like openness, better security, enhanced resource sharing, improved traffic management, and zero-touch network and services management provides the Metaverse with a network that is faster, reliable, cost- effective, automated, and intelligent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' This is will help the Metaverse applications and services to be real-time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' ORAN in 6G will help the users in the Metaverse with high-quality immersive experiences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' The issues related to network soft- ware updates or threats will not affect the transactions in the Metaverse as ORAN in 6G is secured and depends less on hardware compared to the traditional RAN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' ORAN in 6G allows AI to easily analyze the network and provide valuable insights for the Metaverse to persist.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Though ORAN in 6G provides better network capabilities to the Metaverse it still faces challenges related to widespread adoption, technical  support difficulties, system integration problems, and secu- rity risks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='  E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 6G CLOUDIFICATION AND CLOUD NATIVE TECHNOLOGIES 1) Introduction A key aspect of 6G networks will be the cloud-native design of the overall ecosystem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' With the actual realization of the Metaverse, the cloud, infrastructure, and telecom companies will have to provide a fully immersive Metaverse experience challenging servers with a 100x harder compute task than an AAA game server hosting Fortnite today, and telecom access networks facing 24x more traffic in a decade [108].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' To ad- dress these compute-storage requirements, the State-of-the- art Metaverse architectures rely on a cloud-based approach for core Metaverse functions such as avatar physics emula- tion and graphics rendering computation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Specifically, XR places extraordinary demands on networks with native cloud design of 6G networks, on-board computation capability to eliminate external computing device dependency can still be delivered on simpler, lighter, and cheaper end-user devices if computationally intensive tasks can be offloaded to a cloud computing instance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' The Metaverse leads to a clear need for cloud computing, considering the amount of storage and processing required to support a virtual reality universe: compute, storage and network loads [132].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' As more performance and details will be demanded, remote cloud-based computers will become a necessary cost-effective way to solve that problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='  The cloud computing technologies will be heavily exploited in two di- mensions: First, by the Metaverse providers themselves built whether with private data centres or managed services.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Due to their advantages, these compute- and graphics-intensive systems will be built on public cloud providers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Another option is to provide on-demand access compute and storage using pay-as-you-go models which can be done by public cloud providers with points of presence distributed globally.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' However, there is also the latency dimension: navigating the Metaverse smoothly through VR technology depends mainly on the network latency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' As VR technologies are delay- sensitive and required very short latency, communicates with the Metaverse servers plays a pivotal role that leads to telco Faster Data Transmission Open Midhaul Reliable Network vCU OpenRU Fronthaul Cost-Effective Network  Automated Network Recovery  IP  RIC  RU  IP  Virtualized  Packet  Core  Intelligent Network Management  vDU  The Metaverse  ORAN  Backhaul  RoE  eCPRI  EEEAccessAiBartlomiej Siniarski et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' : Need 6G for the Metaverse Realization 21 VOLUME 4, 2016  clouds where this concept is embedded in the telco network itself.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' For example, the validation of Non-Fungible Token (NTF) trading transactions requires tremendous computa- tional power.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' This challenge is also valid for other Metaverse applications such as data processing of digital twin appli- cations or AI-enabled services like storytelling and recom- mendation services that empower the virtual universe sim- ulation [106].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Current state-of-the-art Metaverse implemen- tations perform the computational on the cloud, which may limit the simulation capacity, and increase access latency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Moreover, there are several independent and fragmented Metaverses that rely on different hardware and software tech- nologies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Since the service providers would like to exploit the advantages of controlling users’ Metaverse data in their servers, we may end up with isolated Metaverses rather than a universal Metaverse.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Additionally, due to capacity limitations, the number of users that can access each re- gion may be limited by the cloud service provider’s local computational and communication capacity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Such limitations defeat the purpose of a virtual world, which is supposed to accommodate avatars as much as the real-world location can physically accommodate people.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Mobility support is also crucial since Metaverse will be a pervasive experience.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Cloud can also help there as proposed by [106].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='  In this context, they propose a distributed archi- tecture that can achieve a universal Metaverse, and solves the computational bottleneck.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' The advantage of layered ar- chitecture is twofold.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Firstly, the users control their data, which enables organizations to access a universal Metaverse, rather than multiple separated Meta- verses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Secondly, the computational bottleneck is resolved by distributing the com- putational cost of heavy tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='  2) How 6G cloudification can help the Metaverse The real-time interactive nature and high demands on data storage, streaming rates, and the processing power of Meta- verse applications will accelerate the merging of the cloud into the network, leading to highly distributed tightly- integrated compute- and data- intensive networks becoming universal compute platforms for next-generation digital expe- riences [133].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' For instance, Google Stadia [134] and Nvidia GeForce Now [135] instead offload such rendering tasks to a remote compute cloud—allowing the highest level of quality on weaker devices such as smartphones.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' less latency- and loss-tolerant (to provide satisfying responsiveness to inputs).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' To an even greater extent than AAA video games, VR and MR are highly computationally intensive.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='  3) Summary Cloud computing technologies and their adoption by telecom operators as telco clouds and cloud-native design in 6G have important implications for the Metaverse.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' First, they allow elastic Metaverse services which can be dynamically de- ployed and provisioned.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Moreover, the Metaverse is expected to be a federated entity where different service providers, applications and users are present.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Cloud computing enables such an environment where different Metaverse apps can easily reside together and integrate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Moreover, efficiency gains via consolidation and infrastructure sharing is possible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 6G clouds can support ultra-scalable compute storage for spatiotemporal changes in the Metaverse services.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' However, the trade-off between latency and cloud centralization is an important research topic [133].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='  F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 6G IOE 1) Introduction The growth of IoT applications results in increasing the num- ber of IoT devices, which is expected to grow up to 24 billion by 2030 [136].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Furthermore, the total IoT market will also grow up to USD 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='5 trillion in 2030.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' The dawn of Internet of Everything (IoE) is envisaged to expand the IoT paradigm to weave a hyper-connected network of not only things but also data, people, and processes [137].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Therefore, IoE is expected to integrate “Everything" for connecting, identifying, mon- itoring, and making intelligent decisions towards realizing new applications and services.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' IoE will connect many ecosys- tems involving heterogeneous sensors, actuators, user equip- ment, data types, services, and applications [138].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Numerous heterogeneous sensors in IoE can obtain data related to var- ious parameters ranging from location, speed, acceleration, temperature, ambient light, humidity and air pressure to bio- signals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' This sensory information is paramount for the func- tionality of the Metaverse as real-world information provides inputs to form and update the virtual space and allow interac- tions between the real world and the virtual world.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Further- more, Human-Computer Interaction (HCI) can provide more flexible ways to access the Metaverse through human sensing (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' gesture recognition) [5].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Numerous cameras can capture video sequences from multiple angles to recognize human activities through advanced AI-enabled computer vision al- gorithms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='  In addition, the captured audio-visual information can be used to predict human emotions with the aid of smart wearables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' These smart wearables can also capture data that are useful to obtain health metrics, such as heart rate, oxygen saturation level, body temperature, and electrocardiogram (ECG).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 6G provides the ubiquitous, uninterruptible, ultra- high reliable/available and massive low-latency communi- cation demanded by IoE [5], [137].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' In addition, the edge- 6G capabilities of 6G can process massive amounts of data collected from IoE devices to provide meaningful informa- tion for 6G applications and services.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' The integration of 6G and IoE will have the potential to enable many services, including the internet of medical things, smart healthcare, robotics, industry 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='0, smart grids, smart cities, and body area networks [137].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' The superior connectivity offered through 6G with features such as, near real-time connectivity, extreme data rates, access to powerful computing resources at the network edge, and massive machine-type communication under strict delay constraints between heterogeneous sensory devices will facilitate the smooth operation of the Metaverse services and applications [139], [140].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='  EEEAccessBartlomiej Siniarski et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' : Need 6G for the Metaverse Realization 22 VOLUME 4, 2016  2) How 6G IOE can help the Metaverse 6G IoE plays an important role towards enabling the Meta- verse by supporting an extremely large number of users, sensors, and devices to connect and communicate seamlessly with extremely high data rates, ultra-low delays, and jit- ters [137].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' In addition, the data obtained through heteroge- neous IoE devices can be processed using AI and ML through powerful Multi-access Edge Computing (MEC) resources in envisaged 6G networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' For instance, [141] discusses the expansion of IoE and how a multitude of sensors will enable the Extended Reality (XR) applications in the Metaverse.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' This work also explores the convergence of AI, MEC, Robots, and Distributed Ledger Technologies, such as blockchain, towards expanding the horizons of IoT towards IoE and beyond to provide a beyond smartphone experience.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' The proposed multisensory archi- tecture is capable of integrating ubiquitous and pervasive computing towards enhancing human perception through ad- vanced XR experiences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' This is performed by utilizing wear- ables and nearby network resources in the 6G era.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Hence, the dawn and the evolution of IoE will facilitate cross-reality environments, such as the Metaverse that can fuse real and virtual worlds with networked humans, avatars, and robots.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' In addition, 6G IoE enables “wireless sensing" to sense the behavior of surrounding humans and the environment [5].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='  The functionality of IoT is expanded from simply network- ing a large number of devices towards sensing the wire- less network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Various wireless signals including Wireless Fidelity (WiFi), Zigbee, Bluetooth, and Radio-Frequency IDentification (RFID) are used as sensing mediums through analyzing the signal variation (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' signal blocking, signal reflection, and signal scattering) caused by surrounding hu- mans and objects [142].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' These variations may change signal properties, such as phase, frequency and amplitude, which can be inferred through parameters including Received Sig- nal Strength (RSS), Channel State Information (CSI), and Doppler shift.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Together with signal preprocessing techniques, such as filtering and de-noising to minimize the effect of signal interference and noise, changes in the environment can be recognized by identifying distinguishable unique features owing to ML models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' The accuracy of such predictions can be enhanced through the widespread of mmWave and MIMO technologies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' In addition, an Integrated Sensing and Commu- nication (ISAC) system, where communication systems and IoE hardware are jointly designed can improve the accuracy of wireless sensing while enhancing spectrum efficiency and minimizing hardware implementation cost [143].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='  However, modelling such systems, providing real-time access to pow- erful computational resources for data processing through advanced AI and ML schemes, and providing real-time ultra- low latency communication with seamless coverage requires beyond 5G network capabilities that are expected to be facilitated by emerging 6G networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Ubiquitous and Pervasive Computing Seamless Communication AI and ML XR  6G IoE  Metaverse  Blockchain  Wireless Sensing  Multisensory Inputs  Integrated Sensing and Communication  FIGURE 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 6G IoE for the Metaverse  3) Summary The evolution of IoT towards IoE with the dawn of 6G provides seamless connectivity, extreme data rates, ultra-low latency and ultra-high reliable/available communication, and real-time access to powerful Edge-AI-enabled computational resources to facilitate the Metaverse applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 6G IoE also facilitates advanced wireless sensing with mmWave and MIMO technologies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' The development of ISAC harnessing extreme communication capabilities and Edge-AI processing of 6G networks can further improve the capabilities of 6G IoE that would enable emerging the Metaverse applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 6G IoE features that enable the Metaverse applications are illustrated in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='  G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' OTHER 6G TECHNOLOGIES 1) Extended Reality Extended Reality (XR) combines Virtual Reality (VR), Aug- mented Reality (AR) and Mixed Reality (MR) to blur the border between physical and virtual worlds with wear- ables supporting human-machine interactions with real and computer-generated environments [137].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 6G is capable of facilitating the massive low-latency, extremely low latency and extremely high data rate demanded by XR applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Together with Edge-AI capabilities, 6G can facilitate the seamless 3C (computing, caching and communication) ser- vices for XR applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Many sensors are used for the data collection on user location, orientation and movements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' XR enables telepresence towards facilitating various aspects of human life, such as work, education, shopping, health- care, tourism, and entertainment [144].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' For instance, [145] explores how XR impacts six dimensions of workload, as defined by NASA Task Load Index (NASA-TLX), namely, mental demand, physical demand, temporal demand, per- formance, effort, and frustration, and the overall workload in the retail sector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' The results of the study indicate that albeit VR alone did not have a significant impact on the various dimensions of workload, XR had a significant impact on performing shopping-related tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' In addition, [146]  EEEAccess1Bartlomiej Siniarski et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' : Need 6G for the Metaverse Realization 23 VOLUME 4, 2016  presents how users can actively engage with 3D content to stimulate healthy behaviour using XR in the Metaverse.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' This work discusses how XR can be effectively used in the Metaverse to address long-term health issues and challenges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Accordingly, XR can be identified as an important enabler to provide services efficiently using the Metaverse.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' However, challenges, such as limitations in physical and cognitive resources, lack of experience with VR environments, and dif- ficulties in using existing XR devices for prolonged periods, need to be addressed towards utilizing XR for the Metaverse applications in future 6G networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='  2) Digital Twins The Metaverse applications demand next-generation net- works to facilitate the high processing capabilities demanded by the Metaverse applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' These can be provided through the edge-AI capabilities of emerging 6G networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Digital Twins (DT) can be an important enabler of the cloud-native network paradigm, which can efficiently support the Metaverse [147].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' DTs act as a digital representation of humans and things in cyberspace.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Cybertwins can provide a multitude of services for the Metaverse, including, acting as a communication assistant, logging network behavior, and own digital assets, in a flexible, scalable, secure and reliable manner.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 6G IoE can play a key role towards facilitating DTs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' In [148], the authors discuss how to utilize a cloud network operating system that can work distributively in a real-time multi-agent platform to allocate 3C resources, which are considered to be integral components of envisaged 6G networks [137].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' In addition, the Metaverse applications demand 6G networks to support intelligent and fully au- tonomous operation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' In response [149] proposes a Digital Twin Edge Network (DITEN).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' DITEN is able to combine Multi-access Edge Computing (MEC) together with DT to improve the network throughput, enhance network security, and reduce the cost of 3C services.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='  DITEN continuously monitors the network status for DT modelling, updating and deployment and performs tasks such as routing and resource management efficiently to enable applications such as the Metaverse.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' However, there are several open issues and challenges, including high-precision DT modelling, DT migration for mobility and ensuring security and privacy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='  3) Space-Air-Ground Integrated Network (SAGIN) Global sensing and seamless connectivity are paramount to providing uninterrupted access to the Metaverse appli- cations through 6G networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' However, ground networks alone are not capable of providing ubiquitous connectivity to the Metaverse applications in a reliable and cost-efficient fashion [149].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' This is even evident in mountain areas and in disastrous situations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' As a solution, Non-Terrestrial Net- works (NTN) Towards 3D Networking are proposed with 6G networks [137].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' NTN provides 3D network coverage and backhauling through integrating Unmanned Aerial Ve- hicles (UAVs), satellites, balloons and High Altitude Plat- form (HAP) stations [150].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='3D networking expands the NTN paradigm through incorporating space, underground, and un- derwater communication [151].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' For instance, project 3GPP TR 38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='811 intends to support non-terrestrial networks by considering the architecture and channel models across satellite, air access, and terrestrial cellular networks [137].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' In addition, multi-dimensional networks named Space-Air- Ground Integrated Network (SAGIN) envisage to deeply integrate of space nodes (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' satellites), air nodes (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' UAVs, drones, air balloons), and terrestrial network nodes (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 5G and beyond network nodes) towards providing seamless connectivity [5].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='  However, the seamless inter-operation and resource management among multiple types of networks require unified access methods and network standards to- wards facilitating seamless connectivity for the Metaverse applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='  V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 6G INTEGRATION CHALLENGES In this section, we present the challenges raised by lim- ited backwards compatibility with existing devices, lack of standards, accountability, resilience & privacy preservation, energy inefficiency, and radio design & carrier bandwidths while integrating 6G with the Metaverse.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' LIMITED BACKWARDS COMPATIBILITY WITH EXISTING DEVICES 1) Introduction to issues Effective communication in the Metaverse requires compati- bility with previous-generation networks such as 4G and 5G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Despite that, some Metaverse applications can operate on existing network capabilities devices due to the deployment of 6G these devices become worthless.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='  2) Possible solutions A potential solution to address this issue is the backward compatibility of the 6G network with existing devices that enables the addition of high-capacity communication in the Metaverse and also delivers faster data rates for applications requiring real-time processing and integration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' The 6G net- works should support the features of the previous generations of communications like the 5G network for some time, enabling progressive migration of the Metaverse devices and lowering the overall cost of 6G and the Metaverse integration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' In order to evaluate backward compatibility, mobile operators need to consider how the 5G and 6G core networks are connected and work on the 3GPP standard accordingly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' LACK OF STANDARDS 1) Introduction to issues There is a concern among users about the Metaverse’s po- tential legal consequences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' If a problem arises, there is no agreed-upon policy framework or set of standards for the integration of 6G with the Metaverse.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Any problem with the integration of these technologies will affect the trust and the capabilities of the 6G networks and the Metaverse.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='  EEEAccessBartlomiej Siniarski et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' : Need 6G for the Metaverse Realization 24 VOLUME 4, 2016  TABLE 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Summary of related works  6G for the Metaverse technical perspective  Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='  Validation  of digital  assets  Cross platform  integration and  interoperability  Efficient  support  of AI  High speed  data  connection  Low  Latency  Communication  Computer  Vision  High  transaction  integration  Security  and  privacy  7  x  30 34  x  x  35 38  x  x  39 41  x  42 47  x  x  x  48 49  x  x  x  50 53  x  x  54 56  x  The role of 6G technologies for the Metaverse Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' AI Blockchain Edge OpenRAN Cloud IoE/IoT XR Digital Twin 57-84 x  x  85 104  x  x  105 125  x  x  x  x  126 130  x  131 134  x  135 142  x  x  x  x  2, 143 148  x  x  x  x  x  x  x  2) Possible solutions These challenges may be resolved by establishing a forum involving service providers, researchers, and legal counsel to develop standards and policy frameworks that address con- cerns about user ethics, safety, and privacy while integrating 6G with the Metaverse.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' The users should be provided with complete control and transparency of their data transmit- ted over 6G networks, which ensures their privacy in the Metaverse.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' As a consequence, this will raise the bar for the 6G communication networks and the Metaverse, which will increase trust among the users.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' For example, though ORAN is not yet fully functional it has an alliance focusing on the integration issues of multiple service providers which will enhance the bandwidth availability and security of the overall networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' ACCOUNTABILITY, RESILIENCE AND PRIVACY PRESERVATION 1) Introduction to issues The functionalities across 6G integrated Metaverse will be mostly automated based on the decisions made by AI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Any misclassification made by these decisions that cannot be traced because of the black box nature of AI will have a direct effect on the accountability of the 6G integrated Metaverse.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='  2) Possible solutions Explainable AI (XAI) is a promising solution for this issue which allows us to understand the misclassification issues and improve trust in the decisions made in the 6G inte- grated Metaverse.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' The usage of xAI will aid in pinpointing the problem’s cause, assist the Metaverse’s administrators in understanding the issue, and motivate them to prevent a recurrence - this enhances the transparency of auditing of issues related to the 6G integrated Metaverse.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Addition- ally, existing and newly proposed AI algorithms need to be analysed considering their accountability, resilience and privacy preservation capabilities within the context of future networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' ENERGY INEFFICIENCY 1) Introduction to issues The integration of processing, communication, sensing, and control capabilities inside a 6G network enables a seamless transition between the virtual and physical worlds, conse- quently contributing to the realisation of the Metaverse.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' To support the requirements of the Metaverse, the cellular capacity should be increased on top of the existing network infrastructure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' This will require 6G to deploy more micro- scopic and even micro-cells in the network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' This increases technological and network complexity and will further strain the energy efficiency and sustainability of the Metaverse.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='  2) Possible solutions The integration of AI with 6G will address the issues of energy efficiency and network complexity, opening the door to a sustainable Metaverse ecosystem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' The use of Zero touch network & Service Management (ZSM) in 6G provides an intelligent network for the Metaverse by enabling effective data access and cross-domain data exposure by permitting operational data to be maintained apart from the management applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' This will also improve the reliability of commu- nication in the Metaverse.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='  E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' RADIO DESIGN AND CARRIER BANDWIDTHS  EEEAccessBartlomiej Siniarski et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' : Need 6G for the Metaverse Realization 25 VOLUME 4, 2016  1) Introduction to issues One of the main goals of 6G is to achieve Tb/s data rates, which requires large bandwidths (10-100 GHz spectrum for THz bands), which requires an aggregation of a large number of carriers to create larger bandwidth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Designing radios that work at sub-THz bands present a significant challenge to the industry and research due to the complexity of associated RF circuits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Finding the right balance in terms of transceiver efficiency, power generation, heat dissipation and the cost is critical for the successful adoption of radios to sub-THz bands.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='  2) Possible solutions 6G should provide more bandwidth and lower latency to improve the overall connectivity of the Metaverse.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' On 6G networks, there should be a 10 to 100-fold reduction in latency and an increase in bandwidth capacity for the users of the Metaverse to have the best immersive experiences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Every piece of networking hardware must have its material, component manufacture, and antenna architecture modified.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' To comply with the 6G standard, base station operations must change.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 6G should depend on tightly focused, packaged radio signals rather than "omnidirectional" radio channels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Moreover, tightly focused radio signals use less energy, have high transceiver efficiency, less heat dissipation and less cost.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='  VI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 6G METAVERSE PROJECTS This section provides an overview of research projects and developments that are already underway towards realizing the Metaverse by harnessing the extreme network capabilities of envisioned B5G and 6G mobile networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' META Meta, formerly known as Facebook, is presently working on combining social media with VR and AR towards realizing the Metaverse for users to work, play and interact with other users online [152].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' This is possible due to the extreme mobile broadband capabilities, near zero latency, extreme reliability and availability, and network intelligence of emerging mobile networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Users can join the Metaverse using VR head- sets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' The envisaged applications will range from connecting people, education, training, healthcare and the workplace to gaming.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' For instance, education technologies are expected to broaden their horizons from platforms to passively absorb information to learn by doing and experiencing through 3D immersion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' In addition, Meta is working on building the Metaverse responsibly ensuring a safe, secure, and transpar- ent operation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Meta has also launched the Meta Immersive Learning Academy and Research Fund to collaborate in building a solid and interoperable Metaverse platform.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' In addition, their Spark AR platform enables the creation and sharing of AR experiences through their apps and devices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Furthermore, Meta is working on building economic oppor- tunities in the Metaverse to maintain and thrive in a digital economy in the future.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' VR HIVE VR Hive [153] aims to transform e-learning through VR from the comfort of home or workplace.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='  This project aims to design and develop a fully immersive learning platform over 6G mobile networks to feature the Metaverse that can be used to provide education, training, holographic telepresence, and real-time communication.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' These features will be provided through the extreme network capabilities of emerging 6G networks, such as, near real-time ultra-reliable communica- tion with ultra-low latency and edge intelligence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Relevant infrastructure and network-aware immersive and adaptive en- vironments will be developed to facilitate education through the range of products offered through VR Hive.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 6G LIFE 6G Life [154] aims to facilitate the envisaged digital transfor- mation where 6G mobile networks will play a significant role in this revolution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' The project not only aims to develop the digital infrastructure and high-performance computing plat- forms but also concentrates on political and social issues that are required to realize future 6G applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Realizing 6G applications will require diverse communication capabilities including human-machine interaction in virtual worlds, such as the Metaverse.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' The project aims to provide innovative so- lutions in the areas of scalable communication, flexible soft- ware concepts, and adaptive hardware platforms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' The four key aspects considered by the project are latency, resilience, security and sustainability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' The research work, including both basic and applied research, is mainly performed considering Industry 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='0/5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='0, and intelligent healthcare applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' DECENTRALAND Decentraland [155] is a decentralized virtual world where users can create objects, trade and interact with others in a virtual world.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' This also allows users to control policies on the operation of the virtual world.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Decentraland operates as a De- centralized Autonomous Organization (DAO), where it owns smart contracts and assets on virtual land and estate contracts, wearables and other devices, and the marketplace to trade vir- tual assets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' These developments can be realized through the capabilities of emerging 6G mobile networks, where extreme mobile connectivity will facilitate seamless connectivity to the virtual world.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Furthermore, blockchain operation and smart contract execution will be enabled through the edge computing capabilities of the 6G networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Similar projects, such as Sandbox [156], Axie Infin- ity [157], and Illuvium [158] also envisage harnessing the capabilities of blockchain and emerging mobile networks towards realizing the Metaverse.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='  E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' LUXEMBOURG METAVERSE The Luxembourg Metaverse [159] project aims to build a digital twin of an area of Luxembourg City.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' These digital twins can be explored by the public and the industry to provide multiple working opportunities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Luxemburg 5G-6G network digital twin aims to enable seamless and highly  EEEAccessBartlomiej Siniarski et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' : Need 6G for the Metaverse Realization 26 VOLUME 4, 2016  TABLE 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 6G Metaverse Projects  Project Objective 6G Technologies AI Blockchain Edge OpenRAN Cloud IoE XR Digital Twin Meta Combine social media with VR and AR to facilitate work,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' play and other interactions among users online ✓ ✓ ✓ ✓ ✓  ✓ ✓ VR Hive Transform e-learning through VR to be ac- cessed at home or workplace ✓  ✓  ✓  6G Life Facilitate the digital transformation towards 6G with human machine collaboration ✓ ✓ ✓ ✓ ✓ ✓ ✓ Decentraland Create a virtual world for users to create objects,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' trade and interact with users ✓ ✓ ✓  ✓ ✓ ✓ ✓ Luxembourg Metaverse Build a digital twin of an area of Luxem- bourg city ✓  ✓  ✓  ✓  ✓  capable network connectivity to facilitate real-time services banking on emerging communication networks,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' such as be- yond 5G and 6G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' This project will also raise awareness of the advantages and applications of the Metaverse to the public and the industry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Furthermore, the project expects to optimise and secure the Metaverse deployments while integrating the latest developments of networks in a cost-effective and cost- efficient manner.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' The 6G technological directions explored by the 6G meta- verse projects presented in this section are tabulated in TA- BLE 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='  VII.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' CONCLUSION This paper presents the role of 6G towards realizing the Metaverse applications and services.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' The paper presents the role of 6G technologies in the immersive, smart, scalable and secure realization of the Metaverse.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Furthermore, the paper presents how various 6G capabilities play a key role towards the realization of the Metaverse, including the role of 6G for, cross-platform integration, efficient support for AI, high- speed data connectivity, efficient user interaction, low latency communication, computer vision, high transaction integra- tion, and security and privacy protection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Consequently, the integration challenges of 6G with the Metaverse are elab- orated while providing several research directions towards realizing the Metaverse owing to the capabilities of future 6G networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='  REFERENCES [1] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='-H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Lee, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Braud, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Zhou, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Wang, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Xu, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Lin, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Kumar, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Bermejo, and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Hui, “All one needs to know about metaverse: A complete survey on technological singularity, virtual ecosystem, and research agenda,” arXiv preprint arXiv:2110.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='05352, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' [2] “Cloud vr network solution white paper.” [3] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Huynh-The, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='-V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Pham, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='-Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Pham, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Nguyen, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Han, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='-S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Kim, “Artificial intelligence for the metaverse: A survey,” arXiv preprint arXiv:2202.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='10336, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' [4] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Wang, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Su, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Zhang, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Xing, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Liu, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Luan, and X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Shen, “A survey on metaverse: Fundamentals, security, and privacy,” IEEE Communications Surveys & Tutorials, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 1–1, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' [5] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Tang, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Chen, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Zhao, and N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Kato, “The roadmap of com- munication and networking in 6g for the metaverse,” IEEE Wireless Communications, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' [6] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Mozumder, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Sheeraz, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Athar, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Aich, and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='-C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Kim, “Overview: technology roadmap of the future trend of metaverse based on iot, blockchain, ai technique, and medical domain metaverse activity,” in 2022 24th International Conference on Advanced Communication Technology (ICACT), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 256–261, IEEE, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' [7] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Xu, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Ng, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Lim, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Kang, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Xiong, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Niyato, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Yang, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Sherman Shen, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Miao, “A Full Dive into Realizing the Edge- enabled Metaverse: Visions, Enabling Technologies,and Challenges,” arXiv e-prints, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' arXiv:2203.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='05471, Mar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='  [8] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Chang, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Zhang, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Li, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Xi, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Guo, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Shen, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Xiong, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Kang, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Niyato, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Qiao, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=', “6g-enabled edge ai for metaverse: Challenges, methods, and future research directions,” arXiv preprint arXiv:2204.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='06192, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' [9] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Alwis, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Kalla, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='-V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Pham, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Kumar, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Dev, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='-J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Hwang, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Liyanage, “Survey on 6g frontiers: Trends, applications, require- ments, technologies and future research,” IEEE Open Journal of the Communications Society, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 2, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 836–886, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' [10] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Rappaport, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Xing, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Kanhere, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Ju, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Madanayake, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Mandal, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Alkhateeb, and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Trichopoulos, “Wireless communications and applications above 100 ghz: Opportunities and challenges for 6g and beyond,” IEEE access, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 7, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 78729–78757, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' [11] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Salh, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Audah, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Shah, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Alhammadi, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Abdullah, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Kim, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Al-Gailani, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Hamzah, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Esmail, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Almohammedi, “A survey on deep learning for ultra-reliable and low- latency communications challenges on 6g wireless systems,” IEEE Ac- cess, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 9, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 55098–55131, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' [12] X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Shen, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Liao, and Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Yin, “A novel wireless resource management for the 6g-enabled high-density internet of things,” IEEE Wireless Com- munications, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 29, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 1, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 32–39, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' [13] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Chen, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Liu, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Niu, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Feng, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Hu, and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Jiang, “Pervasive intelligent endogenous 6g wireless systems: Prospects, theories and key technologies,” Digital communications and networks, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 6, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 3, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 312–320, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='  [14] X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Shen, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Liao, and Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Yin, “A novel wireless resource management for the 6g-enabled high-density internet of things,” IEEE Wireless Com- munications, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 29, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 1, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 32–39, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' [15] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Kraus, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Kanbach, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Krysta, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Steinhoff, and N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Tomini, “Facebook and the creation of the metaverse: radical business model innovation or incremental transformation?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=',” International Journal of En- trepreneurial Behavior & Research, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' [16] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Hollensen, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Kotler, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Opresnik, “Metaverse–the new mar- keting universe,” Journal of Business Strategy, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' [17] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Hasan and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Salah, “Proof of delivery of digital assets using blockchain and smart contracts,” IEEE Access, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 6, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 65439–65448, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' [18] Å.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Fast-Berglund, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Gong, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Li, “Testing and validating extended reality (xr) technologies in manufacturing,” Procedia Manufacturing, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 25, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 31–38, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' [19] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Siyaev and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='-S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Jo, “Neuro-symbolic speech understanding in air- craft maintenance metaverse,” IEEE Access, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 9, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 154484–154499, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' [20] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Zhang, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Gao, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' He, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Zhang, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Krishnamachari, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Avestimehr, “Federated learning for the internet of things: Applications, challenges, and opportunities,” IEEE Internet of Things Magazine, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 5, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 1, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 24–29, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' [21] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Lu, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Huang, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Zhang, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Maharjan, and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Zhang, “Communication-efficient federated learning for digital twin edge networks in industrial iot,” IEEE Transactions on Industrial Informatics, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='  17, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 8, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 5709–5718, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='  EEEAccessBartlomiej Siniarski et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' : Need 6G for the Metaverse Realization 27 VOLUME 4, 2016  [22] I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Skalidis, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Muller, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Fournier, “Cardioverse: The cardiovascular medicine in the era of metaverse,” Trends in Cardiovascular Medicine, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' [23] Surfing the Metaverse’s Real Estate Boom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' [24] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Beniiche, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Rostami, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Maier, “Society 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='0: Internet as if people mattered,” IEEE Wireless Communications, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' [25] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Gursoy, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Malodia, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Dhir, “The metaverse in the hospitality and tourism industry: An overview of current trends and future research directions,” Journal of Hospitality Marketing & Management, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 1–8, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' [26] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Shin, “The actualization of meta affordances: Conceptualizing af- fordance actualization in the metaverse games,” Computers in Human Behavior, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 133, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 107292, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' [27] I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Ilyina, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Eltikova, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Uvarova, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Chelysheva, “Metaverse-death to offline communication or empowerment of inter- action?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=',” in 2022 Communication Strategies in Digital Society Seminar (ComSDS), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 117–119, IEEE, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' [28] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Falchuk, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Loeb, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Neff, “The social metaverse: Battle for privacy,” IEEE Technology and Society Magazine, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 37, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 2, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 52– 61, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' [29] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Gadekallu, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Huynh-The, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Wang, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Yenduri, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Ranaweera, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='-V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Pham, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' da Costa, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Liyanage, “Blockchain for the metaverse: A review,” arXiv preprint arXiv:2203.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='09738, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' [30] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Kim, “Advertising in the metaverse: Research agenda,” Journal of Interactive Advertising, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 21, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 3, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 141–144, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='  [31] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Nadini, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Alessandretti, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Di Giacinto, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Martino, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Aiello, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Baronchelli, “Mapping the nft revolution: market trends, trade networks, and visual features,” Scientific reports, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 11, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 1, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 1–11, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' [32] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Ko, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Son, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Lee, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Jang, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Lee, “The economic value of nft: Evidence from a portfolio analysis using mean–variance framework,” Finance Research Letters, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 47, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 102784, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' [33] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Park, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Kietzmann, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Pitt, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Dabirian, “The evolution of nonfun- gible tokens: Complexity and novelty of nft use-cases,” IT Professional, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 24, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 1, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 9–14, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' [34] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Vidal-Tomás, “The new crypto niche: Nfts, play-to-earn, and meta- verse tokens,” Finance Research Letters, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 102742, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' [35] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Hackl, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Lueth, and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Di Bartolo, Navigating the Metaverse: A Guide to Limitless Possibilities in a Web 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='0 World.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' John Wiley & Sons, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' [36] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Lee, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='-D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Seo, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='-R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Oh, and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='-G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Kim, “A survey on standards for interoperability and security in the internet of things,” IEEE Communi- cations Surveys & Tutorials, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 23, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 2, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 1020–1047, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' [37] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Hazra, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Adhikari, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Amgoth, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Srirama, “A comprehen- sive survey on interoperability for iiot: taxonomy, standards, and future directions,” ACM Computing Surveys (CSUR), vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 55, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 1, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 1–35, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' [38] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Sparkes, “What is a metaverse,” 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='  [39] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Khan, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Shayea, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Ergen, and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Mohamad, “Handover man- agement over dual connectivity in 5g technology with future ultra-dense mobile heterogeneous networks: A review,” Engineering Science and Technology, an International Journal, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 101172, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' [40] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Mystakidis, “Metaverse,” Encyclopedia, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 2, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 1, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 486–497, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' [41] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Campbell and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Jovanovic, “Digital self: The next evolution of the digital human,” Computer, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 55, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 04, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 82–86, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' [42] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Wiederhold, “Ready (or not) player one: initial musings on the metaverse,” 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' [43] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Duan, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Li, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Fan, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Lin, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Wu, and W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Cai, “Metaverse for social good: A university campus prototype,” in Proceedings of the 29th ACM International Conference on Multimedia, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 153–161, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' [44] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Inomata, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Yamada, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Kuno, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Sasaki, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Kitao, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Nakamura, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Ishikawa, and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Oda, “Terahertz propagation characteristics for 6g mobile communication systems,” in 2021 15th European Conference on Antennas and Propagation (EuCAP), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 1–5, IEEE, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' [45] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='-I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Han, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Bergs, and N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Moorhouse, “Virtual reality consumer experience escapes: preparing for the metaverse,” Virtual Reality, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 1– 16, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' [46] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Girvan, “What is a virtual world?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' definition and classification,” Educa- tional Technology Research and Development, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 66, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 5, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 1087– 1100, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='  [47] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Markowitz, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Laha, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Perone, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Pea, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Bailenson, “Immersive virtual reality field trips facilitate learning about climate change,” Frontiers in psychology, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 9, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 2364, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' [48] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Mendes, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Caputo, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Giachetti, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Ferreira, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Jorge, “A survey on 3d virtual object manipulation: From the desktop to immersive virtual environments,” in Computer graphics forum, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 38, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 21–45, Wiley Online Library, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' [49] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Suzuki, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Karim, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Xia, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Hedayati, and N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Marquardt, “Augmented reality and robotics: A survey and taxonomy for ar-enhanced human- robot interaction and robotic interfaces,” in CHI Conference on Human Factors in Computing Systems, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 1–33, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' [50] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Adhikari and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Hazra, “6g-enabled ultra-reliable low-latency com- munication in edge networks,” IEEE Communications Standards Maga- zine, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 6, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 1, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 67–74, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' [51] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='-H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Guo, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='-X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Xu, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='-J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Liu, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='-N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Liu, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='-T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Jiang, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='-J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Mu, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='-H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Zhang, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Martin, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='-M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Cheng, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='-M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Hu, “Attention mecha- nisms in computer vision: A survey,” Computational Visual Media, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 1– 38, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' [52] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Braud, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Fernández, and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Hui, “Scaling-up ar: University campus as a physical-digital metaverse,” in 2022 IEEE Conference on Virtual Re- ality and 3D User Interfaces Abstracts and Workshops (VRW), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 169– 175, IEEE, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='  [53] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Kumar et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=', “Epidemiological mucormycosis treatment and diagno- sis challenges using the adaptive properties of computer vision techniques based approach: a review,” Multimedia Tools and Applications, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 1–29, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' [54] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Yeh, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Do Jo, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='-J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Ko, and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Chung, “Perspectives on 6g wireless communications,” ICT Express, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' [55] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Liu, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Yu, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Li, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Ji, and V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Leung, “Decentralized resource allocation for video transcoding and delivery in blockchain-based system with mobile edge computing,” IEEE Transactions on Vehicular Technol- ogy, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 68, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 11, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 11169–11185, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' [56] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Frey, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Royan, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Piegay, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='-M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Kermarrec, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Anceaume, and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Le Fessant, “Solipsis: A decentralized architecture for virtual envi- ronments,” in 1st International Workshop on Massively Multiuser Virtual Environments, 2008.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' [57] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Nguyen, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Hoang, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Nguyen, and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Dutkiewicz, “Metachain: a novel blockchain-based framework for metaverse applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' arxiv,” arXiv preprint arXiv:2201.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='00759, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' [58] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Huynh-The, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='-V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Pham, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='-Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Pham, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Nguyen, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Han, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='-S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Kim, “Artificial intelligence for the metaverse: A survey,” arXiv preprint arXiv:2202.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='10336, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' [59] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Fuad and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Al-Yahya, “Recent developments in arabic conversa- tional ai: A literature review,” IEEE Access, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 10, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 23842–23859, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='  [60] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='-S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Chiu, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='-W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Chang, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='-C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Lee, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='-H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Chen, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='-S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Lee, “En- abling intelligent environment by the design of emotionally aware virtual assistant: A case of smart campus,” IEEE Access, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 8, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 62032– 62041, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' [61] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Cui, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Cui, and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Song, “A survey on learning-based approaches for modeling and classification of human–machine dialog systems,” IEEE Transactions on Neural Networks and Learning Systems, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 32, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 4, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 1418–1432, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' [62] I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Giorgi, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Golosio, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Esposito, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Cangelosi, and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Masala, “Modeling multiple language learning in a developmental cognitive architecture,” IEEE Transactions on Cognitive and Developmental Sys- tems, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 13, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 4, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 922–933, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' [63] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Otter, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Medina, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Kalita, “A survey of the usages of deep learning for natural language processing,” IEEE Transactions on Neural Networks and Learning Systems, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 32, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 2, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 604–624, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' [64] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Xu, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Meng, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Qiu, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Yu, and X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Wu, “Sentiment analysis of comment texts based on bilstm,” IEEE Access, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 7, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 51522–51532, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' [65] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Cheng, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Yao, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Xiang, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Zhang, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Tang, and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Zhong, “Text sen- timent orientation analysis based on multi-channel cnn and bidirectional gru with attention mechanism,” IEEE Access, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 8, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 134964–134975, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' [66] Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Hu, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Bulling, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Li, and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Wang, “Fixationnet: Forecasting eye fixations in task-oriented virtual environments,” IEEE Transactions on Visualization and Computer Graphics, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 27, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='  2681–2690, Mar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' [67] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Miller, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Banerjee, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Banerjee, “Combining real-world constraints on user behavior with deep neural networks for virtual reality (vr) biometrics,” in 2022 IEEE Conference on Virtual Reality and 3D User Interfaces (VR), (Christchurch, New Zealand), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 409–418, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='  EEEAccessBartlomiej Siniarski et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' : Need 6G for the Metaverse Realization 28 VOLUME 4, 2016  [68] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Jin, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Chen, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Goodall, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Patney, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Bovik, “Subjective and objective quality assessment of 2d and 3d foveated video compression in virtual reality,” IEEE Transactions on Image Processing, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 30, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 5905–5919, Jun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' [69] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Huynh-The, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='-H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Hua, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Tu, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Hur, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Bang, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Kim, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Amin, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Kang, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Seung, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='-Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Shin, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=', “Hierarchical topic modeling with pose-transition feature for action recognition using 3d skeleton data,” Information Sciences, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 444, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 20–35, May 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' [70] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Huynh-The, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='-H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Hua, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Tu, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='-S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Kim, “Learning 3d spatiotemporal gait feature by convolutional network for person identi- fication,” Neurocomputing, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 397, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 192–202, Jul.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' [71] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Huynh-The, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='-H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Hua, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='-S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Kim, “Encoding pose features to images with data augmentation for 3-d action recognition,” IEEE Transactions on Industrial Informatics, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 16, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 3100–3111, May 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' [72] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='-H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Hua, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Huynh-The, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Lee, “Convolutional networks with bracket-style decoder for semantic scene segmentation,” in Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 2018 IEEE International Conference on Systems, Man, and Cybernetics (SMC), (Miyazaki, Japan), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 2980–2985, IEEE, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' [73] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='-H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Hua, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Huynh-The, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='-H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Bae, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Lee, “Cross-attentional bracket-shaped convolutional network for semantic image segmentation,” Information Sciences, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 539, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 277–294, Oct.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='  [74] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='-C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Chen, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Papandreou, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Kokkinos, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Murphy, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Yuille, “Deeplab: Semantic image segmentation with deep convolutional nets, atrous convolution, and fully connected crfs,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 40, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 834–848, Apr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' [75] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Kim, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Zeng, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Ghadiyaram, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Lee, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Zhang, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Bovik, “Deep convolutional neural models for picture-quality prediction: Chal- lenges and solutions to data-driven image quality assessment,” IEEE Signal Processing Magazine, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 34, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 130–141, Nov.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' [76] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Ranjan, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Patel, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Chellappa, “Hyperface: A deep multi-task learning framework for face detection, landmark localization, pose esti- mation, and gender recognition,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 41, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 121–135, Dec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' [77] X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Wang, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Gao, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Song, and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Shen, “Beyond frame-level cnn: Saliency-aware 3-d cnn with lstm for video action recognition,” IEEE Signal Processing Letters, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 24, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 510–514, Sep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' [78] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Xin, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Kong, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Liu, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Chen, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Li, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Zhu, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Gao, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Hou, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Wang, “Machine learning and deep learning methods for cybersecu- rity,” IEEE Access, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 6, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 35365–35381, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' [79] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Vinayakumar, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Alazab, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Soman, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Poornachandran, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Al- Nemrat, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Venkatraman, “Deep learning approach for intelligent intrusion detection system,” IEEE Access, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 7, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 41525–41550, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='  [80] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Jamalipour and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Murali, “A taxonomy of machine-learning-based intrusion detection systems for the internet of things: A survey,” IEEE Internet of Things Journal, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 9, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 12, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 9444–9466, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' [81] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Liu, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Wang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Li, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Niu, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Wu, and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Song, “Zero-bias deep- learning-enabled quickest abnormal event detection in iot,” IEEE Internet of Things Journal, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 9, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 11385–11395, Jul.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' [82] Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Lv, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Qiao, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Li, and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Song, “Deep-learning-enabled security issues in the internet of things,” IEEE Internet of Things Journal, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 8, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 9531–9538, Jun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' [83] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Uprety and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Rawat, “Reinforcement learning for iot security: A comprehensive survey,” IEEE Internet of Things Journal, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 8, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 8693–8706, Jun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' [84] X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Liu, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Li, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Xu, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Liu, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Liu, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Lu, “Padl: Privacy-aware and asynchronous deep learning for iot applications,” IEEE Internet of Things Journal, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 7, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 6955–6969, Aug.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' [85] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Zhang, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Jiang, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Li, and X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Lin, “Privacy-preserving aggregate mobility data release: An information-theoretic deep reinforcement learn- ing approach,” IEEE Transactions on Information Forensics and Security, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 17, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 849–864, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' [86] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Deepa, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='-V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Pham, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Nguyen, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Bhattacharya, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Prabadevi, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Gadekallu, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Maddikunta, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Fang, and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Pathirana, “A survey on blockchain for big data: Approaches, opportunities, and future directions,” Future Generation Computer Systems, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 131, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 209–226, Jun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='  [87] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Nguyen, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Hoang, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Nguyen, and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Dutkiewicz, “Metachain: A novel blockchain-based framework for metaverse appli- cations,” arXiv preprint arXiv:2201.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='00759, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' [88] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Cheng, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Quan, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Yan, “A blockchain-based crowdsourcing system for large scale environmental data acquisition,” in 2021 IEEE 24th International Conference on Computer Supported Cooperative Work in Design (CSCWD), (Dailan, China), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 855–860, May 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' [89] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Liu, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Lin, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Wen, “Blockchain-enabled data collection and sharing for industrial iot with deep reinforcement learning,” IEEE Transactions on Industrial Informatics, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 15, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 3516–3526, Jun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' [90] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Li, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Weng, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Yang, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Lu, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Zhang, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Hou, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='-N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Liu, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Xiang, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Deng, “Crowdbc: A blockchain-based decentralized framework for crowdsourcing,” IEEE Transactions on Parallel and Distributed Sys- tems, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 30, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 1251–1266, Jun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' [91] U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Bodkhe, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Tanwar, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Parekh, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Khanpara, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Tyagi, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Kumar, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Alazab, “Blockchain for industry 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='0: A comprehensive review,” IEEE Access, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 8, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 79764–79800, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' [92] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Li, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Song, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Mei, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Li, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Cheng, and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Sun, “Blockchain for large-scale internet of things data storage and protection,” IEEE Transactions on Services Computing, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 12, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 762–771, Sept.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='-Oct.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='  [93] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Shafagh, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Burkhalter, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Hithnawi, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Duquennoy, “Towards blockchain-based auditable storage and sharing of iot data,” in Proceed- ings of the 2017 on Cloud Computing Security Workshop, (Dallas, Texas, USA), p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 45–50, Nov.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' [94] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Liang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Fan, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='-C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Li, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Zhang, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='-L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Gaudiot, “Secure data storage and recovery in industrial blockchain network environments,” IEEE Transactions on Industrial Informatics, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 16, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 6543–6552, Oct.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' [95] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Jabbar, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Fetais, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Krichen, and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Barkaoui, “Blockchain tech- nology for healthcare: Enhancing shared electronic health record inter- operability and integrity,” in 2020 IEEE International Conference on Informatics, IoT, and Enabling Technologies (ICIoT), (Doha, Qatar), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 310–317, Feb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' [96] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Gordon and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Catalini, “Blockchain technology for healthcare: Fa- cilitating the transition to patient-driven interoperability,” Computational and Structural Biotechnology Journal, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 16, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 224–230, Jul.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' [97] X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Liu, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Sun, and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Huang, “Decentralized services computing paradigm for blockchain-based data governance: Programmability, inter- operability, and intelligence,” IEEE Transactions on Services Computing, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 13, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 343–355, Mar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='-Apr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' [98] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Schulte, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Sigwart, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Frauenthaler, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Borkowski, “Towards blockchain interoperability,” in Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' International Conference on Busi- ness Process Management, (Vienna, Austria), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 3–10, Springer, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='  [99] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Jiang, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Wang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Wang, and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Gao, “A cross-chain solution to integrating multiple blockchains for iot data management,” Sensors, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 19, May 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' [100] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Pillai, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Biswas, and V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Muthukkumarasamy, “Cross-chain inter- operability among blockchain-based systems using transactions,” The Knowledge Engineering Review, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 35, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' e23, Jun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' [101] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Wei, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Wang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Zhao, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Tyagi, and N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Kumar, “Blockchain data-based cloud data integrity protection mechanism,” Future Genera- tion Computer Systems, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 102, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 902–911, Jan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' [102] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='-J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Chen, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='-C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Wang, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Wang, “Stochastic blockchain for iot data integrity,” IEEE Transactions on Network Science and Engineering, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 7, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 373–384, Jan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='-March 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' [103] Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Feng, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' He, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Zeadally, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Khan, and N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Kumar, “A survey on privacy protection in blockchain system,” Journal of Network and Computer Applications, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 126, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 45–58, Jan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' [104] X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Xu, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Liu, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Zhang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Zhang, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Qi, and W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Dou, “A blockchain- powered crowdsourcing method with privacy preservation in mobile en- vironment,” IEEE Transactions on Computational Social Systems, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 6, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 1407–1419, Dec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' [105] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Wu, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='-N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Dai, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Wang, and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='-K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Choo, “Blockchain-based privacy preservation for 5g-enabled drone communications,” IEEE Net- work, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 35, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 50–56, Jan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='/Feb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='  [106] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Dhelim, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Kechadi, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Chen, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Aung, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Ning, and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Atzori, “Edge-enabled metaverse: The convergence of metaverse and mobile edge computing,” arXiv preprint arXiv:2205.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='02764, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' [107] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Dionisio, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' III, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Gilbert, “3d virtual worlds and the metaverse: Current status and future possibilities,” ACM Comput.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Surv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=', vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 45, jul 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' [108] Credit Suisse, “Metaverse: A guide to the next-gen internet,” 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Accessed on 27.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='08.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' [109] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Bujari, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Gaggi, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Luglio, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Palazzi, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Quadrio, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Roseti, and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Zampognaro, “Addressing the bandwidth demand of immersive appli- cations through nfv in a 5g network,” Mobile Networks and Applications, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 25, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 3, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 1114–1121, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='  EEEAccessBartlomiej Siniarski et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' : Need 6G for the Metaverse Realization 29 VOLUME 4, 2016  [110] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Hu, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Dhelim, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Ning, and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Qiu, “Survey on fog computing: architecture, key technologies, applications and open issues,” Journal of Network and Computer Applications, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 98, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 27–42, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' [111] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Naouri, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Wu, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Nouri, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Dhelim, and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Ning, “A novel framework for mobile-edge computing by optimizing task offloading,” IEEE Internet of Things Journal, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 8, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 16, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 13065–13076, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' [112] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Zhang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Chen, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Zhang, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Raychaudhuri, “Towards efficient edge cloud augmentation for virtual reality mmogs,” in Proceedings of the Second ACM/IEEE Symposium on Edge Computing, SEC ’17, (New York, NY, USA), Association for Computing Machinery, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' [113] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Lim, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Xiong, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Niyato, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Cao, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Miao, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Sun, and Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Yang, “Realizing the Metaverse with Edge Intelligence: A Match Made in Heaven,” arXiv e-prints, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' arXiv:2201.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='01634, Jan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' [114] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Letaief, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Shi, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Lu, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Lu, “Edge artificial intelligence for 6g: Vision, enabling technologies, and applications,” IEEE Journal on Selected Areas in Communications, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 40, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 1, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 5–36, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' [115] Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Wang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Qiu, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Zhou, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Shi, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Fu, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Chen, and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Letaief, “Federated learning via intelligent reflecting surface,” IEEE Transactions on Wireless Communications, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 21, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 2, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 808–822, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='  [116] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Xu, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Niyato, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Kang, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Xiong, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Miao, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Kim, “Wireless edge-empowered metaverse: A learning-based incentive mechanism for virtual reality,” in ICC 2022-IEEE International Conference on Commu- nications, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 5220–5225, IEEE, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' [117] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Sun, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Chen, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Tao, and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Liu, “Communications, caching, and computing for mobile virtual reality: Modeling and tradeoff,” IEEE Transactions on Communications, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 67, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 11, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 7573–7586, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' [118] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Jiang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Kang, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Niyato, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Ge, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Xiong, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Miao, Xuemin, and Shen, “Reliable Distributed Computing for Metaverse: A Hierarchical Game-Theoretic Approach,” arXiv e-prints, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' arXiv:2111.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='10548, Nov.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' [119] X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Huang, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Zhang, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Wu, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Leng, “Collaborative machine learn- ing for energy-efficient edge networks in 6g,” IEEE Network, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 35, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 6, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 12–19, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' [120] X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Wang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Han, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Wang, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Zhao, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Chen, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Chen, “In-edge ai: Intelligentizing mobile edge computing, caching and communication by federated learning,” IEEE Network, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 33, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 5, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 156–165, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' [121] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Lim, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Luong, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Hoang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Jiao, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='-C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Liang, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Yang, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Niyato, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Miao, “Federated learning in mobile edge networks: A comprehensive survey,” IEEE Communications Surveys & Tutorials, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 22, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 3, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 2031–2063, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='  [122] X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Wang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Han, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Leung, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Niyato, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Yan, and X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Chen, “Convergence of edge computing and deep learning: A comprehensive survey,” IEEE Communications Surveys & Tutorials, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 22, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 2, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 869–904, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' [123] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Liu, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Zhu, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Yu, “Resource-constrained federated edge learn- ing with heterogeneous data: Formulation and analysis,” IEEE Transac- tions on Network Science and Engineering, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 9, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 5, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 3166–3178, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' [124] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Mikolov, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Deoras, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Povey, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Burget, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Cˇ ernocký, “Strategies for training large scale neural network language models,” in 2011 IEEE Workshop on Automatic Speech Recognition & Understanding, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 196– 201, 2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' [125] Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Li, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Zhuang, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Guo, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Zhuo, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Zhang, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Song, and I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Stoica, “Ter- apipe: Token-level pipeline parallelism for training large-scale language models,” in International Conference on Machine Learning, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 6543– 6552, PMLR, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' [126] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Lu, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Huang, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Zhang, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Maharjan, and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Zhang, “Low-latency federated learning and blockchain for edge association in digital twin empowered 6g networks,” IEEE Transactions on Industrial Informatics, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 17, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 7, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 5098–5107, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' [127] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='-N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Dao, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='-V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Pham, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Tu, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Thanh, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Bao, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Lakew, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Cho, “Survey on aerial radio access networks: Toward a comprehensive 6g access infrastructure,” IEEE Communications Surveys & Tutorials, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 23, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 2, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 1193–1225, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='  [128] “Europe urged to act now to build open ran ecosystem.” Accessed on 24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='08.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' [129] “Openran begins work on ai/ml.” Accessed on 24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='08.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' [130] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Abdalla, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Upadhyaya, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Shah, and V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Marojevic, “Toward next generation open radio access networks–what o-ran can and cannot do!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=',” IEEE Network, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' [131] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Tang, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Chen, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Zhao, and N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Kato, “The roadmap of com- munication and networking in 6g for the metaverse,” IEEE Wireless Communications, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 1–15, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' [132] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Linthicum, “Cloud computing and the metaverse,” 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Accessed on 27.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='07.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' [133] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Cai, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Llorca, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Tulino, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Molisch, “Compute-and data- intensive networks: The key to the metaverse,” arXiv preprint arXiv:2204.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='02001, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' [134] Google, “Google Stadia.” Accessed on 27.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='08.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' [135] Nvidia, “Nvidia GeForce Now.” Accessed on 25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='08.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' [136] “Global IoT Market will Grow to 24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='1 Billion Devices in 2030, Gener- ating $1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='5 Trillion Annual Revenue.” Transforma Insights research, May, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' [Accessed on 09.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='06.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='2022].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' [137] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' De Alwis, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Kalla, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='-V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Pham, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Kumar, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Dev, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='-J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Hwang, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Liyanage, “Survey on 6g frontiers: Trends, applications, require- ments, technologies and future research,” IEEE Open Journal of the Communications Society, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 2, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 836–886, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' [138] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Janbi, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Katib, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Albeshri, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Mehmood, “Distributed artificial intelligence-as-a-service (daiaas) for smarter ioe and 6g environments,” Sensors, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 20, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 20, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 5796, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='  [139] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Jagatheesaperumal, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Ahmad, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Al-Fuqaha, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Qadir, “Ad- vancing education through extended reality and internet of everything enabled metaverses: Applications, challenges, and open issues,” arXiv preprint arXiv:2207.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='01512, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' [140] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Nayak and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Patgiri, “6g communication: Envisioning the key issues and challenges,” arXiv preprint arXiv:2004.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='04024, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' [141] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Maier, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Ebrahimzadeh, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Rostami, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Beniiche, “The internet of no things: Making the internet disappear and" see the invisible",” IEEE Communications Magazine, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 58, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 11, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 76–82, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' [142] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Liu, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Liu, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Chen, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Wang, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Wang, “Wireless sensing for human activity: A survey,” IEEE Communications Surveys & Tutorials, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 22, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 3, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 1629–1645, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' [143] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Cui, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Liu, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Jing, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Mu, “Integrating sensing and communi- cations for ubiquitous iot: Applications, trends, and challenges,” IEEE Network, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 35, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 5, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 158–167, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' [144] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Siriwardhana, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Porambage, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Liyanage, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Ylianttila, “A survey on mobile augmented reality with 5g mobile edge computing: ar- chitectures, applications, and technical aspects,” IEEE Communications Surveys & Tutorials, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 23, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 2, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 1160–1192, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' [145] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Xi, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Chen, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Gama, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Riar, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Hamari, “The challenges of entering the metaverse: An experiment on the effect of extended reality on workload,” Information Systems Frontiers, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 1–22, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='  [146] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Plechatá, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Makransky, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Böhm, “Can extended reality in the metaverse revolutionise health communication?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=',” NPJ digital medicine, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 5, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 1, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 1–4, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' [147] Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Yu, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Wang, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Zhou, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Ni, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Chen, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Céspedes, “Guest editorial special issue on cybertwin-driven 6g: Architectures, methods, and applications,” IEEE Internet of Things Journal, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 8, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 22, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 16191–16194, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' [148] Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Yu, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Ren, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Fu, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Li, and W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Zhang, “Cybertwin: An origin of next generation network architecture,” IEEE Wireless Communications, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 26, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 6, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 111–117, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' [149] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Tang, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Chen, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Rodrigues, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Zhao, and N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Kato, “Survey on digital twin edge networks (diten) towards 6g,” IEEE Open Journal of the Communications Society, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' [150] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Saad, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Bennis, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Chen, “A vision of 6g wireless systems: Applications, trends, technologies, and open research problems,” IEEE network, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 34, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 3, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 134–142, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' [151] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Chowdhury, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Shahjalal, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Ahmed, and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Jang, “6g wire- less communication systems: Applications, requirements, technologies, challenges, and research directions,” IEEE Open Journal of the Commu- nications Society, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 1, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' 957–975, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' [152] “Meta.” Accessed on 27.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
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+page_content=' [159] “Luxembourg metaverse.” Accessed on 27.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
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+page_content='  EEEAccessBartlomiej Siniarski et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' : Need 6G for the Metaverse Realization 30 VOLUME 4, 2016  BARTLOMIEJ SINIARSKI is currently a post doctoral researcher and a project manager for the EU H2020 SPATIAL project at University College Dublin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' He completed his undergraduate studies in Computer Science at University College Dublin (Ireland) and University of New South Wales (Australia).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' He was awarded with a doctoral degree in 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' He has a particular interest and experience in the design of the IoT networks and in particular collecting, storing and analysing data gathered from intelligent sensors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Furthermore, he was actively involved in MSCA-ITN-ETN, ICT-52-2020 and H2020-SU-DS-2020 projects which are focused on solving problems in the area of network security, performance and management in 5G and B5G networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' THIEN HUYNH-THE received the B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' degree in Electronics and Telecommunication Engineering and the M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='Sc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' degree in Electronics Engineering from Ho Chi Minh City University of Technol- ogy and Education, Vietnam, in 2011 and 2013, respectively, and the Ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' degree in Computer Science and Engineering from Kyung Hee Uni- versity (KHU), South Korea, in 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' He was a recipient of the Superior Thesis Prize awarded by KHU.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' From March 2018 to August 2018, he was a Postdoctoral Researcher with Ubiquitous Computing Laboratory, KHU.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' From September 2018 to May 2022, he was a Postdoctoral Researcher with the ICT Convergence Research Center, Kumoh National Institute of Technology, South Korea.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='  He is currently a Lecturer in Department of Computer and Communication Engineering, Ho Chi Minh City University of Technology and Education (HCMUTE), Vietnam.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' He was a recipient of Golden Globe Award 2020 for Vietnamese Young Scientist by Central Ho Chi Minh Communist Youth Union associated with Ministry of Science and Technology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' His current research interests include digital image processing, radio signal processing, computer vision, wireless communications, IoT applications, machine learning, and deep learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='  CHAMITHA DE ALWIS (Senior Member, IEEE) is a Lecturer, Researcher and Consultant in Cy- bersecurity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Presently he works as a Lecturer in Cybersecurity in the School of Computer Sci- ence and Technology, University of Bedfordshire, United Kingdom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' He is the founder Head of the Department of Electrical and Electronic Engineer- ing, University of Sri Jayewardenepura, Sri Lanka, where he also served as a Senior Lecturer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' He received the B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='Sc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' (First Class Hons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=') in Electronic and Telecommunication Engineering from University of Moratuwa, Sri Lanka, in 2009, and the Ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' in Electronic Engineering from University of Surrey, United Kingdom, in 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' He has over 13 years of experience in the academia and the industry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' He has published over 30 research arti- cles and serves as guest editor/reviewer/TPC member for reputed journals and conferences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' He was awarded several competitive research grants and actively contributes to various research projects related to network security, 5G/6G, and blockchain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' He also provides consultancy services for ICT and cybersecurity related projects and activities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='  GÜRKAN GÜR (Senior Member, IEEE) is a se- nior lecturer at Zurich University of Applied Sci- ences (ZHAW) – Institute of Applied Information Technology (InIT) in Winterthur, Switzerland.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' He received his B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' degree in electrical engineering in 2001 and Ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' degree in computer engineer- ing in 2013 from Bogazici University in Istan- bul, Turkey.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' His research interests include Future Internet, 5G and Beyond networks, information security, and information-centric networking.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' He has two patents (one in US, one in TR) and published more than 80 academic works.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Currently, he is involved in EU H2020 RIA – INSPIRE- 5Gplus project.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' He is a senior member of IEEE and a member of ACM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' His research interests include Future Internet, information security, next- generation wireless networks and ICN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='  GOKUL YENDURI received his Master’s degree (M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='Tech.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=', IT) from Vellore Institute of Technology in the year 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Currently, he is a senior research fellow at the DIVERSASIA project, co-funded by the Erasmus+ programme of the European Union.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' His areas of interest are machine learning and predictive analysis, software engineering, assistive technologies, and the metaverse.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' He has worked as an assistant professor in the past.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' He attended sev- eral national and international conferences, work- shops, and guest lectures and published papers in peer-reviewed international journals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' He is also acting as a reviewer for many prestigious peer-reviewed international journals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' THIPPA REDDY GADEKALLU is currently working as an Associate Professor in the School of Information Technology and Engineering, Vel- lore Institute of Technology, Vellore, Tamil Nadu, India.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' He obtained his Bachelors in Computer Science and Engineering from Nagarjuna Univer- sity, India, in the year 2003, Masters in Computer Science and Engineering from Anna University, Chennai, Tamil Nadu, India in the year 2011 and his Ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='D in Vellore Institute of Technology, Vel- lore, Tamil Nadu, India in the year 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' He has more than 14 years of experience in teaching.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' He has more than 150 international/national publications in reputed journals and conferences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Currently, his areas of research include Machine Learning, Internet of Things, Deep Neural Net- works, Blockchain, Computer Vision.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='  He is an editor in several publishers like Springer, Hindawi, Plosone, Scientific Reports (Nature), Wiley.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' He also acted as a guest editor in several reputed publishers like IEEE, Elsevier, Springer, Hindawi, MDPI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' He is recently recognized as one among the top 2% scientists in the world as per the survey conducted by Elsevier in the year 2021, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='  EEEAccessBartlomiej Siniarski et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' : Need 6G for the Metaverse Realization 31 VOLUME 4, 2016  MADHUSANKA LIYANAGE (Senior Member, IEEE) is an Assistant Professor/Ad Astra Fellow and Director of Graduate Research at the School of Computer Science, University College Dublin, Ireland.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' He is also acting as a Docent/Adjunct Pro- fessor at the Center for Wireless Communications, University of Oulu, Finland, and Honorary Ad- junct Professor at the Department of Electrical and Information Engineering, University of Ruhuna, Sri Lanka.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' He received his Doctor of Technology degree in communication engineering from the University of Oulu, Oulu, Finland, in 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' From 2011 to 2012, he worked as a Research Scientist at the I3S Laboratory and Inria, Sophia Antipolis, France.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' He was also a recipient of the prestigious Marie Skłodowska-Curie Actions Individual Fellowship and Government of Ireland Postdoctoral Fellowship during 2018-2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' During 2015-2018, he has been a Visiting Research Fellow at the CSIRO, Australia, the Infolabs21, Lancaster University, U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=', Computer Science and Engineering, The University of New South Wales, Australia, School of IT, University of Sydney, Australia, LIP6, Sorbonne University, France and Computer Science and Engineering, The University of Oxford, U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' He is also a senior member of IEEE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' In 2020, he received the "2020 IEEE ComSoc Outstanding Young Researcher" award by IEEE ComSoc EMEA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' In 2021, he was ranked among the World’s Top 2% Scientists (2020) in the List prepared by Elsevier BV, Stanford University, USA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='  Also, he was awarded an Irish Research Council (IRC) Research Ally Prize as part of the IRC Researcher of the Year 2021 awards for the positive impact he has made as a supervisor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Dr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' Liyanage’s research interests are 5G/6G, SDN, IoT, Blockchain, MEC, mobile, and virtual network security.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content=' More info: www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='madhusanka.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
+page_content='com  EEEAccess' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNE1T4oBgHgl3EQfuQVw/content/2301.03386v1.pdf'}
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+SPRING: Situated Conversation Agent Pretrained with
+Multimodal Questions from Incremental Layout Graph
+Yuxing Long 1, Binyuan Hui 2, Fulong Ye 1, Yanyang Li 2, Zhuoxin Han 1,
+Caixia Yuan 1, Yongbin Li 2, Xiaojie Wang 1 *
+1 Beijing University of Posts and Telecommunications, Beijing, China
+2 Independent Researcher
+{longyuxing, fulong ye, hanzhuoxin, yuancx, xjwang}@bupt.edu.cn
+lyb821@gmail.com
+Abstract
+Existing multimodal conversation agents have shown impres-
+sive abilities to locate absolute positions or retrieve attributes
+in simple scenarios, but they fail to perform well when com-
+plex relative positions and information alignments are in-
+volved, which poses a bottleneck in response quality. In this
+paper, we propose a Situated Conversation Agent PRetrained
+with Multimodal Questions from INcremental Layout Graph
+(SPRING) with abilities of reasoning multi-hops spatial rela-
+tions and connecting them with visual attributes in crowded
+situated scenarios. Speciﬁcally, we design two types of Mul-
+timodal Question Answering (MQA) tasks to pretrain the
+agent. All QA pairs utilized during pretraining are gener-
+ated from novel Incremental Layout Graphs (ILG). QA pair
+difﬁculty labels automatically annotated by ILG are used
+to promote MQA-based Curriculum Learning. Experimen-
+tal results verify the SPRING’s effectiveness, showing that it
+signiﬁcantly outperforms state-of-the-art approaches on both
+SIMMC 1.0 and SIMMC 2.0 datasets. We release our code
+and data at https://github.com/LYX0501/SPRING.
+1
+Introduction
+Building multi-modal conversation agents that can commu-
+nicate with people in visual situations is an attractive goal
+for the AI community. Lots of speciﬁc tasks and datasets
+for visual dialog, like VisDial (Das et al. 2017), GuessWhat
+(De Vries et al. 2017), GuessWhich (Chattopadhyay et al.
+2017), are proposed in recent years. Among them, the Sit-
+uated Interactive Multi-modal Conversation (SIMMC 1.0)
+(Moon et al. 2020) aims to study task-oriented dialogues that
+encompass a situated multi-modal user context in the form
+of a virtual reality (VR) environment. The updated dataset
+SIMMC 2.0 (Kottur et al. 2021b) provides a more challeng-
+ing test bed for multi-modal conversation agents. There are
+many assets with a complex layout in each image. Figure
+1 gives an example of a scene and a fragment of dialogue
+in SIMMC 2.0. There are dozens of clothes in the image.
+Each cloth is a digit asset with a unique asset ID and a set of
+attributes (e.g. type, color) in the metadata. But there is no
+information on the scene layout except for a few labels on
+four relations (up, down, left, and right) between the assets.
+*Corresponding author
+Copyright © 2023, Association for the Advancement of Artiﬁcial
+Intelligence (www.aaai.org). All rights reserved.
+Figure 1: An example of a virtual scene and a fragment of
+dialogue in SIMMC 2.0. Since there are many clothes with
+similar visual attributes, it is difﬁcult to talk about a asset
+only by its visual attributes. For this case, the spatial rela-
+tions in the layout are necessary.
+A number of works have been established on SIMMC
+2.0. Based on different multi-modal Visual-Language pre-
+training Models (VLM), previous researchers pay more at-
+tention to learning the visual attributes of assets. QS Goal
+Diggers (Kottur et al. 2021a) and Kakao Enterprise (Lee and
+Han 2021) directly insert visual attributes into models input,
+while Sogang University (Kottur et al. 2021b) and A-STAR
+(Nguyen et al. 2021) build a set of visual attributes predic-
+tion tasks in pre-training stage. KAIST (Lee et al. 2022) de-
+signs an auxiliary task to predict visual attributes. However,
+less attention has been paid to building spatial relations be-
+tween assets. All existing models only use the coordinates of
+asset bounding boxes as positional information, which can-
+not capture spatial relations in the scenes.
+As a result, the models can accurately generate ”the black
+jacket” but fail to describe more natural referring expres-
+sions like ”the black jacket on the leftmost ﬂoor rack”. It is
+obvious that the later expression is more useful in a scene
+including lots of clothes with similar attributes. The combi-
+nation of attributes and spatial relations helps people locate
+assets quickly. To generate this type of expression, a model
+needs to learn not only the visual attributes of each asset but
+also spatial relations between different items.
+To address above problem, we propose Situated Conver-
+sation Agent PRetrained with Multimodal Questions from
+arXiv:2301.01949v1  [cs.CL]  5 Jan 2023
+
+User
+Do you have any clothes match my new bought jeans ?
+Agent
+How
+bout thel
+black jacket on the leftmost floor rack of the
+grey jacket
+ the to, row of the shelf near the entrance ?
+User
+Anything else ? I prefer some fashion t-shirs
+Agent
+The
+purple t-shirt on the back middle shelf may meet your criteriaINcremental Layout Graph (SPRING), which is pretrained
+with multimodal questions generated from incremental lay-
+out graph. In our method, we design Incremental Layout
+Graph (ILG) for each scene to capture rich spatial relations
+between different scene items. Unlike scene graph (Chang
+et al. 2020), an ILG is built using pure textual information
+and can be extended incrementally with newly added dia-
+logue. And then, two types of Multimodal Question An-
+swering (MQA) pre-training tasks and corresponding QA
+pairs are collected by traversing nodes (digital assets and
+background items) on the ILG. According to the spanned
+path length, QA pairs can be automatically annotated with
+difﬁculty levels. Curriculum Learning (Bengio et al. 2009)
+is therefore employed for pre-training on a Transformer
+(Vaswani et al. 2017) encoder-decoder backbone. Experi-
+ments on both SIMMC 1.0 and SIMMC 2.0 show that our
+method improves the response quality by a large margin
+compared to previous best models.
+The main contributions of our work are as follows:
+• We ﬁrst propose a novel approach to build ILGs for vir-
+tual scenes from dialogue text incrementally. The ILGs
+include scene items with relations. It is worth noting that
+this process does not rely on any human annotation.
+• Based on ILGs, we introduce two types of new MQA
+pretraining tasks that can facilitate model understanding
+of visual metadata and spatial relations between different
+assets. Pre-training samples are automatically generated
+by traversing the ILG, which also generates an accompa-
+nying difﬁculty label for curriculum learning.
+• We conduct thorough experiments to verify that our ap-
+proach effectively enhances response quality. Our ap-
+proach outperforms existing state-of-the-art methods by
+a signiﬁcant margin consistently on all metrics on both
+SIMMC 1.0 and SIMMC 2.0.
+2
+Related Works
+Situated Interactive Multimodal Conversations.
+Con-
+versation systems have developed rapidly in recent years,
+e.g., task-oriented conversations pretraining (He et al.
+2022c,a,b), knowledge-based conversations (Hui et al. 2022;
+Wang et al. 2022a) and so on. Among them, multimodal
+conversations are the new trend. META releases multimodal
+conversation datasets SIMMC (Kottur et al. 2021b) based on
+VR shopping stores. There are hundreds of scene snapshots
+from different angles. Compared with the previous multi-
+modal dialogue datasets MMD (Saha, Khapra, and Sankara-
+narayanan 2018) and VisDial (Das et al. 2017), the situ-
+ated agent is required to generate more complex visual at-
+tributes and more detailed spatial relations to infer digital
+assets in the scene. Kottur et al. (2021a) has preliminary
+explorations on utilizing visual attributes and spatial rela-
+tions. Concretely, DialVinVL (Kottur et al. 2021a) incorpo-
+rates slot values about visual attributes with dialogue history
+as textual input and concatenates original box coordinates
+to region features extracted by the object detector as visual
+input. JMGPT (Kottur et al. 2021b) and JointGM (Nguyen
+et al. 2021) apply language model to predict visual attributes
+and system response jointly. MMBart (Lee et al. 2022) adds
+embedded box coordinates to textual embedding as Trans-
+former input and designs auxiliary tasks to predict visual at-
+tributes according to the output of encoder hidden states. We
+can ﬁnd that their utilized spatial information is all from the
+bounding box. Unlike these methods, we ﬁrst notice the lack
+of VLM’s capability for visuality and spatiality, and then
+propose MQA pretraining tasks based on incremental layout
+graphs which have been successfully applied to (Qiu et al.
+2021; Liao et al. 2021; Hui et al. 2021; Qiu et al. 2022).
+Visual Language Pretraining.
+To improve models’ per-
+ception of text and image and help them establish connec-
+tions between multimodal information, kinds of visual lan-
+guage pretraining models are designed. ViLBERT (Lu et al.
+2019) and UNITER (Chen et al. 2020) propose to con-
+sider the raw output of the detector, a distribution of object
+classes, as soft labels and optimize the KL-divergence be-
+tween two distributions. LEXMERT (Tan and Bansal 2019)
+and UNIMO (Li et al. 2021) propose Masked Region Fea-
+ture Regression (MRFR) regresses the masked region fea-
+ture to its corresponding original region feature, where rep-
+resents images as a sequence of region features by Faster
+R-CNN (Ren et al. 2015). Furthermore, SOHO (Huang et al.
+2021b) is designed to avoid information leakage from neigh-
+bor features when images are converted into grid features or
+patch features.
+Recently, CLIP (Radford et al. 2021) and ALIGN (Jia
+et al. 2021) leverage large-scale image-text pairs to learn
+transferable visual representations and exhibit surprising
+zero-shot transfer to image classiﬁcation tasks. VL-T5 (Cho
+et al. 2021) and OFA (Wang et al. 2022b) introduce down-
+stream tasks, like visual grounding and grounded caption,
+into pretraining tasks to narrow the gap between pretrain-
+ing and ﬁne-tuning. Unlike these efforts, we design new pre-
+training tasks through a uniﬁed QA paradigm to improve ex-
+isting methods’ visual attributes and spatial relations model-
+ing without adding new modules.
+3
+Methods
+Let D = {(Ut, Rt, It)}T
+t=1 be an ongoing dialogue between
+a user and an agent with T rounds, where Ut is the user
+utterance at time step t, Rt is the language response to Ut by
+the agent, and It is the accompanying scene image. The task
+here is to predict the optimal language response R
+′
+t, given
+the dialog history Ht = [Ui, Ri]t−1
+i=1, current user utterance
+Ut and scene image It, as modeled in Eq (1)
+R
+′
+t = argmax Pθ (Rt | Ht, Ut, It)
+(1)
+where θ is the model learnable parameters.
+To solve above problem, we propose a mutimodal dia-
+logue model SPRING, which is pretrained with mutlimodal
+questions generated from incremental layout graph. In the
+following sections, we will introduce model architecture,
+ILG generation and MQA pretraining tasks in order.
+3.1
+Architecture
+The backbone of SPRING model is encoder-decoder based
+single-stream VLM framework, which are stacks of Trans-
+former (Vaswani et al. 2017) layers. The scene image It ∈
+
+in
+on
+in
+in
+in
+on
+Do you have a nice coat from 
+Downtown Consignment ?
+I have the black coat in the second row of the third 
+compartment in the leftmost cupboard.
+User
+( Dialogue History  … )
+My next question is whether you 
+have quality t-shirt to show me ?
+How about the pink t-shirt in the top row
+on the back display wall and the blue t-
+shirt in the bottom row?
+User
+Agent
+( Dialogue History  … )
+I need a blouse as well.
+How about the brown blouse in the bottom row on 
+the back display wall and the grey blouse in the 
+middle row in the second compartment in the 
+leftmost cupboard. ?
+User
+Agent
+( Dialogue History  … )
+pink
+t-shirt
+ID 42
+top
+row
+blue
+t-shirt
+ID 33
+bottom
+row
+back
+display
+wall
+brown
+blouse
+ID 9
+bottom
+row
+black
+coat
+ID 16
+second
+row
+third
+compart-
+ment
+leftmost
+cupboard
+grey
+Blouse
+ID 20
+second
+row
+second
+compart-
+ment
+leftmost
+cupboard
+Query Asset ID & BBox 
+by Visual Attribute 
+Query Asset ID & BBox 
+by Visual Attribute 
+Query Asset ID & BBox 
+by Visual Attribute 
+in
+in
+in
+of
+of
+[412, 323, 479, 588]
+[656, 263, 701, 399]
+[699, 410, 740, 598]
+[661, 421, 695, 592]
+[218, 354, 230, 579]
+top/down
+on
+[661, 421, 695, 592]
+black
+coat
+ID 16
+second
+row
+third
+compart-
+ment
+leftmost
+cupboard
+in
+in
+of
+grey
+Blouse
+ID 20
+in
+blue
+t-shirt
+ID 33
+in
+[699, 410, 740, 598]
+second
+row
+third
+compart-
+ment
+of
+[218, 354, 230, 579]
+in
+pink
+t-shirt
+ID 42
+top
+row
+back
+display
+wall
+in
+on
+[656, 263, 701, 399]
+right/left
+brown
+blouse
+ID 9
+bottom
+row
+in
+right/left
+right/left
+right/left
+Part of Background Item
+Background Item
+Digital Asset
+Spatial Relationship
+ILG
+[412, 323, 479, 588]
+Agent
+back
+display
+wall
+Figure 2: Construction of Incremental Layout Graph from dialogue. Digital assets and background items constitute ILG nodes
+while spatial relations form ILG edges. ILG is continuously incremented with newly added dialogue under the same scene.
+Rh×w×c is splitted to P patches. And each patch is projected
+to visual embedding of the model hidden size. The dialogue
+history and current user utterance are converted to sub-word
+sequence by Byte-Pair Encoding (BPE) and then embedded
+to textual embedding. All visual embedding and textual em-
+bedding are concatenated as model input.
+To facilitate SPRING to better understand the informa-
+tion of embodied scenes, we propose a series of MQA pre-
+training tasks based on layout graphs Gi. As there is no an-
+notated layout graph in the SIMMC dataset, we propose an
+unsupervised ILG construction method based on natural lan-
+guage dialog history.
+3.2
+Incremental Layout Graph (ILG)
+We observe that visual attributes and spatial descriptions
+exist in the dialogue history. Compared with dataset an-
+notations, the information from dialogue is more detailed.
+For example, SIMMC 2.0 annotation only gives bounding
+boxes of digital assets and four types of relative position
+(up, down, right, left) between them, while dialogues in-
+clude the absolute position of background items and their
+relative position with assets. A crucial discovery lies in the
+co-coreference between dialogue history and response, the
+same assets present in the responses to be generated.
+Therefore, we propose an ILG generation algorithm to ex-
+tract high quality information from dialogues and generate
+Incremental Layout Graph (ILG) Gi = ⟨Vi, Ei⟩ to dispose
+them, where Vi denotes the node set containing the digital
+assets and background items from dialog history and Ei rep-
+resents the edge set depicting spatial relations between scene
+items Vi.
+Textual Information Extraction and Alignment
+we
+consider adopting a rule-based textual information extrac-
+tion method, i.e. , regular expression, to extract visual at-
+tributes and spatial descriptions from dialogue history with-
+out human annotation. The regular expressions RegExpva
+and RegExpsd for visual attribute and spatial description
+are as follows.
+RegExpva = (art.) (color) (asset type)
+(2)
+RegExpsd = (positional prep.) (art.) (.∗?) (punc.) (3)
+where art. is article, prep. represents preposition and punc.
+means punctuation. Please refer to Appendix for details.
+With these two regular expressions, as left part of Figure 2
+shows, we can extract visual attribute ”black coat” and spa-
+tial description ”in the second row of the third compartment
+in the leftmost cupboard” from dialogue history.
+Although the visual attributes and spatial descriptions
+extracted by the above regular expressions are naturally
+aligned because of language features, they are not aligned
+with asset IDs, making asset box coordinates unusable. To
+solve this problem, we query the color and type of assets
+from the database by their IDs to compose visual attributes
+like ”black coat” and then try pairing them with the ex-
+tracted visual attributes like ”black coat”. If these two visual
+attributes match, the corresponding asset ID ”16” can be de-
+termined, from which we can get the paired asset IDs, visual
+attributes, and spatial descriptions. We further design the fol-
+lowing two regular expressions to extract background item
+and relative spatial relation from extracted spatial descrip-
+tions.
+RegExpbi = (background item)
+(4)
+RegExpsr = (positional prep.)
+(5)
+where RegExpbi and RegExpsr denote regular expressions
+for background item and spatial relation, prep. represents
+preposition. With these two regular expressions, as middle
+part of Figure 2 shows, we can extract background items
+”second row”, ”third compartment” and ”leftmost cup-
+board” and relative spatial relations ”in”, ”of” from spatial
+description obtained previously.
+Incremental Layout Graph Generation
+With rich infor-
+mation extracted from a sample of dialogue history, lay-
+out sub-graph can be generated as middle part of Figure 2
+shows. In the layout sub-graph, digital asset node store its
+visual attributes like ”black coat” and asset ID ”16” while
+background item nodes store background items like ”sec-
+ond row”, ”third compartment” and ”leftmost cupboard”.
+
+[Pure Visual QA]  What is the type of asset 9 and 16 ?
+[Region-Guided Visual QA] What is the color of asset 42 
+in region ? Region: [656, 263, 701, 399]
+[Position-Guided Visual QA]  What are types of asset 20 
+in second row of the third compartment and asset 42 in 
+the top row on the back display wall?
+[Pure Spatial QA] Where is asset 33 , 9 and 20?
+[Region-Guided Spatial QA] Where is asset 16 in region ? 
+Region: [412, 323, 479, 588]
+[Visual Attribute-Guided Spatial QA] Where is the pink 
+t-shirt and grey blouse ?
+Spatial QA
+Visual QA
+SPRING
+Blouse and coat.
+Pink.
+Blouse and t-shirt.
+In the bottom row, in the bottom row on the 
+back display wall and in the second row of the 
+second compartment in leftmost cupboard.
+In the second row of the third compartment in 
+the leftmost cupboard.
+In the top row on the back display wall.
+2
+1
+5
+8
+4
+2
+N
+Difficulty Level
+Curriculum Learning
+ILG
+Figure 3: Demonstration of SPRING model and two types of MQA pretraining tasks, Visual QA and Spatial QA. Curriculum
+learning based on QA pair difﬁculty level activates the potential of MQA tasks.
+SCENE IMAGE
+QA TYPE
+QUESTION TEMPLATE
+ANSWER
+Pure Visual QA
+What is the [visual attribute type] of item [asset ID]?
+[visual attribute value]
+Region-Guided Visual QA
+What is the [visual attribute type] of item [asset ID] in region? Region: [x1, y1, x2, y2]
+[visual attribute value]
+Position-Guided Visual QA
+What is the [visual attribute type] of item [asset ID] [position]?
+[visual attribute value]
+Pure Spatial QA
+Where is the item [asset ID]?
+[position]
+Region-Guided Spatial QA
+Where is the item [asset ID] in region? Region: [x1, y1, x2, y2]
+[position]
+Visual Attribute-Guided Spatial QA
+Where is the [item color] [item type] [asset ID]?
+[position]
+Table 1: QA pair template. Square brackets ‘[∗]’ represent slots to be ﬁlled by traversing ILGs.
+Spatial relations and queried bounding boxes are utilized to
+deﬁne layout sub-graph edges. As the right part of Figure 2
+shows, the scene ILG continuously increments with newly
+added sub-graph about the same scene, which ﬁnally can
+include all digital assets, background items, and spatial rela-
+tions between them under this scene. Mining information on
+the ILG is simple but effective. The visual attributes can be
+easily obtained by traversing the ILG nodes, while multiple
+types of spatial relations can be inferred by walking along
+the ILG edges.
+3.3
+ILG-based MQA Pre-training Tasks
+To enhance response generation quality of visual attributes
+and spatial relations, we design visual QA pre-training task
+and spatial QA pre-training task based on Multimodal Ques-
+tion Answering (MQA), which respectively contain three
+types of novel sub-tasks. As shown in Figure 3 and Table
+1, all QA pairs are automatically generated by traversing
+ILG and ﬁlling the corresponding template. The QA pair
+generation algorithm is displayed in Algorithm 1. Formula-
+rly, we use the question template ﬁlling function Qtype(·) to
+generate question, Atype represents corresponding answer,
+Typeva means visual attribute type, IDasset denotes asset ID,
+Iscene is scene image, BBoxasset means asset region coor-
+dinates, tsr represents spatial relation, tva is visual attribute,
+tbi denotes background item.
+3.3.1 Visual QA
+Pure Visual QA (PVQA)
+As the most basic visual QA
+task, the goal of Pure Visual QA is to help the model es-
+tablish connections between asset ID and corresponding vi-
+sual attributes when a scene image is provided. We design
+PVQA template in which the question prompts the type of
+visual attribute and asset ID. The pure visual question can
+be generated by traversing the asset nodes of ILG and ﬁlling
+[asset ID] slot in the template while answers are gener-
+ated based on the visual attributes stored in asset nodes. The
+objective of PVQA task is the following.
+Lθ = − �N
+i=1 log Pθ (Apv | Qpv(Typeva, IDasset), Iscene)
+(6)
+Region-Guided Visual QA (RVQA)
+To improve the
+model’s ability of locating asset and describing its visual
+attribute by region visual context, we design RVQA tem-
+plate based on PVQA, in which the question is guided by
+asset region coordinates and asset ID. The region-guided
+visual question can be generated by traversing asset nodes
+of ILG and ﬁlling [asset ID], bounding box coordinates
+[x1, y1, x2, y2] slots in the template. The corresponding
+answer is produced based on the visual attributes stored in
+asset nodes. The objective of RVQA task is the following.
+Lθ = − �N
+i=1 log Pθ (Argv | Qrgv(Typeva, IDasset, BBoxasset), Iscene)
+(7)
+Position-Guided Visual QA (PoVQA)
+In the conversa-
+tions, instead of region coordinates, an agent has to locate
+asset by its spatial information no matter when understand-
+ing user utterances or making recommendations. To bring
+the question closer to a real conversation, we design PoVQA
+template by replacing region coordinates in RVQA with spa-
+tial relations. For position-guided visual question template,
+the [asset ID] slot can be ﬁlled by traversing asset nodes
+of ILG while the [position] slot is ﬁlled by spatial rela-
+tion path between asset nodes and background item nodes.
+The corresponding answer is produced based on the visual
+attribute stored in asset nodes. The objective of PoVQA task
+is the following.
+Lθ = − �N
+i=1 log Pθ (Apgv | Qpgv(Typeva, IDasset, tsr), Iscene)
+(8)
+
+口8Algorithm 1: QA Pair Generation
+Input:
+ILG Gi = ⟨Vi, Ei⟩, QA template list T
+Output:
+QA pair list QA, difﬁculty label list DL
+1: Initialize QA pair list QA and difﬁculty label list DL
+2: for node in Ei do
+3:
+if TypeOf(node) = ”background item” then
+4:
+Skip node
+5:
+/* Get information from digtal asset node */
+6:
+(tva, IDasset, BBoxasset) ← GetInfo(Gi, node)
+7:
+/* Walk from node to get spatial relations */
+8:
+(tbi, tsr) ← Walk(Gi, node)
+9:
+tslot ← (tva, tbi, tsr, BBoxasset, IDasset)
+10:
+for template in T do
+11:
+/* Fill in the template */
+12:
+(qa, dl) ← FillIn(template, tslot)
+13:
+Add QA ← qa, DL ← dl
+3.3.2 Spatial QA
+Pure Spatial QA (PSQA)
+As the most basic spatial QA
+task, the goal of PSQA is to help the model establish connec-
+tions between asset ID and corresponding spatial relations
+when a scene image is provided. We design PSQA template
+in which the question only prompts ”where” and asset ID.
+The pure spatial question can be generated by traversing the
+asset nodes of ILG and ﬁlling [asset ID] slot in the tem-
+plate, while answers are generated based on the spatial rela-
+tion paths between the background item node and the asset
+node. The objective of PSQA task is the following.
+Lθ = − �N
+i=1 log Pθ (Aps | Qps(IDasset), Iscene)
+(9)
+Region-Guided Spatial QA (RSQA)
+To improve the
+model’s ability of locating an asset and describing its spatial
+relations by region visual context, we design RSQA tem-
+plate based on PSQA, in which the question is guided by
+asset region coordinates and asset ID. The region-guided vi-
+sual question can be generated by traversing asset nodes of
+ILG and ﬁlling the slots of [asset ID], bounding box coor-
+dinates [x1, y1, x2, y2] in the template. The correspond-
+ing answer is produced based on the spatial relation paths
+between the background item node and the asset node. The
+objective of RSQA task is the following.
+Lθ = − �N
+i=1 log Pθ (Args | Qrgs(IDasset, BBoxasset), Iscene)
+(10)
+Visual Attribute-Guided Spatial QA (VSQA)
+In the
+conversations, instead of region coordinates, an agent has
+to locate an asset by its visual attribute no matter when un-
+derstanding user utterances or making recommendations. To
+bring the question closer to a real conversation, we design
+VSQA template by replacing region coordinates in RSQA
+with visual attributes (e.g. color, type). For spatial-guided vi-
+sual question template, the [asset ID] slot can be ﬁlled by
+traversing asset nodes of ILG while the [item color] and
+[item types] slots are ﬁlled by the visual attribute stored
+in asset nodes. The corresponding answer is produced based
+on the spatial relation paths between the background item
+node and the asset node. The objective of VSQA task is the
+following.
+Lθ = − �N
+i=1 log Pθ (Avags | Qvags(IDasset, tva), Iscene)
+(11)
+3.4
+MQA-Based Curriculum Learning
+Automatic Difﬁculty Level Annotation
+When generat-
+ing QA pairs by walking on the ILG, the number of nodes
+spanned by the pathway can be recorded. The more nodes
+the path passes through, the more scene information con-
+tained in the corresponding QA pair, which means that the
+multimodal dialogue model needs more hops to make infer-
+ences. Therefore, we automatically label the difﬁculty level
+of each QA pair according to the number of nodes the path
+spans. For example, when generating the question “Where is
+the brown jacket 83 & 1055?” and the answer “it is on the
+ﬂoor rack near the entrance.”, one asset node “brown jack
+83 & 1055” and two background item nodes are spanned on
+the ILG. The difﬁculty level of this QA pair is annotated as
+3. The following is the formal expression.
+d = |Vspanned|
+D
+(12)
+where d denotes the normalized difﬁculty level of QA pair,
+|Vspanned| represents the number of ILG nodes spanned by
+corresponding path, D is the maximum value of ILG nodes
+spanned by the QA pair path in the dataset.
+Pretraining Strategy
+With automatically annotated difﬁ-
+culty labels, we propose MQA based curriculum learning
+to activate the potential of our designed MQA pretraining
+tasks. We deﬁne the model competence c as follows.
+c(t) = γ
+�
+α t
+T + β
+�
+1 − t
+T
+�
+min2(d)
+(13)
+where t is the index of current training step, T represents
+the maximum number of training steps, min2(d) means the
+minimum value of difﬁculty level d, α and β are hyper-
+parameters, γ is determined by α as
+�
+1
+α. Here we set α
+to 1.2 and β to 0.8. At a given training step t, QA pair with
+difﬁculty smaller than or equal to c(t) (i.e. d ≤ c(t)) will be
+sampled for training. As such, our pretraining strategy fo-
+cuses on QA pairs with lower difﬁculty in the early stage,
+aiming at helping the model form preliminary perception
+and inference capabilities for scene items. In the middle and
+late stages, more difﬁcult QA pairs are added, which im-
+proves the model’s ability to generate visual attributes and
+spatial relations for multiple assets.
+After MQA pretraining, SPRING model is ﬁne-tuned on
+the SIMMC response generation task. The auto-regressive
+language modeling objective is the following.
+Lθ = − �N
+i=1 log Pθ (Ri | Hi, Ui, Ii)
+(14)
+where N denotes the total number of training samples.
+4
+Experiment
+4.1
+Set up
+Datasets.
+To evaluate the performance of the proposed
+model, we ﬁrst conduct experiments on widely-used situated
+multimodal dialogue datasets SIMMC 1.0 and SIMMC 2.0.
+
+MODELS
+BLEU-1
+BLEU-2
+BLEU-3
+BLEU-4
+METEOR
+ROUGE
+CIDEr
+VISUAL
+SPATIAL
+SIMMC 1.0
+MN-MAG (Kim et al. 2021)
+27.28
+16.75
+12.32
+9.50
+16.62
+32.35
+0.8694
+9.49
+9.10
+Tom (Jeong et al. 2021)
+28.95
+18.81
+14.23
+11.10
+18.83
+38.18
+1.5014
+11.13
+10.17
+JBi-encoder (Huang et al. 2021a)
+26.76
+16.76
+12.49
+9.60
+17.65
+36.46
+1.2345
+9.73
+9.43
+SPRING (Ours)
+32.46
+22.15
+17.23
+13.77
+20.75
+40.51
+1.6329
+13.53
+12.60
+SIMMC 2.0
+MTN (Kottur et al. 2021b)
+62.38
+44.52
+32.90
+21.70
+21.38
+38.50
+1.1207
+19.91
+14.95
+JMGPT (Kottur et al. 2021b)
+51.05
+35.03
+24.66
+19.20
+14.73
+29.18
+0.7738
+13.67
+11.54
+JMGPT-BS (Kottur et al. 2021a)
+64.86
+48.86
+37.91
+28.38
+22.43
+43.88
+1.9669
+22.10
+14.56
+JointGM (Nguyen et al. 2021)
+64.40
+48.54
+37.69
+34.62
+21.91
+42.44
+1.8265
+21.77
+15.82
+MMBart (Lee et al. 2022)
+69.89
+52.99
+41.32
+33.10
+24.79
+46.60
+2.1887
+26.19
+21.11
+DialVinVL (Kottur et al. 2021a)
+75.38
+57.42
+44.92
+34.90
+27.09
+51.24
+2.3426
+29.92
+22.55
+GPTDeIT (Lee and Han 2021)
+68.43
+52.23
+40.95
+28.50
+24.81
+47.80
+2.2271
+25.04
+18.06
+GLIMMeR (Hemanthage et al. 2021)
+74.05
+56.85
+44.88
+35.31
+27.48
+50.92
+2.4952
+32.70
+22.58
+SPRING (Ours)
+83.29
+64.75
+52.41
+42.49
+31.90
+57.12
+3.1351
+38.87
+30.77
+Table 2: Comparison on SIMMC 1.0, SIMMC 2.0 dataset, visual and spatial subsets. Our model consistently outperforms strong
+baselines by a large margin on 7 widely-used metrics. Specially, evaluation on Visual Subset and Spatial Subset by BLEU-4
+effectively verify the huge improvement of our model comes from better response about visual attribute and spatial relation.
+The SIMMC 2.0 dataset contains 7.2k fashion dialogs and 4k
+furniture dialogs, respectively. There are around 290 digital
+assets for fashion and 110 assets for furniture, which are re-
+arranged within seed scenes to generate 160 different scenes.
+The SIMMC 1.0 dataset includes 6.6k fashion dialogs and
+6.4k furniture dialogs. We evaluate model performance on
+the dev-test split of SIMMC 1.0 and SIMMC 2.0, which has
+the same scale as the test-std 1 dataset.
+In addition, we invite human experts to ﬁlter responses
+with visual attribute or spatial relation from SIMMC 1.0 and
+SIMMC 2.0 dev-test split to construct Visual Subset and
+Spatial Subset. We further evaluate models on these two
+subsets to prove the effectiveness of our model.
+Evaluation Metrics.
+The ofﬁcial metric adopted by
+SIMMC 2.0 response generation task is BLEU-4, which only
+focuses on n-grams overlap between the predicted and tar-
+get response. For a more comprehensive comparison, we add
+widely-used machine generation metrics: BLUE-n (Papineni
+et al. 2002), METEOR (Banerjee and Lavie 2005), ROUGE
+(Lin and Hovy 2003) and CIDEr (Vedantam, Zitnick, and
+Parikh 2015) metrics. Compared with the accuracy based
+BLEU metric, METOR and ROUGH pay attention to recall
+and calculate how many n-grams from the target response
+exist in the predicted response, while CIDEr uses TF-IDF to
+assign larger weights to infrequent phrases.
+Implementation Details.
+Our model is based on Trans-
+former (Vaswani et al. 2017) structure with 12 layers, where
+ever Transformer block has 768 hidden units and 12 atten-
+tion heads. Each patch is projected to features of the same
+size as the hidden units. We initialize SPRING parameters
+from pretrained VLM, i.e. , OFA (Wang et al. 2022b). Dur-
+ing pretraining, our model is trained for 4 epochs with 8
+batch sizes on 8 TESLA V100 GPU. Adam (Kingma and
+Ba 2015) is adopted as optimizer with a 4e-4 learning rate.
+Besides, the dropout rate is set to 0.2 to prevent over-ﬁtting.
+During ﬁne-tuning stage, we train 60 epochs on the SIMMC
+train set with a learning rate of 4e-5 and a batch size of 16.
+1Not publicly available as a test set for the DSTC competition.
+Compared Methods.
+We compare SPRING with strong
+baseline methods from SIMMC 1.0 and SIMMC 2.0. On
+SIMMC 1.0, MN-MAG (Kim et al. 2021) adopts a memory
+network as encoder and designs multimodal fusion gate to
+fuse information. Tom (Jeong et al. 2021) esambles predic-
+tion results from several GPT-2 models. JBi-encoder (Huang
+et al. 2021a) is jointly trained to predict belief state and re-
+sponse. On SIMMC 2.0, MTN (Le et al. 2019) separately en-
+codes multimodal input while the visual encoder is guided
+by a query-aware attention encoder. JMGPT (Kottur et al.
+2021b) trains a multi-task GPT2-large, which takes dialogue
+history and ﬂattened multimodal contexts as input. Further-
+more, JMGPT-BS (Kottur et al. 2021a) extends JMGPT by
+inferring with different beam search sizes. MMBart (Lee
+et al. 2022) adds box coordinates embedding to textual in-
+put and proposes auxiliary tasks to predict asset attributes.
+DialVinVL (Kottur et al. 2021a) is based on VinVL-Base
+(Zhang et al. 2021), concatenates original box coordinates
+to region features as visual input, and incorporates dialogue
+history with dialogue policy as textual input. GPTDeIT (Lee
+and Han 2021) utilizes GPT2-large (Radford et al. 2019)
+as the text model to encode dialogue history and ﬂattened
+slot values and DeIT-I (Touvron et al. 2021) as the image
+model to encode assets referenced by current turn utterance.
+JointGM (Nguyen et al. 2021) leverages BART-large (Lewis
+et al. 2020) to predict disambiguation label, belief state and
+response jointly according to inputted dialogue history. Sim-
+ilar to GPTDeIT, GLIMMeR (Hemanthage et al. 2021) also
+leverages GPT2-large and utilizes asset scene ID to help
+the model understand the semantics of each asset. Notably,
+GLIMMeR is the state-of-the-art method on SIMMC 2.0 and
+achieves the winner of the DSTC10.
+4.2
+Overall Performance
+Table 2 displays the results of the model on the SIMMC
+1.0 and SIMMC 2.0 dataset response generation task. It
+can be seen that SPRING has exceeded previous models by
+a large margin and achieved state-of-the-art results on all
+representative machine generation metrics. On SIMMC 2.0,
+
+TASK
+MODELS
+SIMMC 2.0
+VISUAL
+SPATIAL
+VLM
+38.22
+34.67
+25.04
+Visual QA
+VLM
+w/ PVQA
+40.75
+36.54
+27.58
+w/ RVQA
+41.27
+37.02
+27.22
+w/ PoVQA
+40.89
+35.94
+28.08
+w/ (PVQA + RVQA + PoVQA)
+41.36
+37.59
+28.24
+Spatial QA
+VLM
+w/ PSQA
+41.18
+36.05
+28.30
+w/ RSQA
+40.77
+35.42
+28.18
+w/ VSQA
+40.40
+36.34
+27.97
+w/ (PSQA + RSQA + VSQA)
+41.56
+36.25
+28.49
+All
+VLM
+w/ all QA
+41.92
+38.52
+30.18
+w/ (all QA + CL)
+42.49
+38.87
+30.77
+Table 3: Ablation study on SIMMC 2.0 dataset with BLEU-4
+metric. Red and green shades represent a stronger advantage
+in the visual and spatial subsets, respectively.
+SPRING is respectively 7.91, 7.33, 7.49, and 7.18 higher
+than previous best models on BLEU-n, varying n from 1 to
+4. The signiﬁcant increased percentage on BLEU-n mani-
+fests our model successfully utilizing more accurate words
+and phrases to make responses. Our model also shows ex-
+cellent performance on recall-based metrics METEOR and
+ROUGE, of which the score improvements reach 4.42 and
+6.2. When the CIDEr metric pays more attention to infre-
+quent n-grams, SPRING still outperforms GLIMMeR with
+0.64 on CIDEr. Besides, according to the right part of Ta-
+ble 2, our model exhibits the highest BLEU-4 scores on the
+visual subset and spatial subset, which veriﬁes the improve-
+ment of our model is produced by its better understanding
+of visual attribute and spatial relation and ability to conduct
+reasoning with aligned information to generate more accu-
+rate responses.
+4.3
+Detailed Analysis
+Ablation Study.
+As shown in Table 3, we perform abla-
+tion experiments to evaluate the effectiveness of each pre-
+training task and curriculum learning strategy in SPRING.
+It can be observed that each MQA pretraining task brings
+signiﬁcantly BLEU-4 improvement on the complete SIMMC
+2.0 dataset compared with the basic VLM model. Speciﬁ-
+cally, VLM models pretrained with all visual QA tasks per-
+form 2.92 higher than baseline on the Visual Subset, while
+VLM models pretrained with all spatial QA tasks display
+3.45 improvement compared with baseline on the Spatial
+Subset, which can verify that visual QA and spatial QA re-
+spectively prompt model’s ability of describing visual at-
+tribute and spatial relation. Besides, the last two rows fur-
+ther prove that our designed curriculum learning pretraining
+strategy effectively activates the potential of QA pretraining
+tasks and boosts model performance.
+Human Evaluation.
+The human evaluation mainly fo-
+cuses on 4 aspects: ﬂuency, relevance, correctness, and
+informativeness, which are important for task-oriented di-
+alogue systems. We randomly select 500 dialogues from
+SIMMC 2.0 dev-test dataset as candidates, and then ﬁlter
+these dialogues from the results generated by DialVinVL,
+GLIMMeR, and our model. We release evaluation task on
+Fluency
+Relevance
+Correctness
+Informativeness
+1.0
+1.5
+2.0
+2.5
+3.0
+3.5
+4.0
+4.5
+5.0
+Human Evaluation Score
+4.47
+4.66
+2.77
+1.86
+4.83
+4.85
+3.20
+2.24
+4.96
+4.94
+4.04
+3.13
+DialVinVL
+GLIMMeR
+Ours
+Figure 4: The human evaluation results on SIMMC 2.0 with
+four aspects. Our model displays signiﬁcant improvement
+on correctness and informativeness.
+Amazon Mechanical Turk (AMT) and make the last re-
+sponse of every selected dialogue evaluated by 10 different
+evaluators. Each evaluator scores 1500 generated responses
+on 4 aspects according to golden response in blind review
+from 1 to 5, simulating a real-life multimodal dialogue sce-
+nario. As shown in 4, it can be observed that our model con-
+sistently outperforms the other two models on all metrics,
+which is in line with automatic evaluation results.
+Case Study.
+To better illustrate the advantage of our
+model and display how SPRING prompts model’s ability of
+predicting visual attributes and spatial relations related to
+background items, we visualize several generated responses
+from our model and existing SOTA model with correspond-
+ing user utterance and scene snapshot, as shown in Figure 5.
+It can be explicitly observed that: (1) our model is able to
+adopt background items to describe the position of target as-
+sets. (2) The relative spatial relations between target assets
+and background items can be accurately predicted by our
+model. (3) our model is equipped with the ability of align-
+ing visual attribute to spatial information when multiple as-
+sets exist in the response.
+Figure 5: Case study on SIMMC 2.0 dataset.
+5
+Conclusion
+In this paper, we propose a novel situated conversation agent
+pretraining method named SPRING. Speciﬁcally, all QA
+pairs and their difﬁculty labels used in pretraining are gener-
+ated from our Incremental Layout Graph without any extra
+human annotations. Experimental results on SIMMC 1.0 and
+SIMMC 2.0 show that SPRING greatly surpasses previous
+models and describes visual attributes and spatial relations
+more accurately.
+
+User: Hello! I want to buy a pair of shoes.
+User : Please recommend some shirts.
+System: How about the white shirt on the back wall ?
+User: Are there any good shoes with size XL?
+User : Are there any nice black shirts in this store?
+GLIMMeR
+Our
+ GLIMMeR
+Ours
+How do you feel about that black one hanging
+Are you into that black one behind the green
+What do you think of the grey shoes?
+the bottom row lon the light closet?
+against the wall to the left or the other black
+hoodielon the left or tne other light black one
+hanging in the back leit against the wall?
+one on the rack to the right?Acknowledgement
+We would like to sincerely thank anonymous reviewers for
+their suggestions and comments. The work was partially
+supported by the National Natural Science Foundation of
+China (NSFC62076032). We also want to express our grati-
+tude for precious advises given by Guanqi Zhan.
+References
+Banerjee, S.; and Lavie, A. 2005. METEOR: An Automatic
+Metric for MT Evaluation with Improved Correlation with
+Human Judgments. In Goldstein, J.; Lavie, A.; Lin, C.; and
+Voss, C. R., eds., Proceedings of the Workshop on Intrinsic
+and Extrinsic Evaluation Measures for Machine Translation
+and/or Summarization @ ACL.
+Bengio, Y.; Louradour, J.; Collobert, R.; and Weston, J.
+2009. Curriculum learning. In Proceedings of the Inter-
+national Conference on Machine Learning (ICML).
+Chang, X.; Ren, P.; Xu, P.; Li, Z.; Chen, X.; and Hauptmann,
+A. 2020. A survery of scene graph: Generation and applica-
+tion. In Proceedings of IEEE Transactions on Neural Net-
+work Learning.
+Chattopadhyay, P.; Yadav, D.; Prabhu, V.; Chandrasekaran,
+A.; Das, A.; Lee, S.; Batra, D.; and Parikh, D. 2017. Evalu-
+ating Visual Conversational Agents via Cooperative Human-
+AI Games. In Proceedings of the Fifth AAAI Conference on
+Human Computation and Crowdsourcing (AAAI).
+Chen, Y.-C.; Li, L.; Yu, L.; El Kholy, A.; Ahmed, F.; Gan,
+Z.; Cheng, Y.; and Liu, J. 2020. Uniter: Universal image-
+text representation learning. In Proceedings of the European
+conference on computer vision (ECCV), 104–120. Springer.
+Cho, J.; Lei, J.; Tan, H.; and Bansal, M. 2021. Unifying
+vision-and-language tasks via text generation. In Proceed-
+ings of the International Conference on Machine Learning
+(ICML).
+Das, A.; Kottur, S.; Gupta, K.; Singh, A.; Yadav, D.; Moura,
+J. M.; Parikh, D.; and Batra, D. 2017. Visual dialog. In
+Proceedings of the IEEE Conference on Computer Vision
+and Pattern Recognition (CVPR).
+De Vries, H.; Strub, F.; Chandar, S.; Pietquin, O.;
+Larochelle, H.; and Courville, A. 2017.
+Guesswhat?! vi-
+sual object discovery through multi-modal dialogue. In Pro-
+ceedings of the IEEE Conference on Computer Vision and
+Pattern Recognition (CVPR).
+He, W.; Dai, Y.; Hui, B.; Yang, M.; Cao, Z.; Dong, J.; Huang,
+F.; Si, L.; and Li, Y. 2022a. SPACE-2: Tree-Structured Semi-
+Supervised Contrastive Pre-training for Task-Oriented Dia-
+log Understanding. In Proceedings of the 29th International
+Conference on Computational Linguistics (COLING).
+He, W.; Dai, Y.; Yang, M.; Sun, J.; Huang, F.; Si, L.; and
+Li, Y. 2022b. SPACE-3: Uniﬁed Dialog Model Pre-training
+for Task-Oriented Dialog Understanding and Generation. In
+Proceedings of the 45th International ACM SIGIR Confer-
+ence on Research and Development in Information Retrieval
+(SIGIR).
+He, W.; Dai, Y.; Zheng, Y.; Wu, Y.; Cao, Z.; Liu, D.; Jiang,
+P.; Yang, M.; Huang, F.; Si, L.; et al. 2022c.
+SPACE:
+A Generative Pre-trained Model for Task-Oriented Dialog
+with Semi-Supervised Learning and Explicit Policy Injec-
+tion. Proceedings of the AAAI Conference on Artiﬁcial In-
+telligence (AAAI).
+Hemanthage, B.; Lemon, O.; Dondrup, C.; and Bartie, P.
+2021. GLIMMeR: Global-Local Information-aware Multi-
+modal grounding with GPT for Co-reference Resolution. In
+DSTC10 challenge wokrshop at AAAI.
+Huang, X.; Tan, C. S.; Ng, Y. B.; Shi, W.; Yeo, K. H.; Jiang,
+R.; and Kim, J. J. 2021a. Joint generation and bi-encoder
+for situated interactive multimodal conversations. In DSTC9
+challenge wokrshop at AAAI.
+Huang, Z.; Zeng, Z.; Huang, Y.; Liu, B.; Fu, D.; and Fu, J.
+2021b. Seeing out of the box: End-to-end pre-training for
+vision-language representation learning. In Proceedings of
+the IEEE/CVF Conference on Computer Vision and Pattern
+Recognition (CVPR).
+Hui, B.; Geng, R.; Ren, Q.; Li, B.; Li, Y.; Sun, J.; Huang, F.;
+Si, L.; Zhu, P.; and Zhu, X. 2021. Dynamic Hybrid Relation
+Exploration Network for Cross-Domain Context-Dependent
+Semantic Parsing. In AAAI.
+Hui, B.; Geng, R.; Wang, L.; Qin, B.; Li, Y.; Li, B.; Sun,
+J.; and Li, Y. 2022. S2SQL: Injecting Syntax to Question-
+Schema Interaction Graph Encoder for Text-to-SQL Parsers.
+In Findings of the Association for Computational Linguis-
+tics: ACL 2022, 1254–1262. Dublin, Ireland: Association for
+Computational Linguistics.
+Jeong, Y.; Lee, S. J.; Ko, Y.; and Seo, J. 2021. Tom: End-to-
+end task-oriented multimodal dialog system with gpt-2. In
+DSTC9 challenge wokrshop at AAAI.
+Jia, C.; Yang, Y.; Xia, Y.; Chen, Y.-T.; Parekh, Z.; Pham, H.;
+Le, Q.; Sung, Y.-H.; Li, Z.; and Duerig, T. 2021. Scaling
+up visual and vision-language representation learning with
+noisy text supervision. In Proceedings of the International
+Conference on Machine Learning (ICML).
+Kim, B.; Lee, I.; Jeong, Y.; Youngjoong, K.; Koo, M.-W.;
+and Seo, J. 2021. Improving multimodal api prediction via
+adding dialog state and various multimodal gates. In DSTC9
+challenge wokrshop at AAAI.
+Kingma, D. P.; and Ba, J. 2015.
+Adam: A Method for
+Stochastic Optimization. In Proceedings of the International
+Conference on Learning Representations (ICLR).
+Kottur, S.; Moon, S.; Geramifard, A.; and Damavandi, B.
+2021a.
+Overview of Situated and Interactive Multimodal
+Conversations (SIMMC) 2.0 Track at DSTC 10. In DSTC10
+challenge wokrshop at AAAI.
+Kottur, S.; Moon, S.; Geramifard, A.; and Damavandi, B.
+2021b.
+SIMMC 2.0: A Task-oriented Dialog Dataset for
+Immersive Multimodal Conversations.
+In Proceedings of
+the 2021 Conference on Empirical Methods in Natural Lan-
+guage Processing (EMNLP).
+Le, H.; Sahoo, D.; Chen, N.; and Hoi, S. 2019. Multimodal
+transformer networks for end-to-end video-grounded dia-
+logue systems. In Proceedings of the 57th Annual Meeting
+of the Association for Computational Linguistics (ACL).
+
+Lee, H.; Kwon, O. J.; Choi, Y.; Kim, J.; Lee, Y.; Han, R.;
+Kim, Y.; Park, M.; Lee, K.; Shin, H.; and Kim, K.-E. 2022.
+Learning to Embed Multi-Modal Contexts for Situated Con-
+versational Agents. In Findings of the Association for Com-
+putational Linguistics (NAACL).
+Lee, J.; and Han, K. 2021. Multimodal Interactions Using
+Pretrained Unimodal Models for SIMMC 2.0. In DSTC10
+challenge wokrshop at AAAI.
+Lewis, M.; Liu, Y.; Goyal, N.; Ghazvininejad, M.; Mo-
+hamed, A.; Levy, O.; Stoyanov, V.; and Zettlemoyer, L.
+2020. BART: Denoising Sequence-to-Sequence Pre-training
+for Natural Language Generation, Translation, and Compre-
+hension. In Proceedings of the 58th Annual Meeting of the
+Association for Computational Linguistics (ACL).
+Li, W.; Gao, C.; Niu, G.; Xiao, X.; Liu, H.; Liu, J.; Wu,
+H.; and Wang, H. 2021. UNIMO: Towards Uniﬁed-Modal
+Understanding and Generation via Cross-Modal Contrastive
+Learning. In Proceedings of the 59th Annual Meeting of the
+Association for Computational Linguistics (ACL).
+Liao, L.; Long, L. H.; Ma, Y.; Lei, W.; and Chua, T.-S.
+2021. Dialogue State Tracking with Incremental Reasoning.
+Transactions of the Association for Computational Linguis-
+tics, 9: 557–569.
+Lin, C.; and Hovy, E. H. 2003. Automatic Evaluation of
+Summaries Using N-gram Co-occurrence Statistics. In Hu-
+man Language Technology Conference of the North Ameri-
+can Chapter of the Association for Computational Linguis-
+tics (HLT-NAACL).
+Lu, J.; Batra, D.; Parikh, D.; and Lee, S. 2019.
+Vilbert:
+Pretraining task-agnostic visiolinguistic representations for
+vision-and-language tasks. In Proceedings of the Advances
+in neural information processing systems (NIPS).
+Moon, S.; Kottur, S.; Crook, P. A.; De, A.; Poddar, S.; Levin,
+T.; Whitney, D.; Difranco, D.; Beirami, A.; Cho, E.; Subba,
+R.; and Geramifard, A. 2020. Situated and Interactive Mul-
+timodal Conversations. In Proceedings of the 28th Interna-
+tional Conference on Computational Linguistics (COLING).
+Nguyen, T.-T.; Shi, W.; Jiang, R.; and jae Kim, J. 2021. Mul-
+timodal and Joint Learning Generation Models for SIMMC
+2.0. In DSTC10 challenge wokrshop at AAAI.
+Papineni, K.; Roukos, S.; Ward, T.; and Zhu, W. 2002. Bleu:
+a Method for Automatic Evaluation of Machine Translation.
+In Proceedings of the 40th Annual Meeting of the Associa-
+tion for Computational Linguistics (ACL).
+Qiu, L.; Liang, Y.; Zhao, Y.; Lu, P.; Peng, B.; Yu, Z.; Wu,
+Y. N.; and Zhu, S. 2021. SocAoG: Incremental Graph Pars-
+ing for Social Relation Inference in Dialogues. In Proceed-
+ings of the 59th Annual Meeting of the Association for Com-
+putational Linguistics and the 11th International Joint Con-
+ference on Natural Language Processing (ACL-IJCNLP.
+Qiu, L.; Zhao, Y.; Liang, Y.; Lu, P.; Shi, W.; Yu, Z.; and Zhu,
+S.-C. 2022. Towards Socially Intelligent Agents with Mental
+State Transition and Human Value. In SIGDIAL.
+Radford, A.; Kim, J. W.; Hallacy, C.; Ramesh, A.; Goh, G.;
+Agarwal, S.; Sastry, G.; Askell, A.; Mishkin, P.; Clark, J.;
+et al. 2021. Learning transferable visual models from natural
+language supervision. In Proceedings of the International
+Conference on Machine Learning (ICML).
+Radford, A.; Wu, J.; Child, R.; Luan, D.; Amodei, D.;
+Sutskever, I.; et al. 2019. Language models are unsupervised
+multitask learners. In Arxiv.
+Ren, S.; He, K.; Girshick, R.; and Sun, J. 2015. Faster r-cnn:
+Towards real-time object detection with region proposal net-
+works. In Proceedings of the Advances in neural informa-
+tion processing systems (NIPS).
+Saha, A.; Khapra, M.; and Sankaranarayanan, K. 2018. To-
+wards building large scale multimodal domain-aware con-
+versation systems. In Proceedings of the AAAI Conference
+on Artiﬁcial Intelligence.
+Tan, H.; and Bansal, M. 2019. LXMERT: Learning Cross-
+Modality Encoder Representations from Transformers. In
+Proceedings of the 2019 Conference on Empirical Meth-
+ods in Natural Language Processing and the 9th Interna-
+tional Joint Conference on Natural Language Processing
+(EMNLP-IJCNLP).
+Touvron, H.; Cord, M.; Douze, M.; Massa, F.; Sablayrolles,
+A.; and J´egou, H. 2021. Training data-efﬁcient image trans-
+formers & distillation through attention. In Proceedings of
+the International Conference on Machine Learning (ICML).
+Vaswani, A.; Shazeer, N.; Parmar, N.; Uszkoreit, J.; Jones,
+L.; Gomez, A. N.; Kaiser, Ł.; and Polosukhin, I. 2017. At-
+tention is all you need. Proceedings of the Advances in neu-
+ral information processing systems (NIPS).
+Vedantam, R.; Zitnick, C. L.; and Parikh, D. 2015. CIDEr:
+Consensus-based image description evaluation.
+In IEEE
+Conference on Computer Vision and Pattern Recognition
+(CVPR).
+Wang, L.; Qin, B.; Hui, B.; Li, B.; Yang, M.; Wang, B.;
+Li, B.; Huang, F.; Si, L.; and Li, Y. 2022a. Proton: Prob-
+ing Schema Linking Information from Pre-trained Language
+Models for Text-to-SQL Parsing. Proceedings of the 28th
+ACM SIGKDD Conference on Knowledge Discovery and
+Data Mining.
+Wang, P.; Yang, A.; Men, R.; Lin, J.; Bai, S.; Li, Z.; Ma,
+J.; Zhou, C.; Zhou, J.; and Yang, H. 2022b. OFA: Unify-
+ing Architectures, Tasks, and Modalities Through a Simple
+Sequence-to-Sequence Learning Framework. In Proceed-
+ings of the International Conference on Machine Learning
+(ICML).
+Zhang, P.; Li, X.; Hu, X.; Yang, J.; Zhang, L.; Wang, L.;
+Choi, Y.; and Gao, J. 2021. Vinvl: Revisiting visual rep-
+resentations in vision-language models. In Proceedings of
+the IEEE/CVF Conference on Computer Vision and Pattern
+Recognition (CVPR).
+
+SLOT TYPE
+SLOT VALUE
+fashion color
+’red, white, yellow’, ’red, white’, ’purple’, ’white, black’, ’black’, ’dark grey’, ’grey, black’, ’brown’, ’dark green’, ’grey’, ’dark blue’, ’blue, white’,
+’grey, brown’, ’white, blue’, ’yellow, white’, ’dark green, dark blue’, ’light grey’, ’white’, ’blue’, ’green’, ’maroon’, ’yellow’, ’red’, ’violet’,
+’black, red, white’, ’yellow, black’, ’blue, black’, ’black, white’, ’light blue’, ’red, black’, ’pink, white’, ’orange’, ’yellow, brown’, ’light pink’,
+’dark brown’, ’pink’, ’dark yellow’, ’light red’, ’green, white’, ’grey, white’, ’black, red’, ’grey, blue’, ’brown, white’, ’white, black, red’, ’beige’,
+’light orange’, ’orange, purple’, ’dirty green’, ’blue, grey’, ’black, grey’, ’white, grey’, ’olive’, ’dark red’, ’olive, black’, ’pink, black’, ’blue, green’,
+’green, black’, ’light blue, light green’, ’dark pink, white’, ’dirty grey’, ’dark pink’, ’red, grey’, ’dark violet’, ’olive, white’, ’black, orange’, ’golden’,
+’maroon, white, blue’, ’green, violet, pink’, ’white, red, violet’, ’brown, black’, ’black, olive’
+fashion type
+’blouse’, ’jacket’, ’shirt’, ’sweater’, ’dress’, ’tshirt’, ’joggers’, ’jeans’, ’hat’, ’tank top’, ’vest’, ’coat’, ’shoes’, ’skirt’, ’suit’, ’trousers’, ’hoodie’
+furniture color
+’red’, ’blue’, ’white’, ’grey’, ’brown’, ’green’, ’black’, ’black and white’, ’wooden’
+furniture type
+’area rug’, ’bed’, ’chair’, ’coffee table’, ’couch chair’, ’end table’, ’lamp’, ’shelves’, ’sofa’, ’table’
+background item
+’rack’, ’wall’, ’mirror’, ’shelf’, ’closet’, ’table’, ’wardrobe’, ’cabinet’, ’window’, ’divider’, ’door’, ’counter’, ’cubby’, ’cubbies’, ’hanger’, ’stand’,
+’cupboard’, ’mannequin’, ’shoe boxes’, ’room divider’, ’wall divider’
+positional preposition
+’in’, ’on’, ’at’, ’behind’, ’toward’, ’to’, ’against’, ’of’, ’along’, ’below’, ’towards’, ’above’
+article and pronoun
+’the’, ’a’, ’that’, ’this’, ’other’, ’another’
+punctuation and conjunctions
+’,’, ’.’, ’;’, ’?’, ’and’, ’or’
+Table 4: Slot types and slot values in the regular expression.
+Appendix
+In the Table 4, we display the slot types and slot values of
+four regular expressions we use to extract visual attribute,
+spatial description, background item, and spatial relation
+from dialogue corpus. All color values and type values are
+from SIMMC 2.0 metadata while background items are com-
+mon furniture words provided by Wikipedia except for those
+appear in SIMMC 2.0 furniture types. The article, pronoun,
+coordinating conjunction and punctuation come from The
+Oxford English Dictionary. To make it clearer, we adopt a
+simple python code snippet to show how to use our designed
+regular expressions to extract visual and spatial information
+in the following.
+1
+immport re
+2
+3
+system_response = ’How about the blue
+4
+tshirt on the shelf or the red jacket
+5
+above the table ?’
+6
+7
+RegExp_vi = ’(a|the|that|this|other|
+8
+another) (red, white, yellow|pink|
+9
+red, white|purple|white, black|black|
+10
+dark grey|light grey|white|blue|green|
+11
+maroon|yellow|red|violet|yellow, black|
+12
+black, red, white|blue, black|
+13
+black, white|light blue|red, black|
+14
+pink, white|orange|yellow, brown|
+15
+light pink|dark brown|pink|dark yellow|
+16
+light red|green, white|grey, white|
+17
+black, red|grey, blue|brown, white|
+18
+white, black, red|light orange|
+19
+orange, purple|dirty green|blue, grey|
+20
+black, grey|white, grey|olive|dark red|
+21
+olive, black|pink, black|blue, green|
+22
+green, black|light blue, light green)
+23
+(blouse|jacket|shirt|sweater|dress|
+24
+tshirt|joggers|jeans|hat|vest|bed|
+25
+coat|shoes|skirt|suit|trousers|hoodie)’
+26
+27
+RegExp_sd = ’(in|on|at|behind|toward|
+28
+to|against|of|along|below|above) (the|
+29
+a|that|this|other) (.*?) (and|or|,|
+30
+\.|\?)’
+31
+32
+RegExp_bi = ’(rack|wall|mirror|shelf|
+33
+closet|table|wardrobe|cabinet|window|
+34
+divider|door|counter|cubby|cubbies)’
+35
+36
+RegExp_sr = ’(in|on|at|behind|toward|
+37
+to|against|of|along|below|towards|
+38
+above)’
+39
+40
+extracted_vi = re.findall(RegExp_vi,
+41
+system_response)
+42
+# [(’the’, ’blue’, ’tshirt’),
+43
+# (’the’, ’red’, ’jacket’)]
+44
+45
+extracted_sd = re.findall(RegExp_sd,
+46
+system_response)
+47
+# [(’on’, ’the’, ’shelf’, ’or’),
+48
+# (’above’, ’the’, ’table’, ’?’)]
+49
+50
+sds = [’ ’.join(item[:-1]) for item
+51
+in extracted_sd]
+52
+# [’on the shelf’, ’above the table’]
+53
+54
+bi_list, sr_list = [], []
+55
+for sd in sds:
+56
+bi = re.findall(RegExp_bi, sd)
+57
+bi_list.append(bi)
+58
+sr = re.findall(RegExp_sr, sd)
+59
+sr_list.append(sr)
+60
+# bi_list [(’shelf’), (’table’)]
+61
+# sr_list [(’on’), (’above’)]
+
diff --git a/_NAzT4oBgHgl3EQf_f58/content/tmp_files/load_file.txt b/_NAzT4oBgHgl3EQf_f58/content/tmp_files/load_file.txt
new file mode 100644
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+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf,len=1597
+page_content='SPRING: Situated Conversation Agent Pretrained with  Multimodal Questions from Incremental Layout Graph  Yuxing Long 1, Binyuan Hui 2, Fulong Ye 1, Yanyang Li 2, Zhuoxin Han 1,  Caixia Yuan 1, Yongbin Li 2, Xiaojie Wang 1 *  1 Beijing University of Posts and Telecommunications, Beijing, China  2 Independent Researcher  {longyuxing, fulong ye, hanzhuoxin, yuancx, xjwang}@bupt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='edu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='cn  lyb821@gmail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='com  Abstract  Existing multimodal conversation agents have shown impres-  sive abilities to locate absolute positions or retrieve attributes  in simple scenarios, but they fail to perform well when com-  plex relative positions and information alignments are in-  volved, which poses a bottleneck in response quality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' In this  paper, we propose a Situated Conversation Agent PRetrained  with Multimodal Questions from INcremental Layout Graph  (SPRING) with abilities of reasoning multi-hops spatial rela-  tions and connecting them with visual attributes in crowded  situated scenarios.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Speciﬁcally, we design two types of Mul-  timodal Question Answering (MQA) tasks to pretrain the  agent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' All QA pairs utilized during pretraining are gener-  ated from novel Incremental Layout Graphs (ILG).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' QA pair  difﬁculty labels automatically annotated by ILG are used  to promote MQA-based Curriculum Learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Experimen-  tal results verify the SPRING’s effectiveness, showing that it  signiﬁcantly outperforms state-of-the-art approaches on both  SIMMC 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='0 and SIMMC 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='0 datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' We release our code  and data at https://github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='com/LYX0501/SPRING.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  1  Introduction  Building multi-modal conversation agents that can commu-  nicate with people in visual situations is an attractive goal  for the AI community.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Lots of speciﬁc tasks and datasets  for visual dialog, like VisDial (Das et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' 2017), GuessWhat  (De Vries et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' 2017), GuessWhich (Chattopadhyay et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  2017), are proposed in recent years.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Among them, the Sit-  uated Interactive Multi-modal Conversation (SIMMC 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='0)  (Moon et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' 2020) aims to study task-oriented dialogues that  encompass a situated multi-modal user context in the form  of a virtual reality (VR) environment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' The updated dataset  SIMMC 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='0 (Kottur et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' 2021b) provides a more challeng-  ing test bed for multi-modal conversation agents.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' There are  many assets with a complex layout in each image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Figure  1 gives an example of a scene and a fragment of dialogue  in SIMMC 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' There are dozens of clothes in the image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  Each cloth is a digit asset with a unique asset ID and a set of  attributes (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' type, color) in the metadata.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' But there is no  information on the scene layout except for a few labels on  four relations (up, down, left, and right) between the assets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  Corresponding author  Copyright © 2023, Association for the Advancement of Artiﬁcial  Intelligence (www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='aaai.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='org).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' All rights reserved.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  Figure 1: An example of a virtual scene and a fragment of  dialogue in SIMMC 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Since there are many clothes with  similar visual attributes, it is difﬁcult to talk about a asset  only by its visual attributes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' For this case, the spatial rela-  tions in the layout are necessary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  A number of works have been established on SIMMC  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Based on different multi-modal Visual-Language pre-  training Models (VLM), previous researchers pay more at-  tention to learning the visual attributes of assets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' QS Goal  Diggers (Kottur et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' 2021a) and Kakao Enterprise (Lee and  Han 2021) directly insert visual attributes into models input,  while Sogang University (Kottur et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' 2021b) and A-STAR  (Nguyen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' 2021) build a set of visual attributes predic-  tion tasks in pre-training stage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' KAIST (Lee et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' 2022) de-  signs an auxiliary task to predict visual attributes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' However,  less attention has been paid to building spatial relations be-  tween assets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' All existing models only use the coordinates of  asset bounding boxes as positional information, which can-  not capture spatial relations in the scenes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  As a result, the models can accurately generate ”the black  jacket” but fail to describe more natural referring expres-  sions like ”the black jacket on the leftmost ﬂoor rack”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' It is  obvious that the later expression is more useful in a scene  including lots of clothes with similar attributes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' The combi-  nation of attributes and spatial relations helps people locate  assets quickly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' To generate this type of expression, a model  needs to learn not only the visual attributes of each asset but  also spatial relations between different items.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  To address above problem, we propose Situated Conver-  sation Agent PRetrained with Multimodal Questions from  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='01949v1  [cs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='CL]  5 Jan 2023  User  Do you have any clothes match my new bought jeans ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  Agent  How  bout thel  black jacket on the leftmost floor rack of the  grey jacket  the to, row of the shelf near the entrance ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  User  Anything else ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' I prefer some fashion t-shirs  Agent  The  purple t-shirt on the back middle shelf may meet your criteriaINcremental Layout Graph (SPRING), which is pretrained  with multimodal questions generated from incremental lay-  out graph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' In our method, we design Incremental Layout  Graph (ILG) for each scene to capture rich spatial relations  between different scene items.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Unlike scene graph (Chang  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' 2020), an ILG is built using pure textual information  and can be extended incrementally with newly added dia-  logue.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' And then, two types of Multimodal Question An-  swering (MQA) pre-training tasks and corresponding QA  pairs are collected by traversing nodes (digital assets and  background items) on the ILG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' According to the spanned  path length, QA pairs can be automatically annotated with  difﬁculty levels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Curriculum Learning (Bengio et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' 2009)  is therefore employed for pre-training on a Transformer  (Vaswani et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' 2017) encoder-decoder backbone.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Experi-  ments on both SIMMC 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='0 and SIMMC 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='0 show that our  method improves the response quality by a large margin  compared to previous best models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  The main contributions of our work are as follows:  We ﬁrst propose a novel approach to build ILGs for vir-  tual scenes from dialogue text incrementally.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' The ILGs  include scene items with relations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' It is worth noting that  this process does not rely on any human annotation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  Based on ILGs, we introduce two types of new MQA  pretraining tasks that can facilitate model understanding  of visual metadata and spatial relations between different  assets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Pre-training samples are automatically generated  by traversing the ILG, which also generates an accompa-  nying difﬁculty label for curriculum learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  We conduct thorough experiments to verify that our ap-  proach effectively enhances response quality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Our ap-  proach outperforms existing state-of-the-art methods by  a signiﬁcant margin consistently on all metrics on both  SIMMC 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='0 and SIMMC 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  2  Related Works  Situated Interactive Multimodal Conversations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  Con-  versation systems have developed rapidly in recent years,  e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=', task-oriented conversations pretraining (He et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  2022c,a,b), knowledge-based conversations (Hui et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' 2022;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  Wang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' 2022a) and so on.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Among them, multimodal  conversations are the new trend.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' META releases multimodal  conversation datasets SIMMC (Kottur et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' 2021b) based on  VR shopping stores.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' There are hundreds of scene snapshots  from different angles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Compared with the previous multi-  modal dialogue datasets MMD (Saha, Khapra, and Sankara-  narayanan 2018) and VisDial (Das et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' 2017), the situ-  ated agent is required to generate more complex visual at-  tributes and more detailed spatial relations to infer digital  assets in the scene.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Kottur et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' (2021a) has preliminary  explorations on utilizing visual attributes and spatial rela-  tions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Concretely, DialVinVL (Kottur et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' 2021a) incorpo-  rates slot values about visual attributes with dialogue history  as textual input and concatenates original box coordinates  to region features extracted by the object detector as visual  input.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' JMGPT (Kottur et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' 2021b) and JointGM (Nguyen  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' 2021) apply language model to predict visual attributes  and system response jointly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' MMBart (Lee et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' 2022) adds  embedded box coordinates to textual embedding as Trans-  former input and designs auxiliary tasks to predict visual at-  tributes according to the output of encoder hidden states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' We  can ﬁnd that their utilized spatial information is all from the  bounding box.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Unlike these methods, we ﬁrst notice the lack  of VLM’s capability for visuality and spatiality, and then  propose MQA pretraining tasks based on incremental layout  graphs which have been successfully applied to (Qiu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Liao et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Hui et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Qiu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  Visual Language Pretraining.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  To improve models’ per-  ception of text and image and help them establish connec-  tions between multimodal information, kinds of visual lan-  guage pretraining models are designed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' ViLBERT (Lu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  2019) and UNITER (Chen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' 2020) propose to con-  sider the raw output of the detector, a distribution of object  classes, as soft labels and optimize the KL-divergence be-  tween two distributions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' LEXMERT (Tan and Bansal 2019)  and UNIMO (Li et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' 2021) propose Masked Region Fea-  ture Regression (MRFR) regresses the masked region fea-  ture to its corresponding original region feature, where rep-  resents images as a sequence of region features by Faster  R-CNN (Ren et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' 2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Furthermore, SOHO (Huang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  2021b) is designed to avoid information leakage from neigh-  bor features when images are converted into grid features or  patch features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  Recently, CLIP (Radford et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' 2021) and ALIGN (Jia  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' 2021) leverage large-scale image-text pairs to learn  transferable visual representations and exhibit surprising  zero-shot transfer to image classiﬁcation tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' VL-T5 (Cho  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' 2021) and OFA (Wang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' 2022b) introduce down-  stream tasks, like visual grounding and grounded caption,  into pretraining tasks to narrow the gap between pretrain-  ing and ﬁne-tuning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Unlike these efforts, we design new pre-  training tasks through a uniﬁed QA paradigm to improve ex-  isting methods’ visual attributes and spatial relations model-  ing without adding new modules.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  3  Methods  Let D = {(Ut, Rt, It)}T  t=1 be an ongoing dialogue between  a user and an agent with T rounds, where Ut is the user  utterance at time step t, Rt is the language response to Ut by  the agent, and It is the accompanying scene image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' The task  here is to predict the optimal language response R  ′  t, given  the dialog history Ht = [Ui, Ri]t−1  i=1, current user utterance  Ut and scene image It, as modeled in Eq (1)  R  ′  t = argmax Pθ (Rt | Ht, Ut, It)  (1)  where θ is the model learnable parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  To solve above problem, we propose a mutimodal dia-  logue model SPRING, which is pretrained with mutlimodal  questions generated from incremental layout graph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' In the  following sections, we will introduce model architecture,  ILG generation and MQA pretraining tasks in order.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='1  Architecture  The backbone of SPRING model is encoder-decoder based  single-stream VLM framework, which are stacks of Trans-  former (Vaswani et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' 2017) layers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' The scene image It ∈  in  on  in  in  in  on  Do you have a nice coat from  Downtown Consignment ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  I have the black coat in the second row of the third  compartment in the leftmost cupboard.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  User  ( Dialogue History  … )  My next question is whether you  have quality t-shirt to show me ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  How about the pink t-shirt in the top row  on the back display wall and the blue t-  shirt in the bottom row?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  User  Agent  ( Dialogue History  … )  I need a blouse as well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  How about the brown blouse in the bottom row on  the back display wall and the grey blouse in the  middle row in the second compartment in the  leftmost cupboard.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  User  Agent  ( Dialogue History  … )  pink  t-shirt  ID 42  top  row  blue  t-shirt  ID 33  bottom  row  back  display  wall  brown  blouse  ID 9  bottom  row  black  coat  ID 16  second  row  third  compart-  ment  leftmost  cupboard  grey  Blouse  ID 20  second  row  second  compart-  ment  leftmost  cupboard  Query Asset ID & BBox  by Visual Attribute  Query Asset ID & BBox  by Visual Attribute  Query Asset ID & BBox  by Visual Attribute  in  in  in  of  of  [412,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' 323,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' 479,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' 588]  [656,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' 263,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' 701,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' 399]  [699,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' 410,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' 740,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' 598]  [661,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' 421,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' 695,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' 592]  [218,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' 354,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' 230,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' 579]  top/down  on  [661,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' 421,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' 695,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' 592]  black  coat  ID 16  second  row  third  compart-  ment  leftmost  cupboard  in  in  of  grey  Blouse  ID 20  in  blue  t-shirt  ID 33  in  [699,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' 410,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' 740,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' 598]  second  row  third  compart-  ment  of  [218,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' 354,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' 230,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' 579]  in  pink  t-shirt  ID 42  top  row  back  display  wall  in  on  [656,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' 263,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' 701,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' 399]  right/left  brown  blouse  ID 9  bottom  row  in  right/left  right/left  right/left  Part of Background Item  Background Item  Digital Asset  Spatial Relationship  ILG  [412,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' 323,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' 479,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' 588]  Agent  back  display  wall  Figure 2: Construction of Incremental Layout Graph from dialogue.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Digital assets and background items constitute ILG nodes  while spatial relations form ILG edges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' ILG is continuously incremented with newly added dialogue under the same scene.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  Rh×w×c is splitted to P patches.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' And each patch is projected  to visual embedding of the model hidden size.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' The dialogue  history and current user utterance are converted to sub-word  sequence by Byte-Pair Encoding (BPE) and then embedded  to textual embedding.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' All visual embedding and textual em-  bedding are concatenated as model input.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  To facilitate SPRING to better understand the informa-  tion of embodied scenes, we propose a series of MQA pre-  training tasks based on layout graphs Gi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' As there is no an-  notated layout graph in the SIMMC dataset, we propose an  unsupervised ILG construction method based on natural lan-  guage dialog history.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='2  Incremental Layout Graph (ILG)  We observe that visual attributes and spatial descriptions  exist in the dialogue history.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Compared with dataset an-  notations, the information from dialogue is more detailed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  For example, SIMMC 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='0 annotation only gives bounding  boxes of digital assets and four types of relative position  (up, down, right, left) between them, while dialogues in-  clude the absolute position of background items and their  relative position with assets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' A crucial discovery lies in the  co-coreference between dialogue history and response, the  same assets present in the responses to be generated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  Therefore, we propose an ILG generation algorithm to ex-  tract high quality information from dialogues and generate  Incremental Layout Graph (ILG) Gi = ⟨Vi, Ei⟩ to dispose  them, where Vi denotes the node set containing the digital  assets and background items from dialog history and Ei rep-  resents the edge set depicting spatial relations between scene  items Vi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  Textual Information Extraction and Alignment  we  consider adopting a rule-based textual information extrac-  tion method, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' , regular expression, to extract visual at-  tributes and spatial descriptions from dialogue history with-  out human annotation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' The regular expressions RegExpva  and RegExpsd for visual attribute and spatial description  are as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  RegExpva = (art.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=') (color) (asset type)  (2)  RegExpsd = (positional prep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=') (art.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=') (.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='∗?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=') (punc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=') (3)  where art.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' is article, prep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' represents preposition and punc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  means punctuation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Please refer to Appendix for details.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  With these two regular expressions, as left part of Figure 2  shows, we can extract visual attribute ”black coat” and spa-  tial description ”in the second row of the third compartment  in the leftmost cupboard” from dialogue history.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  Although the visual attributes and spatial descriptions  extracted by the above regular expressions are naturally  aligned because of language features, they are not aligned  with asset IDs, making asset box coordinates unusable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' To  solve this problem, we query the color and type of assets  from the database by their IDs to compose visual attributes  like ”black coat” and then try pairing them with the ex-  tracted visual attributes like ”black coat”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' If these two visual  attributes match, the corresponding asset ID ”16” can be de-  termined, from which we can get the paired asset IDs, visual  attributes, and spatial descriptions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' We further design the fol-  lowing two regular expressions to extract background item  and relative spatial relation from extracted spatial descrip-  tions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  RegExpbi = (background item)  (4)  RegExpsr = (positional prep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=')  (5)  where RegExpbi and RegExpsr denote regular expressions  for background item and spatial relation, prep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' represents  preposition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' With these two regular expressions, as middle  part of Figure 2 shows, we can extract background items  ”second row”, ”third compartment” and ”leftmost cup-  board” and relative spatial relations ”in”, ”of” from spatial  description obtained previously.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  Incremental Layout Graph Generation  With rich infor-  mation extracted from a sample of dialogue history, lay-  out sub-graph can be generated as middle part of Figure 2  shows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' In the layout sub-graph, digital asset node store its  visual attributes like ”black coat” and asset ID ”16” while  background item nodes store background items like ”sec-  ond row”, ”third compartment” and ”leftmost cupboard”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  [Pure Visual QA]  What is the type of asset 9 and 16 ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  [Region-Guided Visual QA] What is the color of asset 42  in region ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Region: [656, 263, 701, 399]  [Position-Guided Visual QA]  What are types of asset 20  in second row of the third compartment and asset 42 in  the top row on the back display wall?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  [Pure Spatial QA] Where is asset 33 , 9 and 20?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  [Region-Guided Spatial QA] Where is asset 16 in region ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  Region: [412, 323, 479, 588]  [Visual Attribute-Guided Spatial QA] Where is the pink  t-shirt and grey blouse ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  Spatial QA  Visual QA  SPRING  Blouse and coat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  Pink.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  Blouse and t-shirt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  In the bottom row, in the bottom row on the  back display wall and in the second row of the  second compartment in leftmost cupboard.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  In the second row of the third compartment in  the leftmost cupboard.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  In the top row on the back display wall.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  2  1  5  8  4  2  N  Difficulty Level  Curriculum Learning  ILG  Figure 3: Demonstration of SPRING model and two types of MQA pretraining tasks, Visual QA and Spatial QA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Curriculum  learning based on QA pair difﬁculty level activates the potential of MQA tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  SCENE IMAGE  QA TYPE  QUESTION TEMPLATE  ANSWER  Pure Visual QA  What is the [visual attribute type] of item [asset ID]?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  [visual attribute value]  Region-Guided Visual QA  What is the [visual attribute type] of item [asset ID] in region?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Region: [x1, y1, x2, y2]  [visual attribute value]  Position-Guided Visual QA  What is the [visual attribute type] of item [asset ID] [position]?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  [visual attribute value]  Pure Spatial QA  Where is the item [asset ID]?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  [position]  Region-Guided Spatial QA  Where is the item [asset ID] in region?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Region: [x1, y1, x2, y2]  [position]  Visual Attribute-Guided Spatial QA  Where is the [item color] [item type] [asset ID]?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  [position]  Table 1: QA pair template.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Square brackets ‘[∗]’ represent slots to be ﬁlled by traversing ILGs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  Spatial relations and queried bounding boxes are utilized to  deﬁne layout sub-graph edges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' As the right part of Figure 2  shows, the scene ILG continuously increments with newly  added sub-graph about the same scene, which ﬁnally can  include all digital assets, background items, and spatial rela-  tions between them under this scene.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Mining information on  the ILG is simple but effective.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' The visual attributes can be  easily obtained by traversing the ILG nodes, while multiple  types of spatial relations can be inferred by walking along  the ILG edges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='3  ILG-based MQA Pre-training Tasks  To enhance response generation quality of visual attributes  and spatial relations, we design visual QA pre-training task  and spatial QA pre-training task based on Multimodal Ques-  tion Answering (MQA), which respectively contain three  types of novel sub-tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' As shown in Figure 3 and Table  1, all QA pairs are automatically generated by traversing  ILG and ﬁlling the corresponding template.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' The QA pair  generation algorithm is displayed in Algorithm 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Formula-  rly, we use the question template ﬁlling function Qtype(·) to  generate question, Atype represents corresponding answer,  Typeva means visual attribute type, IDasset denotes asset ID,  Iscene is scene image, BBoxasset means asset region coor-  dinates, tsr represents spatial relation, tva is visual attribute,  tbi denotes background item.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='1 Visual QA  Pure Visual QA (PVQA)  As the most basic visual QA  task, the goal of Pure Visual QA is to help the model es-  tablish connections between asset ID and corresponding vi-  sual attributes when a scene image is provided.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' We design  PVQA template in which the question prompts the type of  visual attribute and asset ID.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' The pure visual question can  be generated by traversing the asset nodes of ILG and ﬁlling  [asset ID] slot in the template while answers are gener-  ated based on the visual attributes stored in asset nodes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' The  objective of PVQA task is the following.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  Lθ = − �N  i=1 log Pθ (Apv | Qpv(Typeva, IDasset), Iscene)  (6)  Region-Guided Visual QA (RVQA)  To improve the  model’s ability of locating asset and describing its visual  attribute by region visual context, we design RVQA tem-  plate based on PVQA, in which the question is guided by  asset region coordinates and asset ID.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' The region-guided  visual question can be generated by traversing asset nodes  of ILG and ﬁlling [asset ID], bounding box coordinates  [x1, y1, x2, y2] slots in the template.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' The corresponding  answer is produced based on the visual attributes stored in  asset nodes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' The objective of RVQA task is the following.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  Lθ = − �N  i=1 log Pθ (Argv | Qrgv(Typeva, IDasset, BBoxasset), Iscene)  (7)  Position-Guided Visual QA (PoVQA)  In the conversa-  tions, instead of region coordinates, an agent has to locate  asset by its spatial information no matter when understand-  ing user utterances or making recommendations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' To bring  the question closer to a real conversation, we design PoVQA  template by replacing region coordinates in RVQA with spa-  tial relations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' For position-guided visual question template,  the [asset ID] slot can be ﬁlled by traversing asset nodes  of ILG while the [position] slot is ﬁlled by spatial rela-  tion path between asset nodes and background item nodes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  The corresponding answer is produced based on the visual  attribute stored in asset nodes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' The objective of PoVQA task  is the following.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  Lθ = − �N  i=1 log Pθ (Apgv | Qpgv(Typeva,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' IDasset,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' tsr),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Iscene)  (8)  口8Algorithm 1: QA Pair Generation  Input:  ILG Gi = ⟨Vi,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Ei⟩,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' QA template list T  Output:  QA pair list QA,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' difﬁculty label list DL  1: Initialize QA pair list QA and difﬁculty label list DL  2: for node in Ei do  3:  if TypeOf(node) = ”background item” then  4:  Skip node  5:  /* Get information from digtal asset node */  6:  (tva,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' IDasset,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' BBoxasset) ← GetInfo(Gi,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' node)  7:  /* Walk from node to get spatial relations */  8:  (tbi,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' tsr) ← Walk(Gi,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' node)  9:  tslot ← (tva,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' tbi,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' tsr,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' BBoxasset,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' IDasset)  10:  for template in T do  11:  /* Fill in the template */  12:  (qa,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' dl) ← FillIn(template,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' tslot)  13:  Add QA ← qa,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' DL ← dl  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='2 Spatial QA  Pure Spatial QA (PSQA)  As the most basic spatial QA  task, the goal of PSQA is to help the model establish connec-  tions between asset ID and corresponding spatial relations  when a scene image is provided.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' We design PSQA template  in which the question only prompts ”where” and asset ID.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  The pure spatial question can be generated by traversing the  asset nodes of ILG and ﬁlling [asset ID] slot in the tem-  plate, while answers are generated based on the spatial rela-  tion paths between the background item node and the asset  node.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' The objective of PSQA task is the following.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  Lθ = − �N  i=1 log Pθ (Aps | Qps(IDasset), Iscene)  (9)  Region-Guided Spatial QA (RSQA)  To improve the  model’s ability of locating an asset and describing its spatial  relations by region visual context, we design RSQA tem-  plate based on PSQA, in which the question is guided by  asset region coordinates and asset ID.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' The region-guided vi-  sual question can be generated by traversing asset nodes of  ILG and ﬁlling the slots of [asset ID], bounding box coor-  dinates [x1, y1, x2, y2] in the template.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' The correspond-  ing answer is produced based on the spatial relation paths  between the background item node and the asset node.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' The  objective of RSQA task is the following.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  Lθ = − �N  i=1 log Pθ (Args | Qrgs(IDasset, BBoxasset), Iscene)  (10)  Visual Attribute-Guided Spatial QA (VSQA)  In the  conversations, instead of region coordinates, an agent has  to locate an asset by its visual attribute no matter when un-  derstanding user utterances or making recommendations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' To  bring the question closer to a real conversation, we design  VSQA template by replacing region coordinates in RSQA  with visual attributes (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' color, type).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' For spatial-guided vi-  sual question template, the [asset ID] slot can be ﬁlled by  traversing asset nodes of ILG while the [item color] and  [item types] slots are ﬁlled by the visual attribute stored  in asset nodes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' The corresponding answer is produced based  on the spatial relation paths between the background item  node and the asset node.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' The objective of VSQA task is the  following.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  Lθ = − �N  i=1 log Pθ (Avags | Qvags(IDasset, tva), Iscene)  (11)  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='4  MQA-Based Curriculum Learning  Automatic Difﬁculty Level Annotation  When generat-  ing QA pairs by walking on the ILG, the number of nodes  spanned by the pathway can be recorded.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' The more nodes  the path passes through, the more scene information con-  tained in the corresponding QA pair, which means that the  multimodal dialogue model needs more hops to make infer-  ences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Therefore, we automatically label the difﬁculty level  of each QA pair according to the number of nodes the path  spans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' For example, when generating the question “Where is  the brown jacket 83 & 1055?”' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' and the answer “it is on the  ﬂoor rack near the entrance.”, one asset node “brown jack  83 & 1055” and two background item nodes are spanned on  the ILG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' The difﬁculty level of this QA pair is annotated as  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' The following is the formal expression.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  d = |Vspanned|  D  (12)  where d denotes the normalized difﬁculty level of QA pair,  |Vspanned| represents the number of ILG nodes spanned by  corresponding path, D is the maximum value of ILG nodes  spanned by the QA pair path in the dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  Pretraining Strategy  With automatically annotated difﬁ-  culty labels, we propose MQA based curriculum learning  to activate the potential of our designed MQA pretraining  tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' We deﬁne the model competence c as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  c(t) = γ  �  α t  T + β  �  1 − t  T  �  min2(d)  (13)  where t is the index of current training step, T represents  the maximum number of training steps, min2(d) means the  minimum value of difﬁculty level d, α and β are hyper-  parameters, γ is determined by α as  �  1  α.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Here we set α  to 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='2 and β to 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' At a given training step t, QA pair with  difﬁculty smaller than or equal to c(t) (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' d ≤ c(t)) will be  sampled for training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' As such, our pretraining strategy fo-  cuses on QA pairs with lower difﬁculty in the early stage,  aiming at helping the model form preliminary perception  and inference capabilities for scene items.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' In the middle and  late stages, more difﬁcult QA pairs are added, which im-  proves the model’s ability to generate visual attributes and  spatial relations for multiple assets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  After MQA pretraining, SPRING model is ﬁne-tuned on  the SIMMC response generation task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' The auto-regressive  language modeling objective is the following.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  Lθ = − �N  i=1 log Pθ (Ri | Hi, Ui, Ii)  (14)  where N denotes the total number of training samples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  4  Experiment  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='1  Set up  Datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  To evaluate the performance of the proposed  model, we ﬁrst conduct experiments on widely-used situated  multimodal dialogue datasets SIMMC 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='0 and SIMMC 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  MODELS  BLEU-1  BLEU-2  BLEU-3  BLEU-4  METEOR  ROUGE  CIDEr  VISUAL  SPATIAL  SIMMC 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
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+page_content='05  56.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='85  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='88  35.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='31  27.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='48  50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='92  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='4952  32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='70  22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='58  SPRING (Ours)  83.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='29  64.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='75  52.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='41  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='49  31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='90  57.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='12  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='1351  38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='87  30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='77  Table 2: Comparison on SIMMC 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='0, SIMMC 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='0 dataset, visual and spatial subsets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Our model consistently outperforms strong  baselines by a large margin on 7 widely-used metrics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Specially, evaluation on Visual Subset and Spatial Subset by BLEU-4  effectively verify the huge improvement of our model comes from better response about visual attribute and spatial relation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  The SIMMC 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='0 dataset contains 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='2k fashion dialogs and 4k  furniture dialogs, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' There are around 290 digital  assets for fashion and 110 assets for furniture, which are re-  arranged within seed scenes to generate 160 different scenes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  The SIMMC 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='0 dataset includes 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='6k fashion dialogs and  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='4k furniture dialogs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' We evaluate model performance on  the dev-test split of SIMMC 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='0 and SIMMC 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='0, which has  the same scale as the test-std 1 dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  In addition, we invite human experts to ﬁlter responses  with visual attribute or spatial relation from SIMMC 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='0 and  SIMMC 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='0 dev-test split to construct Visual Subset and  Spatial Subset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' We further evaluate models on these two  subsets to prove the effectiveness of our model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  Evaluation Metrics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  The ofﬁcial metric adopted by  SIMMC 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='0 response generation task is BLEU-4, which only  focuses on n-grams overlap between the predicted and tar-  get response.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' For a more comprehensive comparison, we add  widely-used machine generation metrics: BLUE-n (Papineni  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' 2002), METEOR (Banerjee and Lavie 2005), ROUGE  (Lin and Hovy 2003) and CIDEr (Vedantam, Zitnick, and  Parikh 2015) metrics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Compared with the accuracy based  BLEU metric, METOR and ROUGH pay attention to recall  and calculate how many n-grams from the target response  exist in the predicted response, while CIDEr uses TF-IDF to  assign larger weights to infrequent phrases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  Implementation Details.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  Our model is based on Trans-  former (Vaswani et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' 2017) structure with 12 layers, where  ever Transformer block has 768 hidden units and 12 atten-  tion heads.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Each patch is projected to features of the same  size as the hidden units.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' We initialize SPRING parameters  from pretrained VLM, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' , OFA (Wang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' 2022b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Dur-  ing pretraining, our model is trained for 4 epochs with 8  batch sizes on 8 TESLA V100 GPU.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Adam (Kingma and  Ba 2015) is adopted as optimizer with a 4e-4 learning rate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  Besides, the dropout rate is set to 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='2 to prevent over-ﬁtting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  During ﬁne-tuning stage, we train 60 epochs on the SIMMC  train set with a learning rate of 4e-5 and a batch size of 16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  1Not publicly available as a test set for the DSTC competition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  Compared Methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  We compare SPRING with strong  baseline methods from SIMMC 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='0 and SIMMC 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' On  SIMMC 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='0, MN-MAG (Kim et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' 2021) adopts a memory  network as encoder and designs multimodal fusion gate to  fuse information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Tom (Jeong et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' 2021) esambles predic-  tion results from several GPT-2 models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' JBi-encoder (Huang  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' 2021a) is jointly trained to predict belief state and re-  sponse.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' On SIMMC 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='0, MTN (Le et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' 2019) separately en-  codes multimodal input while the visual encoder is guided  by a query-aware attention encoder.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' JMGPT (Kottur et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  2021b) trains a multi-task GPT2-large, which takes dialogue  history and ﬂattened multimodal contexts as input.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Further-  more, JMGPT-BS (Kottur et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' 2021a) extends JMGPT by  inferring with different beam search sizes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' MMBart (Lee  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' 2022) adds box coordinates embedding to textual in-  put and proposes auxiliary tasks to predict asset attributes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  DialVinVL (Kottur et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' 2021a) is based on VinVL-Base  (Zhang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' 2021), concatenates original box coordinates  to region features as visual input, and incorporates dialogue  history with dialogue policy as textual input.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' GPTDeIT (Lee  and Han 2021) utilizes GPT2-large (Radford et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' 2019)  as the text model to encode dialogue history and ﬂattened  slot values and DeIT-I (Touvron et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' 2021) as the image  model to encode assets referenced by current turn utterance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  JointGM (Nguyen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' 2021) leverages BART-large (Lewis  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' 2020) to predict disambiguation label, belief state and  response jointly according to inputted dialogue history.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Sim-  ilar to GPTDeIT, GLIMMeR (Hemanthage et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' 2021) also  leverages GPT2-large and utilizes asset scene ID to help  the model understand the semantics of each asset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Notably,  GLIMMeR is the state-of-the-art method on SIMMC 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='0 and  achieves the winner of the DSTC10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='2  Overall Performance  Table 2 displays the results of the model on the SIMMC  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='0 and SIMMC 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='0 dataset response generation task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' It  can be seen that SPRING has exceeded previous models by  a large margin and achieved state-of-the-art results on all  representative machine generation metrics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' On SIMMC 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='0,  TASK  MODELS  SIMMC 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='0  VISUAL  SPATIAL  VLM  38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='22  34.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='67  25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='04  Visual QA  VLM  w/ PVQA  40.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='75  36.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='54  27.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='58  w/ RVQA  41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='27  37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='02  27.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='22  w/ PoVQA  40.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='89  35.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='94  28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='08  w/ (PVQA + RVQA + PoVQA)  41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='36  37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='59  28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='24  Spatial QA  VLM  w/ PSQA  41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='18  36.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='05  28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='30  w/ RSQA  40.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='77  35.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='42  28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='18  w/ VSQA  40.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='40  36.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='34  27.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='97  w/ (PSQA + RSQA + VSQA)  41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='56  36.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='25  28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='49  All  VLM  w/ all QA  41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='92  38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='52  30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='18  w/ (all QA + CL)  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='49  38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='87  30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='77  Table 3: Ablation study on SIMMC 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='0 dataset with BLEU-4  metric.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Red and green shades represent a stronger advantage  in the visual and spatial subsets, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  SPRING is respectively 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='91, 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='33, 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='49, and 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='18 higher  than previous best models on BLEU-n, varying n from 1 to  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' The signiﬁcant increased percentage on BLEU-n mani-  fests our model successfully utilizing more accurate words  and phrases to make responses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Our model also shows ex-  cellent performance on recall-based metrics METEOR and  ROUGE, of which the score improvements reach 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='42 and  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' When the CIDEr metric pays more attention to infre-  quent n-grams, SPRING still outperforms GLIMMeR with  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='64 on CIDEr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Besides, according to the right part of Ta-  ble 2, our model exhibits the highest BLEU-4 scores on the  visual subset and spatial subset, which veriﬁes the improve-  ment of our model is produced by its better understanding  of visual attribute and spatial relation and ability to conduct  reasoning with aligned information to generate more accu-  rate responses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='3  Detailed Analysis  Ablation Study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  As shown in Table 3, we perform abla-  tion experiments to evaluate the effectiveness of each pre-  training task and curriculum learning strategy in SPRING.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  It can be observed that each MQA pretraining task brings  signiﬁcantly BLEU-4 improvement on the complete SIMMC  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='0 dataset compared with the basic VLM model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Speciﬁ-  cally, VLM models pretrained with all visual QA tasks per-  form 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='92 higher than baseline on the Visual Subset, while  VLM models pretrained with all spatial QA tasks display  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='45 improvement compared with baseline on the Spatial  Subset, which can verify that visual QA and spatial QA re-  spectively prompt model’s ability of describing visual at-  tribute and spatial relation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Besides, the last two rows fur-  ther prove that our designed curriculum learning pretraining  strategy effectively activates the potential of QA pretraining  tasks and boosts model performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  Human Evaluation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  The human evaluation mainly fo-  cuses on 4 aspects: ﬂuency, relevance, correctness, and  informativeness, which are important for task-oriented di-  alogue systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' We randomly select 500 dialogues from  SIMMC 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='0 dev-test dataset as candidates, and then ﬁlter  these dialogues from the results generated by DialVinVL,  GLIMMeR, and our model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' We release evaluation task on  Fluency  Relevance  Correctness  Informativeness  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='5  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='0  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='5  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='0  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='5  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='0  Human Evaluation Score  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='47  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='66  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='77  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='86  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='83  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='85  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='20  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='24  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='96  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='94  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='04  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='13  DialVinVL  GLIMMeR  Ours  Figure 4: The human evaluation results on SIMMC 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='0 with  four aspects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Our model displays signiﬁcant improvement  on correctness and informativeness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  Amazon Mechanical Turk (AMT) and make the last re-  sponse of every selected dialogue evaluated by 10 different  evaluators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Each evaluator scores 1500 generated responses  on 4 aspects according to golden response in blind review  from 1 to 5, simulating a real-life multimodal dialogue sce-  nario.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' As shown in 4, it can be observed that our model con-  sistently outperforms the other two models on all metrics,  which is in line with automatic evaluation results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  Case Study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  To better illustrate the advantage of our  model and display how SPRING prompts model’s ability of  predicting visual attributes and spatial relations related to  background items, we visualize several generated responses  from our model and existing SOTA model with correspond-  ing user utterance and scene snapshot, as shown in Figure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  It can be explicitly observed that: (1) our model is able to  adopt background items to describe the position of target as-  sets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' (2) The relative spatial relations between target assets  and background items can be accurately predicted by our  model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' (3) our model is equipped with the ability of align-  ing visual attribute to spatial information when multiple as-  sets exist in the response.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  Figure 5: Case study on SIMMC 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='0 dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  5  Conclusion  In this paper, we propose a novel situated conversation agent  pretraining method named SPRING.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Speciﬁcally, all QA  pairs and their difﬁculty labels used in pretraining are gener-  ated from our Incremental Layout Graph without any extra  human annotations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Experimental results on SIMMC 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='0 and  SIMMC 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='0 show that SPRING greatly surpasses previous  models and describes visual attributes and spatial relations  more accurately.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  User: Hello!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' I want to buy a pair of shoes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  User : Please recommend some shirts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  System: How about the white shirt on the back wall ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  User: Are there any good shoes with size XL?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  User : Are there any nice black shirts in this store?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  GLIMMeR  Our  GLIMMeR  Ours  How do you feel about that black one hanging  Are you into that black one behind the green  What do you think of the grey shoes?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  the bottom row lon the light closet?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  against the wall to the left or the other black  hoodielon the left or tne other light black one  hanging in the back leit against the wall?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  one on the rack to the right?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='Acknowledgement  We would like to sincerely thank anonymous reviewers for  their suggestions and comments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' The work was partially  supported by the National Natural Science Foundation of  China (NSFC62076032).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' We also want to express our grati-  tude for precious advises given by Guanqi Zhan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  References  Banerjee, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' and Lavie, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' 2005.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' METEOR: An Automatic  Metric for MT Evaluation with Improved Correlation with  Human Judgments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' In Goldstein, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Lavie, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Lin, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' and  Voss, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=', eds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=', Proceedings of the Workshop on Intrinsic  and Extrinsic Evaluation Measures for Machine Translation  and/or Summarization @ ACL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  Bengio, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Louradour, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Collobert, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' and Weston, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  2009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Curriculum learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' In Proceedings of the Inter-  national Conference on Machine Learning (ICML).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  Chang, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Ren, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Xu, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Li, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Chen, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' and Hauptmann,  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
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+page_content=' In Proceedings of IEEE Transactions on Neural Net-  work Learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  Chattopadhyay, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Yadav, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Prabhu, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Chandrasekaran,  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Das, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Lee, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Batra, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' and Parikh, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Evalu-  ating Visual Conversational Agents via Cooperative Human-  AI Games.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
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+page_content='  Chen, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='-C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Li, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Yu, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' El Kholy, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Ahmed, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Gan,  Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Cheng, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' and Liu, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Uniter: Universal image-  text representation learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' In Proceedings of the European  conference on computer vision (ECCV), 104–120.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Springer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  Cho, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Lei, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Tan, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' and Bansal, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Unifying  vision-and-language tasks via text generation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' In Proceed-  ings of the International Conference on Machine Learning  (ICML).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  Das, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Kottur, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Gupta, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Singh, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Yadav, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Moura,  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Parikh, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' and Batra, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Visual dialog.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' In  Proceedings of the IEEE Conference on Computer Vision  and Pattern Recognition (CVPR).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  De Vries, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Strub, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Chandar, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Pietquin, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  Larochelle, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' and Courville, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  Guesswhat?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' vi-  sual object discovery through multi-modal dialogue.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' In Pro-  ceedings of the IEEE Conference on Computer Vision and  Pattern Recognition (CVPR).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  He, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Dai, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Hui, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Yang, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Cao, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Dong, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
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+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Si, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' and Li, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' 2022a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' SPACE-2: Tree-Structured Semi-  Supervised Contrastive Pre-training for Task-Oriented Dia-  log Understanding.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' In Proceedings of the 29th International  Conference on Computational Linguistics (COLING).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  He, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Dai, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Yang, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Sun, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Huang, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Si, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' and  Li, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' 2022b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' SPACE-3: Uniﬁed Dialog Model Pre-training  for Task-Oriented Dialog Understanding and Generation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' In  Proceedings of the 45th International ACM SIGIR Confer-  ence on Research and Development in Information Retrieval  (SIGIR).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  He, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Dai, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Zheng, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Wu, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Cao, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Liu, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Jiang,  P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Yang, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Huang, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Si, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' 2022c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  SPACE:  A Generative Pre-trained Model for Task-Oriented Dialog  with Semi-Supervised Learning and Explicit Policy Injec-  tion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Proceedings of the AAAI Conference on Artiﬁcial In-  telligence (AAAI).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  Hemanthage, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Lemon, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Dondrup, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' and Bartie, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' GLIMMeR: Global-Local Information-aware Multi-  modal grounding with GPT for Co-reference Resolution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' In  DSTC10 challenge wokrshop at AAAI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  Huang, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Tan, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Ng, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Shi, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Yeo, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Jiang,  R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' and Kim, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' 2021a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Joint generation and bi-encoder  for situated interactive multimodal conversations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' In DSTC9  challenge wokrshop at AAAI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  Huang, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Zeng, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Huang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Liu, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Fu, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' and Fu, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  2021b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Seeing out of the box: End-to-end pre-training for  vision-language representation learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' In Proceedings of  the IEEE/CVF Conference on Computer Vision and Pattern  Recognition (CVPR).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  Hui, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Geng, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Ren, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Li, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Li, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Sun, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Huang, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  Si, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Zhu, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' and Zhu, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Dynamic Hybrid Relation  Exploration Network for Cross-Domain Context-Dependent  Semantic Parsing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' In AAAI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  Hui, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Geng, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Wang, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Qin, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Li, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Li, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Sun,  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
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+page_content=' 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
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+page_content='  Jeong, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
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+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
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+page_content=' Yang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Xia, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Chen, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='-T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
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+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  Le, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
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+page_content='-H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Li, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
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+page_content=' 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
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+page_content=' In Proceedings of the International  Conference on Machine Learning (ICML).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  Kim, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Lee, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Jeong, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
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+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Koo, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='-W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
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+page_content=' 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
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+page_content='  Kingma, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' and Ba, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  Adam: A Method for  Stochastic Optimization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' In Proceedings of the International  Conference on Learning Representations (ICLR).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  Kottur, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Moon, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
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+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' and Damavandi, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  2021a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
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+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Moon, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
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+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
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+page_content='  2021b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  SIMMC 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='0: A Task-oriented Dialog Dataset for  Immersive Multimodal Conversations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  In Proceedings of  the 2021 Conference on Empirical Methods in Natural Lan-  guage Processing (EMNLP).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  Le, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Sahoo, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Chen, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' and Hoi, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Multimodal  transformer networks for end-to-end video-grounded dia-  logue systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' In Proceedings of the 57th Annual Meeting  of the Association for Computational Linguistics (ACL).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  Lee, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Kwon, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Choi, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Kim, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Lee, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Han, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  Kim, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Park, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Lee, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Shin, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' and Kim, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='-E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  Learning to Embed Multi-Modal Contexts for Situated Con-  versational Agents.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' In Findings of the Association for Com-  putational Linguistics (NAACL).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  Lee, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' and Han, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
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+page_content=' Niu, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Xiao, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Liu, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Liu, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Wu,  H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' and Wang, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
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+page_content=' In Proceedings of the 59th Annual Meeting of the  Association for Computational Linguistics (ACL).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  Liao, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Long, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Ma, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Lei, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
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+page_content='-S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
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+page_content='  Lin, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' and Hovy, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' 2003.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Automatic Evaluation of  Summaries Using N-gram Co-occurrence Statistics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
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+page_content='  Lu, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Batra, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Parikh, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' and Lee, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  Vilbert:  Pretraining task-agnostic visiolinguistic representations for  vision-and-language tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' In Proceedings of the Advances  in neural information processing systems (NIPS).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  Moon, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Kottur, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Crook, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' De, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
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+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Levin,  T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Whitney, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
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+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Beirami, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Cho, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
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+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
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+page_content=' 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
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+page_content=' In Proceedings of the 28th Interna-  tional Conference on Computational Linguistics (COLING).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  Nguyen, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='-T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Shi, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Jiang, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' and jae Kim, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Mul-  timodal and Joint Learning Generation Models for SIMMC  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' In DSTC10 challenge wokrshop at AAAI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  Papineni, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Roukos, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Ward, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' and Zhu, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' 2002.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Bleu:  a Method for Automatic Evaluation of Machine Translation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  In Proceedings of the 40th Annual Meeting of the Associa-  tion for Computational Linguistics (ACL).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  Qiu, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Liang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Zhao, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Lu, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Peng, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Yu, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Wu,  Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' and Zhu, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' SocAoG: Incremental Graph Pars-  ing for Social Relation Inference in Dialogues.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' In Proceed-  ings of the 59th Annual Meeting of the Association for Com-  putational Linguistics and the 11th International Joint Con-  ference on Natural Language Processing (ACL-IJCNLP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  Qiu, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Zhao, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Liang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Lu, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Shi, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Yu, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' and Zhu,  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='-C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Towards Socially Intelligent Agents with Mental  State Transition and Human Value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' In SIGDIAL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  Radford, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Kim, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Hallacy, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Ramesh, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Goh, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  Agarwal, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Sastry, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Askell, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Mishkin, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Clark, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Learning transferable visual models from natural  language supervision.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' In Proceedings of the International  Conference on Machine Learning (ICML).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  Radford, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Wu, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Child, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Luan, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Amodei, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  Sutskever, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Language models are unsupervised  multitask learners.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' In Arxiv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  Ren, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' He, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Girshick, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' and Sun, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Faster r-cnn:  Towards real-time object detection with region proposal net-  works.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' In Proceedings of the Advances in neural informa-  tion processing systems (NIPS).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  Saha, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Khapra, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' and Sankaranarayanan, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' To-  wards building large scale multimodal domain-aware con-  versation systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' In Proceedings of the AAAI Conference  on Artiﬁcial Intelligence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  Tan, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' and Bansal, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' LXMERT: Learning Cross-  Modality Encoder Representations from Transformers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' In  Proceedings of the 2019 Conference on Empirical Meth-  ods in Natural Language Processing and the 9th Interna-  tional Joint Conference on Natural Language Processing  (EMNLP-IJCNLP).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  Touvron, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Cord, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Douze, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Massa, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Sablayrolles,  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' and J´egou, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Training data-efﬁcient image trans-  formers & distillation through attention.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' In Proceedings of  the International Conference on Machine Learning (ICML).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  Vaswani, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Shazeer, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Parmar, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Uszkoreit, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Jones,  L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' Gomez, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
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+page_content=' 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
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+page_content=' Qin, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
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+page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
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+page_content=' ’of’,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' ’along’,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' ’below’,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' ’towards’,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' ’above’  article and pronoun  ’the’,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' ’a’,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' ’that’,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' ’this’,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' ’other’,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' ’another’  punctuation and conjunctions  ’,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='’,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' ’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='’,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' ’;’' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=', ’?’' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=', ’and’, ’or’  Table 4: Slot types and slot values in the regular expression.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  Appendix  In the Table 4, we display the slot types and slot values of  four regular expressions we use to extract visual attribute,  spatial description, background item, and spatial relation  from dialogue corpus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' All color values and type values are  from SIMMC 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='0 metadata while background items are com-  mon furniture words provided by Wikipedia except for those  appear in SIMMC 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='0 furniture types.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' The article, pronoun,  coordinating conjunction and punctuation come from The  Oxford English Dictionary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' To make it clearer, we adopt a  simple python code snippet to show how to use our designed  regular expressions to extract visual and spatial information  in the following.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  1  immport re  2  3  system_response = ’How about the blue  4  tshirt on the shelf or the red jacket  5  above the table ?’' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='  6  7  RegExp_vi = ’(a|the|that|this|other|  8  another) (red,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' white,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' yellow|pink|  9  red,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' white|purple|white,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' black|black|  10  dark grey|light grey|white|blue|green|  11  maroon|yellow|red|violet|yellow,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' black|  12  black,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' red,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' white|blue,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' black|  13  black,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' white|light blue|red,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' black|  14  pink,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' white|orange|yellow,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' brown|  15  light pink|dark brown|pink|dark yellow|  16  light red|green,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' white|grey,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' white|  17  black,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' red|grey,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' blue|brown,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' white|  18  white,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' black,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' red|light orange|  19  orange,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' purple|dirty green|blue,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' grey|  20  black,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' grey|white,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' grey|olive|dark red|  21  olive,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' black|pink,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' black|blue,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' green|  22  green,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' black|light blue,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' light green)  23  (blouse|jacket|shirt|sweater|dress|  24  tshirt|joggers|jeans|hat|vest|bed|  25  coat|shoes|skirt|suit|trousers|hoodie)’  26  27  RegExp_sd = ’(in|on|at|behind|toward|  28  to|against|of|along|below|above) (the|  29  a|that|this|other) (.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='*?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=') (and|or|,|  30  \\.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='|\\?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=' )’  31  32  RegExp_bi = ’(rack|wall|mirror|shelf|  33  closet|table|wardrobe|cabinet|window|  34  divider|door|counter|cubby|cubbies)’  35  36  RegExp_sr = ’(in|on|at|behind|toward|  37  to|against|of|along|below|towards|  38  above)’  39  40  extracted_vi = re.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='findall(RegExp_vi,  41  system_response)  42  # [(’the’, ’blue’, ’tshirt’),  43  # (’the’, ’red’, ’jacket’)]  44  45  extracted_sd = re.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='findall(RegExp_sd,  46  system_response)  47  # [(’on’, ’the’, ’shelf’, ’or’),  48  # (’above’, ’the’, ’table’, ’?’' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content=')]  49  50  sds = [’ ’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='join(item[:-1]) for item  51  in extracted_sd]  52  # [’on the shelf’, ’above the table’]  53  54  bi_list, sr_list = [], []  55  for sd in sds:  56  bi = re.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='findall(RegExp_bi, sd)  57  bi_list.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='append(bi)  58  sr = re.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='findall(RegExp_sr, sd)  59  sr_list.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
+page_content='append(sr)  60  # bi_list [(’shelf’), (’table’)]  61  # sr_list [(’on’), (’above’)]' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_NAzT4oBgHgl3EQf_f58/content/2301.01949v1.pdf'}
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+TCC bounds on the static patch of de Sitter space
+Matt´eo Blamart∗, Samuel Laliberte† and Robert Brandenberger‡
+Department of Physics, McGill University, Montr´eal, QC, H3A 2T8, Canada
+Abstract
+Recently, Pei-Ming Ho and Hikaru Kawai [1] have argued that treating particles as wave packets
+can lead to a shutdown of Hawking radiation at late times near the horizon of black holes. This
+shutdown arises from viewing quantum ﬁeld theory near the black hole horizon as an eﬀective ﬁeld
+theory, and imposing an appropriate UV cutoﬀ. We show that this eﬀect is also present in the
+static patch of de Sitter space, leading to a shutdown of Gibbons-Hawking radiation near the de
+Sitter horizon. Assuming this eﬀect is due to the breakdown of eﬀective ﬁeld theory, we obtain a
+bound t ≲ H−1 ln(H−1MP ) on the time scale of validity of eﬀective ﬁeld theory in de Sitter space,
+which matches with the predictions of the Trans-Planckian Censorship Conjecture.
+Contents
+1
+Introduction
+1
+2
+Review of Gibbons-Hawking radiation in de Sitter space
+3
+2.1
+UV cutoﬀ, blue shift and scrambling time . . . . . . . . . . . . . . . . . . . . . . . . .
+6
+3
+Wave packets in de Sitter space
+7
+4
+Shutdown of Gibbons-Hawking radiation in de Sitter space
+9
+4.1
+Late-time and early-time spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+9
+4.2
+Early and late time bounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+10
+4.3
+Relation to the TCC bound . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+12
+5
+Conclusion and discussion
+13
+1
+Introduction
+It is well known that, calculated an eﬀective ﬁeld theory (EFT) in the semiclassical approximation,
+black holes radiate thermally [2]. Speciﬁcally, if matter is treated as a scalar ﬁeld, then an observer
+at late times and far from the horizon will measure a thermal ﬂux of scalar ﬁeld quanta if the initial
+∗e-mail address: matteo.blamart@mail.mcgill.ca
+†e-mail address: samuel.laliberte@mail.mcgill.ca
+‡e-mail address: rhb@physics.mcgill.ca
+1
+arXiv:2301.02741v1  [hep-th]  6 Jan 2023
+
+state is prepared as an appropriate vacuum state. In a similar way, observers at a point x in de
+Sitter space will measure a thermal ﬂux of scalar ﬁeld quanta if the initial state is set up as a local
+vacuum state a Hubble horizon distance away from x [3]. It is these ﬂuctuations which are postulated
+to be the origin of density perturbations [4] and gravitational waves [5] in an inﬂationary universe
+scenario [6].
+In the context of inﬂationary cosmology, it was argued in [7] that there is a “trans-Planckian
+problem” for cosmological ﬂuctuations if the period of inﬂation is long since in that case the physical
+wavelength of the ﬂuctuations observed today was smaller than the Planck length at the beginning
+of inﬂation and thus in a region where the eﬀective ﬁeld theory of ﬂuctuations becomes questionable.
+Based on these considerations, in [8] a “Trans-Planckian Censorship Conjecture” (TCC) was put
+forward according to which in no eﬀective ﬁeld theory emanating from superstring theory modes
+which initially were trans-Planckian could ever have exited the Hubble horizon, i.e.
+a(tR)
+a(ti) lpl < H−1(tR) ,
+(1)
+for any initial time ti and ﬁnal time tR. In the above, a(t) is the cosmological scale factor, and H(t)
+is the Hubble expansion rate at time t (whose inverse is the Hubble horizon). As discussed in [9],
+the TCC severely constrains viable inﬂationary models. In particular, canonical single scalar ﬁeld
+inﬂation models with an energy scale η > 109GeV are ruled out. As argued in [10], the TCC can be
+argued for independently of superstring theory, making use of unitarity arguments and consistency
+with the second law of thermodynamics (see [11]).
+On the other hand, there have been arguments to the eﬀect that there is no trans-Planckian
+problem for inﬂationary cosmology (see e.g. [12–14]). Based on the Einstein equivalence principle it
+is argued that on microscopic scales (in the context of cosmology this means on length scales much
+smaller than the Hubble radius) physics must reduce to that in Minkowski space-time. From the
+point of view of quantum gravity, however, this argument is problematic. Nevertheless, it would be
+useful to have more independent support for the TCC.
+In the case of black holes, one can argue that a similar trans-Planckian problem arises (see
+e.g. [15, 16] for some early work).
+From the point of view of a semiclassical EFT analysis, the
+Hawking radiation [2] which an observer far outside the black hole horizon observes at a frequency
+ω (e.g.
+the frequency corresponding to the Hawking temperature) observes is associated with a
+blueshifted frequency Ω which becomes larger than the Planck scale suﬃciently close to the black
+hole horizon. Hence, one may argue that the semi-classical analysis must break down.
+Once again, it can be argued that there is no problem for the semiclassical description of Hawking
+radiation since there is a “nice slice”, a spatial hypersurface from whose point of view there is no
+divergence of the frequency close to the horizon (see e.g. [17]). But this does not resolve the famous
+black hole information loss problem (see e.g. [18] for early discussions of this problem) associated
+with Hawking radiation. It has been argued [19] that the semiclassical analysis must break down at
+the “Page time”, the time when the entropy of thermal Hawking radiation reaches half of the initial
+2
+
+entropy of the black hole (as determined by the area of the initial black hole horizon).
+In recent work, Pei-Ming Ho and Hikaru Kawai [1] considered the propagation of wave packets in
+a black hole background rather than considering only plane waves. Working in the context of eﬀective
+ﬁeld theory and imposing a UV cutoﬀ, they ﬁnd that Hawking radiation shuts oﬀ at the scrambling
+time. More generally, they ﬁnd that the spectrum of Hawking radiation after the scrambling time
+depends on physics which cannot be described in terms of the EFT.
+We apply a similar analysis to the static patch dS, and ﬁnd that Gibbons-Hawking radiation shuts
+oﬀ after the TCC time scale (if there is an ultraviolet cutoﬀ), and more generally cannot be described
+by the EFT beyond that time. Besides the intrinsic interest of this result, it points to an intriguing
+analogy between the black hole scrambling time and the cosmological TCC time scale.
+This document is structured as follows. In section 2, we review Gibbons-Hawking radiation in de
+Sitter space by using a conventional approach, where particles on a curved background behave like
+plane waves. In section 3, we deﬁne semi-classical wave packets and describe how they can arise as
+ﬂuctuations of quantum ﬁeld ﬁelds. Finally, in section 4, we show how Gibbons-Hawking radiation
+coming from particles that behave as semi-classical wave packets becomes sensitive to UV cutoﬀs
+after a scrambling time tsc = H−1 ln(H−1Mp), leading to a breakdown of eﬀective ﬁeld theory.
+2
+Review of Gibbons-Hawking radiation in de Sitter space
+To see how thermal radiation can be shut down after a ﬁnite amount of time, let us start by reviewing
+the derivation of Gibbons-Hawking radiation when particles are treated as plane waves in a curved
+background. We will roughly follow the approach presented in [20] and work in the static patch of de
+Sitter space where the metric takes the form
+ds2 = −f(r)dt2 + dr2
+f(r) + r2dΩ2
+2
+,
+f(r) = 1 − r2/l2 ,
+(2)
+where l is the radius of the de Sitter horizon. This metric can be rewritten in the more convenient
+Eddington-Finkelstein frame (see [21] for a review) where the metric takes the form
+ds2 = −f(u, v)dudv + r(u, v)2dΩ2
+2 ,
+(3)
+by deﬁning a radial coordinates r∗ = Arctanh (r/l) and light cone-coordinates u = t−r∗ and v = t+r∗.
+Another useful frame is the Kruskal coordinate system. One can move from the Eddington-Finkelstein
+frame to the Kruskal frame using the change of coordinates
+U(u) = leu/l
+,
+V (v) = −le−v/l ,
+(4)
+in which case the space-time metric then takes the form
+ds2 ≈ −4dUdV + r2(U, V )dΩ2
+2 ,
+(5)
+3
+
+in the r ≈ l limit. A useful feature of the Kruskal coordinate system is that space-time looks ﬂat in the
+near horizon limit. In comparison, the Eddington-Finkelstein coordinates look like those of an acceler-
+ated observer in the ”ﬂat” Kruskal background. Consequently, one can derive Gibbons-Hawking radi-
+ation in de Sitter space by computing the spectrum of particles observed by an Eddington-Finkelstein
+observer in the Kruskal vacuum in the near horizon limit.
+To do this, let us consider s-wave modes of a massless scalar ﬁeld φ in the static patch of de
+Sitter space. The mode decomposition of φ for s-wave modes in Kruskal and Eddington-Finkelstein
+coordinates can be written as
+φ =
+� ∞
+0
+dΩ
+√
+4πΩ
+�
+aΩe−iΩU + a†
+ΩeiΩU + ˜aΩe−iΩV + ˜a†
+ΩeiΩV �
+(6)
+=
+� ∞
+0
+dω
+√
+4πω
+�
+bωe−iωu + b†
+ωeiωu + ˜bωe−iωv + ˜b†
+ωeiωv�
+.
+(7)
+Here, aΩ, ˜aΩ and bω,˜bω are annihilation operators deﬁned by
+aΩ|0⟩a = ˜aΩ|0⟩a = 0
+,
+bω|0⟩b = ˜bω|0⟩b = 0
+(8)
+where |0⟩a is the Kruskal coordinates vacuum state, and |0⟩b is the Eddington-Finkelstein coordinates
+vacuum state. Similar creation operators can be obtained by taking the hermitian conjugate of the
+annihilation operators. The creation-annihilation of the two frames can be related by the Bogoliubov
+transformations
+bω =
+� ∞
+0
+dΩ
+�
+αωΩaΩ + βωΩa†
+Ω
+�
+˜bω =
+� ∞
+0
+dΩ
+�
+˜αωΩ˜aΩ + ˜βωΩ˜a†
+Ω
+�
+(9)
+b†
+ω =
+� ∞
+0
+dΩ
+�
+α∗
+ωΩa†
+Ω + β∗
+ωΩaΩ
+�
+˜b†
+ω =
+� ∞
+0
+dΩ
+�
+˜α∗
+ωΩ˜a†
+Ω + ˜β∗
+ωΩ˜aΩ
+�
+,
+(10)
+for appropriate Bogoliubov coeﬃcients αωΩ, βωΩ and ˜αωΩ, ˜βωΩ.
+In the Eddington-Finklestein and Kruskal coordinate systems, the r ≈ l regime corresponds to
+two separate limits. The ﬁrst one, v → ∞ or V → 0, is related to the horizon in the far future. In
+this case, Gibbons-Hawking radiation can be obtained from the left-moving modes of the ﬁeld (see
+Figure 1). The second limit, u → ∞ or U → 0, is related to the horizon in the far past. In this case,
+Gibbons-Hawking radiation can be obtained from the right-moving modes of the ﬁeld. Both limits
+can be taken independently and yield the same spectrum.
+Let us ﬁrst bring our attention to the left moving modes, which are relevant for Gibbons-Hawking
+radiation near the future horizon. The Bogoliubov coeﬃcients for these modes can be derived from
+the normalized left-moving eigenfunctions ˜Gω(v) and ˜HΩ(V ) of the Laplacian operator in Eddington-
+Finkelstein and Kruskal coordinates. These eigenfunctions are given by
+˜Gω(v) = e−iωv
+√
+4πw
+,
+˜HΩ(V ) = e−iΩV
+√
+4πΩ
+.
+(11)
+4
+
+˜
+Gω(v)
+I+
+I−
+v = ∞
+u = −∞
+r = 0
+Gω(u)
+I+
+I−
+v = ∞
+u = −∞
+r = 0
+Figure 1: Space-time diagram of de Sitter space. Left-moving modes contribute to Gibbons-Hawking
+radiation near the future horizon (left) and right-moving modes contribute to Gibbons-Hawking
+radiation near the past horizon (right). Here, left-moving means that the modes are moving towards
+the center of the static patch (r = 0). Similarly, right-moving means that the modes are moving
+away from the center of the static patch (not to be confused with the directions of the arrows on the
+ﬁgure).
+We obtain1
+˜αωΩ = i
+� 0
+−∞
+dV ˜G∗
+ω(v(V ))←→
+∂ V ˜HΩ(V ) = l
+2π
+�ω
+Ω (lΩ)ilω eπlω/2Γ(−ilω)
+(12)
+˜βωΩ = −i
+� 0
+−∞
+dV ˜Gω(v(V ))←→
+∂ V ˜HΩ(V ) = l
+2π
+�ω
+Ω (lΩ)−ilω e−πlω/2Γ(ilω) ,
+(13)
+where Γ(z) is the gamma function. Using the Bogoliubov transformations above, we can compute
+the number of particles an Eddington-Finklestein observer perceives in the Kruskal vacuum. This
+number of particles can be obtained from the expectation value of the number operator ˜nω = ˜b†
+ω˜bω in
+the Kruskal vacuum. For an observer near the future horizon, we obtain
+a⟨0|˜b†
+ω1˜bω2|0⟩a =
+� ∞
+0
+dΩ˜βω1Ω ˜β∗
+ω2Ω
+(14)
+=
+1
+e2πlω1 − 1δ(ω1 − ω2) ,
+(15)
+which is the expected spectrum of Gibbons-Hawking radiation. Here, we made use of the identity
+|e−πlω/2Γ(±ilω)|2 = 2π
+lω
+�
+1
+e2πlω − 1
+�
+(16)
+1Here, we will be using the convention f←→
+∂ xg = f∂xg − g∂xf for the double arrow derivative.
+5
+
+to obtain the result above. A similar spectrum can be obtained from the right-moving modes, which
+are relevant for Gibbons-Hawking radiation near the past horizon. In this case, the normalized wave
+functions are
+Gω(u) = e−iωu
+√
+4πw
+,
+HΩ(U) = e−iΩU
+√
+4πΩ
+,
+(17)
+and the associated Bogoliubov transformations are
+αωΩ = i
+� ∞
+0
+dUG∗
+ω(u(U))←→
+∂ UHΩ(U) = l
+2π
+�ω
+Ω (lΩ)−ilω eπlω/2Γ(ilω)
+(18)
+βωΩ = −i
+� ∞
+0
+dUGω(u(U))←→
+∂ UHΩ(U) = l
+2π
+�ω
+Ω (lΩ)ilω e−πlω/2Γ(−ilω) .
+(19)
+By computing the expectation value of the number operator nω = b†
+ωbω in the Kruskal vacuum, we
+obtain the same result as for the left moving modes:
+a⟨0|b†
+ω1bω2|0⟩a =
+� ∞
+0
+dΩβω1Ωβ∗
+ω2Ω
+(20)
+=
+1
+e2πlω1 − 1δ(ω1 − ω2) .
+(21)
+Consequently, at all times, a static observer in de Sitter space will perceive a thermal bath of particles
+with a temperature given by T = (2πl)−1.
+2.1
+UV cutoﬀ, blue shift and scrambling time
+At ﬁrst glance, the thermal spectrum of Equation 15 and 21 does not seem to change in the UV limit.
+However, we must remember that physics at low energies is described by an eﬀective ﬁeld theory and
+cannot be trusted beyond the Planck scale, where quantum gravity corrections become important. To
+take this into account, let us impose a cutoﬀ ΛΩ ∼ Mp on the frequency Ω. When ΛΩ ≫ H (H = l−1
+is the Hubble expansion rate), Equations 15 and 21 are still approximately valid. However, there are
+two regions of the static patches where we expect that new physics might be important. Given our
+cutoﬀ, these are the regions near the future and past horizon.
+To see why this is the case, let us study how one particle states in Eddington-Finklestein co-
+ordinates behave in the Kruskal frame. In the Eddington-Finklestein frame, the free particle wave
+functions are deﬁned by
+ψR(u) = b⟨0|φ(u, v)b†
+ω|0⟩b = e−iωu
+√
+4πw
+,
+ψL(v) = b⟨0|φ(u, v)˜b†
+ω|0⟩b = e−iωv
+√
+4πw
+(22)
+where ψR(u) describes a right moving particle and ψL(v) a left moving particle. In the Eddington-
+Finklestein frame, ψR(u) and ψL(v) are eigenfunctions of the momentum operators pu = i d
+du and
+pv = i d
+dv with an eigenvalue given by the frequency ω associated to each wave function. Similarly,
+ψR(u) and ψL(v) are also eigenfunctions of the momentum operators pU = i d
+dU and pV = i d
+dV in
+Kruskal coordinates. Acting with these operators, we obtain
+idψR(u)
+dU
+= ω du
+dU ψR(u)
+,
+idψL(v)
+dV
+= ω dv
+dV ψL(v) ,
+(23)
+6
+
+from which we read oﬀ the frequency eigenvalues
+Ω = dv
+dV ω = ev/lω
+,
+Ω = du
+dU ω = e−u/lω .
+(24)
+From the results above, we conclude that the Kruskal frame frequency associated to Eddington-
+Finklestein particles is blue-shifted close the future and past horizon (v → ∞ and u → −∞ limits).
+In these, limits we have to worry about this frequency being blueshifted above our UV cutoﬀ ΛΩ ∼
+Mp. As an example, let us consider Eddington-Finklestein particles with frequencies on the Hubble
+scale (ω ∼ H), which are those that contribute most signiﬁcantly to Gibbons-Hawking radiation. For
+such particles, the blueshifted frequency exceeds the UV cutoﬀ when v ≫ l ln(lMp) for a left-moving
+particle or u ≪ −l ln(lMp) for a right-moving particle. For an observer at the center of the static patch
+(r = 0), these bounds correspond precisely to a scrambling time tsc = l ln(lMp) in the future and in
+the past. After this amount of time, we expect UV eﬀects to become relevant in Gibbons-Hawking
+radiation.
+From what we have seen so far, the Gibbons-Hawking spectrum coming from particles that behave
+as plane waves does not seem sensitive to the eﬀects above. We will see that this is a result of particles
+being described as plane waves as opposed to localized wave packets. The key diﬀerence between the
+two descriptions is that wave-packets are localised within a left or right-moving patch of width ∆v or
+∆u depending on the direction of motion of the wave packet. In comparison, plane waves are fully
+non-local and span the whole static patch at all times. Because the wave-packets are local, they are
+sensitive to the region of the static patch where they propagate. Hence, they will be sensitive to the
+UV cutoﬀ in the blue-shifted regions v ≫ l ln(lMp) and u ≪ −l ln(lMp). In the next sections, we will
+see that this sensitivity leads to a shutdown of Gibbons-Hawking radiation when v ≫ l ln(lMp) or
+u ≪ −l ln(lMp).
+3
+Wave packets in de Sitter space
+Let us now turn our attention to the case where particles are described by semi-classical wave packets.
+We will be interested in left-moving wave packets ψ(w0,v0)(v) and right-moving wave packets ψ(w0,u0)(u)
+of the form
+ψ(w0,v0)(v) =
+� ∞
+0
+dω
+√
+4πwfw0(ω)e−iω(v−v0)
+,
+ψ(w0,u0)(u) =
+� ∞
+0
+dω
+√
+4πwfw0(ω)e−iω(u−u0) .
+(25)
+Here, we will consider frequency distributions fω0(ω) that are peaked around a central frequency ω0,
+and vanishing a distance ∆ω from ω0. This way, the left and right moving wave packets will become
+centered around v0 and u0 respectively. For the wave packets to be properly normalized, we will
+impose the normalisation condition
+� ∞
+−∞
+dvρ(ω0,v0)(v) =
+� ∞
+0
+dω|fω0(ω)|2 = 1 ,
+(26)
+7
+
+where
+ρ(ω0,u0)(v) = iψ∗
+(w0,v0)
+←→
+∂ vψ(w0,v0)
+(27)
+is the relativistic density of the wave packet ψ(w0,v0)(v). (Here, we used the left-moving wave packet
+for this deﬁnition, but a similar condition is true for the right-moving wave packet as well.) One of the
+most simple frequency distributions which satisﬁes the conditions above is the Gaussian distribution
+fω0(ω) =
+�
+ω
+2πω0∆ωe− (ω−ω0)2
+2∆ω2
+,
+(28)
+associated to the left and right-moving Gaussian wave packets
+ψ(w0,v0)(v) ≈
+�
+∆ω
+2√πω0
+e− ∆ω2(v−v0)
+2
+−iω0(v−v0)
+,
+ψ(w0,u0)(u) ≈
+�
+∆ω
+2√πω0
+e− ∆ω2(u−u0)
+2
+−iω0(u−u0) , (29)
+in the limit where ∆ω ≪ ω0. The wave functions above saturate the Heisenberg uncertainty bound.
+Hence, we should view particles described by ψ(w0,v0)(v) and ψ(w0,u0)(u) as free particles in their
+semi-classical limits.
+Such particles can be created in quantum ﬁeld theory by appropriately modifying the raising and
+lowering operators. Using b†
+ω,˜b†
+ω and the frequency distribution fω0(ω) of Equation 28, we can deﬁne
+creation operators ˜b†
+(ω0,v0), b†
+(ω0,u0) associated to the Gaussian wave packets ψ(w0,v0)(v) and ψ(w0,u0)(u).
+Such creation operators are given by
+˜b†
+(ω0,v0) =
+� ∞
+0
+dωfω0(ω)eiωv0˜b†
+ω
+,
+b†
+(ω0,u0) =
+� ∞
+0
+dωfω0(ω)eiωu0b†
+ω .
+(30)
+Similar annihilation operators can be obtained by taking the hermitian conjugate of the operators
+above. One can check that this creation operator lets us create particles with the wave function of
+Equation 25 by evaluating the wave function of a one-particle state in quantum ﬁeld theory. For
+the left-moving particle, the wave function can be obtained by evaluating the vacuum expectation
+value of φ(v)˜b†
+(ω0,v0) in the Eddington-Finkelstein vacuum. Similarly, the wave function of the right
+moving particle can be obtained by computing the Eddington-Finkelstein vacuum expectation value
+of φ(u)b†
+(ω0,u0). This gives us
+b⟨0|φ(v)˜b†
+(ω0,v0)|0⟩b = ψ(ω0,v0)(v)
+,
+b⟨0|φ(u)b†
+(ω0,u0)|0⟩b = ψ(ω0,u0)(u) ,
+(31)
+as expected. The fully quantum limit of this semi-classical particle can be recovered by letting the
+∆ω → 0. In this case, we recover the quantum mechanical wave function of a free particle that
+behaves as a plane wave2:
+ψ(w0,v0)(v) ≈ e−iω0(v−v0)
+√4πω0
+,
+ψ(w0,u0)(u) ≈ e−iω0(u−u0)
+√4πω0
+.
+(32)
+2It’s a bit tricky to see this from Equation 29. However, we can see that this is true when taking the ∆ω → 0
+limit in Equation 28. In this limit, we obtain fω0(ω) ≈
+�
+ω/ω0δ(w − w0). Evaluating Equation 25 using this frequency
+distribution, we obtain the desired result.
+8
+
+Using ˜b†
+(ω0,v0), b†
+(ω0,u0) and the corresponding annihilation operators, it is possible to compute the
+spectrum of Gibbons-Hawking radiation associated to a thermal bath of semi-classical particles in
+the Kruskal vacuum. This can be done by deﬁning number operators ˜
+N(ω0,v0) = ˜b†
+(ω0,v0)˜b(ω0,v0) and
+N(ω0,u0) = b†
+(ω0,u0)b(ω0,u0) associated to the left and right-moving wave packets, and computing their
+expectation values in the Kruskal vacuum in the same way we did in section 2. As we will see in the
+next section, the spectrum we obtain will be similar to our previous result, but also sensitive to UV
+cutoﬀs.
+4
+Shutdown of Gibbons-Hawking radiation in de Sitter space
+We now provide a derivation of Gibbons-Hawking radiation in de Sitter space in the case where
+particles are described as wave packets rather than plane waves. In this case, the Gibbons-Hawking
+spectrum will vary depending on the location v0 or u0 of the contributing wave packets.
+When
+v0 ≪ l ln(lMp) and u0 ≫ −l ln(lMp), the spectrum will remain approximately the same as in equation
+15 and 21. Conversely, the spectrum will shut down in the cases where v0 ≫ l ln(lMp) and u0 ≪
+−l ln(lMp). Since Gibbons-Hawking radiation becomes sensitive to the UV cutoﬀ with the localized
+wave packet formalism, v0 ≈ l ln(lMp) and u0 ≈ −l ln(lMp) give bounds on the validity of eﬀective
+ﬁeld theory near the future and past horizons. We will see that these bounds match the predictions
+from the TCC for an observer at the center of the static patch (r∗ = 0).
+4.1
+Late-time and early-time spectrum
+Following the same steps as in section 2, let us compute the expectation value of the number operators
+˜
+N(ω0,v0) and N(ω0,u0) in the Kruskal vacuum. The ﬁrst step is to substitute the raising operators of
+equation 30 and the corresponding annihiliation operators in the deﬁnition of the number operators.
+We obtain the following expectation values:
+a ⟨0| ˜
+N(ω0,v0) |0⟩a =
+� ∞
+0
+dω1
+� ∞
+0
+dω2fω0(ω1)f∗
+ω0(ω2)ei(ω1−ω2)v0
+� ΛΩ
+0
+dΩ˜β∗
+ω1Ω ˜βω2Ω ,
+(33)
+a ⟨0| N(ω0,u0) |0⟩a =
+� ∞
+0
+dω1
+� ∞
+0
+dω2fω0(ω1)f∗
+ω0(ω2)ei(ω1−ω2)u0
+� ΛΩ
+0
+dΩβ∗
+ω1Ωβω2Ω .
+(34)
+Here, we have imposed the UV cutoﬀ ΛΩ = Mp on the energy scale Ω in order to remove UV eﬀects.
+Moreover, βωΩ and ˜βωΩ are given by 19 and 13 respectively. To see the impacts of the UV cutoﬀ on
+the contribution of wave packets in diﬀerent regions of the static patch, we will then make the change
+of variables Ω = ω0ev/l for the left-moving modes and Ω = ω0e−u/l for the right-moving modes. These
+correspond to the blue-shifted frequency of left or right-moving wave packet of central frequency ω0.
+9
+
+Following the change of variables, the expectation value of the number operators becomes
+a ⟨0| ˜
+N(ω0,v0) |0⟩a =
+� l log(ΛΩ/ω0)
+−∞
+dv
+l | ˜Fω0(v − v0)|2 ,
+(35)
+a ⟨0| N(ω0,u0) |0⟩a =
+� ∞
+−l log(ΛΩ/ω0)
+du
+l |Fω0(u − u0)|2 ,
+(36)
+where ˜Fω0 and Fω0 are given by
+˜Fω0(v − v0) = l
+2π
+� ∞
+0
+dωfω0(ω)e−iω(v−v′
+0)√ωe−πωl/2Γ(ilω) ,
+(37)
+Fω0(u − u0) = l
+2π
+� ∞
+0
+dωfω0(ω)e−iω(u−u′
+0)√ωe−πωl/2Γ(−ilω) .
+(38)
+Here, the centers v′
+0 and u′
+0 for each distribution are given by v′
+0 = v0 − l ln(lω0) and u′
+0 = u0 +
+l ln(lω0). When the frequency distribution fω0(ω) is suﬃciently narrow, it is possible to approximate
+the expressions above as
+˜Fω0(v − v0) ≈
+l
+√πω0e−πω0l/2Γ(ilω0)ψω0,v′
+0(v) ,
+(39)
+˜Fω0(u − u0) ≈
+l
+√πω0e−πω0l/2Γ(−ilω0)ψω0,u′
+0(u) .
+(40)
+For frequencies on cosmic scales ω0 ∼ l, the approximation above holds if ∆ω ≪ ω0. Using the
+expressions above and the identity (16), we can ﬁnally express a ⟨0| ˜
+N(ω0,v′
+0) |0⟩a and a ⟨0| N(ω0,u′
+0) |0⟩a
+as
+a ⟨0| ˜
+N(ω0,v0) |0⟩a ≈
+1
+e2πlω0 − 1
+�� l ln(ΛΩ/ω0)
+−∞
+dvρ(ω0,v′
+0)(v)
+�
+,
+(41)
+a ⟨0| N(ω0,u0) |0⟩a ≈
+1
+e2πlω0 − 1
+�� ∞
+−l ln(lΛΩ/ω0)
+duρ(ω0,u′
+0)(u)
+�
+,
+(42)
+where ρ(ω0,v′
+0)(v) and ρ(ω0,u′
+0)(u) are the relativistic density of the wave-packet ψ(ω0, v′
+0)(v) and
+ψ(ω0, u′
+0)(u) (see Equation 27). As we can see from equations 41 and 42, wave packets above the cos-
+mic scale ω0 ∼ l are exponentially suppressed. Since only wave-packets of frequency ω0 ∼ l and below
+contribute signiﬁcantly to the spectrum, we will be assuming ω0 ∼ l for the rest of the computations.
+For such frequencies, we have v′
+0 = v0 , u′
+0 = u0 and the bounds of integration in equation 41 and 42
+correspond to a scrambling time vsc = l ln(lMp) in the future and usc = −l ln(lMp) in the past.
+4.2
+Early and late time bounds
+The number operators of equation 41 and 42 are simply the Planck distribution multiplied by the
+probabilities
+� vsc
+−∞ dvρ(ω0,v0)(v) ,
+� ∞
+usc duρ(ω0,u0)(u) of ﬁnding the particle described by the wave packet
+in the intervals v ∈ ]−∞, vsc] and u ∈ [usc, ∞[. Here, the wave-packets are found in the regions
+[v0 − ∆v, v0 + ∆v] , [u0 − ∆u, u0 + ∆u], where ∆v and ∆u are related to ∆ω via ∆u = ∆v = 1/∆ω.
+10
+
+I+
+I−
+v = ∞
+u = −∞
+r = 0
+vsc = l ln(lMp)
+2∆v
+I+
+I−
+v = ∞
+u = −∞
+r = 0
+usc = −l ln(lMp)
+2∆u
+Figure 2: Left and right-moving wave packets are peaked in a light-cone region of width 2∆v (left
+ﬁgure) centered around v0 or a light-cone region of width 2∆u centered around u0 (right ﬁgure)
+depending on the direction of motion. The expectation values of the number operators give us the
+Gibbons-Hawking spectrum as long as the light cone regions are found below vsc = l ln(lMp) or above
+usc = −l ln(lMp). When the regions are found above the vsc = l ln(lMp) or below usc = −l ln(lMp),
+the expectation values of the number operators become zero.
+When vsc ≥ v0 + ∆v or usc ≤ u0 − ∆u, the wave packets will almost always be found within the
+bounds of integration. In this case, the probabilities give us
+� vsc
+−∞
+dvρ(ω0,v0)(v) ≈ 1
+,
+� ∞
+usc
+duρ(ω0,u0)(u) ≈ 1 ,
+(43)
+and we recover usual Gibbons-Hawking spectrum. Conversely, when v0 − ∆v ≥ vsc or u0 + ∆u ≤ usc,
+the wave packets will almost always be found in the regions forbidden by the cutoﬀ ΛΩ, which are
+outside the bounds of integration. In this case, the probabilities give us
+� vsc
+−∞
+dvρ(ω0,v0)(v) ≈ 0
+,
+� ∞
+usc
+duρ(ω0,u0)(u) ≈ 0 ,
+(44)
+and the expectation values of the number operators become zero (see Figure 2). This shutdown can
+be illustrated by using the Gaussian wave packets of equation 29 as an example. In this case, the
+wave packet densities are given by
+ρ(ω0,v0)(v) =
+1
+√π∆ve− (v−v0)2
+∆v2
+,
+ρ(ω0,v0)(u) =
+1
+√π∆ue− (u−u0)2
+∆u2
+(45)
+From these densities, we obtain the following expectation values for the number operators.
+a ⟨0| ˜
+N(ω0,v0) |0⟩a = 1
+2
+1
+e2πlω0 − 1erfc
+�v0 − vsc
+∆v
+�
+(46)
+a ⟨0| N(ω0,u0) |0⟩a = 1
+2
+1
+e2πlω0 − 1erfc
+�
+−u0 − usc
+∆u
+�
+.
+(47)
+11
+
+Figure 3: Illustration of the shutdown in the Gaussian wave packets case for the late time bound
+on the left and the early time bound on the right. As soon as the conditions v0 + ∆v ≤ vsc and
+usc ≤ u0 − ∆u are no longer satisﬁed, the Gaussian wave packet ﬁnds itself in the region forbidden
+by the UV cutoﬀ and the spectrum becomes exponentially suppressed due to the cutoﬀ.
+Here, erfc(x) is the complementary error function. As expected, we recover the Gibbons-Hawking
+spectrum when vsc ≥ v0 + ∆v or usc ≤ u0 − ∆u. When v0 − ∆v ≥ vsc or u0 + ∆u ≤ usc, the
+spectrum becomes exponentially suppressed. Eventually, the spectrum becomes zero when v0 ≫ vsc
+and u0 ≪ usc.
+From the wave packet example, we can also see that the shut down is truly an eﬀect that arises
+when particles are localised in space. In the limits ∆v → ∞ and ∆u → ∞, where particles behave
+as plane waves, some particles will always be found the region allowed by the UV cutoﬀ, and the
+complementary error function erfc(x) will always be equal to one.
+In this case, we recover the
+Gibbons-Hawking spectrum of equations 15 and 21 up to an overall factor of 1/2. This extra factor
+of 1/2 arises as a consequence of imposing the UV cutoﬀ. If we take the limit Mp → ∞ in a way that
+vsc ≥ v0 + ∆v and usc ≤ u0 − ∆u are satisﬁed, then equations 15 and 21 are fully recovered.
+4.3
+Relation to the TCC bound
+As we have seen in the previous section, the spectrum of Gibbons-Hawking radiation is shutdown
+in the regions where v > vsc and u < usc when particles are described as wave packets. Since the
+shutdown arises as a consequence of imposing a UV cutoﬀ, one should not necessary view it as a
+physical eﬀect, but rather an indication that new physics must be taken into account in the regions
+where the cutoﬀ is in eﬀect. Using this interpretation, we conclude that eﬀective ﬁeld theory must
+breakdown in the regions v > vsc and u < usc.
+If we assume eﬀective ﬁeld theory stops being valid when v is above vsc and u is below usc, it is
+possible to recover a bound on the time scale of validity of eﬀective ﬁeld theory in de Sitter space. In
+terms of satic patch time t, the bounds v < vcs and u > ucs can be expressed as usc+r∗ < t < vsc−r∗.
+For a static observer sitting at the center of the static patch (r∗ = 0), this implies |t| > l ln(lMp) (See
+Fibure 4). In other words, the eﬀective ﬁeld theory description will only be valid for a time interval
+∆t = 2l ln(lMp) centered around t = 0, which agrees with the time-scale ∆t ∼ l ln(lMp) predicted by
+the TCC. In fact, it is exactly twice the TCC time scale.
+12
+
+sc
+Vo
+一
+erfc
+Usc
+0一 om
+sc
+erfc
+Au
+usc
+uo
+0vsc = l ln(lMp)
+usc = −l ln(lMp)
+∆t = 2lln(lMp)
+I+
+I−
+v = ∞
+u = −∞
+r = 0
+Figure 4: Assuming eﬀective ﬁeld theory is valid for when u > −l ln(lMp) and v < l ln(lMp), we
+obtain a bound |t| > l ln(lMp) on the validity of eﬀective ﬁeld theory for an observer at the center of
+the static patch (r∗ = 0). This region corresponds to time interval ∆t = 2l ln(lMp) centered around
+t = 0.
+The reason why we are obtaining twice the TCC time-scale seems to be because we worked
+under the assumption that space-time is eternally in a de Sitter phase. In this case, we have to
+consider bounds in the far future and the far past, which contribute to the time scale by an amount
+∆t = l ln(lMp) each. In realistic cosmologies, a matter or radiation dominated phase will precede
+the de Sitter phase. If we impose that the de Sitter phase begins at t = 0, then the future bound
+v < vsc imposes the constraint t < l ln(lMp) at r∗ = 0. In this case, we recover ∆t = l ln(lMp), which
+is exactly the amount of time predicted by the TCC. A similar argument can be made to constrain
+eternal inﬂation. If we assume eternal inﬂation ends at t = 0, then the past bound u > usc imposes
+the constraint t > −l ln(lMp) at r∗ = 0. In this case, we also recover ∆t = l ln(lMp), which is exactly
+the amount of time predicted by the TCC.
+5
+Conclusion and discussion
+We have computed the spectrum of Gibbons-Hawking radiation in the static patch of de Sitter space
+using two approaches. First, we used the standard eﬀective ﬁeld theory approach focusing on the
+propagation of Fourier modes. Second, we considered the propagation of particles described as wave
+packets. For this description, we found that the radiation shuts oﬀ beyond the TCC time scale if there
+is a fundamental ultraviolet cutoﬀ. In any case, the spectrum of this radiation cannot be computed
+reliably using the usual eﬀective ﬁeld theory techniques beyond the TCC time.
+Our result supports the Trans-Planckian Censorship Conjecture [8] which implies that the eﬀective
+13
+
+ﬁeld theory of ﬂuctuations about an inﬂationary background cosmology will break down beyond the
+TCC time scale [9].
+Our analysis is based on applying the techniques used for black holes in [1] to the case of cosmology.
+In the case of black holes, the eﬀective ﬁeld theory of ﬂuctuations breaks down beyond the scrambling
+time. Our analysis points out an interesting analogy between the scrambling time for black holes and
+the TCC time scale for an inﬂationary cosmology. Note that there is another interesting analogy
+between diﬀerent time scales: the Page time for black holes [22] plays an analogous role to the
+quantum break time for de Sitter [23], and equivalently to the time scale where the back-reaction of
+cosmological perturbations on the cosmological background becomes important (see [24] for original
+work and [25] for a review).
+The presence of the scrambling time indicates that an analysis beyond standard eﬀective ﬁeld
+theory of ﬂuctuations is required in order to solve the black hole information problem. In a similar
+way, our work lends support to the lesson from the TCC that a long lasting phase of accelerated
+expansion in cosmology can only be reliably analyzed if one goes beyond standard EFT. For attempts
+to construct models of inﬂation going beyond an EFT treatment see e.g. [23,26].
+Acknowledgements
+R.B. is grateful for hospitality by the Institute for Theoretical Physics and the Institute for Particle
+Physics and Astrophysics of the ETH Zurich during the period when some of the work on this project
+was carried out. S.L. is supported in part by FRQNT. The research at McGill is supported in part
+by funds from NSERC and from the Canada Research Chair program.
+References
+[1] P. M. Ho and H. Kawai, “UV And IR Eﬀects On Hawking Radiation,” [arXiv:2207.07122 [hep-
+th]].
+[2] S. W. Hawking, “Particle Creation by Black Holes,” Commun. Math. Phys. 43, 199-220 (1975)
+[erratum: Commun. Math. Phys. 46, 206 (1976)] doi:10.1007/BF02345020
+[3] G. W. Gibbons and S. W. Hawking, “Cosmological Event Horizons, Thermodynamics, and Par-
+ticle Creation,” Phys. Rev. D 15, 2738 (1977). doi:10.1103/PhysRevD.15.2738
+[4] V. Mukhanov and G. Chibisov, “Quantum Fluctuation And Nonsingular Universe. (In Russian),”
+JETP Lett. 33, 532 (1981) [Pisma Zh. Eksp. Teor. Fiz. 33, 549 (1981)].
+[5] A. A. Starobinsky, “Spectrum of relict gravitational radiation and the early state of the universe,”
+JETP Lett. 30, 682-685 (1979).
+14
+
+[6] A. H. Guth, “The Inﬂationary Universe: A Possible Solution to the Horizon and Flatness Prob-
+lems,” Phys. Rev. D 23, 347 (1981) [Adv. Ser. Astrophys. Cosmol. 3, 139 (1987)];
+R. Brout, F. Englert and E. Gunzig, “The Creation Of The Universe As A Quantum Phe-
+nomenon,” Annals Phys. 115, 78 (1978);
+A. A. Starobinsky, “A New Type Of Isotropic Cosmological Models Without Singularity,” Phys.
+Lett. B 91, 99 (1980);
+K. Sato, “First Order Phase Transition Of A Vacuum And Expansion Of The Universe,” Mon.
+Not. Roy. Astron. Soc. 195, 467 (1981).
+[7] J. Martin and R. H. Brandenberger, “The TransPlanckian problem of inﬂationary cosmology,”
+Phys. Rev. D 63, 123501 (2001) doi:10.1103/PhysRevD.63.123501 [arXiv:hep-th/0005209 [hep-
+th]].
+[8] A. Bedroya and C. Vafa, “Trans-Planckian Censorship and the Swampland,” JHEP 09, 123
+(2020) doi:10.1007/JHEP09(2020)123 [arXiv:1909.11063 [hep-th]].
+[9] A. Bedroya, R. Brandenberger, M. Loverde and C. Vafa, “Trans-Planckian Censorship and Inﬂa-
+tionary Cosmology,” Phys. Rev. D 101, no.10, 103502 (2020) doi:10.1103/PhysRevD.101.103502
+[arXiv:1909.11106 [hep-th]].
+[10] R. Brandenberger, “String Cosmology and the Breakdown of Local Eﬀective Field Theory,”
+[arXiv:2112.04082 [hep-th]];
+R. Brandenberger and V. Kamali, “Unitarity Problems for an Eﬀective Field Theory Description
+of Early Universe Cosmology,” [arXiv:2203.11548 [hep-th]].
+[11] S. Brahma, O. Alaryani and R. Brandenberger, “Entanglement Entropy of Cosmological
+Perturbations,” Phys. Rev. D 102, no. 4, 043529 (2020) doi:10.1103/PhysRevD.102.043529
+[arXiv:2005.09688 [hep-th]].
+[12] A. A. Starobinsky, “Robustness of the inﬂationary perturbation spectrum to transPlanckian
+physics,” Pisma Zh. Eksp. Teor. Fiz. 73, 415-418 (2001) doi:10.1134/1.1381588 [arXiv:astro-
+ph/0104043 [astro-ph]].
+[13] G. Dvali, A. Kehagias and A. Riotto, “Inﬂation and Decoupling,” [arXiv:2005.05146 [hep-th]].
+[14] C. P. Burgess, S. P. de Alwis and F. Quevedo, “Cosmological Trans-Planckian Conjectures are
+not Eﬀective,” JCAP 05, 037 (2021) doi:10.1088/1475-7516/2021/05/037 [arXiv:2011.03069 [hep-
+th]].
+[15] W. G. Unruh, “Sonic analog of black holes and the eﬀects of high frequencies on black hole evapo-
+ration,” Phys. Rev. D 51, 2827-2838 (1995) doi:10.1103/PhysRevD.51.2827 [arXiv:gr-qc/9409008
+[gr-qc]];
+15
+
+W. G. Unruh and R. Schutzhold, “On the universality of the Hawking eﬀect,” Phys. Rev. D 71,
+024028 (2005) doi:10.1103/PhysRevD.71.024028 [arXiv:gr-qc/0408009 [gr-qc]].
+[16] S. Corley and T. Jacobson, “Hawking spectrum and high frequency dispersion,” Phys. Rev. D
+54, 1568-1586 (1996) doi:10.1103/PhysRevD.54.1568 [arXiv:hep-th/9601073 [hep-th]].
+[17] S. B. Giddings, “(Non)perturbative gravity, nonlocality, and nice slices,” Phys. Rev. D 74, 106009
+(2006) doi:10.1103/PhysRevD.74.106009 [arXiv:hep-th/0606146 [hep-th]].
+[18] J. Preskill, “Do black holes destroy information?,” [arXiv:hep-th/9209058 [hep-th]];
+S. B. Giddings, “The Black hole information paradox,” [arXiv:hep-th/9508151 [hep-th]].
+[19] D. N. Page, “Time Dependence of Hawking Radiation Entropy,” JCAP 09, 028 (2013)
+doi:10.1088/1475-7516/2013/09/028 [arXiv:1301.4995 [hep-th]].
+[20] R. Brout, S. Massar, R. Parentani and P. Spindel, “A Primer for black hole quantum physics,”
+Phys. Rept. 260, 329-454 (1995) doi:10.1016/0370-1573(95)00008-5 [arXiv:0710.4345 [gr-qc]].
+[21] M. Spradlin, A. Strominger and A. Volovich, “Les Houches lectures on de Sitter space,”
+[arXiv:hep-th/0110007 [hep-th]].
+[22] Y. Sekino and L. Susskind, “Fast Scramblers,” JHEP 10, 065 (2008) doi:10.1088/1126-
+6708/2008/10/065 [arXiv:0808.2096 [hep-th]].
+[23] G. Dvali, C. Gomez and S. Zell, “Quantum Break-Time of de Sitter,” JCAP 06, 028 (2017)
+doi:10.1088/1475-7516/2017/06/028 [arXiv:1701.08776 [hep-th]];
+G. Dvali, C. Gomez and S. Zell, “Quantum Breaking Bound on de Sitter and Swampland,”
+Fortsch. Phys. 67, no.1-2, 1800094 (2019) doi:10.1002/prop.201800094 [arXiv:1810.11002 [hep-
+th]].
+[24] V. F. Mukhanov,
+L. R. W. Abramo and R. H. Brandenberger,
+“On the Back re-
+action problem for gravitational perturbations,” Phys. Rev. Lett. 78, 1624-1627 (1997)
+doi:10.1103/PhysRevLett.78.1624 [arXiv:gr-qc/9609026 [gr-qc]];
+L. R. W. Abramo,
+R. H. Brandenberger and V. F. Mukhanov,
+“The Energy - mo-
+mentum
+tensor
+for
+cosmological
+perturbations,”
+Phys.
+Rev.
+D
+56,
+3248-3257
+(1997)
+doi:10.1103/PhysRevD.56.3248 [arXiv:gr-qc/9704037 [gr-qc]].
+[25] R. H. Brandenberger, “Back reaction of cosmological perturbations and the cosmological constant
+problem,” [arXiv:hep-th/0210165 [hep-th]].
+[26] S. Brahma, K. Dasgupta and R. Tatar, “Four-dimensional de Sitter space is a Glauber-Sudarshan
+state in string theory,” JHEP 07, 114 (2021) doi:10.1007/JHEP07(2021)114 [arXiv:2007.00786
+[hep-th]];
+S. Brahma, K. Dasgupta and R. Tatar, “de Sitter Space as a Glauber-Sudarshan State,” JHEP
+16
+
+02, 104 (2021) doi:10.1007/JHEP02(2021)104 [arXiv:2007.11611 [hep-th]];
+H. Bernardo, S. Brahma, K. Dasgupta, M. M. Faruk and R. Tatar, “de Sitter Space as a Glauber-
+Sudarshan State: II,” Fortsch. Phys. 69, no.11-12, 2100131 (2021) doi:10.1002/prop.202100131
+[arXiv:2108.08365 [hep-th]];
+S. Brahma, K. Dasgupta, M. M. Faruk, B. Kulinich, V. Meruliya, B. Pym and R. Tatar,
+“Resurgence of a de Sitter Glauber-Sudarshan State: Nodal Diagrams and Borel Resummation,”
+[arXiv:2211.09181 [hep-th]].
+17
+
diff --git a/bdE0T4oBgHgl3EQf4wIO/content/tmp_files/load_file.txt b/bdE0T4oBgHgl3EQf4wIO/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..ff260f104550572c8934297a7056339259a83eaf
--- /dev/null
+++ b/bdE0T4oBgHgl3EQf4wIO/content/tmp_files/load_file.txt
@@ -0,0 +1,626 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf,len=625
+page_content='TCC bounds on the static patch of de Sitter space  Matt´eo Blamart∗, Samuel Laliberte† and Robert Brandenberger‡  Department of Physics, McGill University, Montr´eal, QC, H3A 2T8, Canada  Abstract  Recently, Pei-Ming Ho and Hikaru Kawai [1] have argued that treating particles as wave packets  can lead to a shutdown of Hawking radiation at late times near the horizon of black holes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' This  shutdown arises from viewing quantum ﬁeld theory near the black hole horizon as an eﬀective ﬁeld  theory, and imposing an appropriate UV cutoﬀ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' We show that this eﬀect is also present in the  static patch of de Sitter space, leading to a shutdown of Gibbons-Hawking radiation near the de  Sitter horizon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' Assuming this eﬀect is due to the breakdown of eﬀective ﬁeld theory, we obtain a  bound t ≲ H−1 ln(H−1MP ) on the time scale of validity of eﬀective ﬁeld theory in de Sitter space,  which matches with the predictions of the Trans-Planckian Censorship Conjecture.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='  Contents  1  Introduction  1  2  Review of Gibbons-Hawking radiation in de Sitter space  3  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='1  UV cutoﬀ, blue shift and scrambling time .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
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+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
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+page_content='  6  3  Wave packets in de Sitter space  7  4  Shutdown of Gibbons-Hawking radiation in de Sitter space  9  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='1  Late-time and early-time spectrum .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
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+page_content='  9  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='2  Early and late time bounds .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
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+page_content='  10  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='3  Relation to the TCC bound .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
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+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='  12  5  Conclusion and discussion  13  1  Introduction  It is well known that, calculated an eﬀective ﬁeld theory (EFT) in the semiclassical approximation,  black holes radiate thermally [2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' Speciﬁcally, if matter is treated as a scalar ﬁeld, then an observer  at late times and far from the horizon will measure a thermal ﬂux of scalar ﬁeld quanta if the initial  ∗e-mail address: matteo.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='blamart@mail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='mcgill.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='ca  †e-mail address: samuel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='laliberte@mail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='mcgill.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='ca  ‡e-mail address: rhb@physics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='mcgill.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='ca  1  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='02741v1  [hep-th]  6 Jan 2023  state is prepared as an appropriate vacuum state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' In a similar way, observers at a point x in de  Sitter space will measure a thermal ﬂux of scalar ﬁeld quanta if the initial state is set up as a local  vacuum state a Hubble horizon distance away from x [3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' It is these ﬂuctuations which are postulated  to be the origin of density perturbations [4] and gravitational waves [5] in an inﬂationary universe  scenario [6].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='  In the context of inﬂationary cosmology, it was argued in [7] that there is a “trans-Planckian  problem” for cosmological ﬂuctuations if the period of inﬂation is long since in that case the physical  wavelength of the ﬂuctuations observed today was smaller than the Planck length at the beginning  of inﬂation and thus in a region where the eﬀective ﬁeld theory of ﬂuctuations becomes questionable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='  Based on these considerations, in [8] a “Trans-Planckian Censorship Conjecture” (TCC) was put  forward according to which in no eﬀective ﬁeld theory emanating from superstring theory modes  which initially were trans-Planckian could ever have exited the Hubble horizon, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='  a(tR)  a(ti) lpl < H−1(tR) ,  (1)  for any initial time ti and ﬁnal time tR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' In the above, a(t) is the cosmological scale factor, and H(t)  is the Hubble expansion rate at time t (whose inverse is the Hubble horizon).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' As discussed in [9],  the TCC severely constrains viable inﬂationary models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' In particular, canonical single scalar ﬁeld  inﬂation models with an energy scale η > 109GeV are ruled out.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' As argued in [10], the TCC can be  argued for independently of superstring theory, making use of unitarity arguments and consistency  with the second law of thermodynamics (see [11]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='  On the other hand, there have been arguments to the eﬀect that there is no trans-Planckian  problem for inﬂationary cosmology (see e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' [12–14]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' Based on the Einstein equivalence principle it  is argued that on microscopic scales (in the context of cosmology this means on length scales much  smaller than the Hubble radius) physics must reduce to that in Minkowski space-time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' From the  point of view of quantum gravity, however, this argument is problematic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' Nevertheless, it would be  useful to have more independent support for the TCC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='  In the case of black holes, one can argue that a similar trans-Planckian problem arises (see  e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' [15, 16] for some early work).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='  From the point of view of a semiclassical EFT analysis, the  Hawking radiation [2] which an observer far outside the black hole horizon observes at a frequency  ω (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='  the frequency corresponding to the Hawking temperature) observes is associated with a  blueshifted frequency Ω which becomes larger than the Planck scale suﬃciently close to the black  hole horizon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' Hence, one may argue that the semi-classical analysis must break down.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='  Once again, it can be argued that there is no problem for the semiclassical description of Hawking  radiation since there is a “nice slice”, a spatial hypersurface from whose point of view there is no  divergence of the frequency close to the horizon (see e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' [17]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' But this does not resolve the famous  black hole information loss problem (see e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' [18] for early discussions of this problem) associated  with Hawking radiation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' It has been argued [19] that the semiclassical analysis must break down at  the “Page time”, the time when the entropy of thermal Hawking radiation reaches half of the initial  2  entropy of the black hole (as determined by the area of the initial black hole horizon).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='  In recent work, Pei-Ming Ho and Hikaru Kawai [1] considered the propagation of wave packets in  a black hole background rather than considering only plane waves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' Working in the context of eﬀective  ﬁeld theory and imposing a UV cutoﬀ, they ﬁnd that Hawking radiation shuts oﬀ at the scrambling  time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' More generally, they ﬁnd that the spectrum of Hawking radiation after the scrambling time  depends on physics which cannot be described in terms of the EFT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='  We apply a similar analysis to the static patch dS, and ﬁnd that Gibbons-Hawking radiation shuts  oﬀ after the TCC time scale (if there is an ultraviolet cutoﬀ), and more generally cannot be described  by the EFT beyond that time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' Besides the intrinsic interest of this result, it points to an intriguing  analogy between the black hole scrambling time and the cosmological TCC time scale.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='  This document is structured as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' In section 2, we review Gibbons-Hawking radiation in de  Sitter space by using a conventional approach, where particles on a curved background behave like  plane waves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' In section 3, we deﬁne semi-classical wave packets and describe how they can arise as  ﬂuctuations of quantum ﬁeld ﬁelds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' Finally, in section 4, we show how Gibbons-Hawking radiation  coming from particles that behave as semi-classical wave packets becomes sensitive to UV cutoﬀs  after a scrambling time tsc = H−1 ln(H−1Mp), leading to a breakdown of eﬀective ﬁeld theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='  2  Review of Gibbons-Hawking radiation in de Sitter space  To see how thermal radiation can be shut down after a ﬁnite amount of time, let us start by reviewing  the derivation of Gibbons-Hawking radiation when particles are treated as plane waves in a curved  background.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' We will roughly follow the approach presented in [20] and work in the static patch of de  Sitter space where the metric takes the form  ds2 = −f(r)dt2 + dr2  f(r) + r2dΩ2  2  ,  f(r) = 1 − r2/l2 ,  (2)  where l is the radius of the de Sitter horizon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' This metric can be rewritten in the more convenient  Eddington-Finkelstein frame (see [21] for a review) where the metric takes the form  ds2 = −f(u, v)dudv + r(u, v)2dΩ2  2 ,  (3)  by deﬁning a radial coordinates r∗ = Arctanh (r/l) and light cone-coordinates u = t−r∗ and v = t+r∗.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='  Another useful frame is the Kruskal coordinate system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' One can move from the Eddington-Finkelstein  frame to the Kruskal frame using the change of coordinates  U(u) = leu/l  ,  V (v) = −le−v/l ,  (4)  in which case the space-time metric then takes the form  ds2 ≈ −4dUdV + r2(U, V )dΩ2  2 ,  (5)  3  in the r ≈ l limit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' A useful feature of the Kruskal coordinate system is that space-time looks ﬂat in the  near horizon limit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' In comparison, the Eddington-Finkelstein coordinates look like those of an acceler-  ated observer in the ”ﬂat” Kruskal background.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' Consequently, one can derive Gibbons-Hawking radi-  ation in de Sitter space by computing the spectrum of particles observed by an Eddington-Finkelstein  observer in the Kruskal vacuum in the near horizon limit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='  To do this, let us consider s-wave modes of a massless scalar ﬁeld φ in the static patch of de  Sitter space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' The mode decomposition of φ for s-wave modes in Kruskal and Eddington-Finkelstein  coordinates can be written as  φ =  � ∞  0  dΩ  √  4πΩ  �  aΩe−iΩU + a†  ΩeiΩU + ˜aΩe−iΩV + ˜a†  ΩeiΩV �  (6)  =  � ∞  0  dω  √  4πω  �  bωe−iωu + b†  ωeiωu + ˜bωe−iωv + ˜b†  ωeiωv�  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='  (7)  Here, aΩ, ˜aΩ and bω,˜bω are annihilation operators deﬁned by  aΩ|0⟩a = ˜aΩ|0⟩a = 0  ,  bω|0⟩b = ˜bω|0⟩b = 0  (8)  where |0⟩a is the Kruskal coordinates vacuum state, and |0⟩b is the Eddington-Finkelstein coordinates  vacuum state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' Similar creation operators can be obtained by taking the hermitian conjugate of the  annihilation operators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' The creation-annihilation of the two frames can be related by the Bogoliubov  transformations  bω =  � ∞  0  dΩ  �  αωΩaΩ + βωΩa†  Ω  �  ˜bω =  � ∞  0  dΩ  �  ˜αωΩ˜aΩ + ˜βωΩ˜a†  Ω  �  (9)  b†  ω =  � ∞  0  dΩ  �  α∗  ωΩa†  Ω + β∗  ωΩaΩ  �  ˜b†  ω =  � ∞  0  dΩ  �  ˜α∗  ωΩ˜a†  Ω + ˜β∗  ωΩ˜aΩ  �  ,  (10)  for appropriate Bogoliubov coeﬃcients αωΩ, βωΩ and ˜αωΩ, ˜βωΩ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='  In the Eddington-Finklestein and Kruskal coordinate systems, the r ≈ l regime corresponds to  two separate limits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' The ﬁrst one, v → ∞ or V → 0, is related to the horizon in the far future.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' In  this case, Gibbons-Hawking radiation can be obtained from the left-moving modes of the ﬁeld (see  Figure 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' The second limit, u → ∞ or U → 0, is related to the horizon in the far past.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' In this case,  Gibbons-Hawking radiation can be obtained from the right-moving modes of the ﬁeld.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' Both limits  can be taken independently and yield the same spectrum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='  Let us ﬁrst bring our attention to the left moving modes, which are relevant for Gibbons-Hawking  radiation near the future horizon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' The Bogoliubov coeﬃcients for these modes can be derived from  the normalized left-moving eigenfunctions ˜Gω(v) and ˜HΩ(V ) of the Laplacian operator in Eddington-  Finkelstein and Kruskal coordinates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' These eigenfunctions are given by  ˜Gω(v) = e−iωv  √  4πw  ,  ˜HΩ(V ) = e−iΩV  √  4πΩ  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='  (11)  4  ˜  Gω(v)  I+  I−  v = ∞  u = −∞  r = 0  Gω(u)  I+  I−  v = ∞  u = −∞  r = 0  Figure 1: Space-time diagram of de Sitter space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' Left-moving modes contribute to Gibbons-Hawking  radiation near the future horizon (left) and right-moving modes contribute to Gibbons-Hawking  radiation near the past horizon (right).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' Here, left-moving means that the modes are moving towards  the center of the static patch (r = 0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' Similarly, right-moving means that the modes are moving  away from the center of the static patch (not to be confused with the directions of the arrows on the  ﬁgure).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='  We obtain1  ˜αωΩ = i  � 0  −∞  dV ˜G∗  ω(v(V ))←→  ∂ V ˜HΩ(V ) = l  2π  �ω  Ω (lΩ)ilω eπlω/2Γ(−ilω)  (12)  ˜βωΩ = −i  � 0  −∞  dV ˜Gω(v(V ))←→  ∂ V ˜HΩ(V ) = l  2π  �ω  Ω (lΩ)−ilω e−πlω/2Γ(ilω) ,  (13)  where Γ(z) is the gamma function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' Using the Bogoliubov transformations above, we can compute  the number of particles an Eddington-Finklestein observer perceives in the Kruskal vacuum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' This  number of particles can be obtained from the expectation value of the number operator ˜nω = ˜b†  ω˜bω in  the Kruskal vacuum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' For an observer near the future horizon, we obtain  a⟨0|˜b†  ω1˜bω2|0⟩a =  � ∞  0  dΩ˜βω1Ω ˜β∗  ω2Ω  (14)  =  1  e2πlω1 − 1δ(ω1 − ω2) ,  (15)  which is the expected spectrum of Gibbons-Hawking radiation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' Here, we made use of the identity  |e−πlω/2Γ(±ilω)|2 = 2π  lω  �  1  e2πlω − 1  �  (16)  1Here, we will be using the convention f←→  ∂ xg = f∂xg − g∂xf for the double arrow derivative.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='  5  to obtain the result above.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' A similar spectrum can be obtained from the right-moving modes, which  are relevant for Gibbons-Hawking radiation near the past horizon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' In this case, the normalized wave  functions are  Gω(u) = e−iωu  √  4πw  ,  HΩ(U) = e−iΩU  √  4πΩ  ,  (17)  and the associated Bogoliubov transformations are  αωΩ = i  � ∞  0  dUG∗  ω(u(U))←→  ∂ UHΩ(U) = l  2π  �ω  Ω (lΩ)−ilω eπlω/2Γ(ilω)  (18)  βωΩ = −i  � ∞  0  dUGω(u(U))←→  ∂ UHΩ(U) = l  2π  �ω  Ω (lΩ)ilω e−πlω/2Γ(−ilω) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='  (19)  By computing the expectation value of the number operator nω = b†  ωbω in the Kruskal vacuum, we  obtain the same result as for the left moving modes:  a⟨0|b†  ω1bω2|0⟩a =  � ∞  0  dΩβω1Ωβ∗  ω2Ω  (20)  =  1  e2πlω1 − 1δ(ω1 − ω2) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='  (21)  Consequently, at all times, a static observer in de Sitter space will perceive a thermal bath of particles  with a temperature given by T = (2πl)−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='1  UV cutoﬀ, blue shift and scrambling time  At ﬁrst glance, the thermal spectrum of Equation 15 and 21 does not seem to change in the UV limit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='  However, we must remember that physics at low energies is described by an eﬀective ﬁeld theory and  cannot be trusted beyond the Planck scale, where quantum gravity corrections become important.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' To  take this into account, let us impose a cutoﬀ ΛΩ ∼ Mp on the frequency Ω.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' When ΛΩ ≫ H (H = l−1  is the Hubble expansion rate), Equations 15 and 21 are still approximately valid.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' However, there are  two regions of the static patches where we expect that new physics might be important.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' Given our  cutoﬀ, these are the regions near the future and past horizon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='  To see why this is the case, let us study how one particle states in Eddington-Finklestein co-  ordinates behave in the Kruskal frame.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' In the Eddington-Finklestein frame, the free particle wave  functions are deﬁned by  ψR(u) = b⟨0|φ(u, v)b†  ω|0⟩b = e−iωu  √  4πw  ,  ψL(v) = b⟨0|φ(u, v)˜b†  ω|0⟩b = e−iωv  √  4πw  (22)  where ψR(u) describes a right moving particle and ψL(v) a left moving particle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' In the Eddington-  Finklestein frame, ψR(u) and ψL(v) are eigenfunctions of the momentum operators pu = i d  du and  pv = i d  dv with an eigenvalue given by the frequency ω associated to each wave function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' Similarly,  ψR(u) and ψL(v) are also eigenfunctions of the momentum operators pU = i d  dU and pV = i d  dV in  Kruskal coordinates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' Acting with these operators, we obtain  idψR(u)  dU  = ω du  dU ψR(u)  ,  idψL(v)  dV  = ω dv  dV ψL(v) ,  (23)  6  from which we read oﬀ the frequency eigenvalues  Ω = dv  dV ω = ev/lω  ,  Ω = du  dU ω = e−u/lω .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='  (24)  From the results above, we conclude that the Kruskal frame frequency associated to Eddington-  Finklestein particles is blue-shifted close the future and past horizon (v → ∞ and u → −∞ limits).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='  In these, limits we have to worry about this frequency being blueshifted above our UV cutoﬀ ΛΩ ∼  Mp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' As an example, let us consider Eddington-Finklestein particles with frequencies on the Hubble  scale (ω ∼ H), which are those that contribute most signiﬁcantly to Gibbons-Hawking radiation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' For  such particles, the blueshifted frequency exceeds the UV cutoﬀ when v ≫ l ln(lMp) for a left-moving  particle or u ≪ −l ln(lMp) for a right-moving particle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' For an observer at the center of the static patch  (r = 0), these bounds correspond precisely to a scrambling time tsc = l ln(lMp) in the future and in  the past.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' After this amount of time, we expect UV eﬀects to become relevant in Gibbons-Hawking  radiation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='  From what we have seen so far, the Gibbons-Hawking spectrum coming from particles that behave  as plane waves does not seem sensitive to the eﬀects above.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' We will see that this is a result of particles  being described as plane waves as opposed to localized wave packets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' The key diﬀerence between the  two descriptions is that wave-packets are localised within a left or right-moving patch of width ∆v or  ∆u depending on the direction of motion of the wave packet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' In comparison, plane waves are fully  non-local and span the whole static patch at all times.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' Because the wave-packets are local, they are  sensitive to the region of the static patch where they propagate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' Hence, they will be sensitive to the  UV cutoﬀ in the blue-shifted regions v ≫ l ln(lMp) and u ≪ −l ln(lMp).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' In the next sections, we will  see that this sensitivity leads to a shutdown of Gibbons-Hawking radiation when v ≫ l ln(lMp) or  u ≪ −l ln(lMp).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='  3  Wave packets in de Sitter space  Let us now turn our attention to the case where particles are described by semi-classical wave packets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='  We will be interested in left-moving wave packets ψ(w0,v0)(v) and right-moving wave packets ψ(w0,u0)(u)  of the form  ψ(w0,v0)(v) =  � ∞  0  dω  √  4πwfw0(ω)e−iω(v−v0)  ,  ψ(w0,u0)(u) =  � ∞  0  dω  √  4πwfw0(ω)e−iω(u−u0) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='  (25)  Here, we will consider frequency distributions fω0(ω) that are peaked around a central frequency ω0,  and vanishing a distance ∆ω from ω0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' This way, the left and right moving wave packets will become  centered around v0 and u0 respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' For the wave packets to be properly normalized, we will  impose the normalisation condition  � ∞  −∞  dvρ(ω0,v0)(v) =  � ∞  0  dω|fω0(ω)|2 = 1 ,  (26)  7  where  ρ(ω0,u0)(v) = iψ∗  (w0,v0)  ←→  ∂ vψ(w0,v0)  (27)  is the relativistic density of the wave packet ψ(w0,v0)(v).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' (Here, we used the left-moving wave packet  for this deﬁnition, but a similar condition is true for the right-moving wave packet as well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=') One of the  most simple frequency distributions which satisﬁes the conditions above is the Gaussian distribution  fω0(ω) =  �  ω  2πω0∆ωe− (ω−ω0)2  2∆ω2  ,  (28)  associated to the left and right-moving Gaussian wave packets  ψ(w0,v0)(v) ≈  �  ∆ω  2√πω0  e− ∆ω2(v−v0)  2  −iω0(v−v0)  ,  ψ(w0,u0)(u) ≈  �  ∆ω  2√πω0  e− ∆ω2(u−u0)  2  −iω0(u−u0) , (29)  in the limit where ∆ω ≪ ω0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' The wave functions above saturate the Heisenberg uncertainty bound.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='  Hence, we should view particles described by ψ(w0,v0)(v) and ψ(w0,u0)(u) as free particles in their  semi-classical limits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='  Such particles can be created in quantum ﬁeld theory by appropriately modifying the raising and  lowering operators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' Using b†  ω,˜b†  ω and the frequency distribution fω0(ω) of Equation 28, we can deﬁne  creation operators ˜b†  (ω0,v0), b†  (ω0,u0) associated to the Gaussian wave packets ψ(w0,v0)(v) and ψ(w0,u0)(u).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='  Such creation operators are given by  ˜b†  (ω0,v0) =  � ∞  0  dωfω0(ω)eiωv0˜b†  ω  ,  b†  (ω0,u0) =  � ∞  0  dωfω0(ω)eiωu0b†  ω .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='  (30)  Similar annihilation operators can be obtained by taking the hermitian conjugate of the operators  above.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' One can check that this creation operator lets us create particles with the wave function of  Equation 25 by evaluating the wave function of a one-particle state in quantum ﬁeld theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' For  the left-moving particle, the wave function can be obtained by evaluating the vacuum expectation  value of φ(v)˜b†  (ω0,v0) in the Eddington-Finkelstein vacuum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' Similarly, the wave function of the right  moving particle can be obtained by computing the Eddington-Finkelstein vacuum expectation value  of φ(u)b†  (ω0,u0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' This gives us  b⟨0|φ(v)˜b†  (ω0,v0)|0⟩b = ψ(ω0,v0)(v)  ,  b⟨0|φ(u)b†  (ω0,u0)|0⟩b = ψ(ω0,u0)(u) ,  (31)  as expected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' The fully quantum limit of this semi-classical particle can be recovered by letting the  ∆ω → 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' In this case, we recover the quantum mechanical wave function of a free particle that  behaves as a plane wave2:  ψ(w0,v0)(v) ≈ e−iω0(v−v0)  √4πω0  ,  ψ(w0,u0)(u) ≈ e−iω0(u−u0)  √4πω0  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='  (32)  2It’s a bit tricky to see this from Equation 29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' However, we can see that this is true when taking the ∆ω → 0  limit in Equation 28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' In this limit, we obtain fω0(ω) ≈  �  ω/ω0δ(w − w0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' Evaluating Equation 25 using this frequency  distribution, we obtain the desired result.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='  8  Using ˜b†  (ω0,v0), b†  (ω0,u0) and the corresponding annihilation operators, it is possible to compute the  spectrum of Gibbons-Hawking radiation associated to a thermal bath of semi-classical particles in  the Kruskal vacuum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' This can be done by deﬁning number operators ˜  N(ω0,v0) = ˜b†  (ω0,v0)˜b(ω0,v0) and  N(ω0,u0) = b†  (ω0,u0)b(ω0,u0) associated to the left and right-moving wave packets, and computing their  expectation values in the Kruskal vacuum in the same way we did in section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' As we will see in the  next section, the spectrum we obtain will be similar to our previous result, but also sensitive to UV  cutoﬀs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='  4  Shutdown of Gibbons-Hawking radiation in de Sitter space  We now provide a derivation of Gibbons-Hawking radiation in de Sitter space in the case where  particles are described as wave packets rather than plane waves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' In this case, the Gibbons-Hawking  spectrum will vary depending on the location v0 or u0 of the contributing wave packets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='  When  v0 ≪ l ln(lMp) and u0 ≫ −l ln(lMp), the spectrum will remain approximately the same as in equation  15 and 21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' Conversely, the spectrum will shut down in the cases where v0 ≫ l ln(lMp) and u0 ≪  −l ln(lMp).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' Since Gibbons-Hawking radiation becomes sensitive to the UV cutoﬀ with the localized  wave packet formalism, v0 ≈ l ln(lMp) and u0 ≈ −l ln(lMp) give bounds on the validity of eﬀective  ﬁeld theory near the future and past horizons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' We will see that these bounds match the predictions  from the TCC for an observer at the center of the static patch (r∗ = 0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='1  Late-time and early-time spectrum  Following the same steps as in section 2, let us compute the expectation value of the number operators  ˜  N(ω0,v0) and N(ω0,u0) in the Kruskal vacuum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' The ﬁrst step is to substitute the raising operators of  equation 30 and the corresponding annihiliation operators in the deﬁnition of the number operators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='  We obtain the following expectation values:  a ⟨0| ˜  N(ω0,v0) |0⟩a =  � ∞  0  dω1  � ∞  0  dω2fω0(ω1)f∗  ω0(ω2)ei(ω1−ω2)v0  � ΛΩ  0  dΩ˜β∗  ω1Ω ˜βω2Ω ,  (33)  a ⟨0| N(ω0,u0) |0⟩a =  � ∞  0  dω1  � ∞  0  dω2fω0(ω1)f∗  ω0(ω2)ei(ω1−ω2)u0  � ΛΩ  0  dΩβ∗  ω1Ωβω2Ω .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='  (34)  Here, we have imposed the UV cutoﬀ ΛΩ = Mp on the energy scale Ω in order to remove UV eﬀects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='  Moreover, βωΩ and ˜βωΩ are given by 19 and 13 respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' To see the impacts of the UV cutoﬀ on  the contribution of wave packets in diﬀerent regions of the static patch, we will then make the change  of variables Ω = ω0ev/l for the left-moving modes and Ω = ω0e−u/l for the right-moving modes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' These  correspond to the blue-shifted frequency of left or right-moving wave packet of central frequency ω0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='  9  Following the change of variables, the expectation value of the number operators becomes  a ⟨0| ˜  N(ω0,v0) |0⟩a =  � l log(ΛΩ/ω0)  −∞  dv  l | ˜Fω0(v − v0)|2 ,  (35)  a ⟨0| N(ω0,u0) |0⟩a =  � ∞  −l log(ΛΩ/ω0)  du  l |Fω0(u − u0)|2 ,  (36)  where ˜Fω0 and Fω0 are given by  ˜Fω0(v − v0) = l  2π  � ∞  0  dωfω0(ω)e−iω(v−v′  0)√ωe−πωl/2Γ(ilω) ,  (37)  Fω0(u − u0) = l  2π  � ∞  0  dωfω0(ω)e−iω(u−u′  0)√ωe−πωl/2Γ(−ilω) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='  (38)  Here, the centers v′  0 and u′  0 for each distribution are given by v′  0 = v0 − l ln(lω0) and u′  0 = u0 +  l ln(lω0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' When the frequency distribution fω0(ω) is suﬃciently narrow, it is possible to approximate  the expressions above as  ˜Fω0(v − v0) ≈  l  √πω0e−πω0l/2Γ(ilω0)ψω0,v′  0(v) ,  (39)  ˜Fω0(u − u0) ≈  l  √πω0e−πω0l/2Γ(−ilω0)ψω0,u′  0(u) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='  (40)  For frequencies on cosmic scales ω0 ∼ l, the approximation above holds if ∆ω ≪ ω0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' Using the  expressions above and the identity (16), we can ﬁnally express a ⟨0| ˜  N(ω0,v′  0) |0⟩a and a ⟨0| N(ω0,u′  0) |0⟩a  as  a ⟨0| ˜  N(ω0,v0) |0⟩a ≈  1  e2πlω0 − 1  �� l ln(ΛΩ/ω0)  −∞  dvρ(ω0,v′  0)(v)  �  ,  (41)  a ⟨0| N(ω0,u0) |0⟩a ≈  1  e2πlω0 − 1  �� ∞  −l ln(lΛΩ/ω0)  duρ(ω0,u′  0)(u)  �  ,  (42)  where ρ(ω0,v′  0)(v) and ρ(ω0,u′  0)(u) are the relativistic density of the wave-packet ψ(ω0, v′  0)(v) and  ψ(ω0, u′  0)(u) (see Equation 27).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' As we can see from equations 41 and 42, wave packets above the cos-  mic scale ω0 ∼ l are exponentially suppressed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' Since only wave-packets of frequency ω0 ∼ l and below  contribute signiﬁcantly to the spectrum, we will be assuming ω0 ∼ l for the rest of the computations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='  For such frequencies, we have v′  0 = v0 , u′  0 = u0 and the bounds of integration in equation 41 and 42  correspond to a scrambling time vsc = l ln(lMp) in the future and usc = −l ln(lMp) in the past.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='2  Early and late time bounds  The number operators of equation 41 and 42 are simply the Planck distribution multiplied by the  probabilities  � vsc  −∞ dvρ(ω0,v0)(v) ,  � ∞  usc duρ(ω0,u0)(u) of ﬁnding the particle described by the wave packet  in the intervals v ∈ ]−∞, vsc] and u ∈ [usc, ∞[.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' Here, the wave-packets are found in the regions  [v0 − ∆v, v0 + ∆v] , [u0 − ∆u, u0 + ∆u], where ∆v and ∆u are related to ∆ω via ∆u = ∆v = 1/∆ω.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='  10  I+  I−  v = ∞  u = −∞  r = 0  vsc = l ln(lMp)  2∆v  I+  I−  v = ∞  u = −∞  r = 0  usc = −l ln(lMp)  2∆u  Figure 2: Left and right-moving wave packets are peaked in a light-cone region of width 2∆v (left  ﬁgure) centered around v0 or a light-cone region of width 2∆u centered around u0 (right ﬁgure)  depending on the direction of motion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' The expectation values of the number operators give us the  Gibbons-Hawking spectrum as long as the light cone regions are found below vsc = l ln(lMp) or above  usc = −l ln(lMp).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' When the regions are found above the vsc = l ln(lMp) or below usc = −l ln(lMp),  the expectation values of the number operators become zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='  When vsc ≥ v0 + ∆v or usc ≤ u0 − ∆u, the wave packets will almost always be found within the  bounds of integration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' In this case, the probabilities give us  � vsc  −∞  dvρ(ω0,v0)(v) ≈ 1  ,  � ∞  usc  duρ(ω0,u0)(u) ≈ 1 ,  (43)  and we recover usual Gibbons-Hawking spectrum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' Conversely, when v0 − ∆v ≥ vsc or u0 + ∆u ≤ usc,  the wave packets will almost always be found in the regions forbidden by the cutoﬀ ΛΩ, which are  outside the bounds of integration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' In this case, the probabilities give us  � vsc  −∞  dvρ(ω0,v0)(v) ≈ 0  ,  � ∞  usc  duρ(ω0,u0)(u) ≈ 0 ,  (44)  and the expectation values of the number operators become zero (see Figure 2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' This shutdown can  be illustrated by using the Gaussian wave packets of equation 29 as an example.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' In this case, the  wave packet densities are given by  ρ(ω0,v0)(v) =  1  √π∆ve− (v−v0)2  ∆v2  ,  ρ(ω0,v0)(u) =  1  √π∆ue− (u−u0)2  ∆u2  (45)  From these densities, we obtain the following expectation values for the number operators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='  a ⟨0| ˜  N(ω0,v0) |0⟩a = 1  2  1  e2πlω0 − 1erfc  �v0 − vsc  ∆v  �  (46)  a ⟨0| N(ω0,u0) |0⟩a = 1  2  1  e2πlω0 − 1erfc  �  −u0 − usc  ∆u  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='  (47)  11  Figure 3: Illustration of the shutdown in the Gaussian wave packets case for the late time bound  on the left and the early time bound on the right.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' As soon as the conditions v0 + ∆v ≤ vsc and  usc ≤ u0 − ∆u are no longer satisﬁed, the Gaussian wave packet ﬁnds itself in the region forbidden  by the UV cutoﬀ and the spectrum becomes exponentially suppressed due to the cutoﬀ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='  Here, erfc(x) is the complementary error function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' As expected, we recover the Gibbons-Hawking  spectrum when vsc ≥ v0 + ∆v or usc ≤ u0 − ∆u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' When v0 − ∆v ≥ vsc or u0 + ∆u ≤ usc, the  spectrum becomes exponentially suppressed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' Eventually, the spectrum becomes zero when v0 ≫ vsc  and u0 ≪ usc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='  From the wave packet example, we can also see that the shut down is truly an eﬀect that arises  when particles are localised in space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' In the limits ∆v → ∞ and ∆u → ∞, where particles behave  as plane waves, some particles will always be found the region allowed by the UV cutoﬀ, and the  complementary error function erfc(x) will always be equal to one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='  In this case, we recover the  Gibbons-Hawking spectrum of equations 15 and 21 up to an overall factor of 1/2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' This extra factor  of 1/2 arises as a consequence of imposing the UV cutoﬀ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' If we take the limit Mp → ∞ in a way that  vsc ≥ v0 + ∆v and usc ≤ u0 − ∆u are satisﬁed, then equations 15 and 21 are fully recovered.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='3  Relation to the TCC bound  As we have seen in the previous section, the spectrum of Gibbons-Hawking radiation is shutdown  in the regions where v > vsc and u < usc when particles are described as wave packets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' Since the  shutdown arises as a consequence of imposing a UV cutoﬀ, one should not necessary view it as a  physical eﬀect, but rather an indication that new physics must be taken into account in the regions  where the cutoﬀ is in eﬀect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' Using this interpretation, we conclude that eﬀective ﬁeld theory must  breakdown in the regions v > vsc and u < usc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='  If we assume eﬀective ﬁeld theory stops being valid when v is above vsc and u is below usc, it is  possible to recover a bound on the time scale of validity of eﬀective ﬁeld theory in de Sitter space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' In  terms of satic patch time t, the bounds v < vcs and u > ucs can be expressed as usc+r∗ < t < vsc−r∗.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='  For a static observer sitting at the center of the static patch (r∗ = 0), this implies |t| > l ln(lMp) (See  Fibure 4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' In other words, the eﬀective ﬁeld theory description will only be valid for a time interval  ∆t = 2l ln(lMp) centered around t = 0, which agrees with the time-scale ∆t ∼ l ln(lMp) predicted by  the TCC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' In fact, it is exactly twice the TCC time scale.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='  12  sc  Vo  一  erfc  Usc  0一 om  sc  erfc  Au  usc  uo  0vsc = l ln(lMp)  usc = −l ln(lMp)  ∆t = 2lln(lMp)  I+  I−  v = ∞  u = −∞  r = 0  Figure 4: Assuming eﬀective ﬁeld theory is valid for when u > −l ln(lMp) and v < l ln(lMp), we  obtain a bound |t| > l ln(lMp) on the validity of eﬀective ﬁeld theory for an observer at the center of  the static patch (r∗ = 0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' This region corresponds to time interval ∆t = 2l ln(lMp) centered around  t = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='  The reason why we are obtaining twice the TCC time-scale seems to be because we worked  under the assumption that space-time is eternally in a de Sitter phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' In this case, we have to  consider bounds in the far future and the far past, which contribute to the time scale by an amount  ∆t = l ln(lMp) each.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' In realistic cosmologies, a matter or radiation dominated phase will precede  the de Sitter phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' If we impose that the de Sitter phase begins at t = 0, then the future bound  v < vsc imposes the constraint t < l ln(lMp) at r∗ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' In this case, we recover ∆t = l ln(lMp), which  is exactly the amount of time predicted by the TCC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' A similar argument can be made to constrain  eternal inﬂation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' If we assume eternal inﬂation ends at t = 0, then the past bound u > usc imposes  the constraint t > −l ln(lMp) at r∗ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' In this case, we also recover ∆t = l ln(lMp), which is exactly  the amount of time predicted by the TCC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='  5  Conclusion and discussion  We have computed the spectrum of Gibbons-Hawking radiation in the static patch of de Sitter space  using two approaches.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' First, we used the standard eﬀective ﬁeld theory approach focusing on the  propagation of Fourier modes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' Second, we considered the propagation of particles described as wave  packets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' For this description, we found that the radiation shuts oﬀ beyond the TCC time scale if there  is a fundamental ultraviolet cutoﬀ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' In any case, the spectrum of this radiation cannot be computed  reliably using the usual eﬀective ﬁeld theory techniques beyond the TCC time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='  Our result supports the Trans-Planckian Censorship Conjecture [8] which implies that the eﬀective  13  ﬁeld theory of ﬂuctuations about an inﬂationary background cosmology will break down beyond the  TCC time scale [9].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='  Our analysis is based on applying the techniques used for black holes in [1] to the case of cosmology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='  In the case of black holes, the eﬀective ﬁeld theory of ﬂuctuations breaks down beyond the scrambling  time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' Our analysis points out an interesting analogy between the scrambling time for black holes and  the TCC time scale for an inﬂationary cosmology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' Note that there is another interesting analogy  between diﬀerent time scales: the Page time for black holes [22] plays an analogous role to the  quantum break time for de Sitter [23], and equivalently to the time scale where the back-reaction of  cosmological perturbations on the cosmological background becomes important (see [24] for original  work and [25] for a review).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='  The presence of the scrambling time indicates that an analysis beyond standard eﬀective ﬁeld  theory of ﬂuctuations is required in order to solve the black hole information problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' In a similar  way, our work lends support to the lesson from the TCC that a long lasting phase of accelerated  expansion in cosmology can only be reliably analyzed if one goes beyond standard EFT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' For attempts  to construct models of inﬂation going beyond an EFT treatment see e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' [23,26].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='  Acknowledgements  R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' is grateful for hospitality by the Institute for Theoretical Physics and the Institute for Particle  Physics and Astrophysics of the ETH Zurich during the period when some of the work on this project  was carried out.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' is supported in part by FRQNT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' The research at McGill is supported in part  by funds from NSERC and from the Canada Research Chair program.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='  References  [1] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' Ho and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' Kawai, “UV And IR Eﬀects On Hawking Radiation,” [arXiv:2207.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='07122 [hep-  th]].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='  [2] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' Hawking, “Particle Creation by Black Holes,” Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' 43, 199-220 (1975)  [erratum: Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' 46, 206 (1976)] doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='1007/BF02345020  [3] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' Gibbons and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' Hawking, “Cosmological Event Horizons, Thermodynamics, and Par-  ticle Creation,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' D 15, 2738 (1977).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='1103/PhysRevD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='2738  [4] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' Mukhanov and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' Chibisov, “Quantum Fluctuation And Nonsingular Universe.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' (In Russian),”  JETP Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' 33, 532 (1981) [Pisma Zh.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' Eksp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' Teor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' Fiz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' 33, 549 (1981)].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='  [5] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' Starobinsky, “Spectrum of relict gravitational radiation and the early state of the universe,”  JETP Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' 30, 682-685 (1979).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='  14  [6] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' Guth, “The Inﬂationary Universe: A Possible Solution to the Horizon and Flatness Prob-  lems,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' D 23, 347 (1981) [Adv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' Ser.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' Astrophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' Cosmol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' 3, 139 (1987)];' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='  R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' Brout, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' Englert and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' Gunzig, “The Creation Of The Universe As A Quantum Phe-  nomenon,” Annals Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' 115, 78 (1978);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' Starobinsky, “A New Type Of Isotropic Cosmological Models Without Singularity,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='  Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' B 91, 99 (1980);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='  K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' Sato, “First Order Phase Transition Of A Vacuum And Expansion Of The Universe,” Mon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='  Not.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' Roy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' Astron.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' 195, 467 (1981).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='  [7] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' Martin and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' Brandenberger, “The TransPlanckian problem of inﬂationary cosmology,”  Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' D 63, 123501 (2001) doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='1103/PhysRevD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='63.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='123501 [arXiv:hep-th/0005209 [hep-  th]].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='  [8] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' Bedroya and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' Vafa, “Trans-Planckian Censorship and the Swampland,” JHEP 09, 123  (2020) doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='1007/JHEP09(2020)123 [arXiv:1909.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='11063 [hep-th]].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='  [9] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' Bedroya, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' Brandenberger, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' Loverde and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' Vafa, “Trans-Planckian Censorship and Inﬂa-  tionary Cosmology,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' D 101, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='10, 103502 (2020) doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='1103/PhysRevD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='101.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='103502  [arXiv:1909.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='11106 [hep-th]].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='  [10] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' Brandenberger, “String Cosmology and the Breakdown of Local Eﬀective Field Theory,”  [arXiv:2112.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='04082 [hep-th]];' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='  R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' Brandenberger and V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' Kamali, “Unitarity Problems for an Eﬀective Field Theory Description  of Early Universe Cosmology,” [arXiv:2203.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='11548 [hep-th]].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='  [11] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' Brahma, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' Alaryani and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' Brandenberger, “Entanglement Entropy of Cosmological  Perturbations,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' D 102, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' 4, 043529 (2020) doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='1103/PhysRevD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='102.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='043529  [arXiv:2005.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='09688 [hep-th]].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='  [12] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' Starobinsky, “Robustness of the inﬂationary perturbation spectrum to transPlanckian  physics,” Pisma Zh.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' Eksp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' Teor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' Fiz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' 73, 415-418 (2001) doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='1134/1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='1381588 [arXiv:astro-  ph/0104043 [astro-ph]].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='  [13] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' Dvali, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' Kehagias and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' Riotto, “Inﬂation and Decoupling,” [arXiv:2005.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='05146 [hep-th]].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='  [14] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' Burgess, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' de Alwis and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' Quevedo, “Cosmological Trans-Planckian Conjectures are  not Eﬀective,” JCAP 05, 037 (2021) doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='1088/1475-7516/2021/05/037 [arXiv:2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='03069 [hep-  th]].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='  [15] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' Unruh, “Sonic analog of black holes and the eﬀects of high frequencies on black hole evapo-  ration,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' D 51, 2827-2838 (1995) doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='1103/PhysRevD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='51.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='2827 [arXiv:gr-qc/9409008  [gr-qc]];' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='  15  W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' Unruh and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' Schutzhold, “On the universality of the Hawking eﬀect,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' D 71,  024028 (2005) doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='1103/PhysRevD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='71.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='024028 [arXiv:gr-qc/0408009 [gr-qc]].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='  [16] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' Corley and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' Jacobson, “Hawking spectrum and high frequency dispersion,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' D  54, 1568-1586 (1996) doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='1103/PhysRevD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='54.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='1568 [arXiv:hep-th/9601073 [hep-th]].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='  [17] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' Giddings, “(Non)perturbative gravity, nonlocality, and nice slices,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' D 74, 106009  (2006) doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='1103/PhysRevD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='74.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='106009 [arXiv:hep-th/0606146 [hep-th]].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='  [18] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' Preskill, “Do black holes destroy information?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=',” [arXiv:hep-th/9209058 [hep-th]];' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' Giddings, “The Black hole information paradox,” [arXiv:hep-th/9508151 [hep-th]].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='  [19] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' Page, “Time Dependence of Hawking Radiation Entropy,” JCAP 09, 028 (2013)  doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='1088/1475-7516/2013/09/028 [arXiv:1301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='4995 [hep-th]].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='  [20] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' Brout, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' Massar, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' Parentani and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' Spindel, “A Primer for black hole quantum physics,”  Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' Rept.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' 260, 329-454 (1995) doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='1016/0370-1573(95)00008-5 [arXiv:0710.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='4345 [gr-qc]].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='  [21] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' Spradlin, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' Strominger and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' Volovich, “Les Houches lectures on de Sitter space,”  [arXiv:hep-th/0110007 [hep-th]].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='  [22] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' Sekino and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' Susskind, “Fast Scramblers,” JHEP 10, 065 (2008) doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='1088/1126-  6708/2008/10/065 [arXiv:0808.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='2096 [hep-th]].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='  [23] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' Dvali, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' Gomez and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' Zell, “Quantum Break-Time of de Sitter,” JCAP 06, 028 (2017)  doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='1088/1475-7516/2017/06/028 [arXiv:1701.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='08776 [hep-th]];' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='  G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' Dvali, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' Gomez and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' Zell, “Quantum Breaking Bound on de Sitter and Swampland,”  Fortsch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' 67, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='1-2, 1800094 (2019) doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='1002/prop.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='201800094 [arXiv:1810.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='11002 [hep-  th]].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='  [24] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' Mukhanov,  L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' Abramo and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' Brandenberger,  “On the Back re-  action problem for gravitational perturbations,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' 78, 1624-1627 (1997)  doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='1103/PhysRevLett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='78.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='1624 [arXiv:gr-qc/9609026 [gr-qc]];' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='  L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' Abramo,  R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' Brandenberger and V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' Mukhanov,  “The Energy - mo-  mentum  tensor  for  cosmological  perturbations,”  Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='  Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='  D  56,  3248-3257  (1997)  doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='1103/PhysRevD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='56.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='3248 [arXiv:gr-qc/9704037 [gr-qc]].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='  [25] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' Brandenberger, “Back reaction of cosmological perturbations and the cosmological constant  problem,” [arXiv:hep-th/0210165 [hep-th]].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='  [26] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' Brahma, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' Dasgupta and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' Tatar, “Four-dimensional de Sitter space is a Glauber-Sudarshan  state in string theory,” JHEP 07, 114 (2021) doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='1007/JHEP07(2021)114 [arXiv:2007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='00786  [hep-th]];' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' Brahma, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' Dasgupta and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' Tatar, “de Sitter Space as a Glauber-Sudarshan State,” JHEP  16  02, 104 (2021) doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='1007/JHEP02(2021)104 [arXiv:2007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='11611 [hep-th]];' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='  H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' Bernardo, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' Brahma, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' Dasgupta, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' Faruk and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' Tatar, “de Sitter Space as a Glauber-  Sudarshan State: II,” Fortsch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' 69, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='11-12, 2100131 (2021) doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='1002/prop.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='202100131  [arXiv:2108.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='08365 [hep-th]];' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' Brahma, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' Dasgupta, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' Faruk, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' Kulinich, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' Meruliya, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' Pym and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content=' Tatar,  “Resurgence of a de Sitter Glauber-Sudarshan State: Nodal Diagrams and Borel Resummation,”  [arXiv:2211.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='09181 [hep-th]].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
+page_content='  17' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE0T4oBgHgl3EQf4wIO/content/2301.02741v1.pdf'}
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+Rotation of galaxies and dark matter 
+ 
+V. A.  Golovko 
+Moscow Polytechnic University 
+Bolshaya Semenovskaya 38, Moscow 107023, Russia 
+E-mail: fizika.mgvmi@mail.ru 
+ 
+ 
+Abstract 
+In a previous paper by the author was proposed a new metric for the gravitational field of a 
+thin rotating disk physically different from the Kerr metric. The metric is admissible for any 
+angular momentum of the disk. As demonstrated in the present paper the parameter determining 
+the angular momentum of the Milky Way greatly exceeds its gravitational radius so that the Kerr 
+metric physically admissible only if the angular momentum is sufficiently small is completely 
+inapplicable to the Milky Way. It is shown on the basis of the new metric that the rotation of the 
+Milky Way plays a decisive role in the motion of satellites in its gravitational field. The effects 
+due to the rotation can imitate the presence of hypothetical dark matter. 
+ 
+ 
+Keywords: General relativity; Rotation of galaxies; Milky Way; Dark matter. 
+ 
+
+ 
+2
+1. Introduction 
+ 
+In Ref. [1] (hereafter referred to as I) were proposed metrics for the gravitational field of a 
+charged and rotating mass which are physically different from the Kerr-Newman one. The metric 
+the most adequate in this case is given in Eq. (3.1) of I. The metric is singular only at the surface 
+of an infinitely thin rotating disk which creates the gravitational field. And what is more 
+important, the metric is admissible for any angular momentum of the disk in contradistinction to 
+the Kerr-Newman metric which is physically admissible only if the angular momentum is 
+sufficiently small. Therefore the new metric opens up possibilities for studies of the rotation of 
+galaxies, in which case the Kerr-Newman metric is completely inapplicable because of a large 
+value of the angular momentum of the galaxies as shown in Appendix A with the Milky Way. 
+Seeing that celestial bodies are practically noncharged, we shall restrict our consideration to the 
+situation where the central rotating disk and other bodies are not charged. 1
+In this paper we investigate the rotation of the Milky Way Galaxy and its influence on the 
+Milky Way’s gravitational field. The Milky Way will be approximated by an infinitely thin 
+rotating disk. Although this approximation is rather simplified and does not reflect the structure 
+of the Milky Way’s disk, the approximation enables one to find out principal effects due to the 
+rotation. Unexpectedly the effects are clearly pronounced and imitate the presence of 
+hypothetical dark matter. In addition the effects explain the existence of the central bulge of the 
+Milky Way. 
+In Sec. 2 we write out equations of I required for our studies. Section 3 is devoted to the 
+treatment of the radial motion in the gravitational field of the Milky Way, and Sec 4 is concerned 
+with the motion in its equatorial plane. Remarks as to the results obtained are made in the 
+concluding section. 
+ 
+2. Basic equations 
+ 
+In the present paper we employ the metric given in Eq. (3.1) of I, the metric describing the 
+gravitational field created by an infinitely thin rotating disk. As mentioned in Introduction we 
+consider noncharged bodies. This being so, we put rq = 0 in Eqs. (3.2)−(3.3) of I. Now Eqs. 
+(3.1)−(3.3) of I acquire the form 
+                                                 
+1 If the rotating disk is charged, its charge should not be too large. The restriction on the charge is not 
+relevant to general relativity but is due to the limits of applicability of classical electrodynamics used in 
+this case [1]. 
+
+ 
+3
+ds2= Σ
+Λ c2dt2− 
+(
+)
+2
+4
+/
+g
+4
+/
+g
+2
+4
+g
+d
+e
+1
+e
+r
+r
+r
+r
+r
+r
+r
+Δ
+−
+Σ
+−
+−
+ − Σdθ 2 − Σ
+Y sin2θ dϕ 2 + Σ
+aZ
+2
+ sin2θ cdtdϕ,        (2.1) 
+where 
+Δ =
+(
+)
+2
+/
+/
+2
+g
+g
+g
+e
+1
+e
+r
+r
+r
+r
+r
+−
+−
+−
++ a2,   Σ =
+(
+)
+2
+/
+2
+g
+g
+e
+1
+r
+r
+r
+−
+−
++ a2cos2θ,   Λ = 
+(
+)
+2
+/
+/
+2
+g
+g
+g
+e
+1
+e
+r
+r
+r
+r
+r
+−
+−
+−
++ a2cos2θ, 
+(
+)
+θ
+Δ
+−
+⎥
+⎥
+⎦
+⎤
+⎢
+⎢
+⎣
+⎡
++
+−
+=
+−
+2
+2
+2
+2
+2
+/
+g
+2
+g
+sin
+e
+1
+a
+a
+r
+Y
+r
+r
+,    
+r
+r
+r
+Z
+/
+g
+2
+g
+e
+1
+−
+−
+=
+.                          (2.2) 
+We recall that rg = 2Gm/c2 is the gravitational radius of the disk of mass m and of radius a, 
+and the rotation of the disk is characterized by the angular momentum L = amc. The metric is 
+singular only at r = 0, the value r = 0 corresponding to the surface of the rotating disk.  
+For the present studies we need the equations of motion for the metric. Since we imply 
+noncharged bodies, we put rq = ε = 0 in Eqs. (3.11)−(3.14) of I with the result 
+ΔΣ
+−
+β
+=
+ahZ
+Y
+t
+c ds
+d
+,                                                            (2.3) 
+(
+)
+(
+)
+2
+2
+/
+2
+/
+2
+2
+g
+2
+4
+g
+/
+2
+4
+2
+g
+g
+g
+e
+1
+e
+1
+e
+d
+d
+⎭⎬⎫
+⎩⎨⎧
+−
+−
+⎥⎦
+⎤
+⎢⎣
+⎡
+−
++
+β
+Σ
+=
+⎟
+⎠
+⎞
+⎜
+⎝
+⎛
+−
+−
+r
+r
+r
+r
+r
+r
+ah
+a
+r
+r
+r
+s
+r
+ 
+(
+)
+(
+⎥⎦
+⎤
+⎢⎣
+⎡
+−
+κ
++
+Σ
+Δ
+−
+−
+−
+−
+2
+/
+2
+g
+2
+4
+g
+2
+/
+/
+2
+4
+g
+g
+g
+e
+1
+e
+1
+e
+r
+r
+r
+r
+r
+r
+r
+r
+r
+)
+,                            (2.4) 
+⎥
+⎥
+⎦
+⎤
+⎢
+⎢
+⎣
+⎡
+⎟
+⎠
+⎞
+⎜
+⎝
+⎛
+θ
+−
+θ
+β
+−
+θ
+−
+κ
+Σ
+=
+⎟
+⎠
+⎞
+⎜
+⎝
+⎛ θ
+2
+2
+2
+2
+2
+sin
+sin
+cos
+1
+d
+d
+h
+a
+a
+s
+,                              (2.5) 
+⎟
+⎠
+⎞
+⎜
+⎝
+⎛
+β
++
+θ
+Λ
+ΔΣ
+=
+ϕ
+Z
+a
+h
+s
+2
+sin
+1
+d
+d
+.                                               (2.6) 
+In these equations, β = Ε0/(μc2) where Ε0 is the energy of a test particle and μ is its mass, h = 
+L0/(μc) where L0 is the angular momentum of the test particle. In other words, the constants β 
+and h are the dimensionless energy (the total energy divided by the rest energy of the test 
+particle) and a magnitude of the angular momentum of the particle (with dimension of length), 
+respectively. The last constant κ (with dimension of square of length) is related to the constant K 
+of Landau and Lifshitz [2], problem 1 in § 104, by κ = K/(μ2c2). 
+We also write down the expression for the nontensorial velocity v of the test particle 
+measured by an observer stationed at infinity and given in Eq. (3.17) of I: 
+2
+2
+2
+2
+2
+2
+)
+(
+)
+(
+ahZ
+Y
+c
+v
+−
+β
+Λ
+Λ
+−
+Σ
+β
+Σ
+Δ
+=
+.                                                      (2.7) 
+
+ 
+4
+3. Radial motion 
+ 
+The radial motion in the above metric is considered in I. Here we analyze the motion in more 
+detail. If a ≠ 0, the radial motion of a test particle is possible only along the axis of rotation of the 
+gravitating disk where θ = 0. From (2.5) we see that now h = 0 and κ = a2. Substituting this into 
+(2.3) and (2.4) results in the following equation for the dependence of the coordinate r upon the 
+time t 
+(
+)
+1
+2
+4
+g
+2
+2
+4
+/
+g
+/
+g
+2
+4
+2
+2
+e
+1
+e
+d
+d
+R
+R
+r
+R
+r
+c
+t
+r
+r
+r
+r
+r
+Σ
+Δ
+−
+β
+−
+=
+⎟
+⎠
+⎞
+⎜
+⎝
+⎛
+,                                    (3.1) 
+in which 
+(
+)
+2
+/
+g
+2
+/
+g
+2
+g
+e
+1
+e
+r
+r
+r
+r
+a
+r
+R
+−
+−
+Δ
+−
++
+=
+,     
+(
+)
+2
+/
+2
+2
+g
+g
+e
+1
+r
+r
+a
+r
+R
+−
+Σ
+−
++
+=
+, 
+(
+)
+(
+)
+2
+/
+g
+2
+2
+g
+2
+/
+g
+2
+/
+g
+2
+g
+2
+1
+e
+1
+e
+1
+e
+r
+r
+r
+r
+r
+r
+a
+r
+a
+r
+R
+−
+−
+−
+−
++
+−
++
+−
+β
+=
+.                                         (3.2) 
+In Eq. (3.1), only the factor R1 can be negative. Recalling that β is the dimensionless energy 
+of a test particle, in parallel with Landau and Lifshitz [2], problem 1 in § 102, we introduce a 
+positive dimensionless “effective potential energy” (the positive effective potential energy 
+divided by the rest energy of the test particle) 
+(
+)
+(
+)
+2
+/
+1
+2
+/
+g
+2
+2
+g
+2
+/
+g
+2
+/
+g
+2
+g
+e
+1
+e
+1
+e
+)
+(
+⎥
+⎥
+⎥
+⎦
+⎤
+⎢
+⎢
+⎢
+⎣
+⎡
+−
++
+−
++
+=
+−
+−
+−
+r
+r
+r
+r
+r
+r
+a
+r
+a
+r
+r
+U
+,                                         (3.3) 
+so that R1 = β2 − U 2(r). The motion of the test particle is possible only if β ≥ U(r) when R1 ≥ 0. 
+To examine U(r) we calculate the derivative 
+(
+)
+(
+)
+2
+2
+/
+g
+2
+2
+g
+2
+/
+g
+2
+2
+g
+2
+/
+g
+3
+g
+e
+1
+e
+1
+2
+e
+d
+d
+⎥⎦
+⎤
+⎢⎣
+⎡
+−
++
+−
+−
+=
+−
+−
+−
+r
+r
+r
+r
+r
+r
+a
+r
+a
+r
+U
+r
+r
+r
+U
+.                                         (3.4) 
+It follows from this (r ≠ 0) that, if a < rg, then always dU/dr > 0. If a > rg, the effective potential 
+energy U(r) is a minimum at 
+⎟⎟
+⎠
+⎞
+⎜⎜
+⎝
+⎛ −
+−
+=
+a
+r
+r
+r
+g
+g
+1
+ln
+.                                                           (3.5) 
+If a >> rg, the minimum is at r ≈ a, which amounts to saying that in this case the position of the 
+minimum is practically independent of the gravitational constant G. 
+
+ 
+5
+Figure 1 shows the behavior of U(r) for different values of the parameter a that determines 
+the angular momentum of the gravitating disk. If a > rg, we have a potential well (this conforms 
+with the results of I). The particle oscillates in the well along the axis of rotation of the disk. The 
+well comes into being only if the rotation of the disk is sufficiently rapid. 
+ 
+0,5
+0,6
+0,7
+0,8
+0,9
+1
+0
+2
+4
+6
+8
+10
+r/r g
+U
+2
+ 
+Fig. 1. Dependence of the effective potential U(r) of (3.3) upon r in the radial motion 
+perpendicularly to the disk. Curve 1: a/rg = 0.5, curve 2: a/rg = 5. 
+ 
+ 
+As to the Milky Way, Appendix A shows that a > rg for it and thereby there is a potential 
+well on the axis of rotation. Neighboring stars are captured by the well, which gives rise to 
+formation of a bulge. Consequently the central bulge of the Milky Way is due to the Milky 
+Way’s rotation. All of this can be imitated by the presence of dark matter near the axis of 
+rotation, dark matter attracting the neighboring stars. To obtain a comprehensive picture of the 
+potential well and not only on the axis of rotation it is necessary to analyze the equations of 
+motion when 0 ≤ θ < π/2, which is beyond the scope of the present paper. Here we can only 
+remark that the motion along the axis of rotation is unstable because an arbitrary small 
+perturbation perpendicular to the axis will lead the star away from the axis. The stable orbits in 
+the central bulge of the Milky Way are parallel to its disk, which is considered at the end of Sec. 
+4. 
+ 
+
+ 
+6
+4. Motion in the equatorial plane 
+ 
+We turn now to the motion in the equatorial plane where θ = π/2. First of all we write out the 
+formula for the velocity v of a star rotating about the Milky Way, the velocity measured by an 
+observer at infinity. If we put  θ = π/2 and substitute the quantities of (2.2) into (2.7), we have 
+(
+)
+(
+)
+(
+)
+r
+r
+r
+r
+r
+r
+r
+r
+r
+r
+r
+r
+r
+r
+ah
+a
+r
+a
+r
+c
+v
+/
+g
+2
+3
+/
+g
+2
+/
+g
+/
+g
+2
+2
+g
+/
+g
+2
+2
+2
+/
+g
+2
+/
+g
+2
+g
+2
+2
+e
+e
+1
+e
+1
+)
+e
+2
+(
+)
+e
+(
+e
+1
+e
+⎥⎦
+⎤
+⎢⎣
+⎡
+−
+−
+−
+−
+β
++
+β
+−
+β
+⎥⎦
+⎤
+⎢⎣
+⎡
+−
++
+=
+−
+−
+−
+−
+−
+−
+.            (4.1) 
+Let us compare this with the case where the gravitating mass does not rotate being a point mass, 
+of course. We mention in passing that this case is considered in Ref. [3]. If a = 0, Eq. (4.1) yields 
+r
+r
+r
+r
+c
+v
+/
+g
+2
+/
+g
+2
+2
+2
+e
+)
+e
+(
+−
+−
+β
+−
+β
+=
+.                                             (4.2) 
+We see a drastic difference between (4.1) and (4.2) when r → 0. According to Eq. (4.1) v → 
+∞ as r → 0 whereas according to Eq. (4.2) v → 0 in the same limit (recall that the value r = 0 
+corresponds to the surface of the rotating disk). It is clear from the physical point of view that the 
+rotating and gravitating disk must drag neighboring objects into rotation. Although the Milky 
+Way is not, of course, a solid disk and the speeds of orbiting stars cannot be infinite; nevertheless 
+the results following from (4.1) demonstrate that the speed of the orbiting stars near the Milky 
+Way can be rather high in contradiction with the Newtonian law of gravitation. The contradiction 
+found experimentally is commonly ascribed to the presence of dark matter. We see that the 
+contradiction may be due to the rotation of the Milky Way. 
+We are coming now to the study of the motion in the equatorial plane. Once θ = π/2, we see 
+from (2.5) that κ = (βa − h)2. Substituting this into (2.4) yields  
+π
+Σ
+=
+⎟
+⎠
+⎞
+⎜
+⎝
+⎛
+R
+r
+r
+s
+r
+r
+r
+2
+4
+g
+/
+g
+2
+4
+2
+e
+d
+d
+,                                                   (4.3) 
+where 
+(
+)
+[
+]
+(
+)
+[
+]
+(
+)
+⎥⎦
+⎤
+⎢⎣
+⎡
+−
+β
++
++
+−
+−
+−
++
+β
+=
+π
+2
+2
+2
+g
+2
+2
+2
+g
+2
+2
+2
+2
+2
+g
+1
+y
+h
+a
+r
+y
+a
+y
+r
+ahy
+y
+a
+r
+R
+.                   (4.4) 
+To simplify the notation we have introduced the quantity 
+1
+0
+,
+e
+1
+/
+g
+≤
+≤
+−
+=
+−
+y
+y
+r
+r
+.                                              (4.5) 
+If necessary, the derivative dr/dt can be found from (4.3) with use made of (2.3). It is worthy of 
+remark that, in the present case and in other cases considered in the paper, Eq. (2.3) leads to no 
+peculiarities. 
+
+ 
+7
+One can introduce an “effective potential energy” U(r) as above only if an expression of the 
+type Rπ of (4.4) does not contain the first power of β. If one considers the motion of a star in the 
+gravitational field of the Milky Way, account must be taken of the fact that the angular 
+momentum of the star characterized by the parameter h is very small as compared to the angular 
+momentum of the Milky Way given by the parameter a so that we can neglect h in (4.4) (h << 
+βa) with the result: 
+(
+) (
+) [
+])
+(
+β
+e
+2
+e
+1
+2
+2
+/
+g
+2
+/
+g
+2
+2
+g
+2
+g
+r
+U
+a
+r
+r
+R
+r
+r
+r
+r
+−
+⎥⎦
+⎤
+⎢⎣
+⎡
+−
+−
++
+=
+−
+−
+π
+,                                (4.6) 
+where 
+(
+)
+(
+) (
+)
+2
+/
+1
+/
+g
+2
+/
+g
+2
+/
+g
+/
+g
+e
+2
+e
+1
+1
+e
+1
+e
+)
+(
+⎥
+⎥
+⎦
+⎤
+⎢
+⎢
+⎣
+⎡
+−
+−
+ξ
++
+−
+ξ
++
+=
+−
+−
+−
+−
+r
+r
+r
+r
+r
+r
+r
+r
+r
+U
+.                                         (4.7) 
+Here we have returned to the previous notation and introduced the positive parameter 
+2
+g
+2
+r
+a
+=
+ξ
+.                                                                   (4.8) 
+For use later we recast Eq. (4.1) in terms of y and ξ: 
+(
+)
+[
+]
+2
+2
+g
+3
+2
+2
+2
+2
+2
+2
+/
+)
+1(
+)
+1(
+)
+1
+(
+1
+r
+ahy
+y
+y
+y
+y
+y
+y
+c
+v
+−
++
+βξ
++
+β
+−
++
+−
+β
+ξ
++
+−
+=
+.                                        (4.9) 
+Before analyzing Eq. (4.7) it is instructive to write Eq. (2.6) in the present case where h << 
+βa (also hΛ << βaΖ as Λ = Ζ when r >> rg and θ = π/2): 
+ΔΣ
+β
+=
+ϕ
+Z
+a
+s
+d
+d
+.                                                                  (4.10) 
+As long as dϕ/ds is positive (we assume throughout the paper that a > 0), the test particle rotates 
+in the same sense as the gravitating disk and the speed of rotation is proportional to a, which 
+amounts to saying that the speed of rotation is very high. Classical mechanics is completely 
+inapplicable to this motion because the particle has a nonzero angular velocity (dϕ/ds ≠ 0) 
+whereas its angular momentum is nil (h = 0). 
+In order to investigate the potential energy U(r) of (4.7) we rewrite Eq. (4.7) in terms of y 
+and ξ as 
+2
+/
+1
+2
+2
+)
+1(
+1
+1
+)
+(
+⎥
+⎦
+⎤
+⎢
+⎣
+⎡
++
+ξ
++
+ξ
++
+−
+=
+y
+y
+y
+y
+y
+U
+.                                                   (4.11) 
+Differentiating we have 
+[
+]
+2
+2
+2
+4
+2
+)
+1(
+1
+2
+1
+)
+1(
+2
+d
+d
+y
+y
+U
+y
+y
+y
+y
+U
++
+ξ
++
++
+−
+ξ
++
+ξ
+−
+=
+.                                            (4.12) 
+
+ 
+8
+Seeing that 0 ≤ y ≤ 1, this derivative is always negative whereas dU/dr = (dU/dy)(dy/dr) is 
+nonnegative because dy/dr ≤ 0 (
+; dy/dr = 0 if r = 0). As a result, U(r) 
+increases monotonically from [ξ/(1+2ξ)]
+2
+/
+g
+/
+e
+d
+/
+d
+r
+r
+r
+y
+r
+rg
+−
+−
+=
+1/2 when r = 0 to 1 as r → ∞. The qualitative behavior of 
+U(r) as a function of r can be schematically represented by a curve similar to curve 1 in Fig. 1. 
+Therefore circular orbits are impossible since U(r) has no extrema if r ≠ 0.  
+If β ≥ 1, the test particle spirals from infinity into the rotating disk because the angle ϕ 
+augments monotonically in view of (4.10). If β ≥ 1, the parameter β is related to the velocity of 
+the test particle at infinity v∞ by Eq. (3.13) of [3]: 
+2
+2 /
+1
+1
+c
+v∞
+−
+=
+β
+.                                                            (4.13) 
+This relation follows from (4.1) as well. 
+When β < 1, the test particle spirals into the rotating disk from the apogalaction, that is, from 
+the most remote point in the orbit where U(r) = β. As an example, we discuss the situation where 
+β ≈ 1. In this situation the motion near the apogalaction should be described by classical 
+mechanics because v << c there. The equation U(r) = β can be written as 
+(
+)
+0
+1
+1
+2
+2
+2
+3
+2
+=
+ξ
+β
+−
+−
+ξ
++
+β
+−
+−
+β
+y
+y
+y
+.                                         (4.14) 
+We have here two small parameters 1 − β2 and 1/ξ (the parameter ξ is considered in Appendix 
+A). The solution to (4.14) in this case is found in Appendix B and is 
+(
+)
+(
+) ⎥⎦
+⎤
+⎢⎣
+⎡
+β
+−
+ξ
++
+β
+−
+=
+3
+2
+2
+1
+ 
+1
+1
+y
+.                                                    (4.15) 
+Seeing that y ≈ 0, we put y = 0 in (4.9) where it is possible with the result 
+2
+2
+2
+2
+1
+β
++
+−
+β
+=
+y
+c
+v
+.                                                               (4.16) 
+We substitute (4.15) with account taken of the fact that y → rg/r as r → ∞ by (4.5): 
+(
+)
+4
+2
+g
+2
+2
+4
+2
+2
+4
+2
+2
+2
+1
+r
+r
+a
+c
+y
+c
+c
+v
+=
+ξ
+≈
+β
+β
+−
+ξ
+=
+.                                           (4.17) 
+This formula is not consistent with classical mechanics where v2 ∝ 1/r. At the same time, v2 of 
+(4.17) may be rather large because of c2a2. Of course, when r → 0, the velocity v tends to infinity 
+inasmuch as y → 1 in (4.9). As a result, we see that the Milky Way’s rotation affects the motion 
+of its satellites even at great distances owing to a in (4.17). 
+Another case where it is possible to introduce an effective potential energy as above is 
+furnished by the relation βa − h = 0. The relation h = βa signifies that the angular momentum of 
+
+ 
+9
+the object in question is comparable to the one of the Milky Way provided that β is not too 
+small. Therefore the case in point is a galaxy orbiting the Milky Way. It should be remarked that 
+the mass of the galaxy may be rather small because the value of h is proportional to the distance 
+between the Milky Way and the galaxy which can be rather great. So, this case matches to a 
+dwarf galaxy located at a specific average distance rotating about the Milky Way. In this case 
+Eq. (4.9) becomes 
+(
+)
+(
+)
+2
+2
+2
+2
+2
+2
+2
+2
+1
+)
+1(
+)
+1
+(
+1
+β
+ξ
++
+−
++
+−
+β
+ξ
++
+−
+=
+y
+y
+y
+y
+y
+c
+v
+.                                         (4.18) 
+Once βa − h = 0, Eq. (4.4) can be written in the form 
+[
+])
+(
+β
+2
+2
+4
+g
+r
+U
+r
+R
+−
+=
+π
+,                                                       (4.19) 
+where 
+(
+)
+2
+/
+1
+2
+/
+g
+/
+g
+e
+1
+e
+)
+(
+⎥⎦
+⎤
+⎢⎣
+⎡
+−
+ξ
++
+=
+−
+−
+r
+r
+r
+r
+r
+U
+.                                            (4.20) 
+Equation (2.6) yields now 
+ΔΣ
++
+Λ
+β
+=
+ϕ
+)
+(
+d
+d
+Z
+a
+s
+.                                                                  (4.21) 
+Here again dϕ/ds > 0, as in (4.10), and the speed of rotation is proportional to a. 
+The qualitative behavior of the effective potential energy U(r) of (4.20) as a function of r is 
+represented in Fig. 2. It follows from the figure that, if 
+ξ
+>
+β
+, the satellite galaxy spirals from 
+infinity into the Milky Way’s disk. When 
+1
+>
+β
+>
+ξ
+, the galaxy spiraling from infinity does not 
+reach the disk going around it and spirals to infinity again. If 
+ξ
+−
+>
+β
+>
+4
+/
+1
+1
+1
+, the galaxy when 
+starting from the apogalaction spirals about the disk and returns to the apogalaction. Finally, if 
+)
+4
+/(
+1
+1
+ξ
+−
+=
+β
+, the dwarf galaxy rotates about the disk in circular orbit with radius r0 = 
+−rg/ln[1−1/(2ξ)]. 
+
+ 
+10
+ 
+Fig. 2. Schematic dependence of the effective potential U(r) of (4.20) upon r (not to scale). Point 
+A corresponds to ξ , point B corresponds to 
+ξ
+−
+4
+/
+1
+1
+. The curve has ξ > 1. 
+ 
+The equation that determines the position of the apogalaction and perigalaction is β2 = U 2(r), 
+which is seen from (4.19) and (4.3) (at these positions dr/ds = 0). We write the equation as 
+0
+1
+2
+2
+=
+β
+−
++
+−
+ξ
+y
+y
+.                                                    (4.22) 
+The solution to the equation is 
+(
+)
+ξ
+−
+β
+ξ
++
+±
+=
+2
+1
+4
+1
+1
+2
+y
+.                                                   (4.23) 
+Recalling that y ≥ 0 we see that, when β > 1, the equation has only one positive solution; and 
+when β < 1, it has two positive solutions existing if 
+ξ
+−
+≥
+β
+4
+/
+1
+1
+. This is consistent with Fig. 2. 
+As above we shall assume that β ≈ 1. Moreover, we suppose that |β2−1| is so small that 
+ξ|β2−1| << 1. In this situation the fist approximate solution valid for β > 1 and β < 1 is 
+ξ
+= 1
+1y
+.                                                              (4.24) 
+This solution corresponds to the perigalaction. When β < 1, the second approximate solution is 
+(
+)
+(
+)
+[
+]
+2
+2
+2
+1
+1
+1
+β
+−
+ξ
++
+β
+−
+=
+y
+.                                          (4.25) 
+This solution corresponds to the apogalaction which exists when β < 1. 
+Considering the motion in the vicinity of the perigalaction we should take into account the 
+fact that y1 of (4.24) is very small [1/ξ ∼ 10−4 according to (A.5)]. Consequently we can set y = 0 
+in (4.18) where it is possible. In the remaining expression (β2 − 1 + y) we use (4.22) so that 
+
+U
+A
+B
+1
+0 
+11
+2
+2
+2
+2
+β
+ξ
+=
+y
+c
+v
+.                                                                    (4.26) 
+Substituting y1 of (4.24) with β ≈ 1 yields 
+ξ
+= c
+v
+.                                                                       (4.27) 
+ If we put ξ ∼ 104 here, we shall obtain the speed of the satellite galaxy at the perigalaction equal 
+to v ∼ 10−2c = 3000 km/s. This enormous speed is due to our approximation according to which 
+the Milky Way is considered to be a solid disk. At the same time this result demonstrates that in 
+the real situation the speed of the satellite galaxy may be rather high. 
+Considering the motion in the vicinity of the apogalaction we remark that y2 of (4.25) is also 
+very small and thereby Eq. (4.26) holds. Instead of substituting this y2 which essentially depends 
+on β, we refer to (4.5) and see that y is small when r → ∞, and y → rg/r in this case. We place 
+this last y with β ≈ 1 in (4.26) to obtain 
+2
+2
+2
+2
+r
+a
+c
+v
+=
+.                                                            (4.28) 
+It is interesting to note that the Newtonian gravitational consonant G disappears from this 
+formula and the role of G goes over to a2. As to the dependence of v2 on r we can make the same 
+comment as the one concerning Eq. (4.17). 
+We turn now to the circular orbit which occurs when
+ξ
+−
+=
+β
+4
+/
+1
+1
+. It follows from (4.23) 
+that then y = 1/(2ξ). Introducing these y and β into (4.18) yields 
+2
+2
+2
+)1
+4
+)(
+1
+2
+(
+)1
+4
+(
+2
++
+ξ
+−
+ξ
+−
+ξ
+ξ
+= c
+v
+.                                                  (4.29) 
+If we take ξ ∼ 104 as in (A.5), we shall have v ∼ 1500 km/s. This speed is of the same order of 
+magnitude as the speed resulting from (4.27). 
+There is yet another case where it is possible to introduce an effective potential energy U(r) 
+as above. We see from (2.5) that θ = constant if 
+2
+2
+2
+sin
+sin
+cos
+⎟
+⎠
+⎞
+⎜
+⎝
+⎛
+θ
+−
+θ
+β
+−
+θ
+=
+κ
+h
+a
+a
+.                                    (4.30) 
+We shall also suppose that 
+θ
+β
+=
+2
+sin
+a
+h
+.                                                                     (4.31) 
+Now (4.30) yields κ = a2 cos2θ. If θ is small, one has h << a. Therefore the case in point will be a 
+star orbiting the Milky Way. 
+Placing these κ and h in (2.4) we see that we can introduce U(r) which is 
+
+ 
+12
+(
+)
+(
+)
+2
+/
+1
+2
+/
+g
+2
+2
+/
+g
+/
+g
+e
+1
+cos
+1
+e
+1
+e
+)
+(
+⎥
+⎥
+⎦
+⎤
+⎢
+⎢
+⎣
+⎡
+−
+θ
+ξ
++
+−
+ξ
++
+=
+−
+−
+−
+r
+r
+r
+r
+r
+r
+r
+U
+.                                         (4.32) 
+If θ = 0, we have (3.3); if θ = π/2, we have (4.20). Consequently, when θ changes from 0 to π/2, 
+we go from Fig. 1 to Fig. 2. In both cases the potential energy U(r) has a minimum and therefore 
+circular orbits are possible. The orbits lie in planes parallel to the equatorial plane. When θ is 
+small, we shall have a star moving in the central bulge of the Milky Way. 
+ 
+5. Concluding remarks 
+ 
+The present paper shows that the rotation of the Milky Way plays a decisive role in the 
+motion of stars or other galaxies in its gravitational field. For example, it is just the rotation that 
+explains the existence of the central bulge of the Milky Way. The effect of the rotation may be so 
+strong that the quantity a2 characterizing the rotation takes the place of the gravitational constant 
+as is seen from Eq. (4.28). Of course, the results obtained in the paper can be applied to other 
+rotating galaxies. The effects due to the rotation can imitate the presence of hypothetical dark 
+matter. It may be that the rotation of the galaxies and of clusters of galaxies influences the 
+evolution of the Universe as long as there must exist an additional energy due to the rotation. 
+Besides, the Universe or its big parts may rotate as a whole and centrifugal forces arising in this 
+case can accelerate their expansion imitating the presence of dark energy. 
+The study of the rotation of the galaxies has become possible when the new metric for the 
+gravitational field of a rotating mass of Ref. [1] was found. The metric is admissible for any 
+angular momentum of the rotating mass whereas the angular momentum of the galaxies can be 
+very large as shown in Appendix A with the Milky Way. The well-known Kerr metric is 
+completely inapplicable in this situation. 
+In this paper we employ rather a simplified model for the Milky Way representing it as an 
+infinitely thin rotating disk. When considering the motion of satellites in the vicinity of the 
+Milky Way the model can yield only qualitative results. At great distances from the Milky Way 
+its structure is not of crucial importance so that the model may produce quantitative results. As is 
+seen from Appendix A the radius a of the disk modeling the Milky Way is small in comparison 
+with its radius R. It would be unreasonable to put a = R because this would yield an enormous 
+angular momentum L = Rmc and an enormous angular velocity ω = L/I for the Milky Way, 
+which would essentially overestimate all effects due to its rotation. 
+
+ 
+13
+We have, in the paper, considered several examples where solutions to relevant equations are 
+rather simple. Nevertheless even these simple examples demonstrate that without regard for the 
+rotation it is impossible to comprehend the actual gravitational field of the Milky Way. 
+Of course, it would be desirable to confirm the results of the paper by comparison with 
+observational data. At this stage of theoretical investigations, however, it will be useless because 
+it is clear in advance that there will be no agreement between the results obtained in the paper 
+and the observational data. This is due to the fact that the Milky Way is not an infinitely thin 
+rotating disk where the velocity of a test particle tends to infinity at the disk’s surface. The main 
+aim in the paper is to attract attention to the fact that the rotation of galaxies plays an important 
+role in their gravitational field and to stimulate further investigations along this line. It is 
+necessary to develop a more realistic model of the rotating Milky Way in order to compare 
+theoretical results and observational data. 
+The results of the present paper do not deny the existence of dark matter. However, 
+properties and the distribution of dark matter cannot be correctly studied if the rotation of 
+galaxies is not taken into proper account, which follows from the results of the paper. 
+ 
+Appendix A. Parameters for the Milky Way 
+ 
+The mass of the Milky Way can be estimated as m = 1.29⋅1012 m☼ [4]. Therefore the 
+gravitational radius of the Milky Way is 
+km
+10
+8.3
+2
+12
+2
+g
+⋅
+=
+=
+c
+Gm
+r
+.                                                   (A.1) 
+The angular momentum of the Milky Way taken from Ref. [5] is L = 0.97⋅1067 J⋅s. 
+Karachentsev [5] uses m = 1.5⋅1011 m☼ and thereby the actual angular momentum of the Milky 
+Way may be greater than the above value. With use made of L = 0.97⋅1067 J⋅s we obtain for the 
+parameter a of the Milky Way that 
+km
+10
+3.1
+13
+⋅
+=
+= mc
+L
+a
+.                                                   (A.2) 
+It should be remarked that in order to be consistent with Karachentsev’s calculations one ought 
+to utilize his mass m = 1.5⋅1011 m☼ with the result 
+km
+10
+1.1
+14
+⋅
+=
+a
+.                                                        (A.3) 
+We see that in any case a > rg and even a >> rg for the Milky Way. If the gravitational field 
+possesses its own angular momentum, this will only augment the value of a. 
+There is another way to evaluate the angular momentum of the Milky Way. We can compute 
+the moment of inertia I with the help of the formula I = mR2/2 for a uniform disk and obtain L 
+
+ 
+14
+from L = Iω. There are different estimates for the radius R of the Milky Way. We take R = 
+4.7⋅1017 km although some authors propose a larger value. The angular velocity ω of the outer 
+parts of the Milky Way is close to the one in the neighborhood of the Sun. The latter is ω = 
+8.94⋅10−16 s−1 [6]. These numbers give 
+km
+10
+3.3
+14
+⋅
+=
+a
+.                                                        (A.4) 
+This estimate is close to (A.3). With this a, we calculate the parameter ξ of (4.8): 
+2
+g
+2
+r
+a
+=
+ξ
+ ∼ 104.                                                                   (A.5) 
+When considering the motion of Milky Way’s satellites in the equatorial plane it is preferable to 
+imply (A.4) or (A.5) because it is the rotation of the outer parts of the Milky Way with the 
+angular velocity ω which plays a leading part in the gravitational field created by the Milky Way 
+in this plane. 
+It may be noted that the Kerr metric is physically admissible only if a ≤ rg/2. Consequently 
+the Kerr metric is absolutely unfit for the gravitational field of the Milky Way. 
+ 
+Appendix B. Equation (4.14) 
+ 
+Equation (4.14) can be recast as 
+(
+)
+(
+)
+[
+]
+(
+)
+0
+1
+1
+1
+2
+2
+2
+3
+2
+=
+ξ
+β
+−
+−
++
+β
+−
+−
++
+β
+−
+−
+y
+y
+y
+y
+.                                         (B.1) 
+Instead of y we introduce y  according to y = 1−β2 + y  and obtain the equation 
+(
+)(
+)
+(
+)
+0
+1
+1
+1
+1
+2
+2
+3
+2
+2
+=
+⎥⎦
+⎤
+⎢⎣
+⎡
+ξ
++
++
+β
+−
++
++
+β
+−
+β
+−
+−
+y
+y
+y
+.                                 (B.2) 
+The first term here is small since we assume the smallness of 1−β2. Upon neglecting this term we 
+arrive at a first approximation y  = 0. We rewrite Eq. (B.2) in the form 
+(
+)(
+)
+(
+)
+ξ
++
++
+β
+−
++
+β
+−
+β
+−
+=
+/
+1
+1
+1
+1
+2
+2
+3
+2
+2
+y
+y
+y
+.                                               (B.3) 
+Placing the first approximation y  = 0 in the right-hand side we obtain the second approximation 
+(
+)
+(
+)
+ξ
++
+β
+−
+β
+−
+=
+/
+1
+1
+1
+2
+2
+4
+2
+y
+.                                                     (B.4) 
+If we return to y, we shall have 
+(
+)
+(
+)
+ξ
++
+β
+−
+β
+−
++
+β
+−
+=
+/
+1
+1
+1
+1
+2
+2
+4
+2
+2
+y
+.                                                     (B.5) 
+
+ 
+15
+The quantity 1−β2 can be arbitrarily small whereas ξ is fixed. Therefore we can neglect 1−β2 in 
+the denominator, which leads to Eq. (4.15). 
+ 
+References 
+ 
+[1] V. A. Golovko, Results in Phys. 15 (2019) 102536. 
+[2] L. D. Landau, E. M. Lifshitz, The Classical Theory of Fields, Butterworth-Heinemann, 
+Oxford, 2000. 
+[3] V. A. Golovko, Results in Phys. 13 (2019) 102288. 
+[4] R. J. J. Grand, A. J. Deason, S. D. M. White, C. M. Simpson, F. A. Gómez, F. Marinacci, R. 
+Pakmor, MNRAS Lett. 487 (1) (2019) L72. 
+[5] I. D. Karachentsev, Binary Galaxies (in Russian), Nauka, Moscow, 1987. 
+[6] T. Camarillo, P. Dredger, B. Ratra, Astroph. Space Sci. 363 (2018) 268.. 
+ 
+
diff --git a/ftFAT4oBgHgl3EQf8B6L/content/tmp_files/load_file.txt b/ftFAT4oBgHgl3EQf8B6L/content/tmp_files/load_file.txt
new file mode 100644
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@@ -0,0 +1,461 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf,len=460
+page_content='Rotation of galaxies and dark matter  V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='  Golovko  Moscow Polytechnic University  Bolshaya Semenovskaya 38, Moscow 107023, Russia  E-mail: fizika.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='mgvmi@mail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='ru  Abstract  In a previous paper by the author was proposed a new metric for the gravitational field of a  thin rotating disk physically different from the Kerr metric.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' The metric is admissible for any  angular momentum of the disk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' As demonstrated in the present paper the parameter determining  the angular momentum of the Milky Way greatly exceeds its gravitational radius so that the Kerr  metric physically admissible only if the angular momentum is sufficiently small is completely  inapplicable to the Milky Way.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' It is shown on the basis of the new metric that the rotation of the  Milky Way plays a decisive role in the motion of satellites in its gravitational field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' The effects  due to the rotation can imitate the presence of hypothetical dark matter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='  Keywords: General relativity;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' Rotation of galaxies;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' Milky Way;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' Dark matter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='  2  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' Introduction  In Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' [1] (hereafter referred to as I) were proposed metrics for the gravitational field of a  charged and rotating mass which are physically different from the Kerr-Newman one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' The metric  the most adequate in this case is given in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='1) of I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' The metric is singular only at the surface  of an infinitely thin rotating disk which creates the gravitational field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' And what is more  important, the metric is admissible for any angular momentum of the disk in contradistinction to  the Kerr-Newman metric which is physically admissible only if the angular momentum is  sufficiently small.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' Therefore the new metric opens up possibilities for studies of the rotation of  galaxies, in which case the Kerr-Newman metric is completely inapplicable because of a large  value of the angular momentum of the galaxies as shown in Appendix A with the Milky Way.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='  Seeing that celestial bodies are practically noncharged, we shall restrict our consideration to the  situation where the central rotating disk and other bodies are not charged.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' 1  In this paper we investigate the rotation of the Milky Way Galaxy and its influence on the  Milky Way’s gravitational field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' The Milky Way will be approximated by an infinitely thin  rotating disk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' Although this approximation is rather simplified and does not reflect the structure  of the Milky Way’s disk, the approximation enables one to find out principal effects due to the  rotation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' Unexpectedly the effects are clearly pronounced and imitate the presence of  hypothetical dark matter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' In addition the effects explain the existence of the central bulge of the  Milky Way.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='  In Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' 2 we write out equations of I required for our studies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' Section 3 is devoted to the  treatment of the radial motion in the gravitational field of the Milky Way, and Sec 4 is concerned  with the motion in its equatorial plane.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' Remarks as to the results obtained are made in the  concluding section.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' Basic equations  In the present paper we employ the metric given in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='1) of I, the metric describing the  gravitational field created by an infinitely thin rotating disk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' As mentioned in Introduction we  consider noncharged bodies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' This being so, we put rq = 0 in Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='2)−(3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='3) of I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' Now Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='1)−(3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='3) of I acquire the form  1 If the rotating disk is charged, its charge should not be too large.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' The restriction on the charge is not  relevant to general relativity but is due to the limits of applicability of classical electrodynamics used in  this case [1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='  3  ds2= Σ  Λ c2dt2−  (  )  2  4  /  g  4  /  g  2  4  g  d  e  1  e  r  r  r  r  r  r  r  Δ  −  Σ  −  −  − Σdθ 2 − Σ  Y sin2θ dϕ 2 + Σ  aZ  2  sin2θ cdtdϕ,        (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='1)  where  Δ =  (  )  2  /  /  2  g  g  g  e  1  e  r  r  r  r  r  −  −  −  + a2,   Σ =  (  )  2  /  2  g  g  e  1  r  r  r  −  −  + a2cos2θ,   Λ =  (  )  2  /  /  2  g  g  g  e  1  e  r  r  r  r  r  −  −  −  + a2cos2θ,  (  )  θ  Δ  −  ⎥  ⎥  ⎦  ⎤  ⎢  ⎢  ⎣  ⎡  +  −  =  −  2  2  2  2  2  /  g  2  g  sin  e  1  a  a  r  Y  r  r  ,  r  r  r  Z  /  g  2  g  e  1  −  −  =  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='2)  We recall that rg = 2Gm/c2 is the gravitational radius of the disk of mass m and of radius a,  and the rotation of the disk is characterized by the angular momentum L = amc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' The metric is  singular only at r = 0, the value r = 0 corresponding to the surface of the rotating disk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='  For the present studies we need the equations of motion for the metric.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' Since we imply  noncharged bodies, we put rq = ε = 0 in Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='11)−(3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='14) of I with the result  ΔΣ  −  β  =  ahZ  Y  t  c ds  d  ,                                                            (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='3)  (  )  (  )  2  2  /  2  /  2  2  g  2  4  g  /  2  4  2  g  g  g  e  1  e  1  e  d  d  ⎭⎬⎫  ⎩⎨⎧  −  −  ⎥⎦  ⎤  ⎢⎣  ⎡  −  +  β  Σ  =  ⎟  ⎠  ⎞  ⎜  ⎝  ⎛  −  −  r  r  r  r  r  r  ah  a  r  r  r  s  r  (  )  (  ⎥⎦  ⎤  ⎢⎣  ⎡  −  κ  +  Σ  Δ  −  −  −  −  2  /  2  g  2  4  g  2  /  /  2  4  g  g  g  e  1  e  1  e  r  r  r  r  r  r  r  r  r  )  ,                            (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='4)  ⎥  ⎥  ⎦  ⎤  ⎢  ⎢  ⎣  ⎡  ⎟  ⎠  ⎞  ⎜  ⎝  ⎛  θ  −  θ  β  −  θ  −  κ  Σ  =  ⎟  ⎠  ⎞  ⎜  ⎝  ⎛ θ  2  2  2  2  2  sin  sin  cos  1  d  d  h  a  a  s  ,                              (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='5)  ⎟  ⎠  ⎞  ⎜  ⎝  ⎛  β  +  θ  Λ  ΔΣ  =  ϕ  Z  a  h  s  2  sin  1  d  d  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='6)  In these equations, β = Ε0/(μc2) where Ε0 is the energy of a test particle and μ is its mass, h =  L0/(μc) where L0 is the angular momentum of the test particle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' In other words, the constants β  and h are the dimensionless energy (the total energy divided by the rest energy of the test  particle) and a magnitude of the angular momentum of the particle (with dimension of length),  respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' The last constant κ (with dimension of square of length) is related to the constant K  of Landau and Lifshitz [2], problem 1 in § 104, by κ = K/(μ2c2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='  We also write down the expression for the nontensorial velocity v of the test particle  measured by an observer stationed at infinity and given in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='17) of I:  2  2  2  2  2  2  )  (  )  (  ahZ  Y  c  v  −  β  Λ  Λ  −  Σ  β  Σ  Δ  =  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='7)  4  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' Radial motion  The radial motion in the above metric is considered in I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' Here we analyze the motion in more  detail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' If a ≠ 0, the radial motion of a test particle is possible only along the axis of rotation of the  gravitating disk where θ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' From (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='5) we see that now h = 0 and κ = a2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' Substituting this into  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='3) and (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='4) results in the following equation for the dependence of the coordinate r upon the  time t  (  )  1  2  4  g  2  2  4  /  g  /  g  2  4  2  2  e  1  e  d  d  R  R  r  R  r  c  t  r  r  r  r  r  Σ  Δ  −  β  −  =  ⎟  ⎠  ⎞  ⎜  ⎝  ⎛  ,                                    (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='1)  in which  (  )  2  /  g  2  /  g  2  g  e  1  e  r  r  r  r  a  r  R  −  −  Δ  −  +  =  ,  (  )  2  /  2  2  g  g  e  1  r  r  a  r  R  −  Σ  −  +  =  ,  (  )  (  )  2  /  g  2  2  g  2  /  g  2  /  g  2  g  2  1  e  1  e  1  e  r  r  r  r  r  r  a  r  a  r  R  −  −  −  −  +  −  +  −  β  =  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='2)  In Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='1), only the factor R1 can be negative.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' Recalling that β is the dimensionless energy  of a test particle,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' in parallel with Landau and Lifshitz [2],' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' problem 1 in § 102,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' we introduce a  positive dimensionless “effective potential energy” (the positive effective potential energy  divided by the rest energy of the test particle)  (  )  (  )  2  /  1  2  /  g  2  2  g  2  /  g  2  /  g  2  g  e  1  e  1  e  )  (  ⎥  ⎥  ⎥  ⎦  ⎤  ⎢  ⎢  ⎢  ⎣  ⎡  −  +  −  +  =  −  −  −  r  r  r  r  r  r  a  r  a  r  r  U  ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='                                         (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='3)  so that R1 = β2 − U 2(r).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' The motion of the test particle is possible only if β ≥ U(r) when R1 ≥ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='  To examine U(r) we calculate the derivative  (  )  (  )  2  2  /  g  2  2  g  2  /  g  2  2  g  2  /  g  3  g  e  1  e  1  2  e  d  d  ⎥⎦  ⎤  ⎢⎣  ⎡  −  +  −  −  =  −  −  −  r  r  r  r  r  r  a  r  a  r  U  r  r  r  U  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='4)  It follows from this (r ≠ 0) that, if a < rg, then always dU/dr > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' If a > rg, the effective potential  energy U(r) is a minimum at  ⎟⎟  ⎠  ⎞  ⎜⎜  ⎝  ⎛ −  −  =  a  r  r  r  g  g  1  ln  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='5)  If a >> rg, the minimum is at r ≈ a, which amounts to saying that in this case the position of the  minimum is practically independent of the gravitational constant G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='  5  Figure 1 shows the behavior of U(r) for different values of the parameter a that determines  the angular momentum of the gravitating disk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' If a > rg, we have a potential well (this conforms  with the results of I).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' The particle oscillates in the well along the axis of rotation of the disk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' The  well comes into being only if the rotation of the disk is sufficiently rapid.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='  0,5  0,6  0,7  0,8  0,9  1  0  2  4  6  8  10  r/r g  U  2  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' Dependence of the effective potential U(r) of (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='3) upon r in the radial motion  perpendicularly to the disk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' Curve 1: a/rg = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='5, curve 2: a/rg = 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='  As to the Milky Way, Appendix A shows that a > rg for it and thereby there is a potential  well on the axis of rotation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' Neighboring stars are captured by the well, which gives rise to  formation of a bulge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' Consequently the central bulge of the Milky Way is due to the Milky  Way’s rotation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' All of this can be imitated by the presence of dark matter near the axis of  rotation, dark matter attracting the neighboring stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' To obtain a comprehensive picture of the  potential well and not only on the axis of rotation it is necessary to analyze the equations of  motion when 0 ≤ θ < π/2, which is beyond the scope of the present paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' Here we can only  remark that the motion along the axis of rotation is unstable because an arbitrary small  perturbation perpendicular to the axis will lead the star away from the axis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' The stable orbits in  the central bulge of the Milky Way are parallel to its disk, which is considered at the end of Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='  6  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' Motion in the equatorial plane  We turn now to the motion in the equatorial plane where θ = π/2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' First of all we write out the  formula for the velocity v of a star rotating about the Milky Way, the velocity measured by an  observer at infinity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' If we put  θ = π/2 and substitute the quantities of (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='2) into (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='7), we have  (  )  (  )  (  )  r  r  r  r  r  r  r  r  r  r  r  r  r  r  ah  a  r  a  r  c  v  /  g  2  3  /  g  2  /  g  /  g  2  2  g  /  g  2  2  2  /  g  2  /  g  2  g  2  2  e  e  1  e  1  )  e  2  (  )  e  (  e  1  e  ⎥⎦  ⎤  ⎢⎣  ⎡  −  −  −  −  β  +  β  −  β  ⎥⎦  ⎤  ⎢⎣  ⎡  −  +  =  −  −  −  −  −  −  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='1)  Let us compare this with the case where the gravitating mass does not rotate being a point mass,  of course.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' We mention in passing that this case is considered in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' [3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' If a = 0, Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='1) yields  r  r  r  r  c  v  /  g  2  /  g  2  2  2  e  )  e  (  −  −  β  −  β  =  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='2)  We see a drastic difference between (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='1) and (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='2) when r → 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' According to Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='1) v →  ∞ as r → 0 whereas according to Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='2) v → 0 in the same limit (recall that the value r = 0  corresponds to the surface of the rotating disk).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' It is clear from the physical point of view that the  rotating and gravitating disk must drag neighboring objects into rotation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' Although the Milky  Way is not, of course, a solid disk and the speeds of orbiting stars cannot be infinite;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' nevertheless  the results following from (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='1) demonstrate that the speed of the orbiting stars near the Milky  Way can be rather high in contradiction with the Newtonian law of gravitation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' The contradiction  found experimentally is commonly ascribed to the presence of dark matter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' We see that the  contradiction may be due to the rotation of the Milky Way.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='  We are coming now to the study of the motion in the equatorial plane.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' Once θ = π/2, we see  from (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='5) that κ = (βa − h)2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' Substituting this into (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='4) yields  π  Σ  =  ⎟  ⎠  ⎞  ⎜  ⎝  ⎛  R  r  r  s  r  r  r  2  4  g  /  g  2  4  2  e  d  d  ,                                                   (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='3)  where  (  )  [  ]  (  )  [  ]  (  )  ⎥⎦  ⎤  ⎢⎣  ⎡  −  β  +  +  −  −  −  +  β  =  π  2  2  2  g  2  2  2  g  2  2  2  2  2  g  1  y  h  a  r  y  a  y  r  ahy  y  a  r  R  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='4)  To simplify the notation we have introduced the quantity  1  0  ,  e  1  /  g  ≤  ≤  −  =  −  y  y  r  r  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='5)  If necessary, the derivative dr/dt can be found from (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='3) with use made of (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' It is worthy of  remark that, in the present case and in other cases considered in the paper, Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='3) leads to no  peculiarities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='  7  One can introduce an “effective potential energy” U(r) as above only if an expression of the  type Rπ of (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='4) does not contain the first power of β.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' If one considers the motion of a star in the  gravitational field of the Milky Way, account must be taken of the fact that the angular  momentum of the star characterized by the parameter h is very small as compared to the angular  momentum of the Milky Way given by the parameter a so that we can neglect h in (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='4) (h <<  βa) with the result:  (  ) (  ) [  ])  (  β  e  2  e  1  2  2  /  g  2  /  g  2  2  g  2  g  r  U  a  r  r  R  r  r  r  r  −  ⎥⎦  ⎤  ⎢⎣  ⎡  −  −  +  =  −  −  π  ,                                (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='6)  where  (  )  (  ) (  )  2  /  1  /  g  2  /  g  2  /  g  /  g  e  2  e  1  1  e  1  e  )  (  ⎥  ⎥  ⎦  ⎤  ⎢  ⎢  ⎣  ⎡  −  −  ξ  +  −  ξ  +  =  −  −  −  −  r  r  r  r  r  r  r  r  r  U  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='7)  Here we have returned to the previous notation and introduced the positive parameter  2  g  2  r  a  =  ξ  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='8)  For use later we recast Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='1) in terms of y and ξ:  (  )  [  ]  2  2  g  3  2  2  2  2  2  2  /  )  1(  )  1(  )  1  (  1  r  ahy  y  y  y  y  y  y  c  v  −  +  βξ  +  β  −  +  −  β  ξ  +  −  =  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='9)  Before analyzing Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='7) it is instructive to write Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='6) in the present case where h <<  βa (also hΛ << βaΖ as Λ = Ζ when r >> rg and θ = π/2):  ΔΣ  β  =  ϕ  Z  a  s  d  d  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='10)  As long as dϕ/ds is positive (we assume throughout the paper that a > 0), the test particle rotates  in the same sense as the gravitating disk and the speed of rotation is proportional to a, which  amounts to saying that the speed of rotation is very high.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' Classical mechanics is completely  inapplicable to this motion because the particle has a nonzero angular velocity (dϕ/ds ≠ 0)  whereas its angular momentum is nil (h = 0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='  In order to investigate the potential energy U(r) of (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='7) we rewrite Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='7) in terms of y  and ξ as  2  /  1  2  2  )  1(  1  1  )  (  ⎥  ⎦  ⎤  ⎢  ⎣  ⎡  +  ξ  +  ξ  +  −  =  y  y  y  y  y  U  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='11)  Differentiating we have  [  ]  2  2  2  4  2  )  1(  1  2  1  )  1(  2  d  d  y  y  U  y  y  y  y  U  +  ξ  +  +  −  ξ  +  ξ  −  =  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='12)  8  Seeing that 0 ≤ y ≤ 1, this derivative is always negative whereas dU/dr = (dU/dy)(dy/dr) is  nonnegative because dy/dr ≤ 0 (  ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' dy/dr = 0 if r = 0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' As a result, U(r)  increases monotonically from [ξ/(1+2ξ)]  2  /  g  /  e  d  /  d  r  r  r  y  r  rg  −  −  =  1/2 when r = 0 to 1 as r → ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' The qualitative behavior of  U(r) as a function of r can be schematically represented by a curve similar to curve 1 in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='  Therefore circular orbits are impossible since U(r) has no extrema if r ≠ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='  If β ≥ 1, the test particle spirals from infinity into the rotating disk because the angle ϕ  augments monotonically in view of (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='10).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' If β ≥ 1, the parameter β is related to the velocity of  the test particle at infinity v∞ by Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='13) of [3]:  2  2 /  1  1  c  v∞  −  =  β  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='13)  This relation follows from (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='1) as well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='  When β < 1, the test particle spirals into the rotating disk from the apogalaction, that is, from  the most remote point in the orbit where U(r) = β.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' As an example, we discuss the situation where  β ≈ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' In this situation the motion near the apogalaction should be described by classical  mechanics because v << c there.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' The equation U(r) = β can be written as  (  )  0  1  1  2  2  2  3  2  =  ξ  β  −  −  ξ  +  β  −  −  β  y  y  y  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='14)  We have here two small parameters 1 − β2 and 1/ξ (the parameter ξ is considered in Appendix  A).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' The solution to (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='14) in this case is found in Appendix B and is  (  )  (  ) ⎥⎦  ⎤  ⎢⎣  ⎡  β  −  ξ  +  β  −  =  3  2  2  1  1  1  y  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='15)  Seeing that y ≈ 0, we put y = 0 in (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='9) where it is possible with the result  2  2  2  2  1  β  +  −  β  =  y  c  v  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='16)  We substitute (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='15) with account taken of the fact that y → rg/r as r → ∞ by (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='5):  (  )  4  2  g  2  2  4  2  2  4  2  2  2  1  r  r  a  c  y  c  c  v  =  ξ  ≈  β  β  −  ξ  =  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='17)  This formula is not consistent with classical mechanics where v2 ∝ 1/r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' At the same time, v2 of  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='17) may be rather large because of c2a2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' Of course, when r → 0, the velocity v tends to infinity  inasmuch as y → 1 in (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='9).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' As a result, we see that the Milky Way’s rotation affects the motion  of its satellites even at great distances owing to a in (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='17).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='  Another case where it is possible to introduce an effective potential energy as above is  furnished by the relation βa − h = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' The relation h = βa signifies that the angular momentum of  9  the object in question is comparable to the one of the Milky Way provided that β is not too  small.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' Therefore the case in point is a galaxy orbiting the Milky Way.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' It should be remarked that  the mass of the galaxy may be rather small because the value of h is proportional to the distance  between the Milky Way and the galaxy which can be rather great.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' So, this case matches to a  dwarf galaxy located at a specific average distance rotating about the Milky Way.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' In this case  Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='9) becomes  (  )  (  )  2  2  2  2  2  2  2  2  1  )  1(  )  1  (  1  β  ξ  +  −  +  −  β  ξ  +  −  =  y  y  y  y  y  c  v  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='18)  Once βa − h = 0, Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='4) can be written in the form  [  ])  (  β  2  2  4  g  r  U  r  R  −  =  π  ,                                                       (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='19)  where  (  )  2  /  1  2  /  g  /  g  e  1  e  )  (  ⎥⎦  ⎤  ⎢⎣  ⎡  −  ξ  +  =  −  −  r  r  r  r  r  U  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='20)  Equation (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='6) yields now  ΔΣ  +  Λ  β  =  ϕ  )  (  d  d  Z  a  s  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='21)  Here again dϕ/ds > 0, as in (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='10), and the speed of rotation is proportional to a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='  The qualitative behavior of the effective potential energy U(r) of (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='20) as a function of r is  represented in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' It follows from the figure that, if  ξ  >  β  , the satellite galaxy spirals from  infinity into the Milky Way’s disk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' When  1  >  β  >  ξ  , the galaxy spiraling from infinity does not  reach the disk going around it and spirals to infinity again.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' If  ξ  −  >  β  >  4  /  1  1  1  , the galaxy when  starting from the apogalaction spirals about the disk and returns to the apogalaction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' Finally, if  )  4  /(  1  1  ξ  −  =  β  , the dwarf galaxy rotates about the disk in circular orbit with radius r0 =  −rg/ln[1−1/(2ξ)].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='  10  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' Schematic dependence of the effective potential U(r) of (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='20) upon r (not to scale).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' Point  A corresponds to ξ , point B corresponds to  ξ  −  4  /  1  1  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' The curve has ξ > 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='  The equation that determines the position of the apogalaction and perigalaction is β2 = U 2(r),  which is seen from (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='19) and (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='3) (at these positions dr/ds = 0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' We write the equation as  0  1  2  2  =  β  −  +  −  ξ  y  y  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='22)  The solution to the equation is  (  )  ξ  −  β  ξ  +  ±  =  2  1  4  1  1  2  y  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='23)  Recalling that y ≥ 0 we see that, when β > 1, the equation has only one positive solution;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' and  when β < 1, it has two positive solutions existing if  ξ  −  ≥  β  4  /  1  1  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' This is consistent with Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='  As above we shall assume that β ≈ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' Moreover, we suppose that |β2−1| is so small that  ξ|β2−1| << 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' In this situation the fist approximate solution valid for β > 1 and β < 1 is  ξ  = 1  1y  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='24)  This solution corresponds to the perigalaction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' When β < 1, the second approximate solution is  (  )  (  )  [  ]  2  2  2  1  1  1  β  −  ξ  +  β  −  =  y  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='25)  This solution corresponds to the apogalaction which exists when β < 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='  Considering the motion in the vicinity of the perigalaction we should take into account the  fact that y1 of (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='24) is very small [1/ξ ∼ 10−4 according to (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='5)].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' Consequently we can set y = 0  in (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='18) where it is possible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' In the remaining expression (β2 − 1 + y) we use (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='22) so that  U  A  B  1  0  11  2  2  2  2  β  ξ  =  y  c  v  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='26)  Substituting y1 of (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='24) with β ≈ 1 yields  ξ  = c  v  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='27)  If we put ξ ∼ 104 here, we shall obtain the speed of the satellite galaxy at the perigalaction equal  to v ∼ 10−2c = 3000 km/s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' This enormous speed is due to our approximation according to which  the Milky Way is considered to be a solid disk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' At the same time this result demonstrates that in  the real situation the speed of the satellite galaxy may be rather high.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='  Considering the motion in the vicinity of the apogalaction we remark that y2 of (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='25) is also  very small and thereby Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='26) holds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' Instead of substituting this y2 which essentially depends  on β, we refer to (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='5) and see that y is small when r → ∞, and y → rg/r in this case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' We place  this last y with β ≈ 1 in (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='26) to obtain  2  2  2  2  r  a  c  v  =  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='28)  It is interesting to note that the Newtonian gravitational consonant G disappears from this  formula and the role of G goes over to a2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' As to the dependence of v2 on r we can make the same  comment as the one concerning Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='17).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='  We turn now to the circular orbit which occurs when  ξ  −  =  β  4  /  1  1  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' It follows from (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='23)  that then y = 1/(2ξ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' Introducing these y and β into (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='18) yields  2  2  2  )1  4  )(  1  2  (  )1  4  (  2  +  ξ  −  ξ  −  ξ  ξ  = c  v  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='29)  If we take ξ ∼ 104 as in (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='5), we shall have v ∼ 1500 km/s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' This speed is of the same order of  magnitude as the speed resulting from (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='27).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='  There is yet another case where it is possible to introduce an effective potential energy U(r)  as above.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' We see from (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='5) that θ = constant if  2  2  2  sin  sin  cos  ⎟  ⎠  ⎞  ⎜  ⎝  ⎛  θ  −  θ  β  −  θ  =  κ  h  a  a  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='30)  We shall also suppose that  θ  β  =  2  sin  a  h  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='31)  Now (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='30) yields κ = a2 cos2θ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' If θ is small, one has h << a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' Therefore the case in point will be a  star orbiting the Milky Way.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='  Placing these κ and h in (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='4) we see that we can introduce U(r) which is  12  (  )  (  )  2  /  1  2  /  g  2  2  /  g  /  g  e  1  cos  1  e  1  e  )  (  ⎥  ⎥  ⎦  ⎤  ⎢  ⎢  ⎣  ⎡  −  θ  ξ  +  −  ξ  +  =  −  −  −  r  r  r  r  r  r  r  U  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='32)  If θ = 0, we have (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='3);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' if θ = π/2, we have (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='20).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' Consequently, when θ changes from 0 to π/2,  we go from Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' 1 to Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' In both cases the potential energy U(r) has a minimum and therefore  circular orbits are possible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' The orbits lie in planes parallel to the equatorial plane.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' When θ is  small, we shall have a star moving in the central bulge of the Milky Way.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' Concluding remarks  The present paper shows that the rotation of the Milky Way plays a decisive role in the  motion of stars or other galaxies in its gravitational field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' For example, it is just the rotation that  explains the existence of the central bulge of the Milky Way.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' The effect of the rotation may be so  strong that the quantity a2 characterizing the rotation takes the place of the gravitational constant  as is seen from Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='28).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' Of course, the results obtained in the paper can be applied to other  rotating galaxies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' The effects due to the rotation can imitate the presence of hypothetical dark  matter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' It may be that the rotation of the galaxies and of clusters of galaxies influences the  evolution of the Universe as long as there must exist an additional energy due to the rotation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='  Besides, the Universe or its big parts may rotate as a whole and centrifugal forces arising in this  case can accelerate their expansion imitating the presence of dark energy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='  The study of the rotation of the galaxies has become possible when the new metric for the  gravitational field of a rotating mass of Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' [1] was found.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' The metric is admissible for any  angular momentum of the rotating mass whereas the angular momentum of the galaxies can be  very large as shown in Appendix A with the Milky Way.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' The well-known Kerr metric is  completely inapplicable in this situation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='  In this paper we employ rather a simplified model for the Milky Way representing it as an  infinitely thin rotating disk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' When considering the motion of satellites in the vicinity of the  Milky Way the model can yield only qualitative results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' At great distances from the Milky Way  its structure is not of crucial importance so that the model may produce quantitative results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' As is  seen from Appendix A the radius a of the disk modeling the Milky Way is small in comparison  with its radius R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' It would be unreasonable to put a = R because this would yield an enormous  angular momentum L = Rmc and an enormous angular velocity ω = L/I for the Milky Way,  which would essentially overestimate all effects due to its rotation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='  13  We have, in the paper, considered several examples where solutions to relevant equations are  rather simple.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' Nevertheless even these simple examples demonstrate that without regard for the  rotation it is impossible to comprehend the actual gravitational field of the Milky Way.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='  Of course, it would be desirable to confirm the results of the paper by comparison with  observational data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' At this stage of theoretical investigations, however, it will be useless because  it is clear in advance that there will be no agreement between the results obtained in the paper  and the observational data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' This is due to the fact that the Milky Way is not an infinitely thin  rotating disk where the velocity of a test particle tends to infinity at the disk’s surface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' The main  aim in the paper is to attract attention to the fact that the rotation of galaxies plays an important  role in their gravitational field and to stimulate further investigations along this line.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' It is  necessary to develop a more realistic model of the rotating Milky Way in order to compare  theoretical results and observational data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='  The results of the present paper do not deny the existence of dark matter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' However,  properties and the distribution of dark matter cannot be correctly studied if the rotation of  galaxies is not taken into proper account, which follows from the results of the paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='  Appendix A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' Parameters for the Milky Way  The mass of the Milky Way can be estimated as m = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='29⋅1012 m☼ [4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' Therefore the  gravitational radius of the Milky Way is  km  10  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='3  2  12  2  g  ⋅  =  =  c  Gm  r  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='1)  The angular momentum of the Milky Way taken from Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' [5] is L = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='97⋅1067 J⋅s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='  Karachentsev [5] uses m = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='5⋅1011 m☼ and thereby the actual angular momentum of the Milky  Way may be greater than the above value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' With use made of L = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='97⋅1067 J⋅s we obtain for the  parameter a of the Milky Way that  km  10  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='1  13  ⋅  =  = mc  L  a  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='2)  It should be remarked that in order to be consistent with Karachentsev’s calculations one ought  to utilize his mass m = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='5⋅1011 m☼ with the result  km  10  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='1  14  ⋅  =  a  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='3)  We see that in any case a > rg and even a >> rg for the Milky Way.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' If the gravitational field  possesses its own angular momentum, this will only augment the value of a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='  There is another way to evaluate the angular momentum of the Milky Way.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' We can compute  the moment of inertia I with the help of the formula I = mR2/2 for a uniform disk and obtain L  14  from L = Iω.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' There are different estimates for the radius R of the Milky Way.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' We take R =  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='7⋅1017 km although some authors propose a larger value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' The angular velocity ω of the outer  parts of the Milky Way is close to the one in the neighborhood of the Sun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' The latter is ω =  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='94⋅10−16 s−1 [6].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' These numbers give  km  10  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='3  14  ⋅  =  a  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='4)  This estimate is close to (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' With this a, we calculate the parameter ξ of (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='8):  2  g  2  r  a  =  ξ  ∼ 104.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='5)  When considering the motion of Milky Way’s satellites in the equatorial plane it is preferable to  imply (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='4) or (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='5) because it is the rotation of the outer parts of the Milky Way with the  angular velocity ω which plays a leading part in the gravitational field created by the Milky Way  in this plane.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='  It may be noted that the Kerr metric is physically admissible only if a ≤ rg/2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' Consequently  the Kerr metric is absolutely unfit for the gravitational field of the Milky Way.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='  Appendix B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' Equation (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='14)  Equation (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='14) can be recast as  (  )  (  )  [  ]  (  )  0  1  1  1  2  2  2  3  2  =  ξ  β  −  −  +  β  −  −  +  β  −  −  y  y  y  y  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='1)  Instead of y we introduce y  according to y = 1−β2 + y  and obtain the equation  (  )(  )  (  )  0  1  1  1  1  2  2  3  2  2  =  ⎥⎦  ⎤  ⎢⎣  ⎡  ξ  +  +  β  −  +  +  β  −  β  −  −  y  y  y  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='2)  The first term here is small since we assume the smallness of 1−β2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' Upon neglecting this term we  arrive at a first approximation y  = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' We rewrite Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='2) in the form  (  )(  )  (  )  ξ  +  +  β  −  +  β  −  β  −  =  /  1  1  1  1  2  2  3  2  2  y  y  y  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='3)  Placing the first approximation y  = 0 in the right-hand side we obtain the second approximation  (  )  (  )  ξ  +  β  −  β  −  =  /  1  1  1  2  2  4  2  y  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='4)  If we return to y, we shall have  (  )  (  )  ξ  +  β  −  β  −  +  β  −  =  /  1  1  1  1  2  2  4  2  2  y  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='5)  15  The quantity 1−β2 can be arbitrarily small whereas ξ is fixed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' Therefore we can neglect 1−β2 in  the denominator, which leads to Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='15).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='  References  [1] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' Golovko, Results in Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' 15 (2019) 102536.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='  [2] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' Landau, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' Lifshitz, The Classical Theory of Fields, Butterworth-Heinemann,  Oxford, 2000.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='  [3] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' Golovko, Results in Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' 13 (2019) 102288.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='  [4] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' Grand, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' Deason, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' White, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' Simpson, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' Gómez, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' Marinacci, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='  Pakmor, MNRAS Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' 487 (1) (2019) L72.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='  [5] I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' Karachentsev, Binary Galaxies (in Russian), Nauka, Moscow, 1987.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='  [6] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' Camarillo, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' Dredger, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' Ratra, Astroph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' Space Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content=' 363 (2018) 268.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
+page_content='.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ftFAT4oBgHgl3EQf8B6L/content/2301.08748v1.pdf'}
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+Towards a Uniﬁed User Interface for Visual Analysis
+of Retinal Data in Ophthalmology
+Martin R¨ohlig1,a, Lars Nonnemann2,a, Hans-J¨org Schulz3,b,
+Oliver Stachs4,c, and Heidrun Schumann5,a
+aInstitute for Visual and Analytic Computing, University of Rostock, Germany
+bDepartment of Computer Science, Aarhus University, Denmark
+cDepartment of Ophthalmology, Rostock University Medical Center, Germany
+Abstract
+The visual analysis of retinal data contributes to the
+understanding of a wide range of eye diseases. For the
+evaluation of cross-sectional studies, ophthalmologists
+rely on workﬂows and toolsets established in their
+work environment. That is, they know what tools
+and data are needed at each step of their workﬂow.
+Yet, manually operating the various tools, including
+activation, data handling, or view arrangement, can be
+cumbersome and time-consuming. We thus introduce
+a new visualization-supported toolchaining approach
+that combines workﬂow, tools, and data. First, we
+provide access to the tools required for each step of
+the workﬂow. Second, we handle the exchange of data
+between these tools. Third, we organize the views of
+the tools on screen using suitable layouts. Fourth, we
+visualize the connection between workﬂow, tools, and
+data to support the data analysis. We demonstrate
+our approach with a use case in ophthalmic research
+and report on initial feedback from experts.
+1
+Introduction
+Over the years, many diﬀerent visual analytics (VA)
+tools have been developed to support the analysis of
+medical data in a wide range of application areas. The
+general goal is to help domain experts in their data
+analyses by providing means for decision making and
+knowledge discovery. This is also true for the area of
+ophthalmology, where VA tools have contributed to the
+understanding of various eye diseases. In collaboration
+with ophthalmologists, we were able to improve the
+detection of early retinal defects using dedicated VA
+tools for retinal data [37, 40]. This was made possible
+by developing the tools speciﬁcally for the needs of
+the ophthalmologists and integrating them into their
+workﬂows for the evaluation of cross-sectional studies.
+1martin.roehlig@uni-rostock.de
+2lars.nonnemann@vcric.igd-r.fraunhofer.de
+3hjschulz@cs.au.dk
+4oliver.stachs@uni-rostock.de
+5heidrun.schumann@uni-rostock.de
+However, a single VA tool is often not enough to fully
+handle complex analysis workﬂows. On the one hand,
+this is because diﬀerent VA tools may be needed for
+diﬀerent steps of the analysis. On the other hand, tools
+for data management and preprocessing are typically
+also required, as well as for statistical analysis and
+compilation of ﬁnal results. In general, the use of VA
+tools is focused on the steps necessary for the actual
+visual data analysis. The remaining steps are typically
+performed with other software solutions, ranging from
+clinical information systems over examination device-
+speciﬁc software to general spreadsheet and statistics
+software. The reason for this is that trying to inte-
+grate all the functionality into a single tool would
+signiﬁcantly increase the eﬀort required for software
+development and maintenance. In certain cases it may
+even simply not be possible due to time and resource
+constraints or because of the proprietary algorithms or
+data formats used. As a result, domain experts have
+to interact with various tools – VA-based or not – and
+exchange data between them to fulﬁll all the necessary
+steps in their analysis workﬂows.
+One of the resulting problems is that for a given
+analysis workﬂow in the domain, it may not be imme-
+diately clear how to coordinate the required tools and
+the corresponding visual output on the screen. For
+each workﬂow step, domain experts must determine
+which tools and what pieces of information to show
+before deciding how to display them on the screen to
+get the current step done. This places an additional
+burden on a given workﬂow, making it more cumber-
+some and time-consuming to execute. At the same
+time, no support is generally oﬀered to complete these
+secondary tasks alongside the actual data analysis. In-
+stead, in practice, experts have to manually switch
+between diﬀerent stages of preprocessing, visual data
+analysis, and result interpretation, and operate the
+tools and their output by hand. Often, this is necessary
+again and again each time a workﬂow is executed.
+We present a novel visualization-supported tool-
+chaining approach that combines workﬂow, tools, and
+data. With a use case in the analysis of retinal data in
+ophthalmology, we show that our approach not only
+1
+arXiv:2301.01840v1  [cs.HC]  4 Jan 2023
+
+provides access to the tools and data needed for each
+workﬂow step, but also helps to organize the tools’ user
+interfaces (UIs) on the screen. This reduces the over-
+head of managing the various tools and data during the
+workﬂow execution. In our collaboration with ophthal-
+mologists, the experts were thus able to concentrate
+on the actual steps of data analysis in the evaluation
+of cross-sectional studies. Our contributions are:
+Integration of workﬂow and tools: We examine
+existing connections between workﬂow, tools, and
+data in the context of our use case and establish
+meaningful links for accessing the right tools, the
+right data, and the right views at the right time.
+Visualization support for toolchaining: We
+present an editor that allows to interactively
+create toolchains and adjust tools and data for
+each step of a workﬂow. We incorporate a uniﬁed
+UI that shows the workﬂow, tools, and data and
+helps to organize multiple tool views on screen.
+Application in practice: We assess our approach
+together with domain experts in a use case in
+ophthalmology. We discuss the diﬀerences with
+current data analysis practices and report initial
+expert feedback.
+The remainder of this paper is structured as follows.
+The background and current analysis workﬂow are
+described in Section 2, followed by an overview of
+related work in Section 3. Our approach to combining
+workﬂows, tools, and data is detailed in Section 4. An
+application example and user feedback are presented
+in Section 5. Finally, a conclusion and topics for future
+work are discussed in Section 6.
+2
+Background
+In ophthalmology, data from various examination
+methods are analyzed to understand the impact of dif-
+ferent eye diseases on the condition of the human retina.
+One widely used examination method is optical coher-
+ence tomography (OCT) [1, 2]. Modern OCT scanners
+enable noninvasive imaging of substructures of the
+multilayered retina with high spatial resolution [3]. By
+analyzing the OCT images, ophthalmologists are able
+to detect common ocular diseases, such as age-related
+macular degeneration [18], diabetic retinopathy [25],
+or glaucoma [20], as well as other pathologies with
+ocular signs, such as multiple sclerosis [17]. OCT ex-
+aminations are therefore now a standard procedure in
+clinics and an integral part of ophthalmic research [26].
+We are particularly interested in OCT data analysis
+in the context of cross-sectional studies in ophthalmic
+research. Here, multiple OCT datasets have to be
+analyzed together with information from other clinical
+records to compare the retinal condition of patients
+with that of healthy controls. This is a complicated
+process. To handle the study data, ophthalmologists
+rely on workﬂows and toolsets that are established
+in their work environment. These workﬂows can be
+divided into three common stages:
+Data preparation: The required data from all study
+participants are collected and processed, including
+ﬁltering and screening based on the study criteria.
+Afterwards, the patient and control groups are
+assembled.
+Data analysis: With the prepared data, the diﬀer-
+ences between the patients and controls are com-
+puted. Data subsets of interest are selected, mea-
+sured, and statistically quantiﬁed.
+Summarization of results: The ﬁndings most rele-
+vant to the study design are compiled. The ﬁnal
+results are presented by a combination of images,
+plots, and tables.
+Throughout these three stages, ophthalmologists are
+dealing with diﬀerent tools for diﬀerent types of data.
+The tools used for the ﬁrst stage typically include
+clinical information systems, OCT device-speciﬁc soft-
+ware, and general spreadsheet software for managing
+and processing the raw electronic health records and
+OCT datasets. In the second stage, mainly statistical
+software is used to analyze the prepared data and,
+more recently, also exploration-oriented VA tools [34,
+38]. Here, the data are often enriched with computed
+measurements as well as reduced to relevant subsets.
+Finally, in the last stage, selected results are summa-
+rized and presented with charting tools.
+This mixture of diﬀerent tools, ranging from general-
+purpose to visualization-speciﬁc, has to be operated
+manually in current analysis practice. Switching be-
+tween the tools can be diﬃcult, however, as ophthal-
+mologists must remember which tools are used in which
+part of the workﬂow, locate those tools at the right
+time, and activate them by hand. The exchange of
+data can also be quite labor intensive due to the dif-
+ferent data formats used and the limited compatibility
+between the various tools. It is therefore not easy to
+keep track of which data was transferred when and
+between which tools. On top of that, the output of the
+tools must be arranged sensibly on the screen, since
+for some workﬂow steps not only one, but several tools
+must be operated simultaneously. This is the case,
+for example, in the data exploration stage, where it is
+often necessary to go back and forth between selection
+of data subsets, their visual analysis, and statistical
+quantiﬁcation. All in all, the limited integration of
+workﬂow steps, tools, and data commonly increased
+the time and eﬀort of performing an analysis workﬂow
+and places an additional burden on ophthalmologists.
+Our objective therefore is to help ophthalmologists
+to show the right tool at the right time, to illustrate
+the ﬂow of data between them, and to make clear
+which output was generated for which step with which
+data. Establishing this level of support will help reduce
+the overhead of managing the various tools and data
+during workﬂow execution.
+2
+
+3
+Related work
+The development of workﬂow-based toolchains relates
+to challenges regarding sustainable data exchange [39]
+and tool interoperability [27]. While these two research
+areas are complex in their own right, dealing with
+multiple VA tools introduces an additional problem
+for workﬂow coordination, namely unifying the UIs of
+independent tools.
+There are many examples for managing multiple
+views, reaching from comprehensive application toolk-
+its with built-in VA tools to loosely coupled, concur-
+rently running applications [10, 9]. Most of the existing
+solutions rely on the following approaches:
+Integrating views: Applications like Tableau [4],
+Dashiki [11], or Fusion [5] allow users to rapidly
+assemble multiple views within a given interface.
+This is usually achieved via web interfaces to cre-
+ate mashups [15] or webcharts [13]. If enough
+screen space is available, even dozens of individual
+views can be incorporated in the same environ-
+ment [32]. However, using integrative approaches
+also has its limitations, as the visual load increases
+with the number of views included.
+Coupling views: Instead of nested or tabbed UIs,
+some approaches rely on loose coupling of inde-
+pendent views for view orchestration. This way,
+the views are interactively assembled into a com-
+mon interface.
+Example are WinCuts [6] and
+Fa¸cades [8], where arbitrary view regions are repli-
+cated in a combined interface to focus on task-
+related areas. Other methods rely on implicit or
+explicit visual links between independent views to
+facilitate the connection between them [16, 23].
+Both the integration of views and the coupling of
+views depend on the number of views and the available
+screen space. This is where the workﬂow-based order
+of tool execution becomes important. By providing a
+toolchain, information is made available about which
+tools need to be active at what time and what data
+needs to be passed from one tool to the next. This
+can reduce the visual load for the current analysis step.
+While this can help users with the data analysis, it
+also means that management of tool views over time
+must be considered. In this regard, two basic types of
+displaying tool views can be distinguished:
+Sequential display: In simple workﬂow scenarios, it
+can be suﬃcient to display information via only
+one tool view at a time. An example is Stack’n’ﬂip
+[19], where views are displayed in a sequential
+order and can be switched interactively through
+a central interface.
+Parallel display: For certain analysis tasks of more
+complex workﬂows, it is necessary to execute
+more than one tool at a time, with the individ-
+ual views displayed concurrently. One example is
+ManyVis [21], where multiple views are shown to-
+gether in an integrated visualization environment.
+When coordinating multiple tools, the toolchain
+itself is also sometimes encoded visually, e.g., as a
+directed graph showing its connections [12, 27]. Con-
+sidering the steps completed and data generated with
+the tools over time, similar visualization approaches
+can be found in the ﬁeld of provenance visualization,
+especially with regard to workﬂow provenance and
+data provenance [29]. Examples are AVOCADO [28]
+for the visualization of workﬂow-derived biomedical
+data, and the systems VisTrails [7], Galaxy [14], or
+Taverna [22] for automated tracking and visualization
+of workﬂow and data provenance. The representations
+of workﬂow steps and related data with these systems
+help users understand the data analysis and make it
+reproducible. However, combined support for the ex-
+ecution of workﬂow steps, the sequential or parallel
+use of tools and their data exchange, and the arrange-
+ment of visual outputs on the screen have hardly been
+addressed so far.
+Against this background, we recently introduced a
+layered toolchaining approach for VA [41]. Our main
+idea is to model the VA tools in a given workﬂow as a
+graph that represents the tools as its nodes and the
+diﬀerent levels of communication between them as di-
+rected edges. This provides ﬂexibility for describing
+diﬀerent couplings, regardless of whether the tools are
+used in a sequence, repeatedly back-and-forth, or si-
+multaneously side-by-side. Based on this model, we
+were able to characterize the data exchange between
+VA tools [39] and introduce ReVize [36], a library for
+adding toolchain support for web-based applications
+using Vega-Lite [30] as a common exchange format.
+We further demonstrated a framework to interactively
+create toolchains via custom data connections between
+independent VA tools [42, 44]. We have not yet ad-
+dressed, however, how to present and interact with
+a uniﬁed UI and how to incorporate the tools’ out-
+put into a sensible assembly during the execution of a
+workﬂow in practice.
+In summary, there are several approaches for the
+uniﬁcation of UI elements. With respect to retinal
+data analysis in ophthalmology, it is not clear how
+to translate these approaches into practice, especially
+when considering complex analysis scenarios such as
+the evaluation of cross-sectional studies. We there-
+fore aim to ﬁll in the missing pieces and develop a
+consistent coordination approach for our application
+example. To this end, we build on our ideas of layered
+toolchaining [41] and investigate (1) what tools to show
+in which part of the workﬂow, (2) what data parts to
+exchange between the tools, (3) how to present the
+tools and the data on screen, and (4) how to establish
+a connection between workﬂow, tools, and data that
+supports the analysis of retinal data.
+3
+
+4
+Workﬂow-based toolchaining
+for visual analytics
+We aim to support toolchaining for VA of retinal data
+in ophthalmology. To ﬁnd suitable solutions, we ﬁrst
+consider the requirements in our use case. On that
+basis, we then present new concepts and visual designs.
+4.1
+Requirements
+We conducted interviews with ophthalmologists and
+job observations to get an overall idea of the current
+analysis practices. Together, we then engaged in the
+statistical analysis of two studies [31, 33] and subse-
+quently two additional studies [37, 40] analyzed with a
+mixture of statistical and VA tools. This allowed us to
+gain deeper insights into their workﬂows and use of VA,
+statistics, and general-purpose analysis software. We
+ﬁnally compiled a list of design requirements related to
+the coordination of VA tools for retinal data analysis.
+Access to tools (R1): In a workﬂow, the temporal
+order of tools and their interplay is typically only
+implicitly deﬁned. On the one hand, this means
+that the ophthalmologists must remember which
+tools to activate for the current work step. On the
+other hand, they also need to determine what con-
+tent to display at the same time with these tools.
+The contents include currently required panels
+and views, but also information about available
+data and information about already used or sub-
+sequent tools. Therefore, access to the right tool
+at the right time must be supported.
+Connection of tools and data (R2): In
+general,
+the entire data are not passed between analysis
+tools over and over again during the execution of
+a workﬂow. Instead, the data are incrementally
+reduced and sometimes even selectively extended
+to extract valuable information. Thus, ophthal-
+mologists must not only supply the original data
+to the tools at the beginning of the workﬂow,
+but also manage the exchange of various data
+pieces between the tools during subsequent steps.
+This includes taking care of all necessary data
+transformations between the tools and updates
+if parts of the data have changed during the
+analysis. Supporting access to the right data at
+the right time and establishing a link between
+the data and the tools is thus a requirement.
+Arrangement of tool views (R3): When
+activat-
+ing diﬀerent tools, the layout of their views should
+correspond to their intended use in the respective
+part of the workﬂow. If the tools are used one
+after the other, their views may simply be inter-
+changed. However, if they are used in parallel,
+their views must be organized on the screen in a
+meaningful way so that they can be used together
+eﬀectively. In addition, navigational features are
+needed that not only give the user control over
+Figure 1: Overview of the coordination components.
+Shown are the workﬂow steps S1 to S5 (a), associated
+toolsets A to D (b), links between workﬂow steps and
+tools L1 to L6, and view layouts V1 to V3 assigned
+to each workﬂow steps and toolset (c).
+switching between workﬂow steps and associated
+view layouts, but also help to maintain orienta-
+tion at the same time. Consequently, support for
+obtaining the right view layout at the right time
+is needed to manage the visual output of tools.
+From a VA perspective, the three requirements (R1)
+to (R3) are related to three fundamental questions that
+need to be answered in order to support toolchaining
+in our use case. The ﬁrst questions is what to show?.
+With respect to requirement (R1), it addresses the
+selection of all relevant information that needs to be
+presented to the user at a given point in time. The
+second question is what data parts to exchange? and
+corresponds to requirement (R2). It aims to identify
+subsets of interesting data and consider when and how
+they should be exchanged between tools. The third
+question is how to show?. Related to requirement (R3),
+it is primarily about the layout and adaptation of views
+and panels of the current tools. In addition, it includes
+presenting information about the workﬂow itself and
+how workﬂow steps, data, and tools are connected. By
+answering these three questions in our VA design, we
+create a meaningful coordination between workﬂow,
+tools, data, and view layouts.
+4.2
+Combination of tools, data, and
+view layout
+To meet our design requirements and answer the three
+corresponding questions, we ﬁrst need to determine
+several pieces of information. For this purpose, we
+build on our earlier work on a layered approach to
+lightweight toolchaining in VA [41]. In particular, we
+implement and adapt the proposed coordination model
+to establish a connection between the four components:
+(i) domain workﬂow, (ii) tools used, (iii) data analyzed,
+and (iv) layout of tool views. Figure 1 illustrates the
+interplay of these components.
+We start by looking at the existing workﬂow and the
+tools used in the application domain. This allows us
+4
+
+to determine a set of tools per workﬂow step (Fig. 1a).
+Generally, one or more tools may be required to per-
+form each step. The sequences in which these tools
+must be activated can be derived from the order of
+the workﬂow steps. The back and forth between the
+steps also determines which data connections must be
+established between which tools. With this informa-
+tion at hand, we build up a coordination graph [41] by
+stepwise deﬁning a link between pairs of tools (Fig. 1b).
+The links capture both the usage ﬂow, i.e., all possible
+activation sequences, and the data ﬂow, i.e., all possi-
+ble data exchanges, between the tools. Based on this,
+we then deﬁne diﬀerent arrangements of tool views
+and assign a suitable layout to each combination of
+workﬂow step and toolset (Fig. 1c). Note that one set
+of tools can be used in multiple workﬂow steps, but the
+content of the tools can be displayed with a diﬀerent
+layout speciﬁc to each particular step. We determine
+these layouts based on user preferences. For example,
+we support choosing from a set of default layouts or
+saving custom arrangements of views per step.
+The ﬁnal coordination graph provides all the infor-
+mation necessary to facilitate toolchaining in our use
+case. That is, it allows us to query at any time which
+tools need to be activated or deactivated, which pieces
+of data need to be transferred from a current tool to
+the next, and which content should be displayed how
+on the screen. In this way, it enables us to answer
+in particularly the questions what to show? (R1) and
+what data parts to exchange? (R2). Incorporating dif-
+ferent view layouts into the graph further provides the
+basis for answering the third question how to show?
+(R3). The actual path through the coordination graph,
+however, is not determined until the workﬂow is ex-
+ecuted at runtime and the user interactively decides
+which steps are to be processed in which order. Hence,
+in addition to the arrangement of the individual tools
+on the screen, it must be possible to access the coor-
+dination graph, the progress of the workﬂow, and the
+results obtained during its execution. To this end, we
+present a new design that provides this information
+both visually and interactively, speciﬁcally addressing
+the third question how to show? (R3) again.
+4.3
+Visualization support for the uniﬁ-
+cation of UI ensembles
+The workﬂow describes the analysis steps to be exe-
+cuted by the user. Per step, one or more tools are
+used. The coordination graph captures the pairwise
+coupling of the tools and the associated data exchange.
+The assigned layouts determine how the tool views are
+displayed on the screen. This results in a toolchain
+that controls the handling of the tools, including going
+back and forth between them.
+To use the coordination graph eﬀectively, the in-
+formation it contains must be made available to the
+user.
+We therefore introduce a uniﬁed UI that vi-
+sualizes the workﬂow together with the coordination
+graph. Our design assists users in creating or adapting
+a coordination graph, retrieving information from it
+for the execution of the workﬂow, and comprehending
+the results obtained. It consists of several views that
+allow switching between the current work step and the
+corresponding toolchain in the background.
+Visualizing
+the
+workﬂow
+and
+coordination
+graph:
+From the user’s point of view, it is important
+to get an idea of the work at hand before executing a
+particular workﬂow. This involves not only the individ-
+ual workﬂow steps that must be performed, but also
+the data to be analyzed and the extent to which tool
+coordination is supported. Therefore, with our uniﬁed
+UI, we provide an overview of the workﬂow along with
+the coordination graph. A toolchain editor makes it
+possible to view individual links between tools in detail
+and make adjustments as needed. Figure 2 illustrates
+our design consisting of three views.
+The workﬂow view displays the workﬂow steps as a
+ﬂowchart (Fig. 2a). The steps are shown as rectangles
+colored according to their workﬂow stage (preparation,
+analysis, summarization). The arrows between the
+rectangles encode the possible back and forth between
+the steps.
+Information about the current progress
+within the workﬂow is provided by highlighting the
+steps and links that have already been performed.
+The coordination graph view shows the toolsets used
+in the workﬂow as a network visualization (Fig. 2b).
+The toolsets are coded as circles and the lines indicate
+their data exchange and activation capabilities. Hov-
+ering over the circles displays additional information,
+e.g., which tools are included in the respective set and
+in which steps they are used.
+The third view consists of a toolchain editor (Fig. 2c).
+Based on our previous work [42, 44], the main purpose
+of the editor is to establish a connection between the
+workﬂow and the coordination graph. It consists of
+three panels showing all available tools (top), all data
+sources (bottom), and the links between the tools
+(middle). Within our interface, the editor performs
+two functions. The ﬁrst is to create a coordination
+graph, if not already available, for a given workﬂow
+and set of tools. Using the three panels, links between
+tools can be added step by step via drag & drop. The
+second function is to specify the data sources to be
+used as input for a planned execution of the workﬂow,
+and to adjust the data transformations between tools.
+Together, the three views provide an overview of the
+work, the tools, and the data involved, and allow tool
+coordination to be set up as required.
+Supporting the workﬂow execution:
+After a
+connection between the workﬂow and the tool coordi-
+nation through the coordination graph has been estab-
+lished, the execution of the individual workﬂow steps
+must be supported. Here, it is important to inform the
+user about what currently needs to be done, as well as
+provide navigation support in terms of what has been
+done before and what comes next. In addition, the
+5
+
+Figure 2: Visualization of workﬂow, coordination graph, and toolchain editor. The workﬂow steps are displayed
+as colored rectangles (a). The coordination graph is represented as a network visualization, where the circles
+depict the tools and the lines encode the links between them (b). The toolchain editor (c) consists of three panels
+showing the available tools (top), the data sources (bottom), and the data connections between tools (middle).
+ability to document the work and progress is required.
+As illustrated in Figure 3, our interface support this by
+showing current steps in detail along with additional
+information about the coordination.
+To focus on the current steps during a workﬂow exe-
+cution, the workﬂow view is switched from an overview
+to a detail view (Fig. 3a). This enlarges the active
+step and shows a description of what needs to be done
+and how the tools needed to do it are arranged on
+the screen. The previous step is displayed above the
+active step and the next possible steps are displayed
+below it. Clicking on these steps allows to go back
+and forth within the workﬂow. Once a workﬂow step
+has been selected, the corresponding tools are auto-
+matically activated and their content is arranged on
+the screen based on the assigned layouts. The data
+exchange between the last and the current tools is also
+handled automatically as deﬁned in the coordination
+graph. This reduces the eﬀort of manually searching
+for the right tools, activating them, transferring the
+work data, and customizing where the content is dis-
+played on screen. To see the actual path taken so far
+through the workﬂow and coordination graph, the user
+can switch back to the overview visualizations (Fig. 2)
+at any time. This highlights the links of the active
+step and tools in the overviews, making adjustments
+in the coordination graph possible on the ﬂy.
+Our interface also helps to document the work per-
+formed. On the one hand, the user can set the status of
+the active workﬂow step (e.g., pending, done, paused,
+canceled) to indicate the state of the work. In addition,
+notes can be added to the steps describing how the
+work was performed and whether it was necessary to
+deviate from the original work description (Fig. 3b).
+On the other hand, intermediate results can be cap-
+tured via screenshots of the tool content currently
+visible on the screen (Fig. 3c). Multiple screenshots
+can be added by selecting any areas of the screen, with
+a reference image showing which areas have already
+been captured. The content of the selected screen areas
+can be updated or removed again if relevant changes
+occur during work. If a workﬂow step is visited mul-
+tiple times, e.g., by navigating back and forth in the
+workﬂow, a new set of notes and captures is created
+for each activation. That way, a detailed history of all
+work performed is generated. Especially when diﬀerent
+paths are taken through the workﬂow, this helps to
+recapitulate which steps were taken to arrive at the
+results achieved in each case.
+Compiling the results:
+During and after the exe-
+cution of the workﬂow, it typically becomes necessary
+to summarize the work performed. Going back and
+forth between workﬂow steps and multiple tools, how-
+6
+
+Workflow * -
+-ox
+ Tool coordination 7.
+-口×
+START
+PREPARATION
+ANALYSIS
+PRESENTATION
+END
+Gather study data
+ Preprocess health records
+ Toolchain editor  - ×
+Preprocess ocT datasets
+ show Advanced Connection Options
+?
+Check data quality
+delberg Eye Expl: TExplorer 4.0.0 (x etinavis_2017100
+Tools:
+Compile study groups
+Reset Default
+delberg Eye Expl
+TExplorer 4.0.0 (x
+indhno
+Input
+Channel
+ReVize Server
+ReVize Server
+etinavis_2017100
+ Graph:
+Analyze clinical health records
+Format
+Path:
+Add Converter
+xa.
+xa.
+Refine groups & analyze individuals
+ corneal
+corneal
+xa
+xa.
+cars
+ corneal
+Data:Figure 3: Visualization of individual workﬂow steps and additional information. On the left side, the current
+step is enlarged to show additional information, and the previous and next possible steps are displayed above
+and below (a). On the right side, a full description and user notes about the current step are depicted (b). In
+addition, intermediate analysis results are displayed as a list of screen captures (c).
+ever, can make it diﬃcult to recapitulate the work after
+completion and extract the most meaningful insights
+from multiple intermediate results. In fact, the end
+results do not have to come from a single workﬂow step
+and a single set of tools. It is rather often a mixture
+of intermediate results from multiple steps and tools
+that need to be reconciled and compared to provide an
+overall picture of the work done and insights gained.
+Therefore, our interface provides an additional sum-
+mary view for compiling results across workﬂow steps
+and tools. Figure 4 illustrates this view.
+The summary view consists of three areas. In the
+lower area, a history of all performed workﬂow steps
+is displayed in the order of their activation (Fig. 4a).
+Each step is represented by a colored rectangle with
+small icons indicating whether intermediate results
+have been captured. In the middle area, the interme-
+diate results are listed grouped by the respective steps
+(Fig. 4b). In the top area, the intermediate results
+can be interactively combined into a single image via
+drag & drop (Fig. 4c). The ﬁnished image can then be
+exported for further use. This allows to bring together
+and compare the main ﬁndings of the data analysis.
+Without our uniﬁed UI, this would hardly be directly
+possible if only the work steps and the associated tools
+were considered individually.
+Overall, the diﬀerent views of our uniﬁed UI estab-
+lish a visual connection between workﬂow, tools, data,
+and displayed content. Our design approach thus as-
+sists users in creating a coordination graph that ﬁts
+a particular workﬂow and provides valuable informa-
+tion for executing the workﬂow and understanding the
+results. To assess the utility, we tested our approach
+with a use case in ophthalmology.
+5
+Application to retinal data
+analysis
+We applied and tested our solution in collaboration
+with ophthalmologists. As brieﬂy described in Sec-
+tion 2, the ophthalmologists were particularly inter-
+ested in the analysis of retinal OCT data in the context
+of cross-sectional studies. In such studies, data from
+a group of patients are compared with data from a
+control group to determine any inﬂuence of the disease
+under study on the condition of the retina and other
+measured clinical parameters. After the data acquisi-
+tion from all study participants, the study evaluation
+follows established workﬂows that are usually divided
+into three stages: (1) data preparation, (2) data anal-
+ysis, and (3) summary of results. Currently, however,
+the ophthalmologist must manually operate the tools
+required to accomplish these stages.
+Together, we
+therefore created a coordination graph according to
+their steps and tools, and compared the execution of
+7
+
+Workflow *-×
+ Tool coordination
+ Toolchain editor
+-口×
+ capture, Note *- ×
+@ Help
+*-口x
+START
+PREPARATION
+ANALYSIS
+PRESENTATION
+END
+ capture *_ ×
+-口X
+?
+Preprocess ocT datasets
+Add
+Refresh all
+e
+Check data quality
+Description
+D: Scan slightly off-center, Bscan #2,4, 7, 13, 16, 71, 147, 185-189, 1
+For each ocT dataset:
+218, 222-223, 228, 234
+OD_HR: Scan slightly off-center, Bscan #1, 3,8, 14, 37, 41, 45-46, 53, 6
+. Visually inspect data quality (ocT images and computes
+206-221, 223, 226, 229-231
+attributes)
+OS: Slightly of center, Bscan #2, 6, 9, 11 12, 15, 17, 26 28, 34 35, 44, 7
+. Try to fix segmentation errors
+Os_HR: Bscan #1-4, 18-19, 23, 40, 42, 46, 53, 63, 80, 84, 92-93 (miss), 2
+: Exclude participants with ocT data of insufficient quality
+231, 234, 237
+Tools
+ Note 7- ×
+7-x
+- Scan has segementation errors
+Compile study groupsFigure 4: Visualization of workﬂow history and result composition. At the bottom, a history of all performed
+workﬂow steps is displayed (a). In the middle, all captured intermediate results are listed (b). At the top, selected
+intermediate results are summarized in an overview that illustrates the main ﬁndings of the data analysis (c).
+the workﬂow supported by our solutions with their
+experience with manual tool coordination in previous
+studies [31, 40].
+5.1
+Connection of workﬂow, tools, and
+data
+For our use case, we reevaluated the data of a previous
+study [40] with focus on the detection of thickness
+changes in intraretinal layers at an early stage of di-
+abetes mellitus. In this study, data from 33 diabetic
+patients and 40 healthy controls were analyzed.
+The data:
+In the study evaluation, we distinguished
+between two types of input data. The ﬁrst type was
+retinal OCT datasets. These datasets consisted of
+3D images and segmented layer boundaries of each
+participant’s retina.
+The second type was clinical
+health records. The record of each participant included
+various parameters such as age, body mass index, blood
+glucose level, and type of medication received.
+The tools:
+A total of 8 diﬀerent tools were used
+to process and analyze the data. On the one hand,
+these were commercial software tools speciﬁcally for
+the acquisition and processing of retinal OCT data.
+For the management of the tabular data from the
+electronic health records also general spreadsheet and
+statistical software was used. On the other hand, we
+applied our own VA tools designed for the exploration
+of retinal OCT data and multivariate data from clinical
+health records [24, 34, 38] For statistical analysis, we
+additionally used custom scripts together with the R
+software environment [43].
+The workﬂow:
+For the evaluation of the study data,
+we built on our prior research on workﬂow-based visual
+analysis of retinal data [38]. Together with the ophthal-
+mologists, we enhanced our approach to include the
+multiple tools and data sources needed for comprehen-
+sive ophthalmic research. In the extended workﬂow,
+the ophthalmologists had to perform 9 steps (Fig. 2a).
+In the ﬁrst 5 steps, they focused on the data prepa-
+ration. This included collecting study data from all
+subjects, calculating retinal thickness, checking data
+quality, and assembling the two groups to be compared.
+In the next 3 steps, the ophthalmologists continued
+with the data analysis. Here, their main focus was on
+analyzing the diﬀerences in thickness values between
+the groups. They also alternated between the analy-
+8
+
+ Result -× History
+Composition
+DAge
+M-CNFD
+28.75
+6
+15.0
+39.06
+Results
+History
+11
+10sis of OCT data and clinical parameters to identify
+outliers and reﬁne the groups accordingly. For this
+purpose, a mixture of visual exploration and statistical
+hypothesis testing was used. Especially at this stage,
+there was therefore a back-and-forth between workﬂow
+steps to narrow down the data to relevant subsets. In
+the ﬁnal step, the ophthalmologists summarized the
+key ﬁndings based on their analysis of the identiﬁed
+subsets. This included extracting images of relevant
+data values and creating additional charts, e.g., to
+highlight interesting statistical results.
+The toolchain:
+The tool coordination for our use
+case was created with the toolchain editor (Fig. 2c).
+First, we imported all tools and datasets into the ed-
+itor. Together with the ophthalmologists, we then
+focused on making the tools available when needed
+by automating their activation. For this purpose, we
+displayed the workﬂow steps in the overview visual-
+ization and created corresponding links between the
+tools using the editor. The visual representation of the
+connections in the editor helped us to get an idea of
+when which tool was used. Using the drag & drop fea-
+tures of the editor, we then set the data input for the
+workﬂow and customized the data transfer between the
+tools. Once the links were established, we performed a
+test run by navigating the workﬂow to ensure that the
+modeled coordination graph met the ophthalmologists’
+expectations. The test run also served to assign a suit-
+able view layout to the automatically activated tools
+for each workﬂow step. Based on the default layouts,
+the ophthalmologists were able to reﬁne where content
+should be displayed and how much space each view
+was given on the screen. The layouts, along with a
+description of the workﬂow and coordination graph,
+were saved for subsequent executions.
+5.2
+Workﬂow execution and testing
+We applied the workﬂow and toolchain according to
+the use case deﬁned together with ophthalmologists.
+During conception of our approach and the testing of
+our solutions, we obtained initial informal feedback in
+discussions with primarily two ophthalmic experts.
+Execution of the workﬂow and toolchain:
+After
+the initial conﬁguration described above, we executed
+the previously saved descriptions of the workﬂow and
+toolchain. Starting from the overview of the work-
+ﬂow (Figure 2a), the UI was switched to the detail
+view (Figure 3a) to walk through the individual steps
+one by one. At each step, the assigned tools were acti-
+vated and their views automatically arranged on screen.
+Based on the displayed description of the actions to be
+performed, the tools were operated with the supplied
+data. Where necessary, we were able to review the
+underlying data exchange and transformation in the
+toolchain for the current step by switching between
+the workﬂow view and the toolchain editor (Figure 2c).
+Throughout the workﬂow execution, user comments
+and screenshots of intermediate results were collected
+using the developed UI controls (Figure 3b, c). These
+results were then summarized in a ﬁnal overview of
+the main ﬁndings, while the visual workﬂow history
+helped to recapitulate in which stage and step each
+part was obtained (Figure 4).
+Overall, the same medical ﬁndings were extracted
+and reproduced with our visualization-supported tool-
+chaining approach that we gained in our earlier analy-
+ses of the same study data [38, 40]. This time, however,
+we were able to support all three stages of the workﬂow
+with our uniﬁed UI, from data preparation over data
+analysis to summary of results. Compared to manual
+coordination in previous studies, this reduced the ef-
+fort required to activate the various tools, manage the
+exchange of data between them, and orchestrate their
+views for sequential and parallel display.
+Discussion and user feedback:
+Given the results
+of the workﬂow execution, the feedback from the ex-
+perts was largely positive. In particular, they pointed
+to the beneﬁts of having a visual representation of the
+workﬂow along with access to related tools and data
+through the uniﬁed UI. Likewise, support for diﬀerent
+layouts for arranging the tool views for each work step
+on the screen was considered advantageous. They also
+liked the idea of summarizing their results based on the
+intermediate comments and screenshots directly in the
+UI, but noted that a future version of the conﬁgured
+toolchain may need to include more tools to produce
+ﬁnal ﬁgures and tables for reporting the study results.
+Nevertheless, they appreciated our solutions towards
+a uniﬁed UI for retinal data analysis.
+On the other hand, given the heterogeneity of the
+tools, not all steps of the use case could be fully au-
+tomated during workﬂow and toolchain conﬁguration.
+Further ﬁne-tuning of our general solutions could help
+to accommodate some of the speciﬁc steps involved in
+the evaluation of this type of ophthalmic study data.
+In general, however, we agreed to coordinate only what
+is necessary, as opposed to what is theoretically possi-
+ble, to balance the eﬀort of conﬁguring the workﬂow
+and toolchain and developing additional controls in
+the uniﬁed UI. Related to this, we discussed the work
+that must be invested up front to force the coupling
+of otherwise seemingly incompatible tools, given the
+amount of actual support gained during execution and
+the generalizability beyond a particular use case. In
+the end, our discussions led to several directions for
+future improvements (Sect. 6).
+Finally, we noted the need for more in-depth testing
+and formal evaluation of our methods to fully assess
+the beneﬁts and limitations of our solutions beyond
+the preliminary results described here. Therefore, we
+are currently continuing our research together with
+ophthalmologists to further develop a uniﬁed UI for
+retinal data analysis. Speciﬁcally, we will also consider
+multi-tool analysis workﬂows with other data types and
+9
+
+study methods, including retinal changes associated
+with cystic ﬁbrosis and longitudinal treatment eﬀects
+in breast cancer patients [45].
+6
+Summary and future work
+We presented a new toolchaining approach for VA of
+retinal data in ophthalmology. Our approach consists
+of two parts. The ﬁrst part is a coordination graph
+that captures the interplay of workﬂow steps, tools
+used, data to be analyzed, and tool contents to be
+displayed on the screen. The second part is a uniﬁed
+UI, which allows to create and customize such a graph
+for a given workﬂow, to access all the information
+needed to execute the workﬂow, and to understand the
+results obtained. By bringing the two parts together,
+we were able to not only answer the three fundamental
+questions what to show?, what data parts to exchange?,
+and how to show?, but also meet the requirements of
+our collaborating ophthalmologists. The initial user
+feedback indicates that our solutions are useful for
+evaluating cross-sectional studies and reduce the co-
+ordination overhead compared to the current manual
+synchronization of individual analysis tools.
+Regarding future work, we see several directions
+to further support the integration of workﬂows and
+toolchaining. For example, we currently display the
+contents of the tools on the screen by ﬁxed layouts of
+the individual tool windows per workﬂow step. This
+prevents the user from having to manually arrange the
+windows each time the tools are activated. It would
+now be interesting to explore how these layouts can be
+dynamically rearranged, either automatically or inter-
+actively, to adapt to the user’s change in focus during
+a data analysis. Approaches such as automated layout
+computations, as explored in multi-display VA [35],
+could be helpful in this regard. Moreover, the entire
+contents of the individual tool windows are displayed
+unchanged at the moment. In the future, it might be
+worthwhile to extract, if possible, only the necessary
+parts of tool views and display them directly inte-
+grated in our uniﬁed UI. Similar to WinCuts [6] and
+Fa¸cades [8], this could reduce clutter on the screen, e.g.,
+by removing redundant interface components, while
+our visualization of the workﬂow and coordination
+graph helps to understand the graphical composition.
+With respect to the coordination graph, we have
+so far only considered tool activation and data ex-
+change between tools. However, during our testing,
+we also observed the need to synchronize the tools
+on the parameter level. These include, in particular,
+visualization-speciﬁc parameters such as applied ﬁlters
+or highlighting as well as selected color scales. Con-
+sistent adjustment of these parameters across tools
+would result in matched visual output, making com-
+posite representations easier to understand on screen.
+Addressing all these topics in the future will require
+additional user studies to assess the applicability of our
+approach and the potential beneﬁts of the extensions.
+Acknowledgments
+This work has been supported by the German Research
+Foundation (project UniVA, grant number 380014305).
+References
+[1]
+D. Huang, E. A. Swanson, C. P. Lin, J. S. Schu-
+man, W. G. Stinson, W. Chang, M. R. Hee, T.
+Flotte, K. Gregory, C. A. Puliaﬁto, and J. G.
+Fujimoto. “Optical Coherence Tomography”. In:
+Science 254.5035 (1991). doi: 10.1126/science.
+1957169.
+[2]
+M. R. Hee, J. A. Izatt, E. A. Swanson, D. Huang,
+J. S. Schuman, C. P. Lin, C. A. Puliaﬁto, and
+J. G. Fujimoto. “Optical Coherence Tomography
+of the Human Retina”. In: JAMA Ophthalmol
+113.3 (1995). doi: 10.1001/archopht.1995.
+01100030081025.
+[3]
+W. Drexler, U. Morgner, R. K. Ghanta, F. X.
+K¨artner, J. S. Schuman, and J. G. Fujimoto.
+“Ultrahigh-resolution ophthalmic optical coher-
+ence tomography”. In: Nat Med 7.4 (2001). doi:
+10.1038/86589.
+[4]
+C. Stolte, D. Tang, and P. Hanrahan. “Polaris:
+a system for query, analysis, and visualization
+of multidimensional relational databases”. In:
+IEEE TVCG 8.1 (2002), pp. 52–65. doi: 10.
+1109/2945.981851.
+[5]
+C. North, N. Conklin, K. Indukuri, V. Saini,
+and Q. Yu. “Fusion: Interactive Coordination
+of Diverse Data, Visualizations, and Mining Al-
+gorithms”. In: Extended Abstracts of CHI’03.
+ACM, 2003, pp. 626–627. doi: 10.1145/765891.
+765897.
+[6]
+D. S. Tan, B. Meyers, and M. Czerwinski.
+“WinCuts: Manipulating Arbitrary Window Re-
+gions for More Eﬀective Use of Screen Space”.
+In: Extended Abstracts of CHI’04. ACM, 2004,
+pp. 1525–1528. doi: 10.1145/985921.986106.
+[7]
+L. Bavoil, S. P. Callahan, P. J. Crossno, J. Freire,
+C. E. Scheidegger, C. T. Silva, and H. T. Vo. “Vis-
+Trails: enabling interactive multiple-view visual-
+izations”. In: IEEE Visualization. 2005, pp. 135–
+142. doi: 10.1109/VISUAL.2005.1532788.
+[8]
+W. Stuerzlinger, O. Chapuis, D. Phillips, and
+N. Roussel. “User Interface Fa¸cades: Towards
+Fully Adaptable User Interfaces”. In: Proc. of
+the Symp. on User Interface Software and Tech-
+nology (UIST). ACM, 2006, pp. 309–318. doi:
+10.1145/1166253.1166301.
+[9]
+J. C. Roberts. “State of the Art: Coordinated &
+Multiple Views in Exploratory Visualization”. In:
+Proc. of the Intl. Conf. on Coordinated and Mul-
+tiple Views in Exploratory Visualization (CMV).
+IEEE, 2007, pp. 61–71. doi: 10.1109/CMV.2007.
+20.
+10
+
+[10]
+M. D¨ork, S. Carpendale, C. Collins, and C.
+Williamson. “VisGets: Coordinated Visualiza-
+tions for Web-based Information Exploration
+and Discovery”. In: IEEE TVCG 14.6 (2008),
+pp. 1205–1212. doi: 10.1109/TVCG.2008.175.
+[11]
+M. McKeon. “Harnessing the web information
+ecosystem with wiki-based visualization dash-
+boards”. In: IEEE TVCG 15.6 (2009), pp. 1081–
+1088. doi: 10.1109/TVCG.2009.148.
+[12]
+M. Tobiasz, P. Isenberg, and S. Carpendale.
+“Lark: Coordinating Co-located Collaboration
+with Information Visualization”. In: IEEE
+TVCG 15.6 (2009), pp. 1065–1072. doi: 10 .
+1109/TVCG.2009.162.
+[13]
+D. Fisher, S. Drucker, R. Fernandez, and S. Ru-
+ble. “Visualizations everywhere: A Multiplat-
+form Infrastructure for Linked Visualizations”.
+In: IEEE TVCG 16.6 (2010), pp. 1157–1163. doi:
+10.1109/TVCG.2010.222.
+[14]
+J. Goecks, A. Nekrutenko, J. Taylor, and The
+Galaxy Team. “Galaxy: a comprehensive ap-
+proach for supporting accessible, reproducible,
+and transparent computational research in the
+life sciences”. In: Genome Biol. 11 (2010), R86.
+doi: 10.1186/gb-2010-11-8-r86.
+[15]
+S. Pietschmann, T. Nestler, and F. Daniel. “Ap-
+plication Composition at the Presentation Layer:
+Alternatives and Open Issues”. In: Proc. of Intl.
+Conf. on Information Integration and Web-based
+Applications & Services (iiWAS). ACM, 2010,
+pp. 461–468. doi: 10.1145/1967486.1967558.
+[16]
+M. Waldner, W. Puﬀ, A. Lex, M. Streit, and D.
+Schmalstieg. “Visual links across applications”.
+In: Proc. of Graphics Interface. 2010, pp. 129–
+136.
+[17]
+J. D¨orr, K. D. Wernecke, M. Bock, G. Gaede,
+J. T. Wuerfel, C. F. Pfueller, J. Bellmann-Strobl,
+A. Freing, A. U. Brandt, and P. Friedemann.
+“Association of Retinal and Macular Damage with
+Brain Atrophy in Multiple Sclerosis”. In: PLOS
+ONE 6.4 (2011). doi: 10.1371/journal.pone.
+0018132.
+[18]
+P. A. Keane, P. J. Patel, S. Liakopoulos, F. M.
+Heussen, S. R. Sadda, and A. Tufail. “Evaluation
+of Age-related Macular Degeneration With Op-
+tical Coherence Tomography”. In: Surv Ophthal-
+mol 57.5 (2012). doi: 10.1016/j.survophthal.
+2012.01.006.
+[19]
+M. Streit, H.-J. Schulz, A. Lex, D. Schmalstieg,
+and H. Schumann. “Model-driven design for the
+visual analysis of heterogeneous data”. In: IEEE
+TVCG 18.6 (2012), pp. 998–1010. doi: 10.1109/
+TVCG.2011.108.
+[20]
+D. S. Grewal and A. P. Tanna. “Diagnosis of
+glaucoma and detection of glaucoma progression
+using spectral domain optical coherence tomog-
+raphy”. In: Curr Opin Ophthalmol 24.2 (2013).
+doi: 10.1097/ICU.0b013e32835d9e27.
+[21]
+A. Rungta, B. Summa, D. Demir, P.-T. Bre-
+mer, and V. Pascucci. “ManyVis: Multiple Ap-
+plications in an Integrated Visualization Environ-
+ment”. In: IEEE TVCG 19.12 (2013), pp. 2878–
+2885. doi: 10.1109/TVCG.2013.174.
+[22]
+K. Wolstencroft, R. Haines, D. Fellows, A.
+Williams, D. Withers, S. Owen, S. Soiland-Reyes,
+I. Dunlop, A. Nenadic, P. Fisher, J. Bhagat, K.
+Belhajjame, F. Bacall, A. Hardisty, A. Nieva de
+la Hidalga, M. P. Balcazar Vargas, S. Suﬁ, and C.
+Goble. “The Taverna workﬂow suite: designing
+and executing workﬂows of web Services on the
+desktop, web or in the cloud”. In: Nucleic Acids
+Research 41.W1 (May 2013), W557–W561. doi:
+10.1093/nar/gkt328.
+[23]
+A. Fourney, B. Lafreniere, P. Chilana, and M.
+Terry. “InterTwine: Creating interapplication in-
+formation scent to support coordinated use of
+software”. In: Proc. of the Symp. on User inter-
+face software and technology (UIST). Ed. by H.
+Benko, M. Dontcheva, and D. Wigdor. ACM,
+2014, pp. 429–438. doi: 10 . 1145 / 2642918 .
+2647420.
+[24]
+M. Luboschik, M. R¨ohlig, G. Kundt, O. Stachs, S.
+Peschel, A. Zhivov, R. F. Guthoﬀ, K. Winter, and
+H. Schumann. “Supporting an Early Detection
+of Diabetic Neuropathy by Visual Analytics”.
+In: Proc. of the EuroVis Workshop on Visual
+Analytics (EuroVA). Eurographics Association,
+2014. doi: 10.2312/eurova.20141145.
+[25]
+G. Virgili, F. Menchini, G. Casazza, R. Hogg,
+R. R. Das, X. Wang, and M. Michelessi. “Op-
+tical coherence tomography (OCT) for detec-
+tion of macular oedema in patients with diabetic
+retinopathy”. In: Cochrane Database Syst Rev
+1 (2015). doi: 10.1002/14651858.CD008081.
+pub3.
+[26]
+J. Fujimoto and E. Swanson. “The Development,
+Commercialization, and Impact of Optical Co-
+herence Tomography”. In: Invest Ophthalmol Vis
+Sci 57.9 (2016). doi: 10.1167/iovs.16-19963.
+[27]
+D. G¨urd¨ur, F. Asplund, J. El-khoury, and F.
+Loiret. “Visual Analytics Towards Tool Inter-
+operabilty: A Position Paper”. In: Proc. of the
+Intl. Conf. on Information Visualization The-
+ory and Applications (IVAPP). SciTePress, 2016,
+pp. 139–145. doi: 10.5220/0005751401390145.
+[28]
+H. Stitz, S. Luger, M. Streit, and N. Gehlenborg.
+“AVOCADO: Visualization of Workﬂow–Derived
+Data Provenance for Reproducible Biomedical
+Research”. In: Comput Graph Forum 35.3 (2016),
+pp. 481–490. doi: 10.1111/cgf.12924.
+11
+
+[29]
+M. Herschel, R. Diestelk¨amper, and H. Ben Lah-
+mar. “A Survey on Provenance: What for? What
+Form? What From?” In: The VLDB Journal
+26.6 (2017), pp. 881–906. doi: 10.1007/s00778-
+017-0486-1.
+[30]
+A. Satyanarayan, D. Moritz, K. Wongsupha-
+sawat, and J. Heer. “Vega-Lite: A Grammar
+of Interactive Graphics”. In: IEEE TVCG 23.1
+(2017), pp. 341–350. doi: 10.1109/TVCG.2016.
+2599030.
+[31]
+A. G¨otze, S. von Keyserlingk, S. Peschel, U. Ja-
+coby, C. Schreiver, B. K¨ohler, S. Allgeier, K.
+Winter, M. R¨ohlig, A. J¨unemann, R. Guthoﬀ, O.
+Stachs, and D.-C. Fischer. “The corneal subbasal
+nerve plexus and thickness of the retinal layers in
+pediatric type 1 diabetes and matched controls”.
+In: Sci Rep 8.1 (2018). doi: 10.1038/s41598-
+017-18284-z.
+[32]
+R. Langner, U. Kister, and R. Dachselt. “Mul-
+tiple Coordinated Views at Large Displays for
+Multiple Users: Empirical Findings on User Be-
+havior, Movements, and Distances”. In: IEEE
+TVCG 25.1 (2018), pp. 608–618. doi: 10.1109/
+TVCG.2018.2865235.
+[33]
+R. K. Prakasam, A. G¨otze, S. von Keyser-
+lingk, A. J¨unemann, M. R¨ohlig, O. Stachs, and
+D.-C. Fischer. “Spectral-Domain Optical Co-
+herence Tomography for Determination of Reti-
+nal Thickness in Pediatric Patients with Mild-
+To-Moderate Chronic Kidney Disease: A Cross-
+Sectional Study”. In: Current Eye Research 44.2
+(2018), pp. 206–211. doi: 10.1080/02713683.
+2018.1522649.
+[34]
+M. R¨ohlig, C. Schmidt, R. K. Prakasam, H. Schu-
+mann, and O. Stachs. “Visual Analysis of Retinal
+Changes with Optical Coherence Tomography”.
+In: Vis Comput 34.9 (2018), pp. 1209–1224. doi:
+10.1007/s00371-018-1486-x.
+[35]
+C. Eichner, H. Schumann, and C. Tominski.
+“Multi-display Visual Analysis: Model, Inter-
+face, and Layout Computation”. In: CoRR
+abs/1912.08558 (2019). url: http : / / arxiv .
+org/abs/1912.08558.
+[36]
+M. Hogr¨afer and H.-J. Schulz. “ReVize: A Li-
+brary for Visualization Toolchaining with Vega-
+Lite”. In: Proc. of Smart Tools and Apps for
+Graphics (STAG). The Eurographics Associa-
+tion, 2019, pp. 129–139. doi: 10.2312/stag.
+20191375.
+[37]
+R. K. Prakasam, M. R¨ohlig, D.-C. Fischer, A.
+G¨otze, A. J¨unemann, H. Schumann, and O.
+Stachs. “Deviation maps for understanding thick-
+ness changes of inner retinal layers in children
+with type 1 diabetes mellitus”. In: Curr Eye
+Res 44.7 (2019), pp. 746–752. doi: 10.1080/
+02713683.2019.1591463.
+[38]
+M. R¨ohlig, R. K. Prakasam, J. St¨uwe, C.
+Schmidt, O. Stachs, and H. Schumann. “En-
+hanced Grid-Based Visual Analysis of Retinal
+Layer Thickness with Optical Coherence Tomog-
+raphy”. In: Information 10.9 (2019), p. 266. doi:
+10.3390/info10090266.
+[39]
+L. Nonnemann, H. Schumann, B. Urban, M.
+Aehnelt, and H.-J. Schulz. “A Characterization
+of Data Exchange between Visual Analytics
+Tools”. In: Proc. of the Int. Conf. on Informa-
+tion Visualisation (IV). 2020, pp. 368–377. doi:
+10.1109/IV51561.2020.00066.
+[40]
+R. K. Prakasam, A. Matuszewska-Iwanicka, D.-C.
+Fischer, H. Schumann, D. Tsch¨ope, B. Strat-
+mann, H.-J. Hettlich, R. F. Guthoﬀ, O. Stachs,
+and M. R¨ohlig. “Thickness of intraretinal lay-
+ers in patients with type 2 diabetes melli-
+tus depending on a concomitant diabetic neu-
+ropathy: results of a cross-sectional study us-
+ing deviation maps for OCT data analysis”.
+In: Biomedicines 8.7 (2020). doi: 10 . 3390 /
+biomedicines8070190.
+[41]
+H.-J. Schulz, M. R¨ohlig, L. Nonnemann, M.
+Hogr¨afer, M. Aehnelt, B. Urban, and H. Schu-
+mann. “A Layered Approach to Lightweight Tool-
+chaining in Visual Analytics”. In: Computer Vi-
+sion, Imaging and Computer Graphics Theory
+and Applications. Springer International Publish-
+ing, 2020, pp. 313–337. doi: 10.1007/978-3-
+030-41590-7_13.
+[42]
+L. Nonnemann, M. Hogr¨afer, H. Schumann, B.
+Urban, and H.-J. Schulz. “Customizable Coordi-
+nation of Independent Visual Analytics Tools”.
+In: Proc. of the EuroVis Workshop on Visual An-
+alytics (EuroVA). The Eurographics Association,
+2021. doi: 10.2312/eurova.20211094.
+[43]
+R Core Team. R: A Language and Environment
+for Statistical Computing. R Foundation for Sta-
+tistical Computing. Vienna, Austria, 2021. url:
+https://www.R-project.org/.
+[44]
+L. Nonnemann, M. Hogr¨afer, M. R¨ohlig, H. Schu-
+mann, B. Urban, and H. Schulz. “A Data-Driven
+Platform for the Coordination of Independent
+Visual Analytics Tools”. In: Comput Graph 106
+(2022), pp. 152–160. doi: 10.1016/j.cag.2022.
+05.023.
+[45]
+N. Stache, S. Bohn, K. A. Sterenczak, C.
+George, H.-V. Do, M. R¨ohlig, A. Stachs, and
+O. Stachs. “Changes in retinal layer thickness
+associated with taxane-induced polyneuropathy
+during breast cancer therapy”. In: Die Ophthal-
+mologie. Vol. 119. Proc. of the DOG congress
+Supplement 3. Springer Medicine, 2022. doi: 10.
+1007/s00347-022-01723-2.
+12
+
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new file mode 100644
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+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf,len=1094
+page_content='Towards a Uniﬁed User Interface for Visual Analysis  of Retinal Data in Ophthalmology  Martin R¨ohlig1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='a,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Lars Nonnemann2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='a,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Hans-J¨org Schulz3,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='b,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  Oliver Stachs4,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='c,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' and Heidrun Schumann5,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='a  aInstitute for Visual and Analytic Computing,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' University of Rostock,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Germany  bDepartment of Computer Science,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Aarhus University,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Denmark  cDepartment of Ophthalmology,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Rostock University Medical Center,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Germany  Abstract  The visual analysis of retinal data contributes to the  understanding of a wide range of eye diseases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' For the  evaluation of cross-sectional studies, ophthalmologists  rely on workﬂows and toolsets established in their  work environment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' That is, they know what tools  and data are needed at each step of their workﬂow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  Yet, manually operating the various tools, including  activation, data handling, or view arrangement, can be  cumbersome and time-consuming.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' We thus introduce  a new visualization-supported toolchaining approach  that combines workﬂow, tools, and data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' First, we  provide access to the tools required for each step of  the workﬂow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Second, we handle the exchange of data  between these tools.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Third, we organize the views of  the tools on screen using suitable layouts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Fourth, we  visualize the connection between workﬂow, tools, and  data to support the data analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' We demonstrate  our approach with a use case in ophthalmic research  and report on initial feedback from experts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  1  Introduction  Over the years, many diﬀerent visual analytics (VA)  tools have been developed to support the analysis of  medical data in a wide range of application areas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' The  general goal is to help domain experts in their data  analyses by providing means for decision making and  knowledge discovery.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' This is also true for the area of  ophthalmology, where VA tools have contributed to the  understanding of various eye diseases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' In collaboration  with ophthalmologists, we were able to improve the  detection of early retinal defects using dedicated VA  tools for retinal data [37, 40].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' This was made possible  by developing the tools speciﬁcally for the needs of  the ophthalmologists and integrating them into their  workﬂows for the evaluation of cross-sectional studies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  1martin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='roehlig@uni-rostock.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='de  2lars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='nonnemann@vcric.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='igd-r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='fraunhofer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='de  3hjschulz@cs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='au.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='dk  4oliver.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='stachs@uni-rostock.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='de  5heidrun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='schumann@uni-rostock.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='de  However, a single VA tool is often not enough to fully  handle complex analysis workﬂows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' On the one hand,  this is because diﬀerent VA tools may be needed for  diﬀerent steps of the analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' On the other hand, tools  for data management and preprocessing are typically  also required, as well as for statistical analysis and  compilation of ﬁnal results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' In general, the use of VA  tools is focused on the steps necessary for the actual  visual data analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' The remaining steps are typically  performed with other software solutions, ranging from  clinical information systems over examination device-  speciﬁc software to general spreadsheet and statistics  software.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' The reason for this is that trying to inte-  grate all the functionality into a single tool would  signiﬁcantly increase the eﬀort required for software  development and maintenance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' In certain cases it may  even simply not be possible due to time and resource  constraints or because of the proprietary algorithms or  data formats used.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' As a result, domain experts have  to interact with various tools – VA-based or not – and  exchange data between them to fulﬁll all the necessary  steps in their analysis workﬂows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  One of the resulting problems is that for a given  analysis workﬂow in the domain, it may not be imme-  diately clear how to coordinate the required tools and  the corresponding visual output on the screen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' For  each workﬂow step, domain experts must determine  which tools and what pieces of information to show  before deciding how to display them on the screen to  get the current step done.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' This places an additional  burden on a given workﬂow, making it more cumber-  some and time-consuming to execute.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' At the same  time, no support is generally oﬀered to complete these  secondary tasks alongside the actual data analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' In-  stead, in practice, experts have to manually switch  between diﬀerent stages of preprocessing, visual data  analysis, and result interpretation, and operate the  tools and their output by hand.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Often, this is necessary  again and again each time a workﬂow is executed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  We present a novel visualization-supported tool-  chaining approach that combines workﬂow, tools, and  data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' With a use case in the analysis of retinal data in  ophthalmology, we show that our approach not only  1  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='01840v1  [cs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='HC]  4 Jan 2023  provides access to the tools and data needed for each  workﬂow step, but also helps to organize the tools’ user  interfaces (UIs) on the screen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' This reduces the over-  head of managing the various tools and data during the  workﬂow execution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' In our collaboration with ophthal-  mologists, the experts were thus able to concentrate  on the actual steps of data analysis in the evaluation  of cross-sectional studies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Our contributions are:  Integration of workﬂow and tools: We examine  existing connections between workﬂow, tools, and  data in the context of our use case and establish  meaningful links for accessing the right tools, the  right data, and the right views at the right time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  Visualization support for toolchaining: We  present an editor that allows to interactively  create toolchains and adjust tools and data for  each step of a workﬂow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' We incorporate a uniﬁed  UI that shows the workﬂow, tools, and data and  helps to organize multiple tool views on screen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  Application in practice: We assess our approach  together with domain experts in a use case in  ophthalmology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' We discuss the diﬀerences with  current data analysis practices and report initial  expert feedback.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  The remainder of this paper is structured as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  The background and current analysis workﬂow are  described in Section 2, followed by an overview of  related work in Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Our approach to combining  workﬂows, tools, and data is detailed in Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' An  application example and user feedback are presented  in Section 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Finally, a conclusion and topics for future  work are discussed in Section 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  2  Background  In ophthalmology, data from various examination  methods are analyzed to understand the impact of dif-  ferent eye diseases on the condition of the human retina.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  One widely used examination method is optical coher-  ence tomography (OCT) [1, 2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Modern OCT scanners  enable noninvasive imaging of substructures of the  multilayered retina with high spatial resolution [3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' By  analyzing the OCT images, ophthalmologists are able  to detect common ocular diseases, such as age-related  macular degeneration [18], diabetic retinopathy [25],  or glaucoma [20], as well as other pathologies with  ocular signs, such as multiple sclerosis [17].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' OCT ex-  aminations are therefore now a standard procedure in  clinics and an integral part of ophthalmic research [26].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  We are particularly interested in OCT data analysis  in the context of cross-sectional studies in ophthalmic  research.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Here, multiple OCT datasets have to be  analyzed together with information from other clinical  records to compare the retinal condition of patients  with that of healthy controls.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' This is a complicated  process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' To handle the study data, ophthalmologists  rely on workﬂows and toolsets that are established  in their work environment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' These workﬂows can be  divided into three common stages:  Data preparation: The required data from all study  participants are collected and processed, including  ﬁltering and screening based on the study criteria.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  Afterwards, the patient and control groups are  assembled.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  Data analysis: With the prepared data, the diﬀer-  ences between the patients and controls are com-  puted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Data subsets of interest are selected, mea-  sured, and statistically quantiﬁed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  Summarization of results: The ﬁndings most rele-  vant to the study design are compiled.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' The ﬁnal  results are presented by a combination of images,  plots, and tables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  Throughout these three stages, ophthalmologists are  dealing with diﬀerent tools for diﬀerent types of data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  The tools used for the ﬁrst stage typically include  clinical information systems, OCT device-speciﬁc soft-  ware, and general spreadsheet software for managing  and processing the raw electronic health records and  OCT datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' In the second stage, mainly statistical  software is used to analyze the prepared data and,  more recently, also exploration-oriented VA tools [34,  38].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Here, the data are often enriched with computed  measurements as well as reduced to relevant subsets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  Finally, in the last stage, selected results are summa-  rized and presented with charting tools.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  This mixture of diﬀerent tools, ranging from general-  purpose to visualization-speciﬁc, has to be operated  manually in current analysis practice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Switching be-  tween the tools can be diﬃcult, however, as ophthal-  mologists must remember which tools are used in which  part of the workﬂow, locate those tools at the right  time, and activate them by hand.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' The exchange of  data can also be quite labor intensive due to the dif-  ferent data formats used and the limited compatibility  between the various tools.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' It is therefore not easy to  keep track of which data was transferred when and  between which tools.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' On top of that, the output of the  tools must be arranged sensibly on the screen, since  for some workﬂow steps not only one, but several tools  must be operated simultaneously.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' This is the case,  for example, in the data exploration stage, where it is  often necessary to go back and forth between selection  of data subsets, their visual analysis, and statistical  quantiﬁcation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' All in all, the limited integration of  workﬂow steps, tools, and data commonly increased  the time and eﬀort of performing an analysis workﬂow  and places an additional burden on ophthalmologists.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  Our objective therefore is to help ophthalmologists  to show the right tool at the right time, to illustrate  the ﬂow of data between them, and to make clear  which output was generated for which step with which  data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Establishing this level of support will help reduce  the overhead of managing the various tools and data  during workﬂow execution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  2  3  Related work  The development of workﬂow-based toolchains relates  to challenges regarding sustainable data exchange [39]  and tool interoperability [27].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' While these two research  areas are complex in their own right, dealing with  multiple VA tools introduces an additional problem  for workﬂow coordination, namely unifying the UIs of  independent tools.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  There are many examples for managing multiple  views, reaching from comprehensive application toolk-  its with built-in VA tools to loosely coupled, concur-  rently running applications [10, 9].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Most of the existing  solutions rely on the following approaches:  Integrating views: Applications like Tableau [4],  Dashiki [11], or Fusion [5] allow users to rapidly  assemble multiple views within a given interface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  This is usually achieved via web interfaces to cre-  ate mashups [15] or webcharts [13].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' If enough  screen space is available, even dozens of individual  views can be incorporated in the same environ-  ment [32].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' However, using integrative approaches  also has its limitations, as the visual load increases  with the number of views included.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  Coupling views: Instead of nested or tabbed UIs,  some approaches rely on loose coupling of inde-  pendent views for view orchestration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' This way,  the views are interactively assembled into a com-  mon interface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  Example are WinCuts [6] and  Fa¸cades [8], where arbitrary view regions are repli-  cated in a combined interface to focus on task-  related areas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Other methods rely on implicit or  explicit visual links between independent views to  facilitate the connection between them [16, 23].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  Both the integration of views and the coupling of  views depend on the number of views and the available  screen space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' This is where the workﬂow-based order  of tool execution becomes important.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' By providing a  toolchain, information is made available about which  tools need to be active at what time and what data  needs to be passed from one tool to the next.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' This  can reduce the visual load for the current analysis step.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  While this can help users with the data analysis, it  also means that management of tool views over time  must be considered.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' In this regard, two basic types of  displaying tool views can be distinguished:  Sequential display: In simple workﬂow scenarios, it  can be suﬃcient to display information via only  one tool view at a time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' An example is Stack’n’ﬂip  [19], where views are displayed in a sequential  order and can be switched interactively through  a central interface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  Parallel display: For certain analysis tasks of more  complex workﬂows, it is necessary to execute  more than one tool at a time, with the individ-  ual views displayed concurrently.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' One example is  ManyVis [21], where multiple views are shown to-  gether in an integrated visualization environment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  When coordinating multiple tools, the toolchain  itself is also sometimes encoded visually, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=', as a  directed graph showing its connections [12, 27].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Con-  sidering the steps completed and data generated with  the tools over time, similar visualization approaches  can be found in the ﬁeld of provenance visualization,  especially with regard to workﬂow provenance and  data provenance [29].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Examples are AVOCADO [28]  for the visualization of workﬂow-derived biomedical  data, and the systems VisTrails [7], Galaxy [14], or  Taverna [22] for automated tracking and visualization  of workﬂow and data provenance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' The representations  of workﬂow steps and related data with these systems  help users understand the data analysis and make it  reproducible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' However, combined support for the ex-  ecution of workﬂow steps, the sequential or parallel  use of tools and their data exchange, and the arrange-  ment of visual outputs on the screen have hardly been  addressed so far.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  Against this background, we recently introduced a  layered toolchaining approach for VA [41].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Our main  idea is to model the VA tools in a given workﬂow as a  graph that represents the tools as its nodes and the  diﬀerent levels of communication between them as di-  rected edges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' This provides ﬂexibility for describing  diﬀerent couplings, regardless of whether the tools are  used in a sequence, repeatedly back-and-forth, or si-  multaneously side-by-side.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Based on this model, we  were able to characterize the data exchange between  VA tools [39] and introduce ReVize [36], a library for  adding toolchain support for web-based applications  using Vega-Lite [30] as a common exchange format.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  We further demonstrated a framework to interactively  create toolchains via custom data connections between  independent VA tools [42, 44].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' We have not yet ad-  dressed, however, how to present and interact with  a uniﬁed UI and how to incorporate the tools’ out-  put into a sensible assembly during the execution of a  workﬂow in practice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  In summary, there are several approaches for the  uniﬁcation of UI elements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' With respect to retinal  data analysis in ophthalmology, it is not clear how  to translate these approaches into practice, especially  when considering complex analysis scenarios such as  the evaluation of cross-sectional studies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' We there-  fore aim to ﬁll in the missing pieces and develop a  consistent coordination approach for our application  example.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' To this end, we build on our ideas of layered  toolchaining [41] and investigate (1) what tools to show  in which part of the workﬂow, (2) what data parts to  exchange between the tools, (3) how to present the  tools and the data on screen, and (4) how to establish  a connection between workﬂow, tools, and data that  supports the analysis of retinal data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  3  4  Workﬂow-based toolchaining  for visual analytics  We aim to support toolchaining for VA of retinal data  in ophthalmology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' To ﬁnd suitable solutions, we ﬁrst  consider the requirements in our use case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' On that  basis, we then present new concepts and visual designs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='1  Requirements  We conducted interviews with ophthalmologists and  job observations to get an overall idea of the current  analysis practices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Together, we then engaged in the  statistical analysis of two studies [31, 33] and subse-  quently two additional studies [37, 40] analyzed with a  mixture of statistical and VA tools.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' This allowed us to  gain deeper insights into their workﬂows and use of VA,  statistics, and general-purpose analysis software.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' We  ﬁnally compiled a list of design requirements related to  the coordination of VA tools for retinal data analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  Access to tools (R1): In a workﬂow, the temporal  order of tools and their interplay is typically only  implicitly deﬁned.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' On the one hand, this means  that the ophthalmologists must remember which  tools to activate for the current work step.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' On the  other hand, they also need to determine what con-  tent to display at the same time with these tools.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  The contents include currently required panels  and views, but also information about available  data and information about already used or sub-  sequent tools.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Therefore, access to the right tool  at the right time must be supported.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  Connection of tools and data (R2): In  general,  the entire data are not passed between analysis  tools over and over again during the execution of  a workﬂow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Instead, the data are incrementally  reduced and sometimes even selectively extended  to extract valuable information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Thus, ophthal-  mologists must not only supply the original data  to the tools at the beginning of the workﬂow,  but also manage the exchange of various data  pieces between the tools during subsequent steps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  This includes taking care of all necessary data  transformations between the tools and updates  if parts of the data have changed during the  analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Supporting access to the right data at  the right time and establishing a link between  the data and the tools is thus a requirement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  Arrangement of tool views (R3): When  activat-  ing diﬀerent tools, the layout of their views should  correspond to their intended use in the respective  part of the workﬂow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' If the tools are used one  after the other, their views may simply be inter-  changed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' However, if they are used in parallel,  their views must be organized on the screen in a  meaningful way so that they can be used together  eﬀectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' In addition, navigational features are  needed that not only give the user control over  Figure 1: Overview of the coordination components.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  Shown are the workﬂow steps S1 to S5 (a), associated  toolsets A to D (b), links between workﬂow steps and  tools L1 to L6, and view layouts V1 to V3 assigned  to each workﬂow steps and toolset (c).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  switching between workﬂow steps and associated  view layouts, but also help to maintain orienta-  tion at the same time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Consequently, support for  obtaining the right view layout at the right time  is needed to manage the visual output of tools.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  From a VA perspective, the three requirements (R1)  to (R3) are related to three fundamental questions that  need to be answered in order to support toolchaining  in our use case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' The ﬁrst questions is what to show?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='.  With respect to requirement (R1), it addresses the  selection of all relevant information that needs to be  presented to the user at a given point in time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' The  second question is what data parts to exchange?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' and  corresponds to requirement (R2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' It aims to identify  subsets of interesting data and consider when and how  they should be exchanged between tools.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' The third  question is how to show?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='. Related to requirement (R3),  it is primarily about the layout and adaptation of views  and panels of the current tools.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' In addition, it includes  presenting information about the workﬂow itself and  how workﬂow steps, data, and tools are connected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' By  answering these three questions in our VA design, we  create a meaningful coordination between workﬂow,  tools, data, and view layouts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='2  Combination of tools, data, and  view layout  To meet our design requirements and answer the three  corresponding questions, we ﬁrst need to determine  several pieces of information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' For this purpose, we  build on our earlier work on a layered approach to  lightweight toolchaining in VA [41].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' In particular, we  implement and adapt the proposed coordination model  to establish a connection between the four components:  (i) domain workﬂow, (ii) tools used, (iii) data analyzed,  and (iv) layout of tool views.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Figure 1 illustrates the  interplay of these components.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  We start by looking at the existing workﬂow and the  tools used in the application domain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' This allows us  4  to determine a set of tools per workﬂow step (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' 1a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  Generally, one or more tools may be required to per-  form each step.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' The sequences in which these tools  must be activated can be derived from the order of  the workﬂow steps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' The back and forth between the  steps also determines which data connections must be  established between which tools.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' With this informa-  tion at hand, we build up a coordination graph [41] by  stepwise deﬁning a link between pairs of tools (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' 1b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  The links capture both the usage ﬂow, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=', all possible  activation sequences, and the data ﬂow, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=', all possi-  ble data exchanges, between the tools.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Based on this,  we then deﬁne diﬀerent arrangements of tool views  and assign a suitable layout to each combination of  workﬂow step and toolset (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' 1c).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Note that one set  of tools can be used in multiple workﬂow steps, but the  content of the tools can be displayed with a diﬀerent  layout speciﬁc to each particular step.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' We determine  these layouts based on user preferences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' For example,  we support choosing from a set of default layouts or  saving custom arrangements of views per step.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  The ﬁnal coordination graph provides all the infor-  mation necessary to facilitate toolchaining in our use  case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' That is, it allows us to query at any time which  tools need to be activated or deactivated, which pieces  of data need to be transferred from a current tool to  the next, and which content should be displayed how  on the screen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' In this way, it enables us to answer  in particularly the questions what to show?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' (R1) and  what data parts to exchange?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' (R2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Incorporating dif-  ferent view layouts into the graph further provides the  basis for answering the third question how to show?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  (R3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' The actual path through the coordination graph,  however, is not determined until the workﬂow is ex-  ecuted at runtime and the user interactively decides  which steps are to be processed in which order.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Hence,  in addition to the arrangement of the individual tools  on the screen, it must be possible to access the coor-  dination graph, the progress of the workﬂow, and the  results obtained during its execution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' To this end, we  present a new design that provides this information  both visually and interactively, speciﬁcally addressing  the third question how to show?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' (R3) again.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='3  Visualization support for the uniﬁ-  cation of UI ensembles  The workﬂow describes the analysis steps to be exe-  cuted by the user.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Per step, one or more tools are  used.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' The coordination graph captures the pairwise  coupling of the tools and the associated data exchange.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  The assigned layouts determine how the tool views are  displayed on the screen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' This results in a toolchain  that controls the handling of the tools, including going  back and forth between them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  To use the coordination graph eﬀectively, the in-  formation it contains must be made available to the  user.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  We therefore introduce a uniﬁed UI that vi-  sualizes the workﬂow together with the coordination  graph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Our design assists users in creating or adapting  a coordination graph, retrieving information from it  for the execution of the workﬂow, and comprehending  the results obtained.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' It consists of several views that  allow switching between the current work step and the  corresponding toolchain in the background.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  Visualizing  the  workﬂow  and  coordination  graph:  From the user’s point of view, it is important  to get an idea of the work at hand before executing a  particular workﬂow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' This involves not only the individ-  ual workﬂow steps that must be performed, but also  the data to be analyzed and the extent to which tool  coordination is supported.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Therefore, with our uniﬁed  UI, we provide an overview of the workﬂow along with  the coordination graph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' A toolchain editor makes it  possible to view individual links between tools in detail  and make adjustments as needed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Figure 2 illustrates  our design consisting of three views.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  The workﬂow view displays the workﬂow steps as a  ﬂowchart (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' 2a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' The steps are shown as rectangles  colored according to their workﬂow stage (preparation,  analysis, summarization).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' The arrows between the  rectangles encode the possible back and forth between  the steps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  Information about the current progress  within the workﬂow is provided by highlighting the  steps and links that have already been performed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  The coordination graph view shows the toolsets used  in the workﬂow as a network visualization (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' 2b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  The toolsets are coded as circles and the lines indicate  their data exchange and activation capabilities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Hov-  ering over the circles displays additional information,  e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=', which tools are included in the respective set and  in which steps they are used.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  The third view consists of a toolchain editor (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' 2c).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  Based on our previous work [42, 44], the main purpose  of the editor is to establish a connection between the  workﬂow and the coordination graph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' It consists of  three panels showing all available tools (top), all data  sources (bottom), and the links between the tools  (middle).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Within our interface, the editor performs  two functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' The ﬁrst is to create a coordination  graph, if not already available, for a given workﬂow  and set of tools.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Using the three panels, links between  tools can be added step by step via drag & drop.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' The  second function is to specify the data sources to be  used as input for a planned execution of the workﬂow,  and to adjust the data transformations between tools.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  Together, the three views provide an overview of the  work, the tools, and the data involved, and allow tool  coordination to be set up as required.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  Supporting the workﬂow execution:  After a  connection between the workﬂow and the tool coordi-  nation through the coordination graph has been estab-  lished, the execution of the individual workﬂow steps  must be supported.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Here, it is important to inform the  user about what currently needs to be done, as well as  provide navigation support in terms of what has been  done before and what comes next.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' In addition, the  5  Figure 2: Visualization of workﬂow, coordination graph, and toolchain editor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' The workﬂow steps are displayed  as colored rectangles (a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' The coordination graph is represented as a network visualization, where the circles  depict the tools and the lines encode the links between them (b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' The toolchain editor (c) consists of three panels  showing the available tools (top), the data sources (bottom), and the data connections between tools (middle).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  ability to document the work and progress is required.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  As illustrated in Figure 3, our interface support this by  showing current steps in detail along with additional  information about the coordination.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  To focus on the current steps during a workﬂow exe-  cution, the workﬂow view is switched from an overview  to a detail view (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' 3a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' This enlarges the active  step and shows a description of what needs to be done  and how the tools needed to do it are arranged on  the screen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' The previous step is displayed above the  active step and the next possible steps are displayed  below it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Clicking on these steps allows to go back  and forth within the workﬂow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Once a workﬂow step  has been selected, the corresponding tools are auto-  matically activated and their content is arranged on  the screen based on the assigned layouts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' The data  exchange between the last and the current tools is also  handled automatically as deﬁned in the coordination  graph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' This reduces the eﬀort of manually searching  for the right tools, activating them, transferring the  work data, and customizing where the content is dis-  played on screen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' To see the actual path taken so far  through the workﬂow and coordination graph, the user  can switch back to the overview visualizations (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' 2)  at any time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' This highlights the links of the active  step and tools in the overviews, making adjustments  in the coordination graph possible on the ﬂy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  Our interface also helps to document the work per-  formed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' On the one hand, the user can set the status of  the active workﬂow step (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=', pending, done, paused,  canceled) to indicate the state of the work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' In addition,  notes can be added to the steps describing how the  work was performed and whether it was necessary to  deviate from the original work description (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' 3b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  On the other hand, intermediate results can be cap-  tured via screenshots of the tool content currently  visible on the screen (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' 3c).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Multiple screenshots  can be added by selecting any areas of the screen, with  a reference image showing which areas have already  been captured.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' The content of the selected screen areas  can be updated or removed again if relevant changes  occur during work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' If a workﬂow step is visited mul-  tiple times, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=', by navigating back and forth in the  workﬂow, a new set of notes and captures is created  for each activation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' That way, a detailed history of all  work performed is generated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Especially when diﬀerent  paths are taken through the workﬂow, this helps to  recapitulate which steps were taken to arrive at the  results achieved in each case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  Compiling the results:  During and after the exe-  cution of the workﬂow, it typically becomes necessary  to summarize the work performed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Going back and  forth between workﬂow steps and multiple tools, how-  6  Workflow * -  ox  Tool coordination 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  口×  START  PREPARATION  ANALYSIS  PRESENTATION  END  Gather study data  Preprocess health records  Toolchain editor  - ×  Preprocess ocT datasets  show Advanced Connection Options  ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  Check data quality  delberg Eye Expl: TExplorer 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='0 (x etinavis_2017100  Tools:  Compile study groups  Reset Default  delberg Eye Expl  TExplorer 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='0 (x  indhno  Input  Channel  ReVize Server  ReVize Server  etinavis_2017100  Graph:  Analyze clinical health records  Format  Path:  Add Converter  xa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  xa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  Refine groups & analyze individuals  corneal  corneal  xa  xa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  cars  corneal  Data:Figure 3: Visualization of individual workﬂow steps and additional information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' On the left side, the current  step is enlarged to show additional information, and the previous and next possible steps are displayed above  and below (a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' On the right side, a full description and user notes about the current step are depicted (b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' In  addition, intermediate analysis results are displayed as a list of screen captures (c).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  ever, can make it diﬃcult to recapitulate the work after  completion and extract the most meaningful insights  from multiple intermediate results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' In fact, the end  results do not have to come from a single workﬂow step  and a single set of tools.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' It is rather often a mixture  of intermediate results from multiple steps and tools  that need to be reconciled and compared to provide an  overall picture of the work done and insights gained.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  Therefore, our interface provides an additional sum-  mary view for compiling results across workﬂow steps  and tools.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Figure 4 illustrates this view.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  The summary view consists of three areas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' In the  lower area, a history of all performed workﬂow steps  is displayed in the order of their activation (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' 4a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  Each step is represented by a colored rectangle with  small icons indicating whether intermediate results  have been captured.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' In the middle area, the interme-  diate results are listed grouped by the respective steps  (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' 4b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' In the top area, the intermediate results  can be interactively combined into a single image via  drag & drop (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' 4c).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' The ﬁnished image can then be  exported for further use.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' This allows to bring together  and compare the main ﬁndings of the data analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  Without our uniﬁed UI, this would hardly be directly  possible if only the work steps and the associated tools  were considered individually.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  Overall, the diﬀerent views of our uniﬁed UI estab-  lish a visual connection between workﬂow, tools, data,  and displayed content.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Our design approach thus as-  sists users in creating a coordination graph that ﬁts  a particular workﬂow and provides valuable informa-  tion for executing the workﬂow and understanding the  results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' To assess the utility, we tested our approach  with a use case in ophthalmology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  5  Application to retinal data  analysis  We applied and tested our solution in collaboration  with ophthalmologists.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' As brieﬂy described in Sec-  tion 2, the ophthalmologists were particularly inter-  ested in the analysis of retinal OCT data in the context  of cross-sectional studies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' In such studies, data from  a group of patients are compared with data from a  control group to determine any inﬂuence of the disease  under study on the condition of the retina and other  measured clinical parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' After the data acquisi-  tion from all study participants, the study evaluation  follows established workﬂows that are usually divided  into three stages: (1) data preparation, (2) data anal-  ysis, and (3) summary of results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Currently, however,  the ophthalmologist must manually operate the tools  required to accomplish these stages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  Together, we  therefore created a coordination graph according to  their steps and tools, and compared the execution of  7  Workflow *-×  Tool coordination  Toolchain editor  口×  capture, Note *- ×  @ Help  *-口x  START  PREPARATION  ANALYSIS  PRESENTATION  END  capture *_ ×  口X  ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  Preprocess ocT datasets  Add  Refresh all  e  Check data quality  Description  D: Scan slightly off-center, Bscan #2,4, 7, 13, 16, 71, 147, 185-189, 1  For each ocT dataset:  218, 222-223, 228, 234  OD_HR: Scan slightly off-center, Bscan #1, 3,8, 14, 37, 41, 45-46, 53, 6  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Visually inspect data quality (ocT images and computes  206-221, 223, 226, 229-231  attributes)  OS: Slightly of center, Bscan #2, 6, 9, 11 12, 15, 17, 26 28, 34 35, 44, 7  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Try to fix segmentation errors  Os_HR: Bscan #1-4, 18-19, 23, 40, 42, 46, 53, 63, 80, 84, 92-93 (miss), 2  : Exclude participants with ocT data of insufficient quality  231, 234, 237  Tools  Note 7- ×  7-x  Scan has segementation errors  Compile study groupsFigure 4: Visualization of workﬂow history and result composition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' At the bottom, a history of all performed  workﬂow steps is displayed (a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' In the middle, all captured intermediate results are listed (b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' At the top, selected  intermediate results are summarized in an overview that illustrates the main ﬁndings of the data analysis (c).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  the workﬂow supported by our solutions with their  experience with manual tool coordination in previous  studies [31, 40].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='1  Connection of workﬂow, tools, and  data  For our use case, we reevaluated the data of a previous  study [40] with focus on the detection of thickness  changes in intraretinal layers at an early stage of di-  abetes mellitus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' In this study, data from 33 diabetic  patients and 40 healthy controls were analyzed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  The data:  In the study evaluation, we distinguished  between two types of input data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' The ﬁrst type was  retinal OCT datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' These datasets consisted of  3D images and segmented layer boundaries of each  participant’s retina.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  The second type was clinical  health records.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' The record of each participant included  various parameters such as age, body mass index, blood  glucose level, and type of medication received.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  The tools:  A total of 8 diﬀerent tools were used  to process and analyze the data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' On the one hand,  these were commercial software tools speciﬁcally for  the acquisition and processing of retinal OCT data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  For the management of the tabular data from the  electronic health records also general spreadsheet and  statistical software was used.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' On the other hand, we  applied our own VA tools designed for the exploration  of retinal OCT data and multivariate data from clinical  health records [24, 34, 38] For statistical analysis, we  additionally used custom scripts together with the R  software environment [43].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  The workﬂow:  For the evaluation of the study data,  we built on our prior research on workﬂow-based visual  analysis of retinal data [38].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Together with the ophthal-  mologists, we enhanced our approach to include the  multiple tools and data sources needed for comprehen-  sive ophthalmic research.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' In the extended workﬂow,  the ophthalmologists had to perform 9 steps (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' 2a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  In the ﬁrst 5 steps, they focused on the data prepa-  ration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' This included collecting study data from all  subjects, calculating retinal thickness, checking data  quality, and assembling the two groups to be compared.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  In the next 3 steps, the ophthalmologists continued  with the data analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Here, their main focus was on  analyzing the diﬀerences in thickness values between  the groups.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' They also alternated between the analy-  8  Result -× History  Composition  DAge  M-CNFD  28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='75  6  15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='0  39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='06  Results  History  11  10sis of OCT data and clinical parameters to identify  outliers and reﬁne the groups accordingly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' For this  purpose, a mixture of visual exploration and statistical  hypothesis testing was used.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Especially at this stage,  there was therefore a back-and-forth between workﬂow  steps to narrow down the data to relevant subsets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' In  the ﬁnal step, the ophthalmologists summarized the  key ﬁndings based on their analysis of the identiﬁed  subsets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' This included extracting images of relevant  data values and creating additional charts, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=', to  highlight interesting statistical results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  The toolchain:  The tool coordination for our use  case was created with the toolchain editor (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' 2c).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  First, we imported all tools and datasets into the ed-  itor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Together with the ophthalmologists, we then  focused on making the tools available when needed  by automating their activation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' For this purpose, we  displayed the workﬂow steps in the overview visual-  ization and created corresponding links between the  tools using the editor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' The visual representation of the  connections in the editor helped us to get an idea of  when which tool was used.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Using the drag & drop fea-  tures of the editor, we then set the data input for the  workﬂow and customized the data transfer between the  tools.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Once the links were established, we performed a  test run by navigating the workﬂow to ensure that the  modeled coordination graph met the ophthalmologists’  expectations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' The test run also served to assign a suit-  able view layout to the automatically activated tools  for each workﬂow step.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Based on the default layouts,  the ophthalmologists were able to reﬁne where content  should be displayed and how much space each view  was given on the screen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' The layouts, along with a  description of the workﬂow and coordination graph,  were saved for subsequent executions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='2  Workﬂow execution and testing  We applied the workﬂow and toolchain according to  the use case deﬁned together with ophthalmologists.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  During conception of our approach and the testing of  our solutions, we obtained initial informal feedback in  discussions with primarily two ophthalmic experts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  Execution of the workﬂow and toolchain:  After  the initial conﬁguration described above, we executed  the previously saved descriptions of the workﬂow and  toolchain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Starting from the overview of the work-  ﬂow (Figure 2a), the UI was switched to the detail  view (Figure 3a) to walk through the individual steps  one by one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' At each step, the assigned tools were acti-  vated and their views automatically arranged on screen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  Based on the displayed description of the actions to be  performed, the tools were operated with the supplied  data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Where necessary, we were able to review the  underlying data exchange and transformation in the  toolchain for the current step by switching between  the workﬂow view and the toolchain editor (Figure 2c).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  Throughout the workﬂow execution, user comments  and screenshots of intermediate results were collected  using the developed UI controls (Figure 3b, c).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' These  results were then summarized in a ﬁnal overview of  the main ﬁndings, while the visual workﬂow history  helped to recapitulate in which stage and step each  part was obtained (Figure 4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  Overall, the same medical ﬁndings were extracted  and reproduced with our visualization-supported tool-  chaining approach that we gained in our earlier analy-  ses of the same study data [38, 40].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' This time, however,  we were able to support all three stages of the workﬂow  with our uniﬁed UI, from data preparation over data  analysis to summary of results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Compared to manual  coordination in previous studies, this reduced the ef-  fort required to activate the various tools, manage the  exchange of data between them, and orchestrate their  views for sequential and parallel display.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  Discussion and user feedback:  Given the results  of the workﬂow execution, the feedback from the ex-  perts was largely positive.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' In particular, they pointed  to the beneﬁts of having a visual representation of the  workﬂow along with access to related tools and data  through the uniﬁed UI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Likewise, support for diﬀerent  layouts for arranging the tool views for each work step  on the screen was considered advantageous.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' They also  liked the idea of summarizing their results based on the  intermediate comments and screenshots directly in the  UI, but noted that a future version of the conﬁgured  toolchain may need to include more tools to produce  ﬁnal ﬁgures and tables for reporting the study results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  Nevertheless, they appreciated our solutions towards  a uniﬁed UI for retinal data analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  On the other hand, given the heterogeneity of the  tools, not all steps of the use case could be fully au-  tomated during workﬂow and toolchain conﬁguration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  Further ﬁne-tuning of our general solutions could help  to accommodate some of the speciﬁc steps involved in  the evaluation of this type of ophthalmic study data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  In general, however, we agreed to coordinate only what  is necessary, as opposed to what is theoretically possi-  ble, to balance the eﬀort of conﬁguring the workﬂow  and toolchain and developing additional controls in  the uniﬁed UI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Related to this, we discussed the work  that must be invested up front to force the coupling  of otherwise seemingly incompatible tools, given the  amount of actual support gained during execution and  the generalizability beyond a particular use case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' In  the end, our discussions led to several directions for  future improvements (Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' 6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  Finally, we noted the need for more in-depth testing  and formal evaluation of our methods to fully assess  the beneﬁts and limitations of our solutions beyond  the preliminary results described here.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Therefore, we  are currently continuing our research together with  ophthalmologists to further develop a uniﬁed UI for  retinal data analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Speciﬁcally, we will also consider  multi-tool analysis workﬂows with other data types and  9  study methods, including retinal changes associated  with cystic ﬁbrosis and longitudinal treatment eﬀects  in breast cancer patients [45].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  6  Summary and future work  We presented a new toolchaining approach for VA of  retinal data in ophthalmology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Our approach consists  of two parts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' The ﬁrst part is a coordination graph  that captures the interplay of workﬂow steps, tools  used, data to be analyzed, and tool contents to be  displayed on the screen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' The second part is a uniﬁed  UI, which allows to create and customize such a graph  for a given workﬂow, to access all the information  needed to execute the workﬂow, and to understand the  results obtained.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' By bringing the two parts together,  we were able to not only answer the three fundamental  questions what to show?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=', what data parts to exchange?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=',  and how to show?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=', but also meet the requirements of  our collaborating ophthalmologists.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' The initial user  feedback indicates that our solutions are useful for  evaluating cross-sectional studies and reduce the co-  ordination overhead compared to the current manual  synchronization of individual analysis tools.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  Regarding future work, we see several directions  to further support the integration of workﬂows and  toolchaining.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' For example, we currently display the  contents of the tools on the screen by ﬁxed layouts of  the individual tool windows per workﬂow step.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' This  prevents the user from having to manually arrange the  windows each time the tools are activated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' It would  now be interesting to explore how these layouts can be  dynamically rearranged, either automatically or inter-  actively, to adapt to the user’s change in focus during  a data analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Approaches such as automated layout  computations, as explored in multi-display VA [35],  could be helpful in this regard.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Moreover, the entire  contents of the individual tool windows are displayed  unchanged at the moment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' In the future, it might be  worthwhile to extract, if possible, only the necessary  parts of tool views and display them directly inte-  grated in our uniﬁed UI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Similar to WinCuts [6] and  Fa¸cades [8], this could reduce clutter on the screen, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=',  by removing redundant interface components, while  our visualization of the workﬂow and coordination  graph helps to understand the graphical composition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  With respect to the coordination graph, we have  so far only considered tool activation and data ex-  change between tools.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' However, during our testing,  we also observed the need to synchronize the tools  on the parameter level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' These include, in particular,  visualization-speciﬁc parameters such as applied ﬁlters  or highlighting as well as selected color scales.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Con-  sistent adjustment of these parameters across tools  would result in matched visual output, making com-  posite representations easier to understand on screen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  Addressing all these topics in the future will require  additional user studies to assess the applicability of our  approach and the potential beneﬁts of the extensions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  Acknowledgments  This work has been supported by the German Research  Foundation (project UniVA, grant number 380014305).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  References  [1]  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Huang, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Swanson, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Lin, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Schu-  man, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Stinson, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Chang, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Hee, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  Flotte, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Gregory, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Puliaﬁto, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  Fujimoto.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' “Optical Coherence Tomography”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' In:  Science 254.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='5035 (1991).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='1126/science.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  1957169.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  [2]  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Hee, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Izatt, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Swanson, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Huang,  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Schuman, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Lin, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Puliaﬁto, and  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Fujimoto.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' “Optical Coherence Tomography  of the Human Retina”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' In: JAMA Ophthalmol  113.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='3 (1995).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='1001/archopht.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='1995.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  01100030081025.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  [3]  W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Drexler, U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Morgner, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Ghanta, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  K¨artner, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Schuman, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Fujimoto.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  “Ultrahigh-resolution ophthalmic optical coher-  ence tomography”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' In: Nat Med 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='4 (2001).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' doi:  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='1038/86589.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  [4]  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Stolte, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Tang, and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Hanrahan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' “Polaris:  a system for query, analysis, and visualization  of multidimensional relational databases”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' In:  IEEE TVCG 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='1 (2002), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' 52–65.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  1109/2945.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='981851.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  [5]  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' North, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Conklin, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Indukuri, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Saini,  and Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Yu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' “Fusion: Interactive Coordination  of Diverse Data, Visualizations, and Mining Al-  gorithms”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' In: Extended Abstracts of CHI’03.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  ACM, 2003, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' 626–627.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='1145/765891.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  765897.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  [6]  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Tan, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Meyers, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Czerwinski.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  “WinCuts: Manipulating Arbitrary Window Re-  gions for More Eﬀective Use of Screen Space”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  In: Extended Abstracts of CHI’04.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' ACM, 2004,  pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' 1525–1528.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='1145/985921.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='986106.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  [7]  L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Bavoil, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Callahan, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Crossno, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Freire,  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Scheidegger, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Silva, and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Vo.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' “Vis-  Trails: enabling interactive multiple-view visual-  izations”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' In: IEEE Visualization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' 2005, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' 135–  142.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='1109/VISUAL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='2005.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='1532788.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  [8]  W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Stuerzlinger, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Chapuis, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Phillips, and  N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Roussel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' “User Interface Fa¸cades: Towards  Fully Adaptable User Interfaces”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' In: Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' of  the Symp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' on User Interface Software and Tech-  nology (UIST).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' ACM, 2006, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' 309–318.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' doi:  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='1145/1166253.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='1166301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  [9]  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Roberts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' “State of the Art: Coordinated &  Multiple Views in Exploratory Visualization”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' In:  Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' of the Intl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Conf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' on Coordinated and Mul-  tiple Views in Exploratory Visualization (CMV).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  IEEE, 2007, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' 61–71.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='1109/CMV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='2007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  10  [10]  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' D¨ork, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Carpendale, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Collins, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  Williamson.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' “VisGets: Coordinated Visualiza-  tions for Web-based Information Exploration  and Discovery”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' In: IEEE TVCG 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='6 (2008),  pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' 1205–1212.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='1109/TVCG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='2008.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='175.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  [11]  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' McKeon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' “Harnessing the web information  ecosystem with wiki-based visualization dash-  boards”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' In: IEEE TVCG 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='6 (2009), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' 1081–  1088.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='1109/TVCG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='2009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='148.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  [12]  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Tobiasz, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Isenberg, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Carpendale.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  “Lark: Coordinating Co-located Collaboration  with Information Visualization”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' In: IEEE  TVCG 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='6 (2009), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' 1065–1072.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' doi: 10 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  1109/TVCG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='2009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='162.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  [13]  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Fisher, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Drucker, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Fernandez, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Ru-  ble.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' “Visualizations everywhere: A Multiplat-  form Infrastructure for Linked Visualizations”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  In: IEEE TVCG 16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='6 (2010), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' 1157–1163.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' doi:  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='1109/TVCG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='2010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='222.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  [14]  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Goecks, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Nekrutenko, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Taylor, and The  Galaxy Team.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' “Galaxy: a comprehensive ap-  proach for supporting accessible, reproducible,  and transparent computational research in the  life sciences”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' In: Genome Biol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' 11 (2010), R86.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='1186/gb-2010-11-8-r86.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  [15]  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Pietschmann, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Nestler, and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Daniel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' “Ap-  plication Composition at the Presentation Layer:  Alternatives and Open Issues”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' In: Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' of Intl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  Conf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' on Information Integration and Web-based  Applications & Services (iiWAS).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' ACM, 2010,  pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' 461–468.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='1145/1967486.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='1967558.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  [16]  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Waldner, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Puﬀ, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Lex, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Streit, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  Schmalstieg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' “Visual links across applications”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  In: Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' of Graphics Interface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' 2010, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' 129–  136.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  [17]  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' D¨orr, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Wernecke, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Bock, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Gaede,  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Wuerfel, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Pfueller, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Bellmann-Strobl,  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Freing, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Brandt, and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
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+page_content='  0018132.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  [18]  P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Keane, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Patel, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
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+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  Heussen, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Sadda, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
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+page_content=' In: Surv Ophthal-  mol 57.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='5 (2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
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+page_content='  2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='01.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='006.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  [19]  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Streit, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='-J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Schulz, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Lex, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Schmalstieg,  and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Schumann.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' “Model-driven design for the  visual analysis of heterogeneous data”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' In: IEEE  TVCG 18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='6 (2012), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' 998–1010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='1109/  TVCG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='108.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  [20]  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Grewal and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Tanna.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' “Diagnosis of  glaucoma and detection of glaucoma progression  using spectral domain optical coherence tomog-  raphy”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' In: Curr Opin Ophthalmol 24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='2 (2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='1097/ICU.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='0b013e32835d9e27.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  [21]  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Rungta, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Summa, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Demir, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='-T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Bre-  mer, and V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Pascucci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' “ManyVis: Multiple Ap-  plications in an Integrated Visualization Environ-  ment”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
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+page_content='12 (2013), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' 2878–  2885.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='1109/TVCG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='174.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  [22]  K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Wolstencroft, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Haines, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Fellows, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  Williams, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Withers, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Owen, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Soiland-Reyes,  I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Dunlop, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Nenadic, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Fisher, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Bhagat, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  Belhajjame, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Bacall, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Hardisty, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Nieva de  la Hidalga, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Balcazar Vargas, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Suﬁ, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  Goble.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' “The Taverna workﬂow suite: designing  and executing workﬂows of web Services on the  desktop, web or in the cloud”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' In: Nucleic Acids  Research 41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='W1 (May 2013), W557–W561.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' doi:  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='1093/nar/gkt328.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  [23]  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Fourney, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Lafreniere, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Chilana, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  Terry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' “InterTwine: Creating interapplication in-  formation scent to support coordinated use of  software”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' In: Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' of the Symp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' on User inter-  face software and technology (UIST).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Ed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' by H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  Benko, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Dontcheva, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Wigdor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' ACM,  2014, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' 429–438.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' doi: 10 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' 1145 / 2642918 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  2647420.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  [24]  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Luboschik, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' R¨ohlig, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Kundt, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Stachs, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  Peschel, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Zhivov, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Guthoﬀ, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Winter, and  H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Schumann.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
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+page_content='  In: Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' of the EuroVis Workshop on Visual  Analytics (EuroVA).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Eurographics Association,  2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
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+page_content='20141145.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  [25]  G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Virgili, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Menchini, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Casazza, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Hogg,  R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Das, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Wang, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Michelessi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' “Op-  tical coherence tomography (OCT) for detec-  tion of macular oedema in patients with diabetic  retinopathy”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' In: Cochrane Database Syst Rev  1 (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='1002/14651858.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='CD008081.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  pub3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  [26]  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Fujimoto and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Swanson.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' “The Development,  Commercialization, and Impact of Optical Co-  herence Tomography”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' In: Invest Ophthalmol Vis  Sci 57.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='9 (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='1167/iovs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='16-19963.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  [27]  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' G¨urd¨ur, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Asplund, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' El-khoury, and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  Loiret.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' “Visual Analytics Towards Tool Inter-  operabilty: A Position Paper”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' In: Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' of the  Intl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Conf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' on Information Visualization The-  ory and Applications (IVAPP).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' SciTePress, 2016,  pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' 139–145.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='5220/0005751401390145.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  [28]  H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Stitz, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Luger, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Streit, and N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Gehlenborg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  “AVOCADO: Visualization of Workﬂow–Derived  Data Provenance for Reproducible Biomedical  Research”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' In: Comput Graph Forum 35.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='3 (2016),  pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' 481–490.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='1111/cgf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='12924.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  11  [29]  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Herschel, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Diestelk¨amper, and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Ben Lah-  mar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' “A Survey on Provenance: What for?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' What  Form?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' What From?”' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' In: The VLDB Journal  26.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='6 (2017), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' 881–906.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='1007/s00778-  017-0486-1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  [30]  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Satyanarayan, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Moritz, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Wongsupha-  sawat, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Heer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' “Vega-Lite: A Grammar  of Interactive Graphics”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' In: IEEE TVCG 23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='1  (2017), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' 341–350.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='1109/TVCG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  2599030.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  [31]  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' G¨otze, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' von Keyserlingk, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Peschel, U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Ja-  coby, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Schreiver, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' K¨ohler, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Allgeier, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  Winter, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' R¨ohlig, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' J¨unemann, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Guthoﬀ, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  Stachs, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='-C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Fischer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' “The corneal subbasal  nerve plexus and thickness of the retinal layers in  pediatric type 1 diabetes and matched controls”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  In: Sci Rep 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='1 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='1038/s41598-  017-18284-z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  [32]  R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Langner, U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Kister, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Dachselt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' “Mul-  tiple Coordinated Views at Large Displays for  Multiple Users: Empirical Findings on User Be-  havior, Movements, and Distances”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' In: IEEE  TVCG 25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='1 (2018), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' 608–618.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
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+page_content='  [33]  R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Prakasam, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
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+page_content=' 206–211.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
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+page_content='1080/02713683.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
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+page_content='  [34]  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' R¨ohlig, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
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+page_content=' Prakasam, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
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+page_content='9 (2018), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' 1209–1224.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
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+page_content='  [35]  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Eichner, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
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+page_content=' Tominski.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
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+page_content=' url: http : / / arxiv .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  org/abs/1912.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='08558.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  [36]  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Hogr¨afer and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='-J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Schulz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' “ReVize: A Li-  brary for Visualization Toolchaining with Vega-  Lite”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
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+page_content=' of Smart Tools and Apps for  Graphics (STAG).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' The Eurographics Associa-  tion, 2019, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' 129–139.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
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+page_content='2312/stag.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  20191375.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  [37]  R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Prakasam, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' R¨ohlig, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='-C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Fischer, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
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+page_content='  Stachs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
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+page_content=' In: Curr Eye  Res 44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='7 (2019), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' 746–752.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='1080/  02713683.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
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+page_content='  [38]  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' R¨ohlig, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Prakasam, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' St¨uwe, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  Schmidt, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
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+page_content='9 (2019), p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' 266.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
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+page_content='  [39]  L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Nonnemann, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Schumann, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
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+page_content='  Aehnelt, and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='-J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Schulz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
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+page_content=' of the Int.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Conf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' on Informa-  tion Visualisation (IV).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' 2020, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' 368–377.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
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+page_content='1109/IV51561.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
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+page_content='00066.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  [40]  R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Prakasam, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Matuszewska-Iwanicka, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='-C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content='  Fischer, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
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+page_content=' Tsch¨ope, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
+page_content=' Strat-  mann, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
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+page_content=' 119.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/gNAzT4oBgHgl3EQf4P4V/content/2301.01840v1.pdf'}
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+Mystique: Accurate and Scalable Production AI
+Benchmarks Generation
+Mingyu Liang1, Wenyin Fu2, Louis Feng2, Zhongyi Lin3, Pavani Panakanti2, Srinivas Sridharan2, and Christina Delimitrou4
+1Cornell University
+2Meta
+3University of California, Davis
+4MIT
+ml2585@cornell.edu
+{wenyinfu,lofe,pavanip,ssrinivas}@meta.com
+zhylin@ucdavis.edu
+delimitrou@csail.mit.edu
+Abstract—Building and maintaining large AI ﬂeets to efﬁ-
+ciently support the fast-growing DL workloads is an active
+research topic for modern cloud infrastructure providers. Gener-
+ating accurate benchmarks plays an essential role in the design
+and evaluation of rapidly evoloving software and hardware
+solutions in this area. Two fundamental challenges to make
+this process scalable are (i) workload representativeness and (ii)
+the ability to quickly incorporate changes to the ﬂeet into the
+benchmarks.
+To overcome these issues, we propose Mystique, an accurate
+and scalable framework for production AI benchmark gener-
+ation. It leverages the PyTorch execution graph (EG), a new
+feature that captures the runtime information of AI models at
+the granularity of operators, in a graph format, together with
+their metadata. By sourcing EG traces from the ﬂeet, we can build
+AI benchmarks that are portable and representative. Mystique is
+scalable, with its lightweight data collection, in terms of runtime
+overhead and user instrumentation efforts. It is also adaptive, as
+the expressiveness and composability of EG format allows ﬂexible
+user control over benchmark creation.
+We evaluate our methodology on several production AI
+workloads, and show that benchmarks generated with Mystique
+closely resemble original AI models, both in execution time
+and system-level metrics. We also showcase the portability of
+the generated benchmarks across platforms, and demonstrate
+several use cases enabled by the ﬁne-grained composability of
+the execution graph.
+I. INTRODUCTION
+Artiﬁcial Intelligence (AI) has experienced a strong resur-
+gence with the recent advances in Deep Learning (DL). It is
+rapidly expanding into many areas, and has led to revolution-
+ary changes, including in natural language processing [7], [12],
+computer vision [18], [42], gaming [41], [43], and recommen-
+dation systems [28], [45]. Almost all cloud enterprises today
+deploy massive amounts of resources towards AI computing
+to support their business. Building and maintaining large AI
+ﬂeets to efﬁciently support these DL workloads has led to both
+hardware and software innovation across the system stack.
+Having representative and agile AI benchmarks based on
+live ﬂeet production workloads would provide an invaluable
+resource for ﬂeet design and efﬁciency optimization. Inter-
+nally, it can be used for system optimization (e.g., GPU
+or ASIC accelerator design), performance characterization
+and analysis, bug reproducibility, etc. It can also be shared
+with external hardware vendors for early-stage performance
+testing, evaluation, and joint HW/SW codesign, with minimal
+infrastructure support and a streamlined IP sharing setup.
+There have been signiﬁcant efforts on AI workloads bench-
+marking over the past few years [1], [3], [9], [25], [39], of
+which the best known is MLPerf. MLPerf is an industry-
+standard benchmark suite that covers diverse ML applications,
+DNN models and optimizers, from training to inference. How-
+ever, its model diversity and updating speed, as Table I shows,
+cannot match the ever-changing, highly-diverse AI production
+workloads across cloud infrastructures.
+TABLE I
+MLPERF TRAINING BENCHMARKS [27].
+Area
+Model
+Last updated
+Vision
+ResNet-50
+May 17, 2021
+Vision
+3D U-Net
+Apr 14, 2021
+Vision
+Mask R-CNN
+Mar 5, 2021
+Language
+RNN-T
+Apr 7, 2021
+Language
+BERT-large
+May 14, 2021
+Commerce
+DLRM
+Feb 9, 2021
+Research
+Mini Go
+Jun 19, 2020
+Additionally, engineers or researchers need to manually
+select and adapt existing production or open-source work-
+loads to a form that can be used for benchmarking. This
+process involves a non-trivial investment, since it requires
+high expertise and comprehensive understanding of the work-
+loads. Also, extracting only the desired components from a
+production environment can be challenging, since production
+1
+arXiv:2301.04122v1  [cs.DC]  16 Dec 2022
+
+workloads have many supporting dependencies (e.g., storage,
+data preprocessing, scheduler), and many proprietary in-house
+libraries and tooling integration. This can lead to a high cost
+for maintaining and updating the derived benchmarks to keep
+up with the fast cadence of AI application design. Therefore,
+there is a strong need for a new methodology which enables
+us to efﬁciently generate AI benchmarks in production scale.
+In this paper, we propose an efﬁcient and scalable frame-
+work to create AI benchmarks directly from production work-
+ﬂows in a “replay as benchmark” manner. We present Mys-
+tique, a benchmark generation framework for AI workloads,
+which leverages the new PyTorch execution graph (EG) capa-
+bility to record the runtime information of a model at operator
+granularity, and faithfully replay it to reproduce the original
+performance. Mystique is efﬁcient and scalable as only a few
+lines of hook code are needed to collect the traces and generate
+a benchmark from a production, cloud-scale AI model.
+Our main contributions are:
+• We build a scalable and automated end-to-end infrastruc-
+ture that proﬁles and replays the execution graph traces
+from real production AI workloads.
+• We evaluate our methodology across several production
+PyTorch workloads running in a warehouse-scale ﬂeet,
+and show that the generated benchmarks closely match
+the original, both in terms of execution time and system-
+level metrics.
+• We showcase the portability of the generated benchmarks
+across platforms and evaluate several use cases the frame-
+work can be applied to.
+II. RELATED WORK
+A. AI benchmarks
+Benchmarks are an easy-to-use representation that cap-
+tures the most essential characteristics of a workload, while
+leaving out non-critical aspects of the original application.
+Benchmarks are powerful tools, as they enable evaluating a
+target system’s performance for a given workload without the
+need for supporting all dependencies the original application
+requires, e.g., libraries, upstream/downstream data pipeline
+setup, job orchestration. These advantages are even more
+desirable for AI workloads, which are built over complex
+programming frameworks, have more interconnected SW com-
+ponents, and often run distributedly in cloud environments.
+Therefore, providing a robust methodology to create realis-
+tic AI benchmarks that closely reﬂect a deployment’s workload
+behavior is an attractive proposition for all levels of system
+design exploration, from AI accelerator design to datacenter
+deployment orchestration.
+Unsurprisingly, there have been numerous proposals on
+benchmarking AI workloads [1], [3], [4], [9], [25], [26],
+[39], [46]. DeepBench [3] provides a set of basic operations
+used by deep neural networks (DNN) and evaluates them on
+different platforms. TBD [46] identiﬁes eight representative
+DNN models, and performs a detailed performance analysis
+on different deep learning frameworks and hardware conﬁgura-
+tions. DAWNBench [9] measures the end-to-end performance
+of training and inference, subject to a speciﬁed accuracy,
+allowing innovation in software, algorithms, communication
+methods, etc. More recently, MLPerf [4], [25], [26], [39]
+has become an industry-standard suite for ML performance,
+encompassing a variety of models in different domains (vision,
+language, recommendation, research) and different deploy-
+ment scenarios, from datacenter, to edge and mobile.
+While this work has enriched and strengthened the avail-
+ability of AI benchmarks to the community, their coverage
+remains limited compared to the vast spectrum of AI work-
+loads deployed in production. For instance, it is not uncommon
+to ﬁnd thousands of AI models in a hyperscaler’s ﬂeet at any
+given time. Curating a small set of benchmarks to approximate
+general behavior characteristics from such a vast collection is
+a signiﬁcant challenge. At the same time, given the rapid pace
+of innovation in the AI space, new AI workloads appear in
+datacenters on a daily basis, further hindering the ability of
+benchmark characteristics to remain up to date.
+In essence, we have a scalability issue both in terms of the
+model space and in terms of time required for benchmark
+generation. For example, diffusion models [37], [40] are a
+new class of generative models that generate diverse high-
+resolution images, however, have not yet been included in any
+widely used benchmarks. On the other hand, production mod-
+els often include adaptations and optimizations on top of open
+source models customized to their own use cases, and thus can
+exhibit signiﬁcantly different performance characteristics from
+their corresponding open-source versions.
+Our insight in dealing with this scalability issue is to rely on
+automation to generate representative AI benchmarks instead
+of the current manual curation approach. Mystique enables
+generating benchmarks at scale with minimal manual input,
+and provides close behavior resemblance to production ﬂows.
+B. Simulation, emulation, and performance modeling
+Simulation, emulation, and performance modeling offer
+another way to approximate a workload’s performance when
+software or hardware is unavailable. Sniper [8] is a parallel
+and scalable CPU simulator using a high-level abstraction for
+simulating multicore and multiprocessor systems. gem5 [6]
+is a modular platform for microarchitectural simulation that
+has been broadly used for GPU architecture modeling [5],
+[10], [34]. GPGPU-Sim [20] provides a cycle-level simulation
+model of NVIDIA GPUs running CUDA and OpenCL work-
+loads, and enables fast and detailed validation. While these
+simulation techniques are not speciﬁc to AI applications, they
+have been extensively used to evaluate software and hardware
+proposals for AI systems.
+Similarly, there has been a lot of work on performance
+modeling of ML workloads [19], [21], [23], [24], [44], [47].
+Daydream [47] predicts model runtime under certain optimiza-
+tions based on the kernel-task dependency graph. Habitat [44]
+uses wave scaling and MLPs to predict the execution time
+of DNN training. Finally, CM-DARE [21] proposes a perfor-
+mance model for distributed training with cloud-based GPU
+servers to achieve cost savings and speedup.
+2
+
+While useful when hardware is unavailable, or requires non-
+negligible changes, these simulators and performance models
+still make approximations on the workload behavior and
+cannot fully capture the complexity of a real system. Also,
+performance models in particular, usually target speciﬁc use
+cases and cannot easily be extended to a wide range of studies.
+C. Performance cloning and synthetic benchmarks
+Performance cloning is an intuitive way to generate syn-
+thetic benchmarks that preserve the performance of real-world
+workloads. Previous work proﬁled the architectural character-
+istics of the target applications, and generated corresponding
+proxy benchmarks [17], [32], [33], [38]. MicroGrad [38]
+collects the CPU metrics and uses a Gradient Descent based
+tuning mechanism to produce workload clones and stress
+tests. PerfProx [32] generates miniature proxies for real-
+world database applications, based on performance metrics
+derived from hardware performance counters. CAMP [33]
+models core-performance, memory locality and the interaction
+between the two to mimic BigData applications. ECHO [11]
+speciﬁcally focuses on cloning the network behavior of dis-
+tributed cloud applications using statistical models, and gener-
+ates synthetic benchmarks that resemble the locality and trafﬁc
+characteristics of the original services. Finally, Ditto [22]
+proposes an automated cloning framework that can capture
+both the low- and high-level performance metrics of distributed
+cloud applications.
+However, these approaches so far only focus on CPU perfor-
+mance and miss the critical performance engines exercised by
+AI workloads, namely GPUs or other accelerators. Extending
+these methods to GPUs is already a challenge due to their
+entirely different ISA and computing paradigm, in addition to
+needing to capture the interactions between CPU and GPU.
+Fortunately, AI models are mostly implemented using high-
+level APIs provided by common frameworks, such as Py-
+Torch and TensorFlow. This means that instead of creating
+benchmarks at instruction level, we can achieve performance
+reconstruction at a higher level, in our case, via leveraging the
+traced execution graph of a model.
+III. BACKGROUND
+Finding realistic benchmarks that resemble production cloud
+workloads is a long-standing problem. Given the limitations
+of open-source benchmarks and of approaches that rely on
+simulation or performance modeling, generating synthetic
+benchmarks that mimic the full stack performance of real
+applications can enable a wide range of system studies.
+Prior work on performance cloning and synthetic bench-
+mark generation focuses on CPU-centric workloads, by col-
+lecting their architectural characteristics and generating ap-
+propriate assembly instructions. Although, in theory we could
+apply the same approach to AI applications, this would be
+overlooking the unique properties that AI workloads exhibit.
+The fact that most AI workloads are implemented on top
+of a handful of popular frameworks (e.g., PyTorch, Ten-
+sorﬂow, JAX), makes capturing a logically complete yet—
+representation-wise—succinct and reproducible snapshot pos-
+sible. In the case of PyTorch, applications invoke underlying
+low-level operators, such as ATen [2], NCCL [29] to fulﬁll
+their execution. By recording the execution information at
+these invocation boundaries, we can faithfully reconstruct the
+execution behavior of a complex AI workload.
+In this work, we focus on generating benchmarks for
+PyTorch AI models. We choose PyTorch as our ﬁrst step
+because of its widespread use in industry (and our worldwide
+production environment speciﬁcally) as well as academia, and
+the rich proﬁling capabilities it offers. Our approach can
+be extended to support other ML frameworks, as discussed
+in Section VIII-B. Below we describe what the execution
+graph (EG) is, and how it enables us to generate realistic AI
+benchmarks.
+A. Execution Graph (EG)
+aten::linear
+aten::t
+aten::transpose
+aten::as_strided
+T16
+T12
+T15
+aten::addmm
+Fig. 1.
+An example of PyTorch’s execution graph (the ﬁgure only shows
+a subgraph for simplicity), in which the boxes are PyTorch operators and
+the ovals are unique tensors. Arrows represent inputs and outputs. Lines
+ending with a diamond show parent-child relationships between the operators.
+Execution order is not shown here.
+The execution graph of a PyTorch model is a runtime
+recording of its operators together with their metadata, such as
+the execution order, operator schema, input/output arguments,
+as well as their parent-child relationships. Figure 1 shows
+an example of such an execution graph, where each node is
+a PyTorch operator and the connections between the nodes
+indicate the parent-child relationships, i.e., the calling stack
+of the operators. Table II shows the key information captured
+for each node in more detail.
+Each tensor argument is tagged with a unique ID (a six
+element tuple) with its shape and data type. This unique ID
+is used to track the data dependencies among operators and
+to distinguish each tensor, as we will discuss in Section IV-D.
+The execution order across operators is not explicitly recorded
+but can be inferred from the node IDs, because they are
+assigned in increasing order, based on execution order.
+3
+
+TABLE II
+EXECUTION GRAPH (EG) NODE SCHEMA.
+Key
+Description
+name
+Name of node
+id
+Unique ID of this node
+parent
+Parent node ID
+op_schema
+PyTorch operator schema
+inputs
+Array of input args
+Actual values for non-tensor args
+input_shapes
+Array of input shapes
+Empty [] for non-tensor args
+input_types
+Array of input types
+Empty [] for non-tensor args
+outputs
+Array of output args
+Actual values for non-tensor args
+output_shapes
+Array of output shapes
+Empty [] for non-tensor args
+output_types
+Array of output types
+Empty [] for non-tensor args
+B. Advantages of EG
+This execution graph records the metadata that is needed
+to reproduce the original execution behavior of each operator,
+offering us a very intuitive way to generate synthetic bench-
+marks by replaying all operators in the graph according to
+their original execution order and data dependencies.
+EG stands out among other similar recording approaches
+because: 1) its API is easy to use and requires minimal
+source level changes (collection can be enabled by a few
+lines of code, no performance counters or architectural char-
+acteristics needed), 2) its hardware agnostic design makes
+it portable across different hardware platforms, 3) it incurs
+very small performance overheads, which facilitates a large-
+scale automated data collection setup in the background, in
+a production environment, 4) it has a compactly deﬁned
+data schema which minimizes the storage support cost in
+production, and 5) as each EG node is a self-contained entity,
+the EG format provides great composability which enable
+more use cases, such as new hardware platform evaluation and
+scaled-down performance emulation (we discuss this in detail
+in Section VII). These traits make EG an ideal candidate for
+encapsulating broad production workload behavior in an agile
+manner.
+C. PyTorch operators
+Operators are the building blocks in the PyTorch framework,
+which deﬁne the mathematical and logical transformations to
+be performed on the data. Every operator includes a set of
+platform-speciﬁc implementations, usually written in C/C++
+or other domain speciﬁc languages, to provide its functionality
+on the supported hardware. The framework is designed to
+allow easy custom implementations for reasons spanning from
+increased performance to enabling new hardware innovations.
+Among the models we have proﬁled, we ﬁnd that operators
+can be roughly divided into four categories based on the
+implications each entails when trying to replay them:
+Count
+CPU time
+GPU time
+(exposed)
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+Operators breakdown
+ATen
+Comms
+Fused
+Custom
+Fig. 2. Fraction of different operators in a production model running on 8
+GPUs, in terms of their count, CPU time, and exposed GPU time.
+• ATen ops: ATen is the low-level tensor library and
+compute backend for PyTorch. It performs the actual
+computation on tensors, such as addition, matrix mul-
+tiplication, and batch normalization.
+• Communication ops: Distributed training across multi-
+ple devices has now become the norm to support large
+scale AI models, as well as to increase the training speed.
+During distributed training, communication operators are
+used for synchronization and data transmission among
+multiple devices. For PyTorch, c10d [35] is the most pop-
+ular communication library, which offers both collective
+communication APIs (e.g., all reduce() and all to all())
+and P2P communication APIs (e.g., send() and recv()).
+• Fused ops: Operator fusion is a common optimization
+technique that merges multiple operators into a single
+execution instance to reduce the memory access and
+kernel dispatch overhead. In PyTorch models, it can be
+easily enabled by applying the @torch.jit.script decorator
+to the model’s function deﬁnition. There are a couple of
+available backends in JIT; the default fuser on CPUs is
+NNC and on GPUs is NVFuser. After PyTorch fuses the
+original operators, it will emit a single fused operator in
+place of them during execution.
+• Custom ops: To support the rapidly changing AI land-
+scape, PyTorch provides a user-friendly interface for users
+to deﬁne custom operators. The interface is commonly
+used to create a novel model architecture building block
+or to provide a better implementation than the default
+routines. Using operators imported from other libraries
+(e.g., FBGEMM [13] and torchrec [15]) in the application
+is another example of leveraging such custom operator
+support.
+Figure 2 shows the fraction of different types of operators
+for one of the most popular production workloads running in
+our warehouse ﬂeet. We show the ratios across three metrics:
+operator count, CPU time, and GPU time, which correspond,
+respectively, to the number of occurrences of the operators, the
+execution time on CPUs, and the execution time of the kernels
+launched on GPUs. In particular, for communication operators,
+4
+
+Execution graph
+Profiler trace
+EG analyzer
+Benchmark generation
+AI workloads
+Trace databases
+EG replayer
+Subgraph replay
+Scale-down simulation
+Trace collection
+EG synthesis
+Use cases
+Similarity measurement
+EG builder
+Fig. 3. Overview of our benchmark generation workﬂow using EG replay.
+we measure the exposed GPU time, which is the time that
+their launched kernels are not running in parallel with any
+other computation kernels. As the default compute backend of
+PyTorch, ATen operators take up the lion share in terms of all
+three metrics. Fused operators are the second in count but have
+the shortest GPU time. Custom and communication operators
+are quantitatively modest, but have long GPU time; the former
+are usually complex in functionality and therefore expensive
+to execute, and the latter can also come at a signiﬁcant cost
+in large-scale distributed deployments.
+Considering the high fraction of ATen and communication
+operators, we mostly focus on them during the operator
+reconstruction phase, discussed in the next section.
+IV. MYSTIQUE DESIGN
+Figure 3 shows a high-level overview of Mystique, our
+benchmark generation framework based on EG replay. First,
+we collect both the execution graph and the proﬁler trace
+of the ﬂeet’s AI workloads under live trafﬁc. Then the EG
+analyzer and builder preprocess the traces and select the most
+commonly-occurring ones. Currently, we pass these EG traces
+to the replayer in their original form and in the future we
+plan to add more sophistication to accommodate additional
+uses, such as operator obfuscation for enhanced IP protection.
+Finally, the EG replayer gets the input traces and creates the
+desired benchmarks or conﬁgures them for different use cases.
+The whole workﬂow is fully automated, so we can constantly
+update the benchmarks using the latest collected traces without
+any human involvement. Additionally, we add the feedback
+loop between the replay and original traces by comparing their
+similarity to validate and improve our methodology. In the
+rest of this section, we describe the trace collection, and each
+essential part of the replay-based benchmarking methodology.
+A. Trace collection
+To collect the EG of a PyTorch model, a user currently needs
+to insert hooks into the code to instantiate an ExecutionGra-
+phObserver and use start() and stop() methods to control when
+the execution is recorded. Typically, we only need to collect
+a single execution iteration, since the execution graph of a
+model is mostly the same across iterations. Each process has
+a single observer instance and if running under a distributed
+setup, multiple execution graphs will be collected, one for
+each process. It is worth noting that these graphs need to be
+collected from the same iteration, as we need to ensure that the
+same communication operators are recorded. The alternative
+can lead to deadlocks during replay, if we cannot match the
+communication operators across multiple EGs.
+1 from torch.profiler import ExecutionGraphObserver
+2
+3 # Instantiate the runtime observer
+4 eg_trace_path = "/tmp/execution_graph.json"
+5 eg_observer = ExecutionGraphObserver()
+6 eg_observer.register_callback(eg_trace_path)
+7
+8 # Insert hooks into execution (e.g., training) loop
+9 def training_loop():
+10
+# Collects profiler trace
+11
+with torch.profiler.profile(
+12
+activities=[ProfilerActivity.CPU,
+13
+ProfilerActivity.CUDA],
+14
+on_trace_ready=profiler_trace_handler,
+15
+) as pf:
+16
+for idx in range(100):
+17
+if idx == 10:
+18
+# Start EG capture
+19
+eg_observer.start()
+20
+if idx == 11:
+21
+# Stop EG capture
+22
+eg_observer.stop()
+23
+model.step()
+24
+pf.step()
+In some cases, collecting the EG trace alone is not enough
+to fully reproduce the behavior of a workload, as it lacks
+the CUDA stream execution information. In those cases, we
+combine EG with another runtime trace, collected by the
+PyTorch Proﬁler [36]. We discuss this in more detail in
+Section IV-E.
+The pseudocode of trace collection is shown above. Adding
+the EG observer and proﬁler to record the runtime infor-
+mation can introduce some overheads to the performance of
+the original AI model. However, this overhead is small and
+only occurs once, and it does not affect the accuracy of the
+generated benchmark, as our replay method does not rely on
+any temporal information captured in these traces or hardware-
+level performance metrics.
+B. Operators selection
+Given an execution graph, we need to select which operators
+to replay, because some of them are redundant. For example,
+aten::linear() has included two of its child operators aten::t()
+and aten::addmm() as part of its implementation. At runtime
+all three operators will be caught in the EG, however, we
+5
+
+only need to replay the parent one, which in this case is
+aten::linear(). To identify these redundant operators, since the
+parent operator is always executed before its children, we can
+traverse the operators in the order of execution, keep each
+operator we encounter and skip all its child operators, based on
+the parent-child relationships captured in the execution graph.
+C. Operators reconstruction
+1) ATen operators: We reconstruct each ATen operator
+through the TorchScript IR (Intermediate Representation) us-
+ing its captured operator schema in EG, which includes
+the operator name and data types for its input and output
+arguments. We implement a string-based parser to extract this
+key information from the schema, which is then used to build
+the canonical textual representation of the IR. Finally, we
+compile the IR with TorchScript to create the callable function
+for each operator to use during replay. The pseudocode below
+demonstrates this procedure:
+1 # Captured op schema in EG
+2 op_schema = "aten::add.Tensor(Tensor self,
+3
+Tensor other, *,
+4
+Scalar alpha=1) -> Tensor"
+5
+6 # Extract name and arguments from schema
+7 op_name, op_args = parser(op_schema)
+8
+9 # Build IR with extracted information
+10 torchscript_ir_str = builder(op_name, op_args) = ""
+11
+graph(%x.1 : Tensor,
+12
+%y.1 : Tensor):
+13
+%4 : int = prim::Constant[value=1]()
+14
+%5 : Tensor = aten::add(%x.1, %y.1, %4)
+15
+return (%5)
+16 ""
+17
+18 # Compile IR to callable function
+19 graph = torch._C.parse_ir(torchscript_ir_str)
+20 cu = torch._C.CompilationUnit()
+21 func = cu.create_function(op_name, graph)
+2) Communication operators: To reproduce the communi-
+cation pattern of the original workload, we need to replay
+the communication operators with their original arguments,
+such as the process group and message size. The metadata
+can be obtained from the execution graph; for the execution of
+the operators during replay, we leverage the existing PyTorch
+distributed infrastructure and implement a wrapper over the
+low-level interfaces to pass the appropriate parameters. We
+create new process groups and map them to the original
+groups, and for each operator, we select the same data type and
+size as the original, to ensure a similar communication pattern
+across servers during replay. Depending on the execution mode
+of the operator, we wait for it to complete if it is blocking, or
+execute it in asynchronous mode by registering its callback to
+check back later.
+3) Custom operators: Custom extension is a mechanism
+that PyTorch developed to allow users to create their out-of-
+source operators, distinct from the default backend. Similar
+to the other operators, their input and output arguments are
+captured in the execution graph, but that is not sufﬁcient for
+replay, as we do not know their speciﬁc implementations. To
+handle this case, we expose an interface, which allows users
+to register their custom operators together with their imple-
+mentations. During replay, we look up the registry and use
+the provided implementation to replay each custom operator.
+4) Fused operators: Pointwise operators can be fused into
+a single kernel to amortize memory access time and kernel
+launch time. However, the metadata of these fused operators
+are not supported by the execution graph, in its current imple-
+mentation. For now, we skip these operators altogether because
+they comprise only a small percentage of the overall operator
+list, and have negligible impact to the overall performance,
+as shown in Figure 2. Fusion behavior can be reproduced via
+PyTorch JIT and we plan to add this support once its EG trace
+is available.
+Note that all operator reconstruction happens during the
+initialization phase of the replay, such that they can be directly
+invoked in the real execution to avoid any runtime overhead.
+D. Arguments and tensor management
+In addition to the functionality, input arguments also play
+an important role to the performance of an operator. For
+arguments with basic types, such as int or bool, we can simply
+save their values and reuse them during replay, however, for
+part of the tensors we need to instantiate them in advance.
+If we track the occurrence of all tensors that are used
+as input, we can divide them into two categories. We call
+one type intermediate tensors, which are generated as the
+output of an operator executed earlier, before being used. The
+other category are external tensors, whose generation is not
+observed in the execution graph. This classiﬁcation can be
+done by tracking the appearance of each tensor based on its
+unique tensor ID, during the traversal of the graph in execution
+order. For intermediate tensors, we need to save them at the
+time of generation, and pass them to the downstream operators,
+according to the data dependencies between operators. For
+external tensors, we have to explicitly instantiate them before
+execution.
+By default, we instantiate a tensor with the same shape and
+data type as the original but with random values, as the perfor-
+mance of an operator is not related to the speciﬁc values of the
+input tensors. We ﬁnd that this holds true for most operators, as
+we will show later in the evaluation section, minus a few rare
+exceptions. One case we have met is the lookup operator
+for embedding tables. One of its input tensors stores the lookup
+indices, whose value directly determines the access pattern
+and has a strong correlation with performance. In this case,
+we would need to specify the values for that tensor based on
+some additional information, such as the table size, indices
+distribution, or pooling factor. Since not all of the above
+information is captured in the EG, for now, we set the default
+values for the missing information empirically, derived by the
+application operators in our production environment, and we
+additionally provide an interface for users to further specify
+them. We leave the automatic processing of such special cases
+to future work.
+6
+
+11/12/22, 9:33 PM
+chrome://tracing
+chrome://tracing
+1/1
+Record
+Save
+Load
+replay_newest_load.json
+Flow events
+Processes
+M
+View Options
+»
+?
+File Size Stats
+Metrics
+Frame Data
+Input Latency
+Alerts
+Nothing selected. Tap stuff.
+[xarexec] (pid 462436): CPU
+X
+[xarexec] (pid 6): GPU 6
+X
+ -1331689920
+ thread 462436 (python3.8)
+ thread 480104 (python3.8)
+stream 7
+stream 20
+stream 22
+stream 84
+stream 85
+stream 86
+stream 87
+stream 88
+stream 89
+stream 90
+stream 91
+stream 92
+stream 93
+stream 94
+stream 95
+stream 96
+stream 97
+stream 98
+stream 99
+stream 100
+stream 101
+stream 102
+stream 103
+stream 104
+stream 105
+stream 106
+stream 107
+stream 108
+stream 109
+stream 110
+stream 111
+stream 112
+stream 113
+stream 114
+stream 115
+stream 116
+stream 117
+stream 118
+stream 119
+stream 120
+11/12/22, 9:33 PM
+chrome://tracing
+chrome://tracing
+1/1
+Record
+Save
+Load
+replay_newest_load.json
+Flow events
+Processes
+M
+View Options
+»
+?
+File Size Stats
+Metrics
+Frame Data
+Input Latency
+Alerts
+Nothing selected. Tap stuff.
+[xarexec] (pid 462436): CPU
+X
+[xarexec] (pid 6): GPU 6
+X
+ -1331689920
+ thread 462436 (python3.8)
+ thread 480104 (python3.8)
+stream 7
+stream 20
+stream 22
+stream 84
+stream 85
+stream 86
+stream 87
+stream 88
+stream 89
+stream 90
+stream 91
+stream 92
+stream 93
+stream 94
+stream 95
+stream 96
+stream 97
+stream 98
+stream 99
+stream 100
+stream 101
+stream 102
+stream 103
+stream 104
+stream 105
+stream 106
+stream 107
+stream 108
+stream 109
+stream 110
+stream 111
+stream 112
+stream 113
+stream 114
+stream 115
+stream 116
+stream 117
+stream 118
+stream 119
+stream 120
+Fig. 4. Example of parallel streams execution, with streams 7, 20, 22 for the
+computation, data loader, and communication, respectively.
+E. Parallel stream execution
+A CUDA stream is a sequence of kernels that execute in
+issue-order on the GPU, and CUDA applications are allowed
+to launch kernels concurrently on different streams to improve
+device utilization and execution efﬁciency. The most repre-
+sentative scenario is the parallel execution of computation and
+communication kernels to hide the networking overhead. Also,
+data transfer between the host and device is often optimized
+to run on a separate stream.
+Figure 4 shows an example trace for one of our evaluated
+production PyTorch models, in which streams 7, 20, 22 are
+used for the computation, data loader, and communication,
+respectively. The stream execution pattern of a model can have
+a signiﬁcant impact on its performance, and we need to take
+this into account during the benchmark generation.
+To do so, we need to identify which stream each kernel is
+executed on, and which operator launches each kernel, so that
+we can prepare multiple streams and dispatch each operator to
+its corresponding stream during replay. Unfortunately, current
+EG does not include any stream or kernel information so we
+need to extract this from another runtime trace, collected via
+the PyTorch proﬁler [36]. This proﬁler has been broadly used
+in the PyTorch community and the extraction can be easily
+performed based on the launching relationships between the
+operators and kernels. For now we use this trace as an EG
+enhancement, and based on our feedback, the EG working
+group is actively working on integrating the kernel information
+into the EG representation.
+F. Putting it all together
+Our EG replay approach ﬁrst collects the execution graph
+and proﬁler trace of a model to capture both the operators with
+their metadata, and their launched GPU kernels. We then walk
+through the graph according to the execution order, distinguish
+individual tensors, and identify the operators to replay. Next,
+we reconstruct the callable function for each operator, prepare
+the necessary tensors, and initialize the distributed environ-
+ment, if necessary. Finally, we replay the operators on different
+streams with the same execution order, input arguments (but
+not values for tensors), and data dependencies as in the original
+workload, to faithfully reproduce their original performance
+characteristics. In case of a distributed deployment, for valida-
+tion purposes, the same number of processes will be spawned
+as the original, each using a separate execution graph, and
+repeating all the steps above. We also enable scaled-down
+replays of an AI workload without the need for retraining,
+as discussed in Section VII-C.
+V. IMPLEMENTATION
+Our framework is built on PyTorch in approximately 8,000
+lines of Python code. It currently supports all basic ATen
+operators, a large fraction of custom operators used in our
+evaluated workloads, a few common libraries like FBGEMM,
+and the c10d distributed library with all four types of backends
+(nccl, gloo, mpi and ucc).
+To leverage our framework, a user ﬁrst inserts hooks into
+their PyTorch model to collect the execution graph and proﬁler
+trace. Our framework then takes the traces as input, follows
+the steps we discussed in Section IV to analyze the traces,
+and generates a single PyTorch program as a benchmark. The
+program contains operators with a hardcoded execution order,
+input arguments and data dependencies, and can directly run
+on any platform as a normal PyTorch application. For the
+distributed training deployment, we use mpirun [30] to create
+the distributed environment and spawn multiple processes,
+each of which uses its own input traces to generate and
+execute the benchmark. Synchronization and data sharing
+between different processes is automatically achieved by the
+communication operators.
+Given the granularity and ﬂexibility of the execution graph,
+our EG replay method can be used to explore more use case
+scenarios, in addition to completely replicating the original
+behavior, as we discuss in Section VII.
+VI. EVALUATION
+A. Platforms
+We evaluate Mystique on a production cluster of 4 servers
+with NVIDIA Tesla A100 GPUs and V100 GPUs, and unless
+explicitly speciﬁed, the results we show are collected on A100
+GPUs. We use CUDA 11.4 and PyTorch 1.14 as our testing
+environment.
+B. Workloads
+• PARAM linear: PARAM [14] is a benchmark suite of
+compute and communication microbenchmarks, as well
+as full workloads for both training and inference. We
+select a representative linear model with 20 linear layers
+and set batch size to 512 and data type to ﬂoat32.
+• ResNet: We choose the ResNet18 model from torchvi-
+sion [16], with batch size set to 128 and data type set
+to ﬂoat32. For its distributed deployment, we use the de-
+fault Distributed Data-Parallel (DDP) training framework
+provided by PyTorch.
+• ASR: We use a production multi-GPU automatic speech
+recognition (ASR) training ﬂow implemented with the
+Fairseq [31] toolkit. At its core, ASR is a neural-network-
+based acoustic model.
+• RM: RM is a leading edge multi-node, multi-GPU pro-
+duction recommendation model that pushes the boundary
+for large-scale training infrastructure. It is the produc-
+tion implementation that the open-source DLRM bench-
+mark [28] aims to approximate. In our experiments,
+7
+
+M.several conﬁgurations of this model are used to cover dif-
+ferent workload setups (e.g., different distributed training
+set sizes).
+C. Operators coverage
+TABLE III
+OPS COVERAGE RATE ACROSS EVALUATED WORKLOADS.
+Model
+Operators coverage
+Count
+Execution time
+PARAM linear
+100%
+100%
+ResNet
+100%
+100%
+ASR
+99.6%
+75.7%
+RM
+96.8%
+90.9%
+Table III shows the current operator coverage rate for
+our framework across the different studied workloads. The
+coverage rate denotes the percentage of operators that we are
+able to replay compared to the total number of operators in a
+workload. We show the fractions in terms of both count and
+execution time. Since we support all ATen operators, which are
+the compute backend of PyTorch, we can achieve a very high
+coverage rate on the operator count for all workloads. Two of
+our production workloads have a relatively lower coverage in
+terms of execution time, since we are currently missing support
+for fused operators and a subset of custom operators, with
+the latter dominating the execution time gap. These custom
+operators normally perform very speciﬁc tasks, for example,
+a LSTM network in NLP models. We provide users with a
+programmable interface that allows them to register more of
+their custom operators, which can lead to higher coverage and
+accuracy.
+D. End-to-end execution time
+Figure 5 shows the runtime traces of a single training
+iteration for the PARAM linear model (top), and its replayed
+benchmark (bottom). Within each trace, we separate execution
+time between threads running on the CPUs (top block for each
+trace) and kernels running on the GPUs (bottom block for each
+trace).
+In the original workload’s trace (top), there are two threads
+on the CPUs since the backward operators are automatically
+performed by PyTorch’s autograd engine on the other thread,
+and we similarly use two threads in replay. The overall
+execution time of the sequence of operators in the replayed
+benchmark is 14.2 ms, very close to the original’s 14.9 ms.
+Moreover, if zoomed in, we can see that the execution time of
+each individual replayed operator, i.e., the length of each bar,
+and the execution pattern across operators, i.e., how these bars
+interleave with each other, is very similar to the original. The
+vertical height of the bars is determined by the call stack depth
+for each operator. The small difference in height between orig-
+inal and replayed benchmark is due to additional wrappers like
+autograd::engine::evaluate function in the original workload,
+which do not perform any meaningful work; in the synthetic
+workload we only replay their underlying operators (“Replay
+targets” regions).
+TABLE IV
+E2E EXECUTION TIME OF A SINGLE ITERATION.
+Model
+Original
+Original
+Replay
+(exclude unsupported)
+PARAM linear
+14.9ms
+14.9ms
+14.1ms
+ResNet
+64.4ms
+64.4ms
+70.7ms
+ASR
+316.3ms
+239.3ms
+229.1ms
+RM
+65.9ms
+59.9ms
+58.4ms
+Table IV shows the original and replayed execution time for
+a single iteration of each workload running on a single GPU.
+For a fair comparison, we also include the original execution
+time that excludes the unsupported operators, and we use this
+calibrated execution time for the rest of our evaluation. This
+table shows to what extent Mystique captures the covered
+operators’ execution time. We obtain high accuracies across
+all studied applications, with 5.4% error on PARAM linear,
+9.8% error on ResNet, 4.3% error on ASR and 2.5% error on
+RM, when comparing the overall performance of all replayed
+operators.
+E. System-level metrics
+In addition to the execution time, system-level metrics are
+also important for a benchmark generation framework to cap-
+ture, in order to ensure similarity with the original workload.
+Speciﬁcally, for these AI workloads, we are more interested in
+GPU-related metrics, such as Streaming Multiprocessor (SM)
+utilization, High Bandwidth Memory (HBM) bandwidth, GPU
+memory utilization, and GPU power.
+Figure 6 shows three representative and widely evaluated
+metrics for AI workloads, in production environments: SM
+utilization, HBM bandwidth, and GPU power, across all
+workloads and their replay counterparts. All models are using
+a single A100 GPU. We collect their performance metrics
+over thousands of iterations, and show their average values.
+Compared to the other three workloads, RM has the highest
+SM utilization, and therefore the highest power usage. The
+HBM bandwidth gap of ASR is a little larger than the others,
+due to the small number of custom operators we do not yet
+support. The results illustrate that different workloads have
+very different performance characteristics, but can be accu-
+rately captured by our replay methodology, and reproduced in
+the generated benchmarks.
+F. Distributed training
+Distributed training is now very common practice for AI
+workloads, as their model sizes and datasets keep rapidly
+growing. To evaluate the scalability of our EG replay-based
+framework, we collect the runtime traces of the RM work-
+load running on 2 nodes with 16 NVIDIA A100 GPUs and
+8
+
+CPU
+GPU
+11/20/22, 9:54 PM
+chrome://tracing
+chrome://tracing
+1/1
+Record
+Save
+Load
+linear_replay_dev_trans.json
+Flow events
+Processes
+M
+View Options
+»
+?
+File Size Stats
+Metrics
+Frame Data
+Input Latency
+Alerts
+Nothing selected. Tap stuff.
+python3.8 (pid 2624623): CPU
+X
+python3.8 (pid 0): GPU 0
+X
+Process Spans
+X
+ thread 2624623 (python3.8)
+ thread 2624624 (python3.8)
+stream 7
+PyTorch Proﬁler
+11/20/22, 9:54 PM
+chrome://tracing
+chrome://tracing
+1/1
+Record
+Save
+Load
+linear_dev.json
+Flow events
+Processes
+M
+View Options
+»
+?
+File Size Stats
+Metrics
+Frame Data
+Input Latency
+Alerts
+Nothing selected. Tap stuff.
+python3.8 (pid 1965390): CPU
+X
+python3.8 (pid 0): GPU 0
+X
+Process Spans
+X
+ thread 1965390 (python3.8)
+ thread 1966752 (python3.8)
+stream 7
+PyTorch Proﬁler
+14.9ms
+14.2ms
+CPU
+GPU
+Replay targets
+Wrappers
+Fig. 5. Runtime proﬁler traces of PARAM linear (top) and its benchmark (bottom) for a single training iteration. Within each trace, the bars on the top are
+PyTorch operators executed on CPU and the bars at the bottom are GPU kernels, with length indicating the real execution time.
+PARAM ResNet
+ASR
+RM
+25
+50
+75
+100
+SM utilization (%)
+PARAM ResNet
+ASR
+RM
+200
+400
+600
+800
+HBM bw (GB/s)
+PARAM ResNet
+ASR
+RM
+100
+200
+300
+400
+GPU power (W)
+Original
+Replay
+Fig. 6. Comparison of SM utilization, HBM bandwidth, and GPU power for each model and their replay counterparts.
+interconnected via NVLink (intra-node) and a 200 Gbps NIC
+(inter-node), and then replay it under the same setting.
+Table V shows the execution time per iteration and the
+system-level metrics per GPU, averaged across the proﬁling
+duration and all 16 GPUs, for the original model and the
+replayed benchmark. Compared to the single GPU results
+mentioned earlier, execution time is now longer, while SM
+utilization, HBM bandwidth, and power are lower, because
+of the communication overhead between the worker nodes.
+The performance of our generated benchmarks successfully
+follows the changes in the original workload under the large
+distributed deployment.
+TABLE V
+SCALABILITY EVALUATION ON 2 NODES WITH 16 GPUS.
+Metric
+Original
+Replay
+Execution time (ms)
+94.5
+90.5
+SM utilization (%)
+71.3
+76.3
+HBM bandwidth (GB/s)
+575.2
+586.1
+GPU power (W)
+253.8
+246.2
+G. Cross platform validation
+Mystique operates at operator-level to reproduce the perfor-
+mance and resource characteristics of an original AI workload.
+9
+
+PyTorch Profiler (0)1This hardware-agnostic operation allows the generated bench-
+mark to be portable across platforms without regeneration. To
+validate this, we test the performance of all four studied work-
+loads and their corresponding generated benchmarks on three
+platforms: Intel Xeon Platinum CPU, NVIDIA Tesla V100,
+and NVIDIA Tesla A100. We only use the trace collected on
+the A100 server to generate the synthetic benchmarks, and
+then run them across the different platforms.
+CPU
+V100
+A100
+Param linear
+0.0
+0.5
+1.0
+Normalized exec. time
+CPU
+V100
+A100
+ResNet
+0.0
+0.5
+1.0
+Normalized exec. time
+CPU
+V100
+A100
+ASR
+0.0
+0.5
+1.0
+Normalized exec. time
+CPU
+V100
+A100
+RM
+0.0
+0.5
+1.0
+Normalized exec. time
+Original
+Replay
+Fig. 7.
+Normalized execution time of all workloads and their replayed
+benchmarks on different platforms.
+Figure 7 shows the validation results of all four workloads.
+We normalize the execution time of the replayed benchmark
+to that of the original workload on each platform. For two
+production workloads ASR and RM, we only show their
+performance on the two GPU platforms, as they cannot directly
+run on CPU. The ﬁgure shows that execution time between
+original and replayed application matches across platforms,
+demonstrating the portability of our replay methodology.
+H. Power efﬁciency sensitivity sweep
+100
+150
+200
+250
+300
+350
+Device power limit (W)
+0.0
+0.5
+1.0
+Energy efficiency
+PARAM
+100
+150
+200
+250
+300
+350
+Device power limit (W)
+0.0
+0.5
+1.0
+ResNet
+100
+150
+200
+250
+300
+350
+Device power limit (W)
+0.0
+0.5
+1.0
+Energy efficiency
+ASR
+100
+150
+200
+250
+300
+350
+Device power limit (W)
+0.0
+0.5
+1.0
+RM
+Original
+Replay
+Fig. 8. Normalized energy efﬁciency under varying power limit.
+Power efﬁciency is an important metric in many system
+designs, and large-scale training is no exception. Due to
+the sheer size of our production training ﬂeet, even a small
+power efﬁciency gain translates to huge infrastructure cost
+savings. Here we demonstrate that the benchmark generated by
+Mystique is able to mimic the power efﬁciency characteristics
+of the original application, when we sweep certain system
+design knobs (the device power limit in this example).
+Figure 8 displays the power efﬁciency sensitivity curves of
+all studied workloads and their corresponding benchmarks, as
+we set the device power limit to different levels. The x axis
+is the device power limit we want to sweep, and the y axis
+is the normalized power efﬁciency, deﬁned as the throughput
+over power. Our generated benchmarks closely track the
+sensitivity trend of the original workloads, demonstrating that
+such a methodology can be effectively used to evaluate system
+performance in the place of real workloads, when they are not
+available.
+VII. USE CASES
+By leveraging the execution graph (EG), Mystique opens up
+many opportunities on how to conduct AI system evaluation.
+In this section we describe several use cases we experimented
+with using our current framework.
+A. Subgraph replay
+Execution graph is made up of nodes (operators) connected
+using parent-child relationships; this composability allows us
+to replay only a subgraph or certain types of operators when
+testing the performance of a speciﬁc component. To do this, a
+user can leverage the record function context manager [36] in
+the PyTorch proﬁler to label an arbitrary range of code with a
+user-provided name. Then in the EG, a new operator appears
+as the parent of all operators within that code range. When
+traversing the graph to select which operators to replay, we can
+use this name to easily locate this operator, and only replay
+the subgraph under it. For example, in Figure 9, we selectively
+replay the subgraph under the ## forward:z ## operator for the
+RM workload and show that partial performance is preserved.
+We show repeated replay traces in the bottom to demonstrate
+that we are actually only replaying the target subgraph.
+11/17/22, 11:36 PM
+chrome://tracing
+chrome://tracing
+1/1
+Record
+Save
+Load
+cmf_1_026.json
+Flow events
+Processes
+M
+View Options
+»
+?
+File Size Stats
+Metrics
+Frame Data
+Input Latency
+Alerts
+Nothing selected. Tap stuff.
+python3.8 (pid 3167047): CPU
+X
+python3.8 (pid 0): GPU 0
+X
+Process Spans
+X
+960644672
+ thread 3167047 (python3.8)
+ thread 3172295 (python3.8)
+stream 7
+stream 20
+stream 22
+PyTorch Proﬁler
+11/13/22, 8:01 PM
+chrome://tracing
+chrome://tracing
+1/1
+Record
+Save
+Load
+cmf_overarch_subgraph_replay copy.json
+Flow events
+Processes
+M
+View Options
+»
+?
+File Size Stats
+Metrics
+Frame Data
+Input Latency
+Alerts
+Nothing selected. Tap stuff.
+[xarexec] (pid 2720388): CPU
+X
+[xarexec] (pid 0): GPU 0
+X
+Process Spans
+X
+1
+ thread 2720388 (python3.8)
+stream 7
+PyTorch Proﬁler
+11/13/22, 8:01 PM
+chrome://tracing
+chrome://tracing
+1/1
+Record
+Save
+Load
+cmf_overarch_subgraph_replay copy.json
+Flow events
+Processes
+M
+View Options
+»
+?
+File Size Stats
+Metrics
+Frame Data
+Input Latency
+Alerts
+Nothing selected. Tap stuff.
+[xarexec] (pid 2720388): CPU
+X
+[xarexec] (pid 0): GPU 0
+X
+Process Spans
+X
+1
+ thread 2720388 (python3.8)
+stream 7
+PyTorch Proﬁler
+9.4ms
+9.8ms
+9.7ms
+Fig. 9.
+Runtime traces of original model (top) and two iterations of
+the subgraph replay (bottom). The original label names are replaced for
+conﬁdentiality reasons.
+Similarly, by ﬁltering operators based on their types, our
+framework can also be easily conﬁgured to replay selected
+types of operators. For example, we have used it to perform a
+network analysis in our production environment, by replaying
+the communication operators exclusively.
+10
+
+ProfilerStep#1912
+## forward ##
+## label:x #:
+#
+## forwa...
+## forward:y ##
+## forward:z ##
+forward
+ autogr...
+torch.:jit...
+ void split_embed...
+amp... voi
+amp...ampamp...
+amp...am
+amp..
+ PyTorch Profiler (0)1amp ampa...a...ampa... amp...
+a...ampa...amp..a...ampampB. Early stage platform evaluation
+An essential application of benchmarks is to obtain per-
+formance indications for new hardware platforms, where the
+full SW environment might not yet have fully matured. Al-
+though we can use simple microbenchmarks to sample the
+performance space and make some best effort performance
+projections, using a production-like benchmark that exercised
+the full stack similarly to the original workload lends signiﬁ-
+cant conﬁdence to the results. In the early stages of design for
+a new platform, it is quite common that an exact copy of the
+PyTorch application cannot properly run on it. Since time is
+usually a critical consideration in these early-stage evaluation
+scenarios, manually forcing the full application stack to run on
+the new platform is cumbersome, time-consuming, and error-
+prone. Due to EG replay’s minimal software dependencies and
+ease of modiﬁcation at operator granularity (e.g., skipping the
+unsupported operators), it is an ideal use case to showcase the
+agility of Mystique. Figure 10 shows a new platform under
+consideration, compared to the mature CPU, V100, and A100
+platforms. We can use the EG replay on the new platform
+to accurately infer the potential performance beneﬁt this new
+platform can offer, as shown with the red line.
+CPU
+V100
+A100
+New plat.
+0
+20
+40
+60
+80
+100
+Speedup over CPU
+Original
+Replay
+Fig. 10. Execution time speedup for new, experimental platform over CPU.
+C. Scaled-down performance emulation
+DL models have been on an exponential growth curve in
+terms of model size, compute complexity, and data needs.
+This trend has led to the rapid adoption of large-scale training
+deployments in production, including in our own global-scale
+production environment. It is now very common to start an AI
+use case using models requiring hundreds of GPUs in training,
+posing a big resource challenge for AI system evaluation.
+Handling a few test systems in the early engineering testing
+phases is manageable, but deploying and supporting testing
+setups with hundreds of GPUs is a serious undertaking and
+investment, or altogether infeasible due to supply chain short-
+ages, datacenter space or cooling limitations, need for custom
+networks, and high failure rate support. Therefore, there is a
+desire to evaluate a model’s large scale training performance
+using a much smaller test setup (e.g., a few GPUs).
+Building a benchmark at the granularity of operators gives
+us the opportunity to evaluate the target large scale execution
+using a much smaller scale setting. For example, you can use
+just 2 nodes to mimic the behavior of the original workloads
+running on 16/32/64 etc. nodes by manipulating the communi-
+cation cost portion during replay. This requires no changes to
+the original training implementation, which would otherwise
+require domain speciﬁc knowledge and coding changes.
+In distributed data-parallel training, workers are performing
+the same computation on their assigned data chunks; this local
+computation does not change with the number of workers. The
+main performance factor that varies with scale is the network
+communication. By approximating the large-scale network
+performance impact, we can emulate the target behavior at
+large scale using a small scale setup.
+There are many ways to achieve this with different trade-
+offs. We started with a simple intuitive approach where dummy
+delays are added to the communication path to account for the
+mismatch between small-scale testing setup and large-scale
+deployment setup. The delay is set empirically, based on the
+network cost model. In many cases, a range estimate for the
+cost is sufﬁcient to sweep the performance space and reveal
+the performance trend. We have demonstrated the feasibility of
+this approach by successfully reproducing the execution time
+of the 16 GPUs RM model training with only 2 GPUs. There
+are clearly many opportunities to improve upon this simple
+approach. Due to the heavy engineering effort required to fully
+explore this area, we defer further exploring it to future work.
+VIII. DISCUSSION
+Mystique has already been used with production AI work-
+loads to accurately generate synthetic benchmarks that have
+been used for several challenging system studies. At the same
+time, there are even more interesting directions we plan to
+explore using this new methodology.
+A. Advanced EG analyzer and builder
+Currently our EG synthesis block is selecting full EG
+traces as replay samples from the trace database, guided by a
+simple EG analyzer based on population weight. This can be
+improved by adding more sophistication on weight calculation
+(e.g., more timing cost). We can also go a step deeper into
+operator level summary and weighting, and take advantage of
+EG’s composability to combine portions from different EGs
+into a single replay trace for more efﬁcient aggregation.
+B. Broader support for other ML frameworks
+Our framework currently targets PyTorch models due to
+their widespread use in our environment, but can be ex-
+tended to support other ML frameworks, such as TensorFlow,
+MXNet. In general, all these frameworks are founded on
+building blocks, such as the tensor manipulation library and
+communication library, and are executed by the operators in
+these libraries, unlike the traditional CPU-centric applications.
+This is highly promising for benchmark generation, as these
+operators are reproducible. Once the proﬁling tool that collects
+the operators’ runtime information is available, our EG-based
+methodology can be easily adapted to support other AI pro-
+gramming frameworks.
+11
+
+C. Improved privacy and IP protection
+Because AI models often offer a competitive advantage for a
+company, great care is taken to safeguard them. Unfortunately,
+this makes sharing the workload to e.g., co-design or co-
+optimize a system with external vendors a very complicated
+process. With Mystique, we can obfuscate the real EG traces
+by automatically swapping the important IP protected blocks
+with performance-equivalent public blocks using a preset
+rule. This way we can still effectively capture the high-level
+behavior of a production workload, while also enabling fast
+sharing of the workload with external partners for performance
+evaluation. Similarly, because EG does not directly capture the
+real training dataset, but only their metadata like dimensions,
+the generated benchmarks do not contain any user privacy-
+sensitive information. This strong separation in the design
+makes sharing EG-based benchmarks a better choice in a
+privacy focused environment.
+IX. CONCLUSION
+We present Mystique, a new generation methodology for
+AI benchmarks, based on execution graphs replay. Mystique
+addresses the scalability issues stemming from both the large
+model variety and the constantly changing workload land-
+scape. We demonstrate that our methodology generates AI
+benchmarks highly similar to the original applications, while
+being easy to use and portable across platforms, without the
+need for regenerating. We have illustrated several use cases for
+Mystique, including early stage platform evaluation, subgraph
+replay, and scaled-down performance testing, all of which are
+highly challenging using existing techniques.
+12
+
+REFERENCES
+[1] R. Adolf, S. Rama, B. Reagen, G.-Y. Wei, and D. Brooks, “Fathom:
+Reference workloads for modern deep learning methods,” in 2016
+IEEE International Symposium on Workload Characterization (IISWC).
+IEEE, 2016, pp. 1–10.
+[2] ATen, “Aten,” https://github.com/pytorch/pytorch/tree/master/aten.
+[3] Baidu, “Deepbench,” https://github.com/baidu-research/DeepBench.
+[4] C. Banbury, V. J. Reddi, P. Torelli, J. Holleman, N. Jeffries, C. Kiraly,
+P. Montino, D. Kanter, S. Ahmed, D. Pau et al., “Mlperf tiny bench-
+mark,” arXiv preprint arXiv:2106.07597, 2021.
+[5] B. M. Beckmann and A. Gutierrez, “The amd gem5 apu simulator: Mod-
+eling heterogeneous systems in gem5,” in Tutorial at the International
+Symposium on Microarchitecture (MICRO), 2015.
+[6] N. Binkert, B. Beckmann, G. Black, S. K. Reinhardt, A. Saidi, A. Basu,
+J. Hestness, D. R. Hower, T. Krishna, S. Sardashti et al., “The gem5
+simulator,” ACM SIGARCH computer architecture news, vol. 39, no. 2,
+pp. 1–7, 2011.
+[7] T. Brown, B. Mann, N. Ryder, M. Subbiah, J. D. Kaplan, P. Dhariwal,
+A. Neelakantan, P. Shyam, G. Sastry, A. Askell et al., “Language mod-
+els are few-shot learners,” Advances in neural information processing
+systems, vol. 33, pp. 1877–1901, 2020.
+[8] T. E. Carlson, W. Heirman, and L. Eeckhout, “Sniper: Exploring the level
+of abstraction for scalable and accurate parallel multi-core simulation,”
+in Proceedings of 2011 International Conference for High Performance
+Computing, Networking, Storage and Analysis, 2011, pp. 1–12.
+[9] C. Coleman, D. Narayanan, D. Kang, T. Zhao, J. Zhang, L. Nardi,
+P. Bailis, K. Olukotun, C. R´e, and M. Zaharia, “Dawnbench: An end-
+to-end deep learning benchmark and competition,” Training, vol. 100,
+no. 101, p. 102, 2017.
+[10] V. M. Del Barrio, C. Gonz´alez, J. Roca, A. Fern´andez, and E. Es-
+pasa, “Attila: a cycle-level execution-driven simulator for modern gpu
+architectures,” in 2006 IEEE International Symposium on Performance
+Analysis of Systems and Software.
+IEEE, 2006, pp. 231–241.
+[11] C. Delimitrou, S. Sankar, A. Kansal, and C. Kozyrakis, “ECHO:
+Recreating Network Trafﬁc Maps for Datacenters of Tens of Thousands
+of Servers,” in Proceedings of the IEEE International Symposium on
+Workload Characterization (IISWC), 2012.
+[12] J. Devlin, M.-W. Chang, K. Lee, and K. Toutanova, “Bert: Pre-training
+of deep bidirectional transformers for language understanding,” arXiv
+preprint arXiv:1810.04805, 2018.
+[13] Facebook, “Fbgemm,” https://github.com/pytorch/FBGEMM.
+[14] Facebook, “Param benchmarks,” https://github.com/facebookresearch/
+param.
+[15] Facebook, “torchrec,” https://github.com/pytorch/torchrec.
+[16] Facebook,
+“torchvision
+models,”
+https://pytorch.org/vision/stable/
+models.html.
+[17] K. Ganesan and L. K. John, “Automatic generation of miniaturized
+synthetic proxies for target applications to efﬁciently design multicore
+processors,” IEEE Transactions on Computers, vol. 63, no. 4, pp. 833–
+846, 2013.
+[18] K. He, X. Zhang, S. Ren, and J. Sun, “Deep residual learning for image
+recognition,” in Proceedings of the IEEE conference on computer vision
+and pattern recognition, 2016, pp. 770–778.
+[19] D. Justus, J. Brennan, S. Bonner, and A. S. McGough, “Predicting the
+computational cost of deep learning models,” in 2018 IEEE international
+conference on big data (Big Data).
+IEEE, 2018, pp. 3873–3882.
+[20] M. Khairy, Z. Shen, T. M. Aamodt, and T. G. Rogers, “Accel-sim:
+An extensible simulation framework for validated gpu modeling,” in
+2020 ACM/IEEE 47th Annual International Symposium on Computer
+Architecture (ISCA).
+IEEE, 2020, pp. 473–486.
+[21] S. Li, R. J. Walls, and T. Guo, “Characterizing and modeling distributed
+training with transient cloud gpu servers,” in 2020 IEEE 40th Interna-
+tional Conference on Distributed Computing Systems (ICDCS).
+IEEE,
+2020, pp. 943–953.
+[22] M. Liang, Y. Gan, Y. Li, C. Torres, A. Dhanotia, M. Ketkar, and
+C. Delimitrou, “Ditto: End-to-End Application Cloning for Networked
+Cloud Services,” in Proceedings of the Twenty Eighth International
+Conference on Architectural Support for Programming Languages and
+Operating Systems (ASPLOS), April 2023.
+[23] Y.-C. Liao, C.-C. Wang, C.-H. Tu, M.-C. Kao, W.-Y. Liang, and S.-H.
+Hung, “Perfnetrt: Platform-aware performance modeling for optimized
+deep neural networks,” in 2020 International Computer Symposium
+(ICS).
+IEEE, 2020, pp. 153–158.
+[24] Z. Lin, L. Feng, E. K. Ardestani, J. Lee, J. Lundell, C. Kim, A. Ke-
+jariwal, and J. D. Owens, “Building a performance model for deep
+learning recommendation model training on gpus,” arXiv preprint
+arXiv:2201.07821, 2022.
+[25] P. Mattson, C. Cheng, G. Diamos, C. Coleman, P. Micikevicius, D. Pat-
+terson, H. Tang, G.-Y. Wei, P. Bailis, V. Bittorf et al., “Mlperf training
+benchmark,” Proceedings of Machine Learning and Systems, vol. 2, pp.
+336–349, 2020.
+[26] P. Mattson, V. J. Reddi, C. Cheng, C. Coleman, G. Diamos, D. Kanter,
+P. Micikevicius, D. Patterson, G. Schmuelling, H. Tang et al., “Mlperf:
+An industry standard benchmark suite for machine learning perfor-
+mance,” IEEE Micro, vol. 40, no. 2, pp. 8–16, 2020.
+[27] MLCommons, “Mlperf training benchmarks,” https://mlcommons.org/
+en/training-normal-21/.
+[28] M. Naumov, D. Mudigere, H.-J. M. Shi, J. Huang, N. Sundaraman,
+J. Park, X. Wang, U. Gupta, C.-J. Wu, A. G. Azzolini et al., “Deep
+learning recommendation model for personalization and recommenda-
+tion systems,” arXiv preprint arXiv:1906.00091, 2019.
+[29] NVIDIA, “nccl,” https://developer.nvidia.com/nccl.
+[30] OpenMPI,
+“mpirun,”
+https://www.open-mpi.org/doc/current/man1/
+mpirun.1.php.
+[31] M. Ott, S. Edunov, A. Baevski, A. Fan, S. Gross, N. Ng, D. Grangier,
+and M. Auli, “fairseq: A fast, extensible toolkit for sequence modeling,”
+in Proceedings of NAACL-HLT 2019: Demonstrations, 2019.
+[32] R. Panda and L. K. John, “Proxy benchmarks for emerging big-
+data workloads,” in 2017 26th International Conference on Parallel
+Architectures and Compilation Techniques (PACT).
+IEEE, 2017, pp.
+105–116.
+[33] R. Panda, X. Zheng, A. Gerstlauer, and L. K. John, “Camp: Accurate
+modeling of core and memory locality for proxy generation of big-data
+applications,” in 2018 Design, Automation & Test in Europe Conference
+& Exhibition (DATE).
+IEEE, 2018, pp. 337–342.
+[34] J. Power, J. Hestness, M. S. Orr, M. D. Hill, and D. A. Wood, “gem5-
+gpu: A heterogeneous cpu-gpu simulator,” IEEE Computer Architecture
+Letters, vol. 14, no. 1, pp. 34–36, 2014.
+[35] PyTorch, “c10d,” https://pytorch.org/docs/stable/distributed.html.
+[36] PyTorch, “Pytorch proﬁler,” https://pytorch.org/tutorials/recipes/recipes/
+proﬁler recipe.html.
+[37] A. Ramesh, P. Dhariwal, A. Nichol, C. Chu, and M. Chen, “Hierarchical
+text-conditional image generation with clip latents,” arXiv preprint
+arXiv:2204.06125, 2022.
+[38] G. S. Ravi, R. Bertran, P. Bose, and M. Lipasti, “Micrograd: A
+centralized framework for workload cloning and stress testing,” in 2021
+IEEE International Symposium on Performance Analysis of Systems and
+Software (ISPASS).
+IEEE, 2021, pp. 70–72.
+[39] V. J. Reddi, C. Cheng, D. Kanter, P. Mattson, G. Schmuelling, C.-J.
+Wu, B. Anderson, M. Breughe, M. Charlebois, W. Chou et al., “Mlperf
+inference benchmark,” in 2020 ACM/IEEE 47th Annual International
+Symposium on Computer Architecture (ISCA).
+IEEE, 2020, pp. 446–
+459.
+[40] C. Saharia, W. Chan, S. Saxena, L. Li, J. Whang, E. Denton, S. K. S.
+Ghasemipour, B. K. Ayan, S. S. Mahdavi, R. G. Lopes et al., “Photoreal-
+istic text-to-image diffusion models with deep language understanding,”
+arXiv preprint arXiv:2205.11487, 2022.
+[41] D. Silver, A. Huang, C. J. Maddison, A. Guez, L. Sifre, G. Van
+Den Driessche, J. Schrittwieser, I. Antonoglou, V. Panneershelvam,
+M. Lanctot et al., “Mastering the game of go with deep neural networks
+and tree search,” nature, vol. 529, no. 7587, pp. 484–489, 2016.
+[42] C. Szegedy, W. Liu, Y. Jia, P. Sermanet, S. Reed, D. Anguelov, D. Erhan,
+V. Vanhoucke, and A. Rabinovich, “Going deeper with convolutions,”
+in Proceedings of the IEEE conference on computer vision and pattern
+recognition, 2015, pp. 1–9.
+[43] O. Vinyals, I. Babuschkin, W. M. Czarnecki, M. Mathieu, A. Dudzik,
+J. Chung, D. H. Choi, R. Powell, T. Ewalds, P. Georgiev et al., “Grand-
+master level in starcraft ii using multi-agent reinforcement learning,”
+Nature, vol. 575, no. 7782, pp. 350–354, 2019.
+[44] G. Yu, Y. Gao, P. Golikov, and G. Pekhimenko, “Computational perfor-
+mance predictions for deep neural network training: A runtime-based
+approach,” CoRR, vol. abs/2102.00527, 2021.
+[45] G. Zhou, X. Zhu, C. Song, Y. Fan, H. Zhu, X. Ma, Y. Yan, J. Jin, H. Li,
+and K. Gai, “Deep interest network for click-through rate prediction,”
+in Proceedings of the 24th ACM SIGKDD international conference on
+knowledge discovery & data mining, 2018, pp. 1059–1068.
+13
+
+[46] H. Zhu, M. Akrout, B. Zheng, A. Pelegris, A. Jayarajan, A. Phanishayee,
+B. Schroeder, and G. Pekhimenko, “Benchmarking and analyzing deep
+neural network training,” in 2018 IEEE International Symposium on
+Workload Characterization (IISWC).
+IEEE, 2018, pp. 88–100.
+[47] H. Zhu, A. Phanishayee, and G. Pekhimenko, “Daydream: Accurately
+estimating the efﬁcacy of optimizations for {DNN} training,” in 2020
+USENIX Annual Technical Conference (USENIX ATC 20), 2020, pp.
+337–352.
+14
+
diff --git a/lNE2T4oBgHgl3EQfygjW/content/tmp_files/load_file.txt b/lNE2T4oBgHgl3EQfygjW/content/tmp_files/load_file.txt
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+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf,len=1048
+page_content='Mystique: Accurate and Scalable Production AI  Benchmarks Generation  Mingyu Liang1, Wenyin Fu2, Louis Feng2, Zhongyi Lin3, Pavani Panakanti2, Srinivas Sridharan2, and Christina Delimitrou4  1Cornell University  2Meta  3University of California, Davis  4MIT  ml2585@cornell.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='edu  {wenyinfu,lofe,pavanip,ssrinivas}@meta.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='com  zhylin@ucdavis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='edu  delimitrou@csail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='mit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='edu  Abstract—Building and maintaining large AI ﬂeets to efﬁ-  ciently support the fast-growing DL workloads is an active  research topic for modern cloud infrastructure providers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Gener-  ating accurate benchmarks plays an essential role in the design  and evaluation of rapidly evoloving software and hardware  solutions in this area.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Two fundamental challenges to make  this process scalable are (i) workload representativeness and (ii)  the ability to quickly incorporate changes to the ﬂeet into the  benchmarks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  To overcome these issues, we propose Mystique, an accurate  and scalable framework for production AI benchmark gener-  ation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' It leverages the PyTorch execution graph (EG), a new  feature that captures the runtime information of AI models at  the granularity of operators, in a graph format, together with  their metadata.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' By sourcing EG traces from the ﬂeet, we can build  AI benchmarks that are portable and representative.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Mystique is  scalable, with its lightweight data collection, in terms of runtime  overhead and user instrumentation efforts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' It is also adaptive, as  the expressiveness and composability of EG format allows ﬂexible  user control over benchmark creation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  We evaluate our methodology on several production AI  workloads, and show that benchmarks generated with Mystique  closely resemble original AI models, both in execution time  and system-level metrics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' We also showcase the portability of  the generated benchmarks across platforms, and demonstrate  several use cases enabled by the ﬁne-grained composability of  the execution graph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' INTRODUCTION  Artiﬁcial Intelligence (AI) has experienced a strong resur-  gence with the recent advances in Deep Learning (DL).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' It is  rapidly expanding into many areas, and has led to revolution-  ary changes, including in natural language processing [7], [12],  computer vision [18], [42], gaming [41], [43], and recommen-  dation systems [28], [45].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Almost all cloud enterprises today  deploy massive amounts of resources towards AI computing  to support their business.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Building and maintaining large AI  ﬂeets to efﬁciently support these DL workloads has led to both  hardware and software innovation across the system stack.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  Having representative and agile AI benchmarks based on  live ﬂeet production workloads would provide an invaluable  resource for ﬂeet design and efﬁciency optimization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Inter-  nally, it can be used for system optimization (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=', GPU  or ASIC accelerator design), performance characterization  and analysis, bug reproducibility, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' It can also be shared  with external hardware vendors for early-stage performance  testing, evaluation, and joint HW/SW codesign, with minimal  infrastructure support and a streamlined IP sharing setup.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  There have been signiﬁcant efforts on AI workloads bench-  marking over the past few years [1], [3], [9], [25], [39], of  which the best known is MLPerf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' MLPerf is an industry-  standard benchmark suite that covers diverse ML applications,  DNN models and optimizers, from training to inference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' How-  ever, its model diversity and updating speed, as Table I shows,  cannot match the ever-changing, highly-diverse AI production  workloads across cloud infrastructures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  TABLE I  MLPERF TRAINING BENCHMARKS [27].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  Area  Model  Last updated  Vision  ResNet-50  May 17, 2021  Vision  3D U-Net  Apr 14, 2021  Vision  Mask R-CNN  Mar 5, 2021  Language  RNN-T  Apr 7, 2021  Language  BERT-large  May 14, 2021  Commerce  DLRM  Feb 9, 2021  Research  Mini Go  Jun 19, 2020  Additionally, engineers or researchers need to manually  select and adapt existing production or open-source work-  loads to a form that can be used for benchmarking.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' This  process involves a non-trivial investment, since it requires  high expertise and comprehensive understanding of the work-  loads.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Also, extracting only the desired components from a  production environment can be challenging, since production  1  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='04122v1  [cs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='DC]  16 Dec 2022  workloads have many supporting dependencies (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=', storage,  data preprocessing, scheduler), and many proprietary in-house  libraries and tooling integration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' This can lead to a high cost  for maintaining and updating the derived benchmarks to keep  up with the fast cadence of AI application design.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Therefore,  there is a strong need for a new methodology which enables  us to efﬁciently generate AI benchmarks in production scale.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  In this paper, we propose an efﬁcient and scalable frame-  work to create AI benchmarks directly from production work-  ﬂows in a “replay as benchmark” manner.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' We present Mys-  tique, a benchmark generation framework for AI workloads,  which leverages the new PyTorch execution graph (EG) capa-  bility to record the runtime information of a model at operator  granularity, and faithfully replay it to reproduce the original  performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Mystique is efﬁcient and scalable as only a few  lines of hook code are needed to collect the traces and generate  a benchmark from a production, cloud-scale AI model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  Our main contributions are:  We build a scalable and automated end-to-end infrastruc-  ture that proﬁles and replays the execution graph traces  from real production AI workloads.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  We evaluate our methodology across several production  PyTorch workloads running in a warehouse-scale ﬂeet,  and show that the generated benchmarks closely match  the original, both in terms of execution time and system-  level metrics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  We showcase the portability of the generated benchmarks  across platforms and evaluate several use cases the frame-  work can be applied to.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' RELATED WORK  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' AI benchmarks  Benchmarks are an easy-to-use representation that cap-  tures the most essential characteristics of a workload, while  leaving out non-critical aspects of the original application.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  Benchmarks are powerful tools, as they enable evaluating a  target system’s performance for a given workload without the  need for supporting all dependencies the original application  requires, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=', libraries, upstream/downstream data pipeline  setup, job orchestration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' These advantages are even more  desirable for AI workloads, which are built over complex  programming frameworks, have more interconnected SW com-  ponents, and often run distributedly in cloud environments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  Therefore, providing a robust methodology to create realis-  tic AI benchmarks that closely reﬂect a deployment’s workload  behavior is an attractive proposition for all levels of system  design exploration, from AI accelerator design to datacenter  deployment orchestration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  Unsurprisingly, there have been numerous proposals on  benchmarking AI workloads [1], [3], [4], [9], [25], [26],  [39], [46].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' DeepBench [3] provides a set of basic operations  used by deep neural networks (DNN) and evaluates them on  different platforms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' TBD [46] identiﬁes eight representative  DNN models, and performs a detailed performance analysis  on different deep learning frameworks and hardware conﬁgura-  tions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' DAWNBench [9] measures the end-to-end performance  of training and inference, subject to a speciﬁed accuracy,  allowing innovation in software, algorithms, communication  methods, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' More recently, MLPerf [4], [25], [26], [39]  has become an industry-standard suite for ML performance,  encompassing a variety of models in different domains (vision,  language, recommendation, research) and different deploy-  ment scenarios, from datacenter, to edge and mobile.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  While this work has enriched and strengthened the avail-  ability of AI benchmarks to the community, their coverage  remains limited compared to the vast spectrum of AI work-  loads deployed in production.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' For instance, it is not uncommon  to ﬁnd thousands of AI models in a hyperscaler’s ﬂeet at any  given time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Curating a small set of benchmarks to approximate  general behavior characteristics from such a vast collection is  a signiﬁcant challenge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' At the same time, given the rapid pace  of innovation in the AI space, new AI workloads appear in  datacenters on a daily basis, further hindering the ability of  benchmark characteristics to remain up to date.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  In essence, we have a scalability issue both in terms of the  model space and in terms of time required for benchmark  generation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' For example, diffusion models [37], [40] are a  new class of generative models that generate diverse high-  resolution images, however, have not yet been included in any  widely used benchmarks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' On the other hand, production mod-  els often include adaptations and optimizations on top of open  source models customized to their own use cases, and thus can  exhibit signiﬁcantly different performance characteristics from  their corresponding open-source versions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  Our insight in dealing with this scalability issue is to rely on  automation to generate representative AI benchmarks instead  of the current manual curation approach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Mystique enables  generating benchmarks at scale with minimal manual input,  and provides close behavior resemblance to production ﬂows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Simulation, emulation, and performance modeling  Simulation, emulation, and performance modeling offer  another way to approximate a workload’s performance when  software or hardware is unavailable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Sniper [8] is a parallel  and scalable CPU simulator using a high-level abstraction for  simulating multicore and multiprocessor systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' gem5 [6]  is a modular platform for microarchitectural simulation that  has been broadly used for GPU architecture modeling [5],  [10], [34].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' GPGPU-Sim [20] provides a cycle-level simulation  model of NVIDIA GPUs running CUDA and OpenCL work-  loads, and enables fast and detailed validation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' While these  simulation techniques are not speciﬁc to AI applications, they  have been extensively used to evaluate software and hardware  proposals for AI systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  Similarly, there has been a lot of work on performance  modeling of ML workloads [19], [21], [23], [24], [44], [47].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  Daydream [47] predicts model runtime under certain optimiza-  tions based on the kernel-task dependency graph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Habitat [44]  uses wave scaling and MLPs to predict the execution time  of DNN training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Finally, CM-DARE [21] proposes a perfor-  mance model for distributed training with cloud-based GPU  servers to achieve cost savings and speedup.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  2  While useful when hardware is unavailable, or requires non-  negligible changes, these simulators and performance models  still make approximations on the workload behavior and  cannot fully capture the complexity of a real system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Also,  performance models in particular, usually target speciﬁc use  cases and cannot easily be extended to a wide range of studies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Performance cloning and synthetic benchmarks  Performance cloning is an intuitive way to generate syn-  thetic benchmarks that preserve the performance of real-world  workloads.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Previous work proﬁled the architectural character-  istics of the target applications, and generated corresponding  proxy benchmarks [17], [32], [33], [38].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' MicroGrad [38]  collects the CPU metrics and uses a Gradient Descent based  tuning mechanism to produce workload clones and stress  tests.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' PerfProx [32] generates miniature proxies for real-  world database applications, based on performance metrics  derived from hardware performance counters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' CAMP [33]  models core-performance, memory locality and the interaction  between the two to mimic BigData applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' ECHO [11]  speciﬁcally focuses on cloning the network behavior of dis-  tributed cloud applications using statistical models, and gener-  ates synthetic benchmarks that resemble the locality and trafﬁc  characteristics of the original services.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Finally, Ditto [22]  proposes an automated cloning framework that can capture  both the low- and high-level performance metrics of distributed  cloud applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  However, these approaches so far only focus on CPU perfor-  mance and miss the critical performance engines exercised by  AI workloads, namely GPUs or other accelerators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Extending  these methods to GPUs is already a challenge due to their  entirely different ISA and computing paradigm, in addition to  needing to capture the interactions between CPU and GPU.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  Fortunately, AI models are mostly implemented using high-  level APIs provided by common frameworks, such as Py-  Torch and TensorFlow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' This means that instead of creating  benchmarks at instruction level, we can achieve performance  reconstruction at a higher level, in our case, via leveraging the  traced execution graph of a model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' BACKGROUND  Finding realistic benchmarks that resemble production cloud  workloads is a long-standing problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Given the limitations  of open-source benchmarks and of approaches that rely on  simulation or performance modeling, generating synthetic  benchmarks that mimic the full stack performance of real  applications can enable a wide range of system studies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  Prior work on performance cloning and synthetic bench-  mark generation focuses on CPU-centric workloads, by col-  lecting their architectural characteristics and generating ap-  propriate assembly instructions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Although, in theory we could  apply the same approach to AI applications, this would be  overlooking the unique properties that AI workloads exhibit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  The fact that most AI workloads are implemented on top  of a handful of popular frameworks (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=', PyTorch, Ten-  sorﬂow, JAX), makes capturing a logically complete yet—  representation-wise—succinct and reproducible snapshot pos-  sible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' In the case of PyTorch, applications invoke underlying  low-level operators, such as ATen [2], NCCL [29] to fulﬁll  their execution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' By recording the execution information at  these invocation boundaries, we can faithfully reconstruct the  execution behavior of a complex AI workload.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  In this work, we focus on generating benchmarks for  PyTorch AI models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' We choose PyTorch as our ﬁrst step  because of its widespread use in industry (and our worldwide  production environment speciﬁcally) as well as academia, and  the rich proﬁling capabilities it offers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Our approach can  be extended to support other ML frameworks, as discussed  in Section VIII-B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Below we describe what the execution  graph (EG) is, and how it enables us to generate realistic AI  benchmarks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Execution Graph (EG)  aten::linear  aten::t  aten::transpose  aten::as_strided  T16  T12  T15  aten::addmm  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  An example of PyTorch’s execution graph (the ﬁgure only shows  a subgraph for simplicity), in which the boxes are PyTorch operators and  the ovals are unique tensors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Arrows represent inputs and outputs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Lines  ending with a diamond show parent-child relationships between the operators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  Execution order is not shown here.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  The execution graph of a PyTorch model is a runtime  recording of its operators together with their metadata, such as  the execution order, operator schema, input/output arguments,  as well as their parent-child relationships.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Figure 1 shows  an example of such an execution graph, where each node is  a PyTorch operator and the connections between the nodes  indicate the parent-child relationships, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=', the calling stack  of the operators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Table II shows the key information captured  for each node in more detail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  Each tensor argument is tagged with a unique ID (a six  element tuple) with its shape and data type.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' This unique ID  is used to track the data dependencies among operators and  to distinguish each tensor, as we will discuss in Section IV-D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  The execution order across operators is not explicitly recorded  but can be inferred from the node IDs, because they are  assigned in increasing order, based on execution order.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  3  TABLE II  EXECUTION GRAPH (EG) NODE SCHEMA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='Key  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='Description  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='name  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='Name of node  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='id  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='Unique ID of this node  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='parent  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='Parent node ID  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='op_schema  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='PyTorch operator schema  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='inputs  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='Array of input args  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='Actual values for non-tensor args  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='input_shapes  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='Array of input shapes  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='Empty [] for non-tensor args  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='input_types  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='Array of input types  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='Empty [] for non-tensor args  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='outputs  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='Array of output args  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='Actual values for non-tensor args  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='output_shapes  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='Array of output shapes  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='Empty [] for non-tensor args  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='output_types  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='Array of output types  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='Empty [] for non-tensor args  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Advantages of EG  This execution graph records the metadata that is needed  to reproduce the original execution behavior of each operator,  offering us a very intuitive way to generate synthetic bench-  marks by replaying all operators in the graph according to  their original execution order and data dependencies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  EG stands out among other similar recording approaches  because: 1) its API is easy to use and requires minimal  source level changes (collection can be enabled by a few  lines of code,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' no performance counters or architectural char-  acteristics needed),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' 2) its hardware agnostic design makes  it portable across different hardware platforms,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' 3) it incurs  very small performance overheads,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' which facilitates a large-  scale automated data collection setup in the background,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' in  a production environment,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' 4) it has a compactly deﬁned  data schema which minimizes the storage support cost in  production,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' and 5) as each EG node is a self-contained entity,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  the EG format provides great composability which enable  more use cases,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' such as new hardware platform evaluation and  scaled-down performance emulation (we discuss this in detail  in Section VII).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' These traits make EG an ideal candidate for  encapsulating broad production workload behavior in an agile  manner.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' PyTorch operators  Operators are the building blocks in the PyTorch framework,  which deﬁne the mathematical and logical transformations to  be performed on the data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Every operator includes a set of  platform-speciﬁc implementations, usually written in C/C++  or other domain speciﬁc languages, to provide its functionality  on the supported hardware.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' The framework is designed to  allow easy custom implementations for reasons spanning from  increased performance to enabling new hardware innovations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  Among the models we have proﬁled, we ﬁnd that operators  can be roughly divided into four categories based on the  implications each entails when trying to replay them:  Count  CPU time  GPU time  (exposed)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='0  Operators breakdown  ATen  Comms  Fused  Custom  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Fraction of different operators in a production model running on 8  GPUs, in terms of their count, CPU time, and exposed GPU time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  ATen ops: ATen is the low-level tensor library and  compute backend for PyTorch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' It performs the actual  computation on tensors, such as addition, matrix mul-  tiplication, and batch normalization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  Communication ops: Distributed training across multi-  ple devices has now become the norm to support large  scale AI models, as well as to increase the training speed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  During distributed training, communication operators are  used for synchronization and data transmission among  multiple devices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' For PyTorch, c10d [35] is the most pop-  ular communication library, which offers both collective  communication APIs (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=', all reduce() and all to all())  and P2P communication APIs (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=', send() and recv()).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  Fused ops: Operator fusion is a common optimization  technique that merges multiple operators into a single  execution instance to reduce the memory access and  kernel dispatch overhead.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' In PyTorch models, it can be  easily enabled by applying the @torch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='jit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='script decorator  to the model’s function deﬁnition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' There are a couple of  available backends in JIT;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' the default fuser on CPUs is  NNC and on GPUs is NVFuser.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' After PyTorch fuses the  original operators, it will emit a single fused operator in  place of them during execution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  Custom ops: To support the rapidly changing AI land-  scape, PyTorch provides a user-friendly interface for users  to deﬁne custom operators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' The interface is commonly  used to create a novel model architecture building block  or to provide a better implementation than the default  routines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Using operators imported from other libraries  (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=', FBGEMM [13] and torchrec [15]) in the application  is another example of leveraging such custom operator  support.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  Figure 2 shows the fraction of different types of operators  for one of the most popular production workloads running in  our warehouse ﬂeet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' We show the ratios across three metrics:  operator count, CPU time, and GPU time, which correspond,  respectively, to the number of occurrences of the operators, the  execution time on CPUs, and the execution time of the kernels  launched on GPUs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' In particular, for communication operators,  4  Execution graph  Profiler trace  EG analyzer  Benchmark generation  AI workloads  Trace databases  EG replayer  Subgraph replay  Scale-down simulation  Trace collection  EG synthesis  Use cases  Similarity measurement  EG builder  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Overview of our benchmark generation workﬂow using EG replay.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  we measure the exposed GPU time, which is the time that  their launched kernels are not running in parallel with any  other computation kernels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' As the default compute backend of  PyTorch, ATen operators take up the lion share in terms of all  three metrics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Fused operators are the second in count but have  the shortest GPU time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Custom and communication operators  are quantitatively modest, but have long GPU time;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' the former  are usually complex in functionality and therefore expensive  to execute, and the latter can also come at a signiﬁcant cost  in large-scale distributed deployments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  Considering the high fraction of ATen and communication  operators, we mostly focus on them during the operator  reconstruction phase, discussed in the next section.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' MYSTIQUE DESIGN  Figure 3 shows a high-level overview of Mystique, our  benchmark generation framework based on EG replay.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' First,  we collect both the execution graph and the proﬁler trace  of the ﬂeet’s AI workloads under live trafﬁc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Then the EG  analyzer and builder preprocess the traces and select the most  commonly-occurring ones.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Currently, we pass these EG traces  to the replayer in their original form and in the future we  plan to add more sophistication to accommodate additional  uses, such as operator obfuscation for enhanced IP protection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  Finally, the EG replayer gets the input traces and creates the  desired benchmarks or conﬁgures them for different use cases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  The whole workﬂow is fully automated, so we can constantly  update the benchmarks using the latest collected traces without  any human involvement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Additionally, we add the feedback  loop between the replay and original traces by comparing their  similarity to validate and improve our methodology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' In the  rest of this section, we describe the trace collection, and each  essential part of the replay-based benchmarking methodology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Trace collection  To collect the EG of a PyTorch model, a user currently needs  to insert hooks into the code to instantiate an ExecutionGra-  phObserver and use start() and stop() methods to control when  the execution is recorded.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Typically, we only need to collect  a single execution iteration, since the execution graph of a  model is mostly the same across iterations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Each process has  a single observer instance and if running under a distributed  setup, multiple execution graphs will be collected, one for  each process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' It is worth noting that these graphs need to be  collected from the same iteration, as we need to ensure that the  same communication operators are recorded.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' The alternative  can lead to deadlocks during replay, if we cannot match the  communication operators across multiple EGs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  1 from torch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='profiler import ExecutionGraphObserver  2  3 # Instantiate the runtime observer  4 eg_trace_path = "/tmp/execution_graph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='json"  5 eg_observer = ExecutionGraphObserver()  6 eg_observer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='register_callback(eg_trace_path)  7  8 # Insert hooks into execution (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=', training) loop  9 def training_loop():  10  # Collects profiler trace  11  with torch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='profiler.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='profile(  12  activities=[ProfilerActivity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='CPU,  13  ProfilerActivity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='CUDA],  14  on_trace_ready=profiler_trace_handler,  15  ) as pf:  16  for idx in range(100):  17  if idx == 10:  18  # Start EG capture  19  eg_observer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='start()  20  if idx == 11:  21  # Stop EG capture  22  eg_observer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='stop()  23  model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='step()  24  pf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='step()  In some cases, collecting the EG trace alone is not enough  to fully reproduce the behavior of a workload, as it lacks  the CUDA stream execution information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' In those cases, we  combine EG with another runtime trace, collected by the  PyTorch Proﬁler [36].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' We discuss this in more detail in  Section IV-E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  The pseudocode of trace collection is shown above.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Adding  the EG observer and proﬁler to record the runtime infor-  mation can introduce some overheads to the performance of  the original AI model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' However, this overhead is small and  only occurs once, and it does not affect the accuracy of the  generated benchmark, as our replay method does not rely on  any temporal information captured in these traces or hardware-  level performance metrics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Operators selection  Given an execution graph, we need to select which operators  to replay, because some of them are redundant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' For example,  aten::linear() has included two of its child operators aten::t()  and aten::addmm() as part of its implementation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' At runtime  all three operators will be caught in the EG, however, we  5  only need to replay the parent one, which in this case is  aten::linear().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' To identify these redundant operators, since the  parent operator is always executed before its children, we can  traverse the operators in the order of execution, keep each  operator we encounter and skip all its child operators, based on  the parent-child relationships captured in the execution graph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Operators reconstruction  1) ATen operators: We reconstruct each ATen operator  through the TorchScript IR (Intermediate Representation) us-  ing its captured operator schema in EG, which includes  the operator name and data types for its input and output  arguments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' We implement a string-based parser to extract this  key information from the schema, which is then used to build  the canonical textual representation of the IR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Finally, we  compile the IR with TorchScript to create the callable function  for each operator to use during replay.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' The pseudocode below  demonstrates this procedure:  1 # Captured op schema in EG  2 op_schema = "aten::add.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='Tensor(Tensor self,  3  Tensor other, *,  4  Scalar alpha=1) -> Tensor"  5  6 # Extract name and arguments from schema  7 op_name, op_args = parser(op_schema)  8  9 # Build IR with extracted information  10 torchscript_ir_str = builder(op_name, op_args) = ""  11  graph(%x.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='1 : Tensor,  12  %y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='1 : Tensor):  13  %4 : int = prim::Constant[value=1]()  14  %5 : Tensor = aten::add(%x.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='1, %y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='1, %4)  15  return (%5)  16 ""  17  18 # Compile IR to callable function  19 graph = torch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='_C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='parse_ir(torchscript_ir_str)  20 cu = torch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='_C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='CompilationUnit()  21 func = cu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='create_function(op_name, graph)  2) Communication operators: To reproduce the communi-  cation pattern of the original workload, we need to replay  the communication operators with their original arguments,  such as the process group and message size.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' The metadata  can be obtained from the execution graph;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' for the execution of  the operators during replay, we leverage the existing PyTorch  distributed infrastructure and implement a wrapper over the  low-level interfaces to pass the appropriate parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' We  create new process groups and map them to the original  groups, and for each operator, we select the same data type and  size as the original, to ensure a similar communication pattern  across servers during replay.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Depending on the execution mode  of the operator, we wait for it to complete if it is blocking, or  execute it in asynchronous mode by registering its callback to  check back later.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  3) Custom operators: Custom extension is a mechanism  that PyTorch developed to allow users to create their out-of-  source operators, distinct from the default backend.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Similar  to the other operators, their input and output arguments are  captured in the execution graph, but that is not sufﬁcient for  replay, as we do not know their speciﬁc implementations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' To  handle this case, we expose an interface, which allows users  to register their custom operators together with their imple-  mentations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' During replay, we look up the registry and use  the provided implementation to replay each custom operator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  4) Fused operators: Pointwise operators can be fused into  a single kernel to amortize memory access time and kernel  launch time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' However, the metadata of these fused operators  are not supported by the execution graph, in its current imple-  mentation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' For now, we skip these operators altogether because  they comprise only a small percentage of the overall operator  list, and have negligible impact to the overall performance,  as shown in Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Fusion behavior can be reproduced via  PyTorch JIT and we plan to add this support once its EG trace  is available.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  Note that all operator reconstruction happens during the  initialization phase of the replay, such that they can be directly  invoked in the real execution to avoid any runtime overhead.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Arguments and tensor management  In addition to the functionality, input arguments also play  an important role to the performance of an operator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' For  arguments with basic types, such as int or bool, we can simply  save their values and reuse them during replay, however, for  part of the tensors we need to instantiate them in advance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  If we track the occurrence of all tensors that are used  as input, we can divide them into two categories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' We call  one type intermediate tensors, which are generated as the  output of an operator executed earlier, before being used.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' The  other category are external tensors, whose generation is not  observed in the execution graph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' This classiﬁcation can be  done by tracking the appearance of each tensor based on its  unique tensor ID, during the traversal of the graph in execution  order.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' For intermediate tensors, we need to save them at the  time of generation, and pass them to the downstream operators,  according to the data dependencies between operators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' For  external tensors, we have to explicitly instantiate them before  execution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  By default, we instantiate a tensor with the same shape and  data type as the original but with random values, as the perfor-  mance of an operator is not related to the speciﬁc values of the  input tensors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' We ﬁnd that this holds true for most operators, as  we will show later in the evaluation section, minus a few rare  exceptions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' One case we have met is the lookup operator  for embedding tables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' One of its input tensors stores the lookup  indices, whose value directly determines the access pattern  and has a strong correlation with performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' In this case,  we would need to specify the values for that tensor based on  some additional information, such as the table size, indices  distribution, or pooling factor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Since not all of the above  information is captured in the EG, for now, we set the default  values for the missing information empirically, derived by the  application operators in our production environment, and we  additionally provide an interface for users to further specify  them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' We leave the automatic processing of such special cases  to future work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  6  11/12/22, 9:33 PM  chrome://tracing  chrome://tracing  1/1  Record  Save  Load  replay_newest_load.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='json  Flow events  Processes  M  View Options  »  ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  File Size Stats  Metrics  Frame Data  Input Latency  Alerts  Nothing selected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Tap stuff.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  [xarexec] (pid 462436): CPU  X  [xarexec] (pid 6): GPU 6  X  1331689920  thread 462436 (python3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='8)  thread 480104 (python3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='8)  stream 7  stream 20  stream 22  stream 84  stream 85  stream 86  stream 87  stream 88  stream 89  stream 90  stream 91  stream 92  stream 93  stream 94  stream 95  stream 96  stream 97  stream 98  stream 99  stream 100  stream 101  stream 102  stream 103  stream 104  stream 105  stream 106  stream 107  stream 108  stream 109  stream 110  stream 111  stream 112  stream 113  stream 114  stream 115  stream 116  stream 117  stream 118  stream 119  stream 120  11/12/22,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' 9:33 PM  chrome://tracing  chrome://tracing  1/1  Record  Save  Load  replay_newest_load.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='json  Flow events  Processes  M  View Options  »  ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  File Size Stats  Metrics  Frame Data  Input Latency  Alerts  Nothing selected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Tap stuff.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  [xarexec] (pid 462436): CPU  X  [xarexec] (pid 6): GPU 6  X  1331689920  thread 462436 (python3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='8)  thread 480104 (python3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='8)  stream 7  stream 20  stream 22  stream 84  stream 85  stream 86  stream 87  stream 88  stream 89  stream 90  stream 91  stream 92  stream 93  stream 94  stream 95  stream 96  stream 97  stream 98  stream 99  stream 100  stream 101  stream 102  stream 103  stream 104  stream 105  stream 106  stream 107  stream 108  stream 109  stream 110  stream 111  stream 112  stream 113  stream 114  stream 115  stream 116  stream 117  stream 118  stream 119  stream 120  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Example of parallel streams execution, with streams 7, 20, 22 for the  computation, data loader, and communication, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Parallel stream execution  A CUDA stream is a sequence of kernels that execute in  issue-order on the GPU, and CUDA applications are allowed  to launch kernels concurrently on different streams to improve  device utilization and execution efﬁciency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' The most repre-  sentative scenario is the parallel execution of computation and  communication kernels to hide the networking overhead.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Also,  data transfer between the host and device is often optimized  to run on a separate stream.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  Figure 4 shows an example trace for one of our evaluated  production PyTorch models, in which streams 7, 20, 22 are  used for the computation, data loader, and communication,  respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' The stream execution pattern of a model can have  a signiﬁcant impact on its performance, and we need to take  this into account during the benchmark generation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  To do so, we need to identify which stream each kernel is  executed on, and which operator launches each kernel, so that  we can prepare multiple streams and dispatch each operator to  its corresponding stream during replay.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Unfortunately, current  EG does not include any stream or kernel information so we  need to extract this from another runtime trace, collected via  the PyTorch proﬁler [36].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' This proﬁler has been broadly used  in the PyTorch community and the extraction can be easily  performed based on the launching relationships between the  operators and kernels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' For now we use this trace as an EG  enhancement, and based on our feedback, the EG working  group is actively working on integrating the kernel information  into the EG representation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Putting it all together  Our EG replay approach ﬁrst collects the execution graph  and proﬁler trace of a model to capture both the operators with  their metadata, and their launched GPU kernels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' We then walk  through the graph according to the execution order, distinguish  individual tensors, and identify the operators to replay.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Next,  we reconstruct the callable function for each operator, prepare  the necessary tensors, and initialize the distributed environ-  ment, if necessary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Finally, we replay the operators on different  streams with the same execution order, input arguments (but  not values for tensors), and data dependencies as in the original  workload, to faithfully reproduce their original performance  characteristics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' In case of a distributed deployment, for valida-  tion purposes, the same number of processes will be spawned  as the original, each using a separate execution graph, and  repeating all the steps above.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' We also enable scaled-down  replays of an AI workload without the need for retraining,  as discussed in Section VII-C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' IMPLEMENTATION  Our framework is built on PyTorch in approximately 8,000  lines of Python code.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' It currently supports all basic ATen  operators, a large fraction of custom operators used in our  evaluated workloads, a few common libraries like FBGEMM,  and the c10d distributed library with all four types of backends  (nccl, gloo, mpi and ucc).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  To leverage our framework, a user ﬁrst inserts hooks into  their PyTorch model to collect the execution graph and proﬁler  trace.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Our framework then takes the traces as input, follows  the steps we discussed in Section IV to analyze the traces,  and generates a single PyTorch program as a benchmark.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' The  program contains operators with a hardcoded execution order,  input arguments and data dependencies, and can directly run  on any platform as a normal PyTorch application.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' For the  distributed training deployment, we use mpirun [30] to create  the distributed environment and spawn multiple processes,  each of which uses its own input traces to generate and  execute the benchmark.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Synchronization and data sharing  between different processes is automatically achieved by the  communication operators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  Given the granularity and ﬂexibility of the execution graph,  our EG replay method can be used to explore more use case  scenarios, in addition to completely replicating the original  behavior, as we discuss in Section VII.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  VI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' EVALUATION  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Platforms  We evaluate Mystique on a production cluster of 4 servers  with NVIDIA Tesla A100 GPUs and V100 GPUs, and unless  explicitly speciﬁed, the results we show are collected on A100  GPUs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' We use CUDA 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='4 and PyTorch 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='14 as our testing  environment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Workloads  PARAM linear: PARAM [14] is a benchmark suite of  compute and communication microbenchmarks, as well  as full workloads for both training and inference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' We  select a representative linear model with 20 linear layers  and set batch size to 512 and data type to ﬂoat32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  ResNet: We choose the ResNet18 model from torchvi-  sion [16], with batch size set to 128 and data type set  to ﬂoat32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' For its distributed deployment, we use the de-  fault Distributed Data-Parallel (DDP) training framework  provided by PyTorch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  ASR: We use a production multi-GPU automatic speech  recognition (ASR) training ﬂow implemented with the  Fairseq [31] toolkit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' At its core, ASR is a neural-network-  based acoustic model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  RM: RM is a leading edge multi-node, multi-GPU pro-  duction recommendation model that pushes the boundary  for large-scale training infrastructure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' It is the produc-  tion implementation that the open-source DLRM bench-  mark [28] aims to approximate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' In our experiments,  7  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='several conﬁgurations of this model are used to cover dif-  ferent workload setups (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=', different distributed training  set sizes).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Operators coverage  TABLE III  OPS COVERAGE RATE ACROSS EVALUATED WORKLOADS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  Model  Operators coverage  Count  Execution time  PARAM linear  100%  100%  ResNet  100%  100%  ASR  99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='6%  75.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='7%  RM  96.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='8%  90.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='9%  Table III shows the current operator coverage rate for  our framework across the different studied workloads.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' The  coverage rate denotes the percentage of operators that we are  able to replay compared to the total number of operators in a  workload.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' We show the fractions in terms of both count and  execution time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Since we support all ATen operators, which are  the compute backend of PyTorch, we can achieve a very high  coverage rate on the operator count for all workloads.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Two of  our production workloads have a relatively lower coverage in  terms of execution time, since we are currently missing support  for fused operators and a subset of custom operators, with  the latter dominating the execution time gap.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' These custom  operators normally perform very speciﬁc tasks, for example,  a LSTM network in NLP models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' We provide users with a  programmable interface that allows them to register more of  their custom operators, which can lead to higher coverage and  accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' End-to-end execution time  Figure 5 shows the runtime traces of a single training  iteration for the PARAM linear model (top), and its replayed  benchmark (bottom).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Within each trace, we separate execution  time between threads running on the CPUs (top block for each  trace) and kernels running on the GPUs (bottom block for each  trace).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  In the original workload’s trace (top), there are two threads  on the CPUs since the backward operators are automatically  performed by PyTorch’s autograd engine on the other thread,  and we similarly use two threads in replay.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' The overall  execution time of the sequence of operators in the replayed  benchmark is 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='2 ms, very close to the original’s 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='9 ms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  Moreover, if zoomed in, we can see that the execution time of  each individual replayed operator, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=', the length of each bar,  and the execution pattern across operators, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=', how these bars  interleave with each other, is very similar to the original.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' The  vertical height of the bars is determined by the call stack depth  for each operator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' The small difference in height between orig-  inal and replayed benchmark is due to additional wrappers like  autograd::engine::evaluate function in the original workload,  which do not perform any meaningful work;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' in the synthetic  workload we only replay their underlying operators (“Replay  targets” regions).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  TABLE IV  E2E EXECUTION TIME OF A SINGLE ITERATION.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  Model  Original  Original  Replay  (exclude unsupported)  PARAM linear  14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='9ms  14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='9ms  14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='1ms  ResNet  64.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='4ms  64.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='4ms  70.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='7ms  ASR  316.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='3ms  239.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='3ms  229.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='1ms  RM  65.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='9ms  59.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='9ms  58.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='4ms  Table IV shows the original and replayed execution time for  a single iteration of each workload running on a single GPU.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  For a fair comparison, we also include the original execution  time that excludes the unsupported operators, and we use this  calibrated execution time for the rest of our evaluation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' This  table shows to what extent Mystique captures the covered  operators’ execution time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' We obtain high accuracies across  all studied applications, with 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='4% error on PARAM linear,  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='8% error on ResNet, 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='3% error on ASR and 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='5% error on  RM, when comparing the overall performance of all replayed  operators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' System-level metrics  In addition to the execution time, system-level metrics are  also important for a benchmark generation framework to cap-  ture, in order to ensure similarity with the original workload.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  Speciﬁcally, for these AI workloads, we are more interested in  GPU-related metrics, such as Streaming Multiprocessor (SM)  utilization, High Bandwidth Memory (HBM) bandwidth, GPU  memory utilization, and GPU power.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  Figure 6 shows three representative and widely evaluated  metrics for AI workloads, in production environments: SM  utilization, HBM bandwidth, and GPU power, across all  workloads and their replay counterparts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' All models are using  a single A100 GPU.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' We collect their performance metrics  over thousands of iterations, and show their average values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  Compared to the other three workloads, RM has the highest  SM utilization, and therefore the highest power usage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' The  HBM bandwidth gap of ASR is a little larger than the others,  due to the small number of custom operators we do not yet  support.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' The results illustrate that different workloads have  very different performance characteristics, but can be accu-  rately captured by our replay methodology, and reproduced in  the generated benchmarks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Distributed training  Distributed training is now very common practice for AI  workloads, as their model sizes and datasets keep rapidly  growing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' To evaluate the scalability of our EG replay-based  framework, we collect the runtime traces of the RM work-  load running on 2 nodes with 16 NVIDIA A100 GPUs and  8  CPU  GPU  11/20/22, 9:54 PM  chrome://tracing  chrome://tracing  1/1  Record  Save  Load  linear_replay_dev_trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='json  Flow events  Processes  M  View Options  »  ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  File Size Stats  Metrics  Frame Data  Input Latency  Alerts  Nothing selected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Tap stuff.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  python3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='8 (pid 2624623): CPU  X  python3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='8 (pid 0): GPU 0  X  Process Spans  X  thread 2624623 (python3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='8)  thread 2624624 (python3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='8)  stream 7  PyTorch Proﬁler  11/20/22, 9:54 PM  chrome://tracing  chrome://tracing  1/1  Record  Save  Load  linear_dev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='json  Flow events  Processes  M  View Options  »  ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  File Size Stats  Metrics  Frame Data  Input Latency  Alerts  Nothing selected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Tap stuff.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  python3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='8 (pid 1965390): CPU  X  python3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='8 (pid 0): GPU 0  X  Process Spans  X  thread 1965390 (python3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='8)  thread 1966752 (python3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='8)  stream 7  PyTorch Proﬁler  14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='9ms  14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='2ms  CPU  GPU  Replay targets  Wrappers  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Runtime proﬁler traces of PARAM linear (top) and its benchmark (bottom) for a single training iteration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Within each trace, the bars on the top are  PyTorch operators executed on CPU and the bars at the bottom are GPU kernels, with length indicating the real execution time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  PARAM ResNet  ASR  RM  25  50  75  100  SM utilization (%)  PARAM ResNet  ASR  RM  200  400  600  800  HBM bw (GB/s)  PARAM ResNet  ASR  RM  100  200  300  400  GPU power (W)  Original  Replay  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Comparison of SM utilization, HBM bandwidth, and GPU power for each model and their replay counterparts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  interconnected via NVLink (intra-node) and a 200 Gbps NIC  (inter-node), and then replay it under the same setting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  Table V shows the execution time per iteration and the  system-level metrics per GPU, averaged across the proﬁling  duration and all 16 GPUs, for the original model and the  replayed benchmark.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Compared to the single GPU results  mentioned earlier, execution time is now longer, while SM  utilization, HBM bandwidth, and power are lower, because  of the communication overhead between the worker nodes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  The performance of our generated benchmarks successfully  follows the changes in the original workload under the large  distributed deployment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  TABLE V  SCALABILITY EVALUATION ON 2 NODES WITH 16 GPUS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  Metric  Original  Replay  Execution time (ms)  94.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='5  90.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='5  SM utilization (%)  71.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='3  76.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='3  HBM bandwidth (GB/s)  575.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='2  586.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='1  GPU power (W)  253.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='8  246.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='2  G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Cross platform validation  Mystique operates at operator-level to reproduce the perfor-  mance and resource characteristics of an original AI workload.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  9  PyTorch Profiler (0)1This hardware-agnostic operation allows the generated bench-  mark to be portable across platforms without regeneration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' To  validate this, we test the performance of all four studied work-  loads and their corresponding generated benchmarks on three  platforms: Intel Xeon Platinum CPU, NVIDIA Tesla V100,  and NVIDIA Tesla A100.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' We only use the trace collected on  the A100 server to generate the synthetic benchmarks, and  then run them across the different platforms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  CPU  V100  A100  Param linear  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='0  Normalized exec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' time  CPU  V100  A100  ResNet  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='0  Normalized exec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' time  CPU  V100  A100  ASR  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='0  Normalized exec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' time  CPU  V100  A100  RM  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='0  Normalized exec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' time  Original  Replay  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  Normalized execution time of all workloads and their replayed  benchmarks on different platforms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  Figure 7 shows the validation results of all four workloads.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  We normalize the execution time of the replayed benchmark  to that of the original workload on each platform.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' For two  production workloads ASR and RM, we only show their  performance on the two GPU platforms, as they cannot directly  run on CPU.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' The ﬁgure shows that execution time between  original and replayed application matches across platforms,  demonstrating the portability of our replay methodology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Power efﬁciency sensitivity sweep  100  150  200  250  300  350  Device power limit (W)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='0  Energy efficiency  PARAM  100  150  200  250  300  350  Device power limit (W)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='0  ResNet  100  150  200  250  300  350  Device power limit (W)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='0  Energy efficiency  ASR  100  150  200  250  300  350  Device power limit (W)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='0  RM  Original  Replay  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Normalized energy efﬁciency under varying power limit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  Power efﬁciency is an important metric in many system  designs, and large-scale training is no exception.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Due to  the sheer size of our production training ﬂeet, even a small  power efﬁciency gain translates to huge infrastructure cost  savings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Here we demonstrate that the benchmark generated by  Mystique is able to mimic the power efﬁciency characteristics  of the original application, when we sweep certain system  design knobs (the device power limit in this example).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  Figure 8 displays the power efﬁciency sensitivity curves of  all studied workloads and their corresponding benchmarks, as  we set the device power limit to different levels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' The x axis  is the device power limit we want to sweep, and the y axis  is the normalized power efﬁciency, deﬁned as the throughput  over power.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Our generated benchmarks closely track the  sensitivity trend of the original workloads, demonstrating that  such a methodology can be effectively used to evaluate system  performance in the place of real workloads, when they are not  available.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  VII.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' USE CASES  By leveraging the execution graph (EG), Mystique opens up  many opportunities on how to conduct AI system evaluation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  In this section we describe several use cases we experimented  with using our current framework.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Subgraph replay  Execution graph is made up of nodes (operators) connected  using parent-child relationships;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' this composability allows us  to replay only a subgraph or certain types of operators when  testing the performance of a speciﬁc component.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' To do this, a  user can leverage the record function context manager [36] in  the PyTorch proﬁler to label an arbitrary range of code with a  user-provided name.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Then in the EG, a new operator appears  as the parent of all operators within that code range.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' When  traversing the graph to select which operators to replay, we can  use this name to easily locate this operator, and only replay  the subgraph under it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' For example, in Figure 9, we selectively  replay the subgraph under the ## forward:z ## operator for the  RM workload and show that partial performance is preserved.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  We show repeated replay traces in the bottom to demonstrate  that we are actually only replaying the target subgraph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  11/17/22, 11:36 PM  chrome://tracing  chrome://tracing  1/1  Record  Save  Load  cmf_1_026.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
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+page_content=' Tap stuff.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
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+page_content='8)  stream 7  stream 20  stream 22  PyTorch Proﬁler  11/13/22, 8:01 PM  chrome://tracing  chrome://tracing  1/1  Record  Save  Load  cmf_overarch_subgraph_replay copy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='json  Flow events  Processes  M  View Options  »  ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
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+page_content=' Tap stuff.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  [xarexec] (pid 2720388): CPU  X  [xarexec] (pid 0): GPU 0  X  Process Spans  X  1  thread 2720388 (python3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='8)  stream 7  PyTorch Proﬁler  11/13/22, 8:01 PM  chrome://tracing  chrome://tracing  1/1  Record  Save  Load  cmf_overarch_subgraph_replay copy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='json  Flow events  Processes  M  View Options  »  ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  File Size Stats  Metrics  Frame Data  Input Latency  Alerts  Nothing selected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Tap stuff.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  [xarexec] (pid 2720388): CPU  X  [xarexec] (pid 0): GPU 0  X  Process Spans  X  1  thread 2720388 (python3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='8)  stream 7  PyTorch Proﬁler  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='4ms  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
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+page_content='7ms  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  Runtime traces of original model (top) and two iterations of  the subgraph replay (bottom).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' The original label names are replaced for  conﬁdentiality reasons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  Similarly, by ﬁltering operators based on their types, our  framework can also be easily conﬁgured to replay selected  types of operators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' For example, we have used it to perform a  network analysis in our production environment, by replaying  the communication operators exclusively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  10  ProfilerStep#1912  ## forward ##  ## label:x #:  #  ## forwa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  ## forward:y ##  ## forward:z ##  forward  autogr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  torch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' :jit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  void split_embed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
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+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' voi  amp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
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+page_content='ampamp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
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+page_content='am  amp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='.  PyTorch Profiler (0)1amp ampa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
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+page_content='ampa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
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+page_content='  a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='ampa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
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+page_content=' Early stage platform evaluation  An essential application of benchmarks is to obtain per-  formance indications for new hardware platforms, where the  full SW environment might not yet have fully matured.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Al-  though we can use simple microbenchmarks to sample the  performance space and make some best effort performance  projections, using a production-like benchmark that exercised  the full stack similarly to the original workload lends signiﬁ-  cant conﬁdence to the results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' In the early stages of design for  a new platform, it is quite common that an exact copy of the  PyTorch application cannot properly run on it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Since time is  usually a critical consideration in these early-stage evaluation  scenarios, manually forcing the full application stack to run on  the new platform is cumbersome, time-consuming, and error-  prone.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Due to EG replay’s minimal software dependencies and  ease of modiﬁcation at operator granularity (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=', skipping the  unsupported operators), it is an ideal use case to showcase the  agility of Mystique.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Figure 10 shows a new platform under  consideration, compared to the mature CPU, V100, and A100  platforms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' We can use the EG replay on the new platform  to accurately infer the potential performance beneﬁt this new  platform can offer, as shown with the red line.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  CPU  V100  A100  New plat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  0  20  40  60  80  100  Speedup over CPU  Original  Replay  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Execution time speedup for new, experimental platform over CPU.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Scaled-down performance emulation  DL models have been on an exponential growth curve in  terms of model size, compute complexity, and data needs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  This trend has led to the rapid adoption of large-scale training  deployments in production, including in our own global-scale  production environment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' It is now very common to start an AI  use case using models requiring hundreds of GPUs in training,  posing a big resource challenge for AI system evaluation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  Handling a few test systems in the early engineering testing  phases is manageable, but deploying and supporting testing  setups with hundreds of GPUs is a serious undertaking and  investment, or altogether infeasible due to supply chain short-  ages, datacenter space or cooling limitations, need for custom  networks, and high failure rate support.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Therefore, there is a  desire to evaluate a model’s large scale training performance  using a much smaller test setup (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=', a few GPUs).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  Building a benchmark at the granularity of operators gives  us the opportunity to evaluate the target large scale execution  using a much smaller scale setting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' For example, you can use  just 2 nodes to mimic the behavior of the original workloads  running on 16/32/64 etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' nodes by manipulating the communi-  cation cost portion during replay.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' This requires no changes to  the original training implementation, which would otherwise  require domain speciﬁc knowledge and coding changes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  In distributed data-parallel training, workers are performing  the same computation on their assigned data chunks;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' this local  computation does not change with the number of workers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' The  main performance factor that varies with scale is the network  communication.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' By approximating the large-scale network  performance impact, we can emulate the target behavior at  large scale using a small scale setup.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  There are many ways to achieve this with different trade-  offs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' We started with a simple intuitive approach where dummy  delays are added to the communication path to account for the  mismatch between small-scale testing setup and large-scale  deployment setup.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' The delay is set empirically, based on the  network cost model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' In many cases, a range estimate for the  cost is sufﬁcient to sweep the performance space and reveal  the performance trend.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' We have demonstrated the feasibility of  this approach by successfully reproducing the execution time  of the 16 GPUs RM model training with only 2 GPUs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' There  are clearly many opportunities to improve upon this simple  approach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Due to the heavy engineering effort required to fully  explore this area, we defer further exploring it to future work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  VIII.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' DISCUSSION  Mystique has already been used with production AI work-  loads to accurately generate synthetic benchmarks that have  been used for several challenging system studies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' At the same  time, there are even more interesting directions we plan to  explore using this new methodology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Advanced EG analyzer and builder  Currently our EG synthesis block is selecting full EG  traces as replay samples from the trace database, guided by a  simple EG analyzer based on population weight.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' This can be  improved by adding more sophistication on weight calculation  (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=', more timing cost).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' We can also go a step deeper into  operator level summary and weighting, and take advantage of  EG’s composability to combine portions from different EGs  into a single replay trace for more efﬁcient aggregation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Broader support for other ML frameworks  Our framework currently targets PyTorch models due to  their widespread use in our environment, but can be ex-  tended to support other ML frameworks, such as TensorFlow,  MXNet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' In general, all these frameworks are founded on  building blocks, such as the tensor manipulation library and  communication library, and are executed by the operators in  these libraries, unlike the traditional CPU-centric applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  This is highly promising for benchmark generation, as these  operators are reproducible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Once the proﬁling tool that collects  the operators’ runtime information is available, our EG-based  methodology can be easily adapted to support other AI pro-  gramming frameworks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  11  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Improved privacy and IP protection  Because AI models often offer a competitive advantage for a  company, great care is taken to safeguard them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Unfortunately,  this makes sharing the workload to e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=', co-design or co-  optimize a system with external vendors a very complicated  process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' With Mystique, we can obfuscate the real EG traces  by automatically swapping the important IP protected blocks  with performance-equivalent public blocks using a preset  rule.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' This way we can still effectively capture the high-level  behavior of a production workload, while also enabling fast  sharing of the workload with external partners for performance  evaluation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Similarly, because EG does not directly capture the  real training dataset, but only their metadata like dimensions,  the generated benchmarks do not contain any user privacy-  sensitive information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' This strong separation in the design  makes sharing EG-based benchmarks a better choice in a  privacy focused environment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  IX.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' CONCLUSION  We present Mystique, a new generation methodology for  AI benchmarks, based on execution graphs replay.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Mystique  addresses the scalability issues stemming from both the large  model variety and the constantly changing workload land-  scape.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' We demonstrate that our methodology generates AI  benchmarks highly similar to the original applications, while  being easy to use and portable across platforms, without the  need for regenerating.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' We have illustrated several use cases for  Mystique, including early stage platform evaluation, subgraph  replay, and scaled-down performance testing, all of which are  highly challenging using existing techniques.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  12  REFERENCES  [1] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Adolf, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Rama, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Reagen, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='-Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Wei, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Brooks, “Fathom:  Reference workloads for modern deep learning methods,” in 2016  IEEE International Symposium on Workload Characterization (IISWC).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  IEEE, 2016, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' 1–10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  [2] ATen, “Aten,” https://github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='com/pytorch/pytorch/tree/master/aten.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  [3] Baidu, “Deepbench,” https://github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='com/baidu-research/DeepBench.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  [4] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Banbury, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Reddi, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Torelli, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Holleman, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Jeffries, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Kiraly,  P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Montino, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Kanter, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Ahmed, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Pau et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=', “Mlperf tiny bench-  mark,” arXiv preprint arXiv:2106.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='07597, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  [5] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Beckmann and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Gutierrez, “The amd gem5 apu simulator: Mod-  eling heterogeneous systems in gem5,” in Tutorial at the International  Symposium on Microarchitecture (MICRO), 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  [6] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Binkert, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Beckmann, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Black, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Reinhardt, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Saidi, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Basu,  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Hestness, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Hower, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Krishna, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Sardashti et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=', “The gem5  simulator,” ACM SIGARCH computer architecture news, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' 39, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' 2,  pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' 1–7, 2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  [7] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Brown, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Mann, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Ryder, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Subbiah, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Kaplan, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Dhariwal,  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Neelakantan, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Shyam, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Sastry, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Askell et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=', “Language mod-  els are few-shot learners,” Advances in neural information processing  systems, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' 33, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' 1877–1901, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  [8] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Carlson, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Heirman, and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Eeckhout, “Sniper: Exploring the level  of abstraction for scalable and accurate parallel multi-core simulation,”  in Proceedings of 2011 International Conference for High Performance  Computing, Networking, Storage and Analysis, 2011, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' 1–12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  [9] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Coleman, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Narayanan, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Kang, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Zhao, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Zhang, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Nardi,  P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Bailis, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Olukotun, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' R´e, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Zaharia, “Dawnbench: An end-  to-end deep learning benchmark and competition,” Training, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' 100,  no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' 101, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' 102, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  [10] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Del Barrio, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Gonz´alez, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Roca, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Fern´andez, and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Es-  pasa, “Attila: a cycle-level execution-driven simulator for modern gpu  architectures,” in 2006 IEEE International Symposium on Performance  Analysis of Systems and Software.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  IEEE, 2006, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' 231–241.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  [11] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Delimitrou, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Sankar, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Kansal, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Kozyrakis, “ECHO:  Recreating Network Trafﬁc Maps for Datacenters of Tens of Thousands  of Servers,” in Proceedings of the IEEE International Symposium on  Workload Characterization (IISWC), 2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  [12] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Devlin, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='-W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Chang, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Lee, and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Toutanova, “Bert: Pre-training  of deep bidirectional transformers for language understanding,” arXiv  preprint arXiv:1810.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='04805, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  [13] Facebook, “Fbgemm,” https://github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='com/pytorch/FBGEMM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  [14] Facebook, “Param benchmarks,” https://github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='com/facebookresearch/  param.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  [15] Facebook, “torchrec,” https://github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='com/pytorch/torchrec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  [16] Facebook,  “torchvision  models,”  https://pytorch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='org/vision/stable/  models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='html.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  [17] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Ganesan and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' John, “Automatic generation of miniaturized  synthetic proxies for target applications to efﬁciently design multicore  processors,” IEEE Transactions on Computers, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' 63, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' 4, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' 833–  846, 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  [18] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' He, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Zhang, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Ren, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Sun, “Deep residual learning for image  recognition,” in Proceedings of the IEEE conference on computer vision  and pattern recognition, 2016, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' 770–778.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  [19] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Justus, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Brennan, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Bonner, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' McGough, “Predicting the  computational cost of deep learning models,” in 2018 IEEE international  conference on big data (Big Data).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  IEEE, 2018, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' 3873–3882.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  [20] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Khairy, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Shen, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Aamodt, and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Rogers, “Accel-sim:  An extensible simulation framework for validated gpu modeling,” in  2020 ACM/IEEE 47th Annual International Symposium on Computer  Architecture (ISCA).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  IEEE, 2020, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' 473–486.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  [21] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Li, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Walls, and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Guo, “Characterizing and modeling distributed  training with transient cloud gpu servers,” in 2020 IEEE 40th Interna-  tional Conference on Distributed Computing Systems (ICDCS).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  IEEE,  2020, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' 943–953.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  [22] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Liang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Gan, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Li, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Torres, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Dhanotia, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Ketkar, and  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Delimitrou, “Ditto: End-to-End Application Cloning for Networked  Cloud Services,” in Proceedings of the Twenty Eighth International  Conference on Architectural Support for Programming Languages and  Operating Systems (ASPLOS), April 2023.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  [23] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='-C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Liao, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='-C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Wang, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='-H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Tu, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='-C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Kao, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='-Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Liang, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='-H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  Hung, “Perfnetrt: Platform-aware performance modeling for optimized  deep neural networks,” in 2020 International Computer Symposium  (ICS).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  IEEE, 2020, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' 153–158.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  [24] Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Lin, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Feng, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Ardestani, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Lee, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Lundell, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Kim, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Ke-  jariwal, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Owens, “Building a performance model for deep  learning recommendation model training on gpus,” arXiv preprint  arXiv:2201.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='07821, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  [25] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Mattson, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Cheng, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Diamos, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Coleman, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Micikevicius, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Pat-  terson, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Tang, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='-Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Wei, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Bailis, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Bittorf et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=', “Mlperf training  benchmark,” Proceedings of Machine Learning and Systems, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' 2, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  336–349, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  [26] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Mattson, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Reddi, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Cheng, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Coleman, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Diamos, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Kanter,  P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Micikevicius, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Patterson, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Schmuelling, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Tang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=', “Mlperf:  An industry standard benchmark suite for machine learning perfor-  mance,” IEEE Micro, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' 40, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' 2, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' 8–16, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  [27] MLCommons, “Mlperf training benchmarks,” https://mlcommons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='org/  en/training-normal-21/.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  [28] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Naumov, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Mudigere, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='-J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Shi, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Huang, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Sundaraman,  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Park, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Wang, U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Gupta, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='-J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Wu, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Azzolini et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=', “Deep  learning recommendation model for personalization and recommenda-  tion systems,” arXiv preprint arXiv:1906.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='00091, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  [29] NVIDIA, “nccl,” https://developer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='nvidia.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='com/nccl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  [30] OpenMPI,  “mpirun,”  https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='open-mpi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='org/doc/current/man1/  mpirun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='php.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  [31] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Ott, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Edunov, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Baevski, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Fan, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Gross, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Ng, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Grangier,  and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Auli, “fairseq: A fast, extensible toolkit for sequence modeling,”  in Proceedings of NAACL-HLT 2019: Demonstrations, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  [32] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Panda and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' John, “Proxy benchmarks for emerging big-  data workloads,” in 2017 26th International Conference on Parallel  Architectures and Compilation Techniques (PACT).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  IEEE, 2017, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  105–116.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  [33] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Panda, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Zheng, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Gerstlauer, and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' John, “Camp: Accurate  modeling of core and memory locality for proxy generation of big-data  applications,” in 2018 Design, Automation & Test in Europe Conference  & Exhibition (DATE).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  IEEE, 2018, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' 337–342.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  [34] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Power, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Hestness, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Orr, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Hill, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Wood, “gem5-  gpu: A heterogeneous cpu-gpu simulator,” IEEE Computer Architecture  Letters, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' 14, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' 1, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' 34–36, 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  [35] PyTorch, “c10d,” https://pytorch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='org/docs/stable/distributed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='html.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  [36] PyTorch, “Pytorch proﬁler,” https://pytorch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='org/tutorials/recipes/recipes/  proﬁler recipe.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='html.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  [37] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Ramesh, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Dhariwal, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Nichol, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Chu, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Chen, “Hierarchical  text-conditional image generation with clip latents,” arXiv preprint  arXiv:2204.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='06125, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  [38] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Ravi, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Bertran, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Bose, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Lipasti, “Micrograd: A  centralized framework for workload cloning and stress testing,” in 2021  IEEE International Symposium on Performance Analysis of Systems and  Software (ISPASS).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  IEEE, 2021, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' 70–72.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  [39] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Reddi, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Cheng, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Kanter, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Mattson, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Schmuelling, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='-J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  Wu, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Anderson, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Breughe, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Charlebois, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Chou et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=', “Mlperf  inference benchmark,” in 2020 ACM/IEEE 47th Annual International  Symposium on Computer Architecture (ISCA).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  IEEE, 2020, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' 446–  459.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  [40] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Saharia, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Chan, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Saxena, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Li, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Whang, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Denton, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  Ghasemipour, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Ayan, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Mahdavi, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Lopes et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=', “Photoreal-  istic text-to-image diffusion models with deep language understanding,”  arXiv preprint arXiv:2205.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='11487, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  [41] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Silver, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Huang, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Maddison, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Guez, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Sifre, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Van  Den Driessche, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Schrittwieser, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Antonoglou, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Panneershelvam,  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Lanctot et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=', “Mastering the game of go with deep neural networks  and tree search,” nature, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' 529, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' 7587, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' 484–489, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  [42] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Szegedy, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Liu, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Jia, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Sermanet, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Reed, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Anguelov, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Erhan,  V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Vanhoucke, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Rabinovich, “Going deeper with convolutions,”  in Proceedings of the IEEE conference on computer vision and pattern  recognition, 2015, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' 1–9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  [43] O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Vinyals, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Babuschkin, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Czarnecki, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Mathieu, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Dudzik,  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Chung, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Choi, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Powell, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Ewalds, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Georgiev et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=', “Grand-  master level in starcraft ii using multi-agent reinforcement learning,”  Nature, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' 575, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' 7782, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' 350–354, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  [44] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Yu, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Gao, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Golikov, and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Pekhimenko, “Computational perfor-  mance predictions for deep neural network training: A runtime-based  approach,” CoRR, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' abs/2102.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='00527, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  [45] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Zhou, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Zhu, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Song, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Fan, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Zhu, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Ma, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Yan, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Jin, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Li,  and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Gai, “Deep interest network for click-through rate prediction,”  in Proceedings of the 24th ACM SIGKDD international conference on  knowledge discovery & data mining, 2018, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' 1059–1068.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  13  [46] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Zhu, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Akrout, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Zheng, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Pelegris, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Jayarajan, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Phanishayee,  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Schroeder, and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Pekhimenko, “Benchmarking and analyzing deep  neural network training,” in 2018 IEEE International Symposium on  Workload Characterization (IISWC).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  IEEE, 2018, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' 88–100.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  [47] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Zhu, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Phanishayee, and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content=' Pekhimenko, “Daydream: Accurately  estimating the efﬁcacy of optimizations for {DNN} training,” in 2020  USENIX Annual Technical Conference (USENIX ATC 20), 2020, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  337–352.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
+page_content='  14' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNE2T4oBgHgl3EQfygjW/content/2301.04122v1.pdf'}
diff --git a/lNFIT4oBgHgl3EQfryt6/content/tmp_files/2301.11333v1.pdf.txt b/lNFIT4oBgHgl3EQfryt6/content/tmp_files/2301.11333v1.pdf.txt
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+Knowing About Knowing: An Illusion of Human Competence
+Can Hinder Appropriate Reliance on AI Systems
+Gaole He
+Delft University of Technology
+Delft, The Netherlands
+g.he@tudelft.nl
+Lucie Kuiper
+Delft University of Technology
+Delft, The Netherlands
+lucieakuiper@gmail.com
+Ujwal Gadiraju
+Delft University of Technology
+Delft, The Netherlands
+u.k.gadiraju@tudelft.nl
+ABSTRACT
+The dazzling promises of AI systems to augment humans in various
+tasks hinge on whether humans can appropriately rely on them.
+Recent research has shown that appropriate reliance is the key to
+achieving complementary team performance in AI-assisted deci-
+sion making. This paper addresses an under-explored problem of
+whether the Dunning-Kruger Effect (DKE) among people can hinder
+their appropriate reliance on AI systems. DKE is a metacognitive
+bias due to which less-competent individuals overestimate their
+own skill and performance. Through an empirical study (𝑁 = 249),
+we explored the impact of DKE on human reliance on an AI sys-
+tem, and whether such effects can be mitigated using a tutorial
+intervention that reveals the fallibility of AI advice, and exploiting
+logic units-based explanations to improve user understanding of AI
+advice. We found that participants who overestimate their perfor-
+mance tend to exhibit under-reliance on AI systems, which hinders
+optimal team performance. Logic units-based explanations did not
+help users in either improving the calibration of their competence
+or facilitating appropriate reliance. While the tutorial intervention
+was highly effective in helping users calibrate their self-assessment
+and facilitating appropriate reliance among participants with over-
+estimated self-assessment, we found that it can potentially hurt
+the appropriate reliance of participants with underestimated self-
+assessment. Our work has broad implications on the design of
+methods to tackle user cognitive biases while facilitating appro-
+priate reliance on AI systems. Our findings advance the current
+understanding of the role of self-assessment in shaping trust and
+reliance in human-AI decision making. This lays out promising
+future directions for relevant HCI research in this community.
+CCS CONCEPTS
+• Human-centered computing → Empirical studies in HCI;
+• Computing methodologies → Artificial intelligence; • Ap-
+plied computing → Law, social and behavioral sciences.
+KEYWORDS
+Human-AI Decision Making, Appropriate Reliance, XAI, Dunning-
+Kruger Effect
+Permission to make digital or hard copies of part or all of this work for personal or
+classroom use is granted without fee provided that copies are not made or distributed
+for profit or commercial advantage and that copies bear this notice and the full citation
+on the first page. Copyrights for third-party components of this work must be honored.
+For all other uses, contact the owner/author(s).
+CHI ’23, April 23–28, 2023, Hamburg, Germany
+© 2023 Copyright held by the owner/author(s).
+ACM ISBN 978-1-4503-9421-5/23/04.
+https://doi.org/10.1145/3544548.3581025
+ACM Reference Format:
+Gaole He, Lucie Kuiper, and Ujwal Gadiraju. 2023. Knowing About Knowing:
+An Illusion of Human Competence Can Hinder Appropriate Reliance on
+AI Systems. In Proceedings of the 2023 CHI Conference on Human Factors in
+Computing Systems (CHI ’23), April 23–28, 2023, Hamburg, Germany. ACM,
+New York, NY, USA, 18 pages. https://doi.org/10.1145/3544548.3581025
+1
+INTRODUCTION
+In the last decade, powerful AI systems (especially deep learning
+systems) have shown better performance than human experts on
+many tasks, sometimes outperforming humans by a large mar-
+gin [58, 87]. Attracted by the predictive capability of such AI sys-
+tems, researchers and practitioners have started to adopt such sys-
+tems to support human decision makers in critical domains (e.g., fi-
+nancial [33], medical domains [48]). With the wish of complemen-
+tary team performance, one goal of such human-AI collaboration is
+appropriate reliance: human decision makers rely on an AI system
+when it is accurate (or perhaps more precisely, when it is more
+accurate than humans) and do not rely on it when the system is
+inaccurate (or, ideally, whenever it is wrong). In such a collabo-
+rative decision process, human factors (e.g., knowledge, mindset,
+cognitive bias) and the explanations for AI advice are important
+for trust in the AI system and for human reliance on the system.
+Several prior works have carried out empirical studies within this
+context of human-AI decision making, to explore the effectiveness
+of different kinds of explanations and the role of human factors in
+shaping such collaboration [3, 8, 24, 33, 52, 62, 79, 87].
+In recent literature exploring human-AI interaction, researchers
+have shown a great interest in understanding what shapes user trust
+and reliance on AI systems. They found that factors like first impres-
+sion [76], AI literacy [8], risk perception [33, 34], and performance
+feedback [55, 61] among others, play important roles in shaping
+human trust and reliance on AI systems. Explanations (e.g., feature
+attribution of input) have been found to be useful in promoting hu-
+man understanding and adoption of AI advice [3, 52, 79, 87] and He
+et al. [35] recently proposed analogies as an instrument to increase
+the intelligibility of explanations. However, prior studies observed
+improvements in performance in the presence of explanations only
+when the AI system outperformed both the human and the best
+team [3]. One reason for such phenomenon is under-reliance, which
+indicates humans do not rely on accurate AI predictions as of-
+ten as it is ideal to [23, 79, 82]. In this work, we explore whether
+Dunning-Kruger effect (DKE) [43] – a metacognitive bias due to
+which individuals overestimate their competence and performance
+– affects user reliance on AI systems. This a particularly important
+metacognitive bias to understand in the context of human-AI de-
+cision making, since one can intuitively understand how inflated
+self-assessments and illusory superiority over an AI system can
+arXiv:2301.11333v1  [cs.HC]  25 Jan 2023
+
+CHI ’23, April 23–28, 2023, Hamburg, Germany
+Gaole He, Lucie Kuiper, Ujwal Gadiraju
+result in overly relying on oneself or exhibiting under-reliance
+on AI advice. This can cloud human behavior in their interaction
+with AI systems. However, to the best of our knowledge no prior
+work has addressed this. In addition, DKE is closely related to user
+confidence in decision making, which has been identified as an
+important user factor and has been recently explored in the con-
+text of human-AI decision making [10, 33]. To achieve the goal
+of appropriate reliance, users are expected to adequately calibrate
+their self-confidence and their confidence in the AI system. Our
+work can lead to fundamental HCI insights that can help facilitate
+appropriate reliance of humans on AI systems.
+To explore the impact of DKE on user reliance, we need to first
+identify participants who demonstrate the DKE (i.e., participants
+who perform relatively poorly but overestimate their performance).
+According to existing research on the DKE [16, 18], the participants
+representing the bottom performance quartile tend to overestimate
+their skill and depict an illusory superiority, while those in the
+top performance quartile do not exhibit such a trend. Researchers
+have also operationalized self-assessments to serve as indicators of
+competence in different online tasks [29]. Informed by such prior
+work, we consider overestimated self-assessments in the context of
+human-AI decision making as an indicator of the DKE and explore
+it further. Through an explicit analysis of participants’ performance
+in the bottom quartile, we verified that the overestimation in their
+performance is highly indicative of DKE in our study. In this scope,
+we explore whether we can design interventions to help users
+improve their own calibration of their skills in the task at hand.
+Inspired by existing work in mitigating cognitive biases such
+as the DKE [43] and promoting appropriate reliance [8, 45, 79],
+we propose to leverage tutorials to calibrate their self-assessment
+through revealing the actual performance level of participants with
+performance feedback. In such a tutorial, after the initial decision
+making, participants are provided with correct answers and expla-
+nations to contrast with their final choice (if they make a wrong
+choice). As pointed out by existing research [17], one cause of DKE
+can be that people place too much confidence in the insightfulness
+of their judgments. When the correct answer differs from their
+own choice, they may refrain from trusting such ground truth in
+the absence of additional rationale. To ensure the effectiveness of
+revealing users’ shortcomings, we provide them with contrastive
+explanations which point out not only the reason for correct an-
+swers, but also why their choice was incorrect. Based on prior work,
+we expect such a training session to help users realize their errors
+and calibrate their self-assessment. Furthermore, they become more
+skillful at the task, which is also highlighted by Kruger et al. [43]
+in mitigating DKE.
+When AI advice disagrees with human decisions, the lack of ra-
+tionales may be a reason not to adopt AI advice. To help participants
+interpret the AI advice, we leverage logic units-based explanations
+which reveal the AI system’s internal states. When users recognize
+that an explanation provides reasonable evidence for supporting AI
+advice, it is much easier for them to resolve disagreement in their
+decision making. As a result, participants have a better opportunity
+to know and understand when they “should” in fact rely on AI
+systems. From this standpoint, effective explanations alongside the
+tutorial may help mitigate the impact of the Dunning-Kruger Effect
+on user reliance. To analyze the impact of DKE on user reliance on
+AI systems in this paper, we aim to find answers for the following
+two research questions:
+RQ1: How does the Dunning-Kruger Effect shape reliance
+on AI systems?
+RQ2: How can the Dunning-Kruger Effect be mitigated in
+human-AI decision making tasks?
+To answer these questions, and based on existing literature, we
+proposed four hypotheses considering the effect of the overesti-
+mation of performance on (appropriate) reliance, the effect of the
+tutorial intervention on self-assessment calibration and reliance
+for participants with miscalibrated self-assessment, the effect of
+logic units-based explanations and tutorial intervention on reliance
+and team performance. We tested these hypotheses in an empirical
+study (𝑁 = 249) of human-AI collaborative decision making in a
+logical reasoning task (i.e., multi-choice logical question answer-
+ing based on a context paragraph). We found a negative impact
+of the DKE on human reliance behavior, where participants with
+DKE relied significantly less on the AI system than their counter-
+parts without DKE. To mitigate such effects, we designed a tutorial
+intervention for making users aware of their miscalibrated self-
+assessment and provided logic units-based explanations to help
+explain AI advice. Although we found that the intervention tutorial
+was highly effective in improving participants’ self-assessments,
+their improvement in appropriate reliance and performance is lim-
+ited (statistically non-significant). Moreover, no obvious benefits
+were found with introducing logic units-based explanations in the
+logical reasoning task.
+Our results highlight that the overestimation of performance will
+result in under-reliance, and such miscalibrated self-assessment can
+be improved with our proposed tutorial intervention. We also found
+that participants who overestimated their performance demon-
+strated an increased appropriate reliance, which the calibration of
+self-assessment can partially explain. However, this was in contrast
+to participants who initially underestimated their performance –
+while they calibrated their self-assessment, they achieved signifi-
+cantly worse appropriate reliance and performance. One potential
+cause is that such tutorials help them recognize their actual per-
+formance but also cause the illusion of superiority to AI systems.
+Such finding is also in line with algorithm aversion [12], where
+users are less tolerant of the mistakes made by AI systems. In ad-
+dition, we found that the users’ general propensity to trust goes
+a long way in shaping trust in AI systems, despite our tutorial
+not having an effect in reshaping subjective trust. Based on the
+results from our empirical study, we provide guidelines for design-
+ing more comprehensive user tutorials and point out promising
+future directions for further research around self-assessments in
+the context of human-AI decision making. Although we found that
+miscalibrated self-assessments may hinder appropriate reliance
+(i.e., participants with DKE relied less on AI systems), the par-
+ticipants with accurate self-assessment did not necessarily show
+optimal appropriate reliance (e.g., we found that participants with
+underestimation showed better appropriate reliance and perfor-
+mance). This interplay between self-assessment and reliance on AI
+
+Knowing About Knowing: An Illusion of Human Competence Can Hinder Appropriate Reliance on AI Systems
+CHI ’23, April 23–28, 2023, Hamburg, Germany
+systems is potentially more complex than what can be explained
+by a linear relationship and, therefore, deserves further research.
+In summary, we explored the effectiveness of a tutorial inter-
+vention to mitigate the DKE and, in turn, facilitate appropriate
+reliance. We found evidence suggesting its effectiveness through an
+empirical study in a logical reasoning task. Our work has important
+implications for HCI research in the realm of human-AI interaction.
+Our findings indicate that incorrect self-assessments and a preva-
+lent meta-cognitive bias can affect user objective reliance on the AI
+system. Thus, while designing for optimal human-AI interaction, it
+is important to consider the extent to which users are aware of their
+own abilities and that of the AI system. Our work is an important
+first step towards furthering our understanding of how cognitive
+biases shape human reliance on AI systems, an understudied aspect
+in this quickly evolving realm of research. Considering the unique
+and evolving landscape of AI systems, the associated metaphors,
+and end-user expectations that are mediated through abstractions
+and their own experiences, we believe that studying the role of
+the DKE in the human-AI decision making context is a timely and
+unique contribution. We hope that our work can inform future
+research on designing human-AI interactions that can facilitate
+appropriate reliance on AI systems.
+2
+BACKGROUND AND RELATED WORK
+This paper contributes to the growing literature on human-AI
+interaction, collaboration, and teaming, by exploring how the
+Dunning-Kruger Effect shapes user reliance on AI systems
+and whether such effect can be mitigated with a user tutorial
+that highlights the fallibility of AI advice and logic units-
+based explanation. Thus, we position our work in different strands
+of related literature: the general literature on AI-assisted decision
+making and what roles explanations play in such collaboration (2.1),
+more specific literature on promoting appropriate reliance (2.2),
+the contradicting literature on algorithm aversion and algorithm
+appreciation (2.3), and finally the literature on self-assessments,
+which has been explored in both psychology and other HCI studies
+(2.4).
+2.1
+Human-AI Collaborative Decision Making
+In recent years, AI-assisted decision making has received more and
+more attention. In such collaboration, user factors and interaction
+with AI systems are observed to be of much impact on final user be-
+haviors. Among these work, most researchers are interested in how
+users shape their trust in AI systems and how user behaviors will
+be affected by AI systems. Topics like performance feedback [2, 55],
+risk perception [27, 34], uncertainty [77] and confidence [10, 79, 87]
+of machine learning models, impact of explanations [3, 46] have
+been extensively studied in human-AI decision making. Meanwhile,
+fairness, accountability, and transparency of incorporating AI sys-
+tems for collaborative decision making received more and more
+attention from a wide range of stakeholders [19, 21]. For a more
+comprehensive survey of existing work on Human-AI decision
+making, readers can refer to [44].
+According to GDPR, the users of AI systems should have the
+right to access meaningful explanations of model predictions [68].
+Under this perspective, more and more researchers have started to
+provide human-centered explainable AI (XAI) solutions to promote
+human-AI collaboration [20–22, 50, 78]. Up to now, the benefits
+of incorporating XAI methods in human-AI collaboration are still
+limited [3, 44]. As reported by most existing work, though XAI
+methods can aid understanding of AI advice, such effect does not
+necessarily lead to clear performance improvement [3, 52]. For in-
+stance, Liu et al. [52] observed that interactive explanations may
+“reinforce human biases and lead to limited performance improve-
+ment”. Based on a comprehensive literature review, Wang et al. [79]
+proposed three desiderata of AI explanations to promote appropri-
+ate reliance: (1) critical for people to understand the AI, (2) recognize
+the uncertainty underlying the AI, and (3) calibrate their trust in
+the AI in AI-assisted decision making. With such ideal properties,
+effective explanations may also potentially help participant realize
+their weakness and mistake when they disagree with AI advice.
+Under this perspective, we also explored whether logic units-based
+explanations can help participants calibrate their self-assessment
+and promote appropriate reliance.
+2.2
+Empirical Studies on Appropriate Reliance
+AI systems and human decision makers are supposed to achieve
+complementary team performance through taking advantage of
+both powerful predictive capability of AI systems and flexibility of
+human users to handle complex decision tasks. However, existing
+literature still struggles to find such complementary team perfor-
+mance — in most empirical studies, AI alone performs much better
+than human-AI team [44, 52]. With further analysis, researchers
+point out two main causes: (1) under-reliance, users fail to fully take
+advantage of powerful AI systems, and (2) over-reliance, users fail
+to rely on themselves when they actually outperform AI systems.
+To promote appropriate reliance, existing research mainly fo-
+cused on mitigating under-reliance and over-reliance. Different in-
+terventions like cognitive forcing functions [5], user tutorial [8, 9]
+and explanations [79] are proved to be highly effective in mitigating
+such unexpected reliance patterns. Buçinca et al. [5] introduced
+three types of cognitive functions to mitigate over-reliance: show
+AI advice on demand, update decision with AI advice after the
+initial decision, and keep participants waiting for a while before
+providing advice. Their experimental results indicate that such cog-
+nitive forcing functions are even more effective than simple XAI
+methods in mitigating over-reliance. With a comparative study
+of four types of different explanations, Wang et al. [79] reported
+that feature importance and feature contribution explanations can
+promote appropriate reliance with mitigating under-reliance.
+“User tutorials, when presented in appropriate forms, can help
+some people rely on ML models more appropriately” [8]. Another
+important branch is educating users with user tutorials, which
+stands out in recent years. On one hand, such user tutorials make
+users aware of the weakness of AI systems, which further calibrate
+user trust and reliance on AI systems. For example, Chiang et al. [9]
+found that a brief education session (to increase people’s awareness
+of the machine learning model’s possible performance disparity
+on different data) can effectively reduce over-reliance on out-of-
+distribution data. On the other hand, such a system can educate
+participants with domain-specific knowledge extracted from an
+AI system, which further improves users’ capability. As a typical
+
+CHI ’23, April 23–28, 2023, Hamburg, Germany
+Gaole He, Lucie Kuiper, Ujwal Gadiraju
+example, Lai et al. [45] proposed model-driven tutorials to help
+humans understand patterns learned by models in a training phase.
+Inspired by this series of research, we also explored whether DKE
+can be mitigated with user tutorial. For the purpose of calibrating
+self-assessment, we include performance feedback and explanations
+to contrast wrong user choice with correct answers.
+2.3
+Algorithm Aversion and Algorithm
+Appreciation
+In the face of intelligent predictive agents, which may outperform
+human experts, people show two contradicting altitudes: Algo-
+rithm Aversion and Algorithm Appreciation. Compared to human
+forecasters, people more quickly lose confidence in AI systems af-
+ter seeing them make the same mistakes [12]. Thus, some users
+are reluctant to use superior but imperfect algorithms [6]. Such a
+phenomenon is called “Algorithm Aversion,” which has been ob-
+served across multiple domains, like moral decision making [31],
+economic bargains [23], medical diagnosis [54], and autonomous
+driving [14]. Burton et al. [6] summarized the cause and solution
+of algorithm aversion with five aspects: expectations and exper-
+tise, decision autonomy, incentivization, cognitive compatibility,
+and divergent rationalities. Meanwhile, Dietvorst et al. [13] found
+that such algorithm aversion can be overcome with the chance to
+modify algorithm advice. Readers can refer to two recent survey
+papers [6, 40] for a comprehensive literature review. In contrast,
+Logg et al. [53] found that users were influenced more by the algo-
+rithmic decision instead of human decision, and they first coined
+the notion of “Algorithm Appreciation” to describe such a phenom-
+enon. Others revealed similar findings in contexts where tasks are
+perceived as being more objective [7], machines share rationale
+with humans [75] or with prior exposure to similar systems [42].
+Besides contradicting attitudes towards the use of AI systems,
+prior work has shown how different human factors such as algorith-
+mic literacy [72], expertise [53], and cognitive load [84] can affect
+users’ final adoption of algorithmic advice. For example, users’
+algorithmic literacy [71–73] about fairness, accountability, trans-
+parency, and explainability is found to greatly affect their trust and
+privacy concern in adopting the advice from AI systems [70, 74].
+Logg et al. [53] found that experts may even show more tendency
+to discount algorithmic advice when compared to laypeople. Fur-
+thermore, these factors can also affect the extent to which users
+show algorithm aversion or algorithm appreciation. For instance,
+You et al. [84] argue that algorithm appreciation declines when the
+transparency of the advice source’s prediction performance further
+increases. In their study, they used a series of numbers instead of
+aggregated average performance, which increases the transparency
+of prediction performance. But they observed a decrease in algo-
+rithm appreciation, which was explained by the greater cognitive
+load imposed by the elaborated format. A recent work [37] found
+that the choice of framings of human agents and algorithmic agents
+may affect user perception of agent competence (i.e., expert power),
+which further affects user behavior and cause inconsistent obser-
+vations of algorithm aversion and algorithm appreciation. In this
+work, since we explore means to facilitate appropriate reliance of
+humans on AI systems, we position our findings in the context of
+the research breaching algorithm aversion and appreciation. Future
+work can further explore the role of algorithmic aversion and ap-
+preciation in the context of interventions to facilitate appropriate
+reliance on AI systems.
+2.4
+Self-assessment in HCI Studies
+Evaluating one’s own performance on a task, typically known as
+“self-assessment”, is perceived as a fundamental skill, but people
+appear to calibrate their abilities [39] poorly. In general, most people
+tend to overestimate their own abilities. The cause of such an effect
+is multi-fold, like people tend to think they are above average and
+people place too much confidence in the insightfulness of their
+judgments [17]. With self-assessment, existing HCI research has
+explored using it as a measure for different purposes: Gadiraju et
+al. [29] used self-assessment for competence-based pre-selection
+in crowdsourcing marketplaces, Green et al. [33] measured users’
+risk assessment with comparing self-reported confidence with their
+actual performance, and Chromik et al. [11] compared perceived
+understanding of XAI methods with their actual understanding to
+reveal users’ illusion of explanatory depth.
+Dunning-Kruger effect (DKE) [43] described the dual burden the
+unskilled suffer from, besides the low performance, the unskilled
+will also lack the skill to estimate their own ability. Kruger et al.
+also found that a training session to increase the skills of partic-
+ipants is highly successful in mitigating such effect [43]. It had
+some positive effects and showed that by increasing knowledge, the
+overestimation could also be reduced. Further work also proved the
+effectiveness of such training in different domains like medicine [4]
+and economics [64].
+Besides the popularity in psychology research, Dunning-Kruger
+effect was also studied in human-computer interaction field. In a
+recent study, Schaffer et al. [65] conducted a user study based on
+Diner’s Dilemma game. They found that participants who consid-
+ered themselves very familiar with the task domain showed more
+trust in an intelligent assistant but relied less on it. Presenting ex-
+planations was not as effective as expected, and sometimes even
+resulted in automation bias. Using logical reasoning tasks with
+varying difficulty levels, Gadiraju et al. [29] showed that online
+crowd workers also fall prey to the DKE. The authors proposed
+the use of self-assessments in a pre-selection strategy to improve
+quality-related outcomes. Informed by prior literature, we selected
+logical reasoning tasks as the exploratory lens to address our re-
+search questions since the tasks themselves are straightforward to
+understand for laypeople, but with increasing difficulty, they also
+create room for inviting AI advice. This serves suitably to study the
+DKE in the context of human-AI decision making.
+3
+METHOD AND HYPOTHESIS
+In this section, we describe the logical reasoning task (i.e., multi-
+choice logical question answering based on a context paragraph)
+and present our hypotheses.
+3.1
+Logical Reasoning Task
+Prior work in the human-AI decision making context has explored
+how one can reliably study human behavior in proxy tasks. These
+work has established the importance of designing tasks, where
+users can find that there is a need to rely on AI (e.g., owing to the
+
+Knowing About Knowing: An Illusion of Human Competence Can Hinder Appropriate Reliance on AI Systems
+CHI ’23, April 23–28, 2023, Hamburg, Germany
+Figure 1: An example of a logical reasoning task used to
+obtain an initial human decision in the two-stage decision
+making process.
+task difficulty or a perceivable benefit) and where there is a risk
+associated with such reliance (e.g., dealing with an imperfect AI
+system) [5, 76]. This follows from the work of Lee and See [47]
+who defined trust in the Human-AI interaction context as “the
+attitude that an agent will help achieve an individual’s goals in a
+situation characterized by uncertainty and vulnerability.” The basis
+for our experimental setup is a task where participants are asked
+to choose an option in a multi-choice setting based on a paragraph
+of context presented to them (an example of the interface page
+is shown in Figure 1). We use the publicly available Reclor1 [85]
+dataset to this end. The dataset corresponds to characteristically
+high difficulty of logical reasoning tasks and has been used in prior
+work exploring Human-AI team performance [3]. This task was
+chosen as a realistic scenario for human-AI collaboration, where
+humans incentivized to complete the task accurately, may have the
+capability to reason accurately and find the right answer, but may
+also evidently perceive a benefit in adopting AI advice. In addition,
+the Dunning-Kruger Effect which has been widely replicated in a
+variety of contexts has been shown to be prevalent in the domain
+of logical reasoning as well [16, 43].
+In the basic setting of the task, participants are presented with
+three snippets of information: (1) a context paragraph, (2) a question
+related to this context, and (3) four different options corresponding
+to the question. Among the four options, a single option is deemed
+to be the best match to the question (i.e., ground truth). Participants
+are asked to first go through the context paragraph, and then make
+a choice based on the question. This simulates a realistic scenario
+where participants make decisions in a reading comprehension set-
+ting. While humans are capable of handling such tasks, AI systems
+may outperform them by extracting useful information and dealing
+1https://whyu.me/reclor/
+with complex reasoning structures which require a larger working
+memory capacity. The task interface is shown in Figure 2(a).
+Two-stage Decision Making. To analyze human reliance on AI
+systems, all participants in our study worked on tasks with a two-
+stage decision making process. In the first stage, only task informa-
+tion was provided, and participants were asked to make decisions
+themselves (example shown in Figure 1). After that, we showed
+the same task with AI advice (and explanations depending on the
+experimental condition) and provided an opportunity for the par-
+ticipants to alter their initial choice. An example of second stage is
+shown in Figure 2(a), where “Your choice” shows the initial decision
+participants made in the first stage. This setup of an initial unaided
+decision and the presentation of advice from an AI system in order
+to make a second and final choice is similar to the update condition
+in [33], and in line with findings that people first make a decision
+on their own and only then decide whether to incorporate system
+advice [32]. It also fits with the research of Dietvorst et al. [13] on
+trust in two-stage decision making.
+Quality Control. To ensure participant reliability and that partici-
+pants worked on the logical reasoning tasks genuinely (i.e., read
+the context paragraph and question carefully), we employed three
+attention check questions during the study process [56]. For this
+purpose, we embedded explicit instructions asking participants to
+select a specific option either in the context paragraph (once) or
+the question (twice). For example, we embedded the instruction,
+“Confirm that you have read the context by selecting answer B.” into
+a context paragraph on the task interface (which looks nearly iden-
+tical to other tasks). A conservative estimate through trial runs
+reflected that participants would take at least 1 minute to complete
+each task. As a further quality control measure, we deactivated the
+submit button corresponding to each task page (including tasks in
+tutorial phase) for 30 seconds. Since attention check pages do not
+require deliberation, we reduced that time to 5 seconds.
+3.2
+Logic Units-based Explanations
+In natural language processing tasks, feature attribution methods
+(e.g., text highlights on input) are the most popular in existing
+literature. However, multiple pieces of research work point out that
+such token-level highlights are still hard to interpret [69, 81, 86].
+Meanwhile, since logical reasoning tasks highlight the potential for
+logical reasoning congruent to human understanding, explanations
+based on logic units (i.e., text spans) may be a better choice to reveal
+how AI systems reach their final decision. With this perspective,
+we drew inspiration from LogiFormer, proposed by Xu et al. [80],
+who conducted logical reasoning with logic units based on pre-
+trained language models to generate such explanations. LogiFormer
+adopted a graph transformer network for logical reasoning of logic
+units, where the logic units are text spans connected with causal
+relations. Following this interpretability design, we also relied on
+the self-attention matrix A ∈ R𝑛×𝑛 (n indicates the number of logic
+units) from the last layer of the graph transformer network and
+identified the important logic units with the following formula:
+𝐸 = 𝐴𝑟𝑔𝑚𝑎𝑥𝑘 (
+𝑗=𝑛
+∑︁
+𝑗=1
+A𝑖𝑗),
+(1)
+
+Tasks
+Context
+Physician: In comparing our country with two other countries of roughly the same population size,
+I found that even though we face the same dietary, bacterial, and stress-related causes of ulcers as
+they do, prescriptions for ulcer medicines in all socioeconomic strata are much rarer here than in
+those two countries. It's clear that we suffer significantly fewer ulcers, per capita, than they do.
+Task 1/16
+Which one of the following, if true, most strengthens the physician's argument?
+The two countries that were compared
+The physician's country has a much better
+with the physician's country had
+system for reporting the number of
+approximately the same ulcer rates as
+prescriptions of a given type that are
+each other.
+obtained each year than is present in
+either of the other two countries.
+A person in the physician's country who is
+Several other countries not covered in the
+suffering from ulcers is just as likely to
+physician's comparisons have more
+obtain a prescription for the ailment as is
+prescriptions for ulcer medication than
+a person suffering from ulcers in one of
+does the physician's country.
+the other two countries.
+Confirm and continueCHI ’23, April 23–28, 2023, Hamburg, Germany
+Gaole He, Lucie Kuiper, Ujwal Gadiraju
+(a) Logical question answering page with AI advice.
+(b) Tutorial page with manual explanation.
+Figure 2: Screenshots of the task interface. In panel (a), the logic units-based explanations are highlighted with a light blue
+background color in the context paragraph and the option suggested by the AI system. In panel (b), we show the rationale of
+correct answers in contrast with users’ final choice at the bottom (when users do not select the correct answer in the decision
+making stage) at the bottom.
+where 𝐸 is the top-𝑘 logic units which receive most attention
+from other logic units (i.e., we calculated it with the sum along
+each column of the self-attention matrix). One example of such
+explanation is shown in figure 2(a).
+Our implementation and extracted logic units-based explana-
+tions can be found in Github repo.2 To generate the explanations
+described above, we first trained the LogiFormer model on the Re-
+clor dataset. With the trained model, we generated logic units-based
+explanations according to Equation 1. In this study, we specify𝑘 = 5
+to highlight the most important logic units for each task. Notice
+that, such explanations are generated for each option, and the spans
+are only extracted from the context paragraph and each option. For
+more details about the LogiFormer model, we refer readers to the
+original paper [80] and the corresponding implementation.3
+3.3
+Proposing a Tutorial Intervention to Help
+Users Calibrate Their Skills
+To answer RQ2, we need to verify whether our proposed interven-
+tion can help mitigate the DKE among the same participants who
+demonstrated it in the absence of the intervention. This requires
+two batches of tasks that can facilitate comparative performance
+2https://github.com/RichardHGL/CHI2023_DKE
+3https://github.com/xufangzhi/Logiformer
+assessment and on which participants can be asked to self-assess
+their performance. Based on the effectiveness of tutorials as inter-
+ventions in previous HCI literature [8, 9, 45], we designed a tutorial
+as a means to shed light on the fallibility of AI advice. In our pa-
+per, we, therefore, considered the tutorial as an intervention and
+analyzed its effectiveness by comparing participants’ reliance and
+self-assessment before and after the tutorial was delivered. Inspired
+by existing work to mitigate different kinds of cognitive biases
+through revealing such biases to users [1, 38], we decided to adopt
+a tutorial to help users calibrate their skills through self-assessment
+on logical reasoning tasks. To this end, we designed a tutorial with
+the aim of revealing to users that they may not be as capable in such
+tasks as they may believe. Furthermore, to ensure the effectiveness
+of revealing their mistakes, we designed persuasive explanations
+for users. To achieve that goal, we chose to provide contrastive
+explanations which point out not only the reason for correct an-
+swers but also the reason to reject users’ wrong choices. As none
+of the existing off-the-shelf toolkits can be used to obtain such
+strongly persuasive explanations, we manually created explana-
+tions for each option in the four tasks considered in the tutorial
+phase. These explanations corresponding to each task have also
+been made available on the Open Science Framework companion
+page. An example of such performance feedback and contrastive
+explanation can be found in Figure 2(b). On this page, we showed
+
+Tasks
+Context
+A study of young children's ability to learn foreign languages found that those with
+parents who read them more than one book per week in their native language were
+75% more proficient in the foreign languages that they learned than children whose
+that children's ability to remember new vocabulary in a second language drops off
+sharply after the age of 6, when it becomes 75% more difficult to retain new words
+learned in the second language
+Task 2/16
+Assuming the statements above are true, which of the following can be inferred from
+them?
+A
+The ease of learning a second
+ Students whose parents enter
+B
+language depends almost
+them in early education and who
+exclusively on environmental
+read to them frequently are more
+Al advice
+factors.
+likely to have extra income and
+more free time.
+D
+Students who begin studying a
+Proficient speakers of a second
+language later in life would have
+languagearelikelyto havebegur
+Your choice
+had an easier time learning some
+learning it before the age of 6
+aspects of that language if they
+D
+had begun studying it as a young
+child.
+Confirm and continueTasks
+Context
+When doctors vaccinate a patient, their intention is to expose him or her to a
+Correct
+weakened form of a disease-causing pathogen and thus to make the patient better
+answer
+able to resist the pathogen and less likely to develop a severe form of that disease
+later.
+D
+Task 8/16
+Which one of the following best illustrates the principle that the passage illustrates?
+A In some circumstances, firefighters B Some police departments
+use fire to fight fire by creating an
+energetically pursue those who
+Al advice
+intense explosion very close to an
+commit minor crimes; in doing so
+uncontrollable blaze that they wish
+they intend to provide examples to
+A
+to extinguish, thus momentarily
+deter people who might be
+depriving it of the oxygen it needs
+tempted to commit more-serious
+to continue burning.
+crimes.
+Your choice
+C In some cases, a business will
+ Some parents read their children
+close down some of its operations,
+fairy tales containing allegorical
+its intention being to position the
+treatments of treachery and
+company to be more profitable
+cruelty, with the intention of
+later even though this involves
+making them less emotionally
+expenses in the current period.
+vulnerable to these phenomena
+when they encounter them later in
+life.
+The answer is D rather than C. In answer C the problem is solved by cutting down profit in the
+beginning but growing it later on. However, in this context, the problem is solved by giving exposure
+to a weakened version. In answer D the fairy tales also act as a weakened version of treachery and
+cruelty to which the children are exposed, thus making the principles align.
+Confirm and continueKnowing About Knowing: An Illusion of Human Competence Can Hinder Appropriate Reliance on AI Systems
+CHI ’23, April 23–28, 2023, Hamburg, Germany
+the correct answer in a box with light blue background color. The
+final decision of the participant after receiving AI advice, and the AI
+advice itself are shown in boxes with a dark blue background color.
+The contrastive explanation is shown at the bottom of this page.
+Through such a performance feedback intervention, we hope that
+users with inflated self-assessments can realize their true capability
+with respect to the tasks and recalibrate their self-assessment. Such
+an intervention can potentially help users improve their reliance
+on AI systems [36].
+3.4
+Pilot Study for Task Selection
+To answer our research questions, we need to analyze the impact
+of the Dunning-Kruger effect on reliance measures and the effec-
+tiveness of the proposed intervention to mitigate such an effect.
+Note that the Dunning-Kruger effect corresponds to one’s skills in a
+given task [16]. To operationalize this, we need two batches of tasks
+with similar difficulty levels, through which we can verify the effec-
+tiveness of the intervention by comparing performance before and
+after the intervention. Meanwhile, for the tutorial tasks, we need
+tasks that may trigger the Dunning-Kruger effect. In other words,
+tasks that participants may make mistakes on with high confidence.
+For these purposes, we conducted a pilot study with 10 participants
+from the Prolific crowdsourcing platform.4 In the pilot study, each
+participant worked on 30 questions randomly sampled from the
+validation set of the Reclor dataset. We collected their choice and
+confidence level for each task. With six participants who passed all
+the attention checks, we assessed the difficulty of each task based
+on the number of participants who answered the task correctly.
+Considering that most participants spend around 1 minute to fully
+understand a task and make a decision, we considered the batch
+size to be six. We collected two batches of tasks which are of similar
+difficulty (informed by the average accuracy on the tasks in the
+pilot study). To make the tutorial effective but not cumbersome, we
+selected four tasks for the tutorial. The tasks for the tutorial were
+selected in a similar fashion as the other batches, as the tutorial
+only has four questions instead of six, the tasks with the lowest and
+highest accuracy were removed. Such selection strategy creates
+a batch similar in difficulty to the other batches. Among the four
+tasks, we configured the AI advice to be correct on two of them and
+misleading on the other two. All participants were rewarded with
+hourly wage of £7.5 (estimated completion time was 33 minutes),
+and extra bonus of £0.05 for each correct decision.
+3.5
+Hypotheses
+Our experiment was designed to answer questions surrounding the
+impact of Dunning-Kruger effect on user reliance on AI systems,
+and how to mitigate such potentially undesirable impact. People
+who are less competent in a task struggle more with estimating their
+own performance in the task, compared to the more competent
+counterparts [43]. Impacted by DKE, users with the option to rely
+on AI advice may overestimate their own performance in a task and
+tend to rely on themselves when they are actually less capable than
+the AI systems. Apart from them, some users can exhibit accurate
+self-assessment. Such accurate self-assessments can be indicative
+of a good understanding of the task difficulty and personal skills,
+4https://www.prolific.co/
+which may help these users rely on AI systems more appropriately.
+Meanwhile, effective explanations may amplify such an effect. Thus,
+we hypothesize that:
+(H1) Users overestimating their own performance will
+demonstrate relatively less reliance on AI systems than users
+demonstrating accurate self-assessment.
+According to previous work [26, 57], interventions that provide
+users with feedback on their performance may help improve their
+self-assessment. By providing users with an opportunity to reflect
+on their skills and recalibrate their skills on the given task, we
+argue that the impact of the DKE can be mitigated. As a result of an
+improved calibration of oneself, such users are better suited to rely
+on AI systems appropriately when making decisions. Therefore, we
+hypothesize that:
+(H2) Making users aware of their miscalibrated self-
+assessment, will help them improve their self-assessment.
+(H3) Making users aware of their miscalibrated self-
+assessment will result in relatively more appropriate reliance
+on AI systems.
+Performance feedback can potentially help participants improve
+their self-assessment, which may facilitate appropriate reliance.
+At the same time, explanations have been shown to improve the
+human understanding and interpretation of AI advice [3, 52, 79],
+which can also potentially contribute to appropriate reliance. Thus,
+we hypothesize to observe the following in a human-AI decision
+making context:
+(H4) Providing performance feedback and meaningful ex-
+planations can facilitate appropriate reliance on the AI system.
+4
+STUDY DESIGN
+This section describes our experimental conditions, variables, sta-
+tistical analysis, procedure, and participants in our main study.
+4.1
+Experimental Conditions
+In our study, all participants worked on logical reasoning tasks
+with two-stage decision making process (described in Sec. 3.1). The
+only difference is whether tutorial is presented and whether ex-
+planations are provided along with AI advice. To comprehensively
+study the effect of each factor and their interaction effect, we con-
+sidered a 2 × 2 factorial design with four experimental conditions:
+(1) no tutorial, no XAI (represented as × Tutorial,× XAI), (2)
+with tutorial, no XAI (represented as ✓ Tutorial,× XAI), (3) no
+tutorial, with XAI (represented as × Tutorial,✓ XAI), (4) with
+tutorial, with XAI (represented as ✓ Tutorial,✓ XAI). In condi-
+tions with tutorial, participants were presented with four selected
+tasks with performance feedback and contrastive explanation for
+correct answers against wrong choice (when participants missed
+the wrong answer). While in conditions without tutorial, the four
+
+CHI ’23, April 23–28, 2023, Hamburg, Germany
+Gaole He, Lucie Kuiper, Ujwal Gadiraju
+Table 1: The different appropriate reliance patterns consid-
+ered in [66]. 𝑑𝑖 is initial human decision, while 𝑑𝑓 is the final
+decision after AI advice.
+𝑑𝑖
+AI advice
+𝑑𝑓
+Reliance
+Incorrect
+Correct
+Correct
+Positive AI reliance
+Incorrect
+Correct
+Incorrect
+Negative self-reliance
+Correct
+Incorrect
+Correct
+Positive self-reliance
+Correct
+Incorrect
+Incorrect
+Negative AI reliance
+tasks selected are presented as normal tasks without any perfor-
+mance feedback or explanation for correct answers, to prevent any
+learning effect. In conditions with XAI, the top-5 most important
+logic units are highlighted as an explanation for AI advice.
+For each batch of six tasks, the AI system was configured to
+provide correct advice on four of them and misleading advice on
+two tasks. So the accuracy of AI systems is around 66.7%. To avoid
+any ordering effect, we randomly assign one batch of tasks as first
+batch of tasks for each participant and further shuffled the order of
+tasks within each batch.
+4.2
+Measures and Variables
+We measure the reliance of participants on the AI system via two
+metrics: the Agreement Fraction and the Switch Fraction. These
+look at the degree to which participants are in agreement with AI
+advice, and how often they adopt AI advice in cases of initial dis-
+agreement. They are commonly used in the literature, for example
+in [83, 87]. In addition, we consider the accuracy in batches to
+measure participants’ performance with AI assistance. Since cases
+without initial disagreement do not clearly signal reliance on the
+system we restrict the scope of the appropriate reliance measure to
+accurately understand how participants handle divergent system
+advice. Max et al. [66] presented four conditions of appropriate
+reliance patterns (see Table 1) when the disagreement exists and
+correct answer exists in human initial decision or AI advice. We
+followed them to adopt Relative positive AI reliance (RAIR) and Rel-
+ative positive self-reliance (RSR) as appropriate reliance measures.
+The two measures assessed users’ appropriate reliance from two
+dimensions, which can help analyze the dynamics of reliance. To
+provide an overview of participants’ appropriate reliance under
+initial disagreement, we considered Accuracy-wid (i.e., accuracy
+with initial disagreement). These measures are computed as follows:
+Agreement Fraction = Number of decisions same as the system
+Total number of decisions
+,
+Switch Fraction = Number of decisions user switched to agree with the system
+Total number of decisions with initial disagreement
+,
+Accuracy = Number of correct final decisions
+Total number of decisions
+,
+Accuracy-wid = Number of correct final decisions with initial disagreement
+Total number of decisions with initial disagreement
+,
+RAIR =
+Positive AI reliance
+Positive AI reliance + Negative self-reliance,
+RSR =
+Positive self-reliance
+Positive self-reliance + Negative AI reliance .
+To measure the self-assessment of users, we gathered responses on
+the following question after each batch of tasks – “From the previ-
+ous 6 questions, how many questions do you estimate to have been
+answered correctly? (after receiving AI advice)”. Comparing that es-
+timation with the actual correct number, we can calculate the degree
+of miscalibration and self-assessment as: Degree of Miscalibra-
+tion = |Estimated correct number - Actual correct number|, Self-
+assessment = Estimated correct number - Actual correct number.
+Meanwhile, for conditions with explanations, we also assessed the
+helpfulness of explanations with the question, “To what extent
+was the explanation (i.e., the highlighted words/phrases) helpful in
+making your final decision?” Responses were gathered on a 5-point
+Likert scale from 1 to 5 corresponding to the labels not helpful, very
+slightly helpful, slightly helpful, helpful, very helpful.
+For a deeper analysis of our results, a number of additional
+measures were considered based on observations from existing
+literature [49, 67, 76]:
+• Trust in Automation (TiA) questionnaire [41], a validated
+instrument to measure (subjective) trust [76]. In this study
+we adopted two subscales: Propensity to Trust (TiA-PtT),
+Trust in Automation (TiA-Trust). Thus, we consider possible
+effects of trust on reliance, in accordance with Lee et al. [47].
+• Affinity for Technology Interaction Scale (ATI) [28], admin-
+istered in the pre-task questionnaire. Thus, we account for
+the effect of participants’ affinity with technology on their
+reliance on systems [76].
+Table 2 presents an overview of all the variables considered in
+our study.
+4.3
+Participants
+Sample Size Estimation. Before recruiting participants, we com-
+puted the required sample size in a power analysis for the 2 × 2
+factorial design using G*Power [25]. To correct for error-inflation as
+a result of testing multiple hypotheses, we applied a Bonferroni cor-
+rection so that the significance threshold decreased to 0.05
+4
+= 0.0125.
+We specified the default effect size 𝑓 = 0.25 (i.e., indicating a mod-
+erate effect), a significance threshold 𝛼 = 0.0125 (i.e., due to testing
+multiple hypotheses), a statistical power of (1 − 𝛽) = 0.8, and the
+consideration of 4 different experimental conditions. This resulted
+in a required sample size of 244 participants. We thereby recruited
+314 participants from the crowdsourcing platform Prolific5, in order
+to accommodate potential exclusion.
+Compensation. All participants were rewarded with £2.5, amount-
+ing to an hourly wage of £7.5 (estimated completion time was 20
+minutes). We rewarded participants with extra bonuses of £0.1 for
+every correct decision in the 16 trial cases. By incentivizing partici-
+pants to reach a correct decision, we operationalize the concomitant
+"vulnerability" discussed by Lee and See [47] as a contextual re-
+quirement to encourage appropriate system reliance.
+Filter Criteria. All participants were proficient English speakers
+above the age of 18 and they had an approval rate of at least 90% on
+the Prolific platform. We excluded participants from our analysis
+if they failed at least one attention check (65 participants). The
+resulting sample of 249 participants had an average age of 38 (𝑆𝐷 =
+12.8) and a gender distribution (48.6% female, 51.4% male).
+5https://www.prolific.co
+
+Knowing About Knowing: An Illusion of Human Competence Can Hinder Appropriate Reliance on AI Systems
+CHI ’23, April 23–28, 2023, Hamburg, Germany
+Table 2: The different variables considered in our experimental study. “DV” refers to the dependent variable. RAIR, RSR, and
+Accuracy-wid are indicators of appropriate reliance.
+Variable Type
+Variable Name
+Value Type
+Value Scale
+Performance (DV)
+Accuracy
+Continuous, Interval
+[0.0, 1.0]
+Accuracy-wid
+Continuous
+[0.0, 1.0]
+Reliance (DV)
+Agreement Fraction
+Continuous, Interval
+[0.0, 1.0]
+Switch Fraction
+Continuous
+[0.0, 1.0]
+RAIR
+Continuous
+[0.0, 1.0]
+RSR
+Continuous
+[0.0, 1.0]
+Assessment (DV)
+Degree of Miscalibration
+Continuous, Interval
+[0,6]
+Self-assessment
+Continuous, Interval
+[-6,6]
+Trust (DV)
+TiA-Trust
+Likert
+5-point, 1:strong distrust, 5: strong trust
+Covariates
+ATI
+Likert
+6-point, 1: low, 6: high
+TiA-PtT
+Likert
+5-point, 1: tend to distrust, 5: tend to trust
+Other
+Helpfulness of Explanation
+Likert
+5-point, 1: not helpful, 5: very helpful
+4.4
+Procedure
+The full procedure that participants followed in our study is illus-
+trated in Figure 3. All participants first read the same basic instruc-
+tions on the logical reasoning task. Next, participants were asked
+to complete a pre-task questionnaire to measure their propensity
+to trust and affinity for technology interaction.
+Instructions
+Pre-task
+Questionnaire
+Task Batch 1
+Tutorial Batch
+Task Batch 2
+Post-task
+Questionnaire
+ATI, TiA-PtT
+Post-task
+Questionnaire
+Done
+Start
+Self-assessment,
+TiA-trust
+Self-assessment, TiA-
+trust, helpfulness of
+explanations
+6 trial cases
+4 trial cases,
+Performance feedback
+6 trial cases
+Figure 3: Illustration of the procedure participants followed
+within our study. This flow chart describes the experimen-
+tal condition ✓ Tutorial,✓ XAI. Blue boxes represent the
+questionnaire phase, orange boxes represent the task phase.
+Participants were then assigned to one experimental condition,
+which differed in whether or not tutorial feedback is provided and
+the system’s prediction is supplemented with explanation. In ×
+Tutorial,× XAI and × Tutorial,✓ XAI conditions, participants
+worked on the four trial cases without any difference with the task
+batch, no extra information was provided. After that, participants
+will work on 16 tasks (two task phases with six tasks, and one
+tutorial phase with four tasks). Selection of these cases is described
+in section 3.4. After each task phase, post-task questionnaires were
+adopted to assess their self-assessment and trust in AI systems (TiA-
+trust). Participants in the × Tutorial,✓ XAI and ✓ Tutorial,✓
+XAI conditions were additionally asked for their perceived help-
+fulness of the explanations they were presented with. To further
+ensure the reliability of responses gathered in the questionnaire and
+the task phases, we added four attention check questions spread
+out at random through the different stages of the procedure [30].
+5
+RESULTS
+In this section, we present the results of our study. We discuss
+descriptive statistics, the outcomes of the hypothesis tests we con-
+ducted, and our exploratory findings. Our code and data can be
+found on Github.6
+5.1
+Descriptive Statistics
+In our analysis, we only kept participants who passed all atten-
+tion checks, which deemed to be more reliable. Participants were
+distributed in a balanced fashion over the four experimental condi-
+tions as follows: 63 (× Tutorial,× XAI), 62 (✓ Tutorial,× XAI),
+62 (× Tutorial,✓ XAI), 62 (✓ Tutorial,✓ XAI). On average,
+participants spend around 32 minutes (𝑆𝐷 = 11 minutes) in our
+study. We found no significant difference in the time spent across
+the four experimental conditions.
+Figure 4: Distribution of participants with underestimated,
+accurate, and overestimated self-assessment across all ex-
+perimental conditions in the first batch of tasks.
+Distribution of Covariates. The covariates’ distribution is as fol-
+lows: ATI (𝑀 = 3.73, 𝑆𝐷 = 0.99, 6-point Likert scale, and 1: low, 6:
+6https://github.com/RichardHGL/CHI2023_DKE
+
+Under
+25
+Accurate
+Over
+20
+15
+10
+5
+NoTutorial.
+With Tutorial.
+NoTutorial
+WithTutorial.
+No XAI
+No XAI
+WithXAI
+WithXAI
+ConditionCHI ’23, April 23–28, 2023, Hamburg, Germany
+Gaole He, Lucie Kuiper, Ujwal Gadiraju
+Table 3: Kruskal-Wallis H-test results for inflated self-assessments (H1) on reliance-based dependent variables. “††” indicates
+the effect of variable is significant at the level of 0.0125. “Under”, “Accurate”, abd “Over” refers to participants who underesti-
+mated , accurately estimated, and overestimated their performance on the first batch of tasks, respectively.
+Dependent Variables
+𝐻
+𝑝
+𝑀 ± 𝑆𝐷(Under)
+𝑀 ± 𝑆𝐷(Accurate)
+𝑀 ± 𝑆𝐷(Over)
+Post-hoc results
+Accuracy
+74.06
+<.001††
+0.72 ± 0.16
+0.61 ± 0.15
+0.45 ± 0.19
+Under > Accurate > Over
+Agreement Fraction
+10.87
+.004††
+0.70 ± 0.18
+0.69 ± 0.21
+0.59 ± 0.24
+Under, Accurate > Over
+Switch Fraction
+23.31
+<.001††
+0.50 ± 0.28
+0.53 ± 0.31
+0.32 ± 0.32
+Under, Accurate > Over
+Accuracy-wid
+87.94
+<.001††
+0.65 ± 0.21
+0.53 ± 0.27
+0.28 ± 0.22
+Under > Accurate > Over
+RAIR
+46.91
+<.001††
+0.65 ± 0.36
+0.58 ± 0.37
+0.27 ± 0.33
+Under, Accurate > Over
+RSR
+30.23
+<.001††
+0.67 ± 0.44
+0.41 ± 0.47
+0.27 ± 0.43
+Under > Accurate, Over
+high), TiA-Propensity to Trust (𝑀 = 2.95, 𝑆𝐷 = 0.60, 5-point Likert
+scale, 1: tend to distrust, 5: tend to trust).
+Distribution of Participants. Among 249 participants, we identi-
+fied the participants who underestimated their performance (i.e., Self-
+assessment < 0), those with an accurate self-assessment (i.e., Self-
+assessment = 0), and those with overestimation of their perfor-
+mance (i.e., Self-assessment > 0) according to their performance in
+the first batch of tasks (shown in Figure 4). In general, participants
+showed relatively balanced distribution into the three types of self-
+assessment across conditions: (1) the number of participants with
+underestimated self-assessment lies in the range of 15 ∼ 20, (2) the
+number of participants with accurate self-assessment lies in the
+range of 15 ∼ 25, (3) the number of participants with overestimated
+self-assessment was in the range of 20 ∼ 30. We also compared
+the time spent by participants with different self-assessment and
+participants with different experimental conditions, and found no
+statistically significant difference with Kruskal-Wallis H-tests.
+Figure 5: Distribution of participants with perceived helpful-
+ness of logic units-based explanations.
+For participants in conditions with explanation (i.e., [× Tutorial,
+✓ XAI] and [✓ Tutorial,✓ XAI]), we assessed the helpfulness of
+logic units-based explanations. The ratios of perceived helpfulness
+are illustrated with Figure 5. As we can see, most people (57.2%)
+think it slightly or very slightly helpful, while only 28.3% partici-
+pants show positive feedback to the logic units-based explanations.
+Performance Overview. On average across all conditions, par-
+ticipants achieved an accuracy of 56.9% (𝑆𝐷 = 0.16) over the two
+batches of tasks, still lower than the aforementioned AI accuracy
+of 66.7%. The agreement fraction is 0.665 (𝑆𝐷 = 0.17) while the
+switching fraction is 0.453 (𝑆𝐷 = 0.27). With these measures, we
+confirm that when disagreement appears participants in our study
+did not always switch to AI advice or blindly rely on the AI system.
+As all dependent variables are not normally distributed, we used
+non-parametric statistical tests to verify our hypotheses.
+5.2
+Hypothesis Tests
+5.2.1
+H1: effect of inflated self-assessments on AI system reliance.
+To analyze the main effect of participants’ inflated self-assessment
+(i.e., overestimation of performance) on their reliance on the AI
+system, we conducted Kruskal-Wallis H-tests by considering how
+participants varied in their self-assessment. We categorize all partic-
+ipants into three groups according to the self-assessment: (1) partic-
+ipants who underestimated their performance (i.e., Self-assessment
+< 0), (2) participants with accurate performance self-assessment
+(i.e., Self-assessment = 0), and (3) participants who overestimated
+their performance (i.e., Self-assessment > 0). For this analysis, we
+considered all participants across the four experimental conditions,
+and the performance metrics are calculated based on the first batch
+of tasks (i.e., 6 tasks). The results are shown in Table 3.
+Effect of Overestimated Self-Assessments on Objective Re-
+liance. For all reliance-based measures, we found a statistically
+significant difference between the performance of the participants
+who overestimated their performance and those with accurate
+self-assessment. Post-hoc Mann-Whitney tests using a Bonferroni-
+adjusted alpha level of 0.0125 ( 0.05
+4 ) were used to make pairwise
+comparisons of performance, revealing that participants who did
+not overestimate their performance in fact performed significantly
+better than those who did (The only exception is on metric RSR).
+Overall, participants with accurate self-assessment and underes-
+timation of their own performance performed much better than
+participants who overestimated their own performance. The main
+reason is that they showed more reliance on the AI system and
+achieved better appropriate reliance when their initial decision dis-
+agreed with AI advice. The results indicate that participants who
+overestimate their own performance rely significantly less on AI
+systems compared to those who do not. Due to such under-reliance
+and inappropriate reliance when initial disagreement exists, they
+achieved a significantly lower accuracy on average. Thus, we find
+support for hypothesis H1.
+We also found that participants who underestimated their per-
+formance achieved significantly higher Accuracy, Accuracy-wid,
+
+Very Slightly Helpful
+39.5%
+Not Helpful
+14.5%
+6.5%
+Very Helpful
+17.7%
+21.8%
+Slightly Helpful
+HelpfulKnowing About Knowing: An Illusion of Human Competence Can Hinder Appropriate Reliance on AI Systems
+CHI ’23, April 23–28, 2023, Hamburg, Germany
+Table 4: Wilcoxon signed ranks test results for H3 on reliance-based dependent variables. For participants with initial underes-
+timation, we report results with one-sided hypothesis that the performance / reliance decrease after tutorial. For participants
+with initial overestimation, we report results with one-sided hypothesis that the performance / reliance increase after tutorial.
+“†” and “††” indicates the effect of variable is significant at the level of 0.05 and 0.0125, respectively.
+Participants
+Underestimation
+Overestimation
+Dependent Variables
+𝑇
+𝑝
+𝑀 ± 𝑆𝐷(first)
+𝑀 ± 𝑆𝐷(second)
+Trend
+𝑇
+𝑝
+𝑀 ± 𝑆𝐷(first)
+𝑀 ± 𝑆𝐷(second)
+Trend
+Accuracy
+407.5
+.000††
+0.73 ± 0.17
+0.55 ± 0.21
+↓
+303.0
+.075
+0.46 ± 0.18
+0.51 ± 0.22
+-
+Agreement Fraction
+212.5
+.543
+0.68 ± 0.20
+0.70 ± 0.23
+-
+451.0
+.605
+0.60 ± 0.23
+0.57 ± 0.23
+-
+Switch Fraction
+267.5
+.592
+0.47 ± 0.29
+0.48 ± 0.36
+-
+367.5
+.147
+0.31 ± 0.33
+0.36 ± 0.31
+-
+Accuracy-wid
+418.0
+.000††
+0.68 ± 0.22
+0.44 ± 0.29
+↓
+338.0
+.013†
+0.27 ± 0.20
+0.41 ± 0.28
+↑
+RAIR
+313.0
+.006††
+0.68 ± 0.37
+0.45 ± 0.38
+↓
+194.0
+.038†
+0.24 ± 0.32
+0.36 ± 0.36
+↑
+RSR
+204.0
+.000††
+0.72 ± 0.43
+0.30 ± 0.44
+↓
+151.0
+.020†
+0.29 ± 0.45
+0.52 ± 0.48
+↑
+and RSR than participants demonstrating accurate self-assessment.
+Since they showed similar degrees of reliance (Agreement Frac-
+tion and Switch Fraction) on the AI system, the improvement of
+overall accuracy is mainly due to appropriate reliance. In general,
+they showed significantly better RSR, which indicates that they
+have a better chance to rely on themselves to make correct decisions
+when they initially disagree with misleading AI advice.
+In the first batch of tasks, we found no difference (with Kruskal-
+Wallis H-tests) in reliance and accuracy metrics when comparing
+participants in XAI conditions (i.e., × Tutorial,✓ XAI and ✓
+Tutorial,✓ XAI) with participants in non-XAI (i.e., × Tutorial,×
+XAI and ✓ Tutorial,× XAI). To verify how the provided logic
+units-based explanations affect participants with different self-
+assessments, we compared the performance and reliance measures
+of participants with XAI and without XAI in underestimation, ac-
+curate self-assessment, and overestimation. No significant effects
+were found from the logic units-based explanation on performance
+and reliance for participants with overestimated self-assessment.
+5.2.2
+H2: effect of the tutorial on self-assessment.
+To verify H2, we used Wilcoxon signed rank tests to compare
+the performance of participants before and after the tutorial. We
+considered participants who are provided with the tutorial for self-
+assessment calibration (i.e., ✓ Tutorial,× XAI and ✓ Tutorial,✓
+XAI). Meanwhile, we exclude participants who have accurate as-
+sessment on the first batch of tasks from this analysis. Finally, we
+have 87 participants reserved for analysis of H2. On average, the
+participants’ self-assessment get improved after receiving the tuto-
+rial (i.e., decreased Degree of Miscalibration, 𝑀 ±𝑆𝐷(first) = 1.67
+± 0.91, 𝑀 ±𝑆𝐷(second) = 1.14 ± 1.04; a smaller value indicates more
+accurate self-assessment). A Wilcoxon signed rank test indicated
+that the difference was statistically significant, 𝑇=1175.0, 𝑝<0.001,
+which supports H2. To further check how the tutorial intervention
+has an impact on participants with different types of miscalibration,
+we separately conducted Wilcoxon signed rank tests on partici-
+pants underestimating their own performance and overestimating
+their own performance separately. The results indicate that: (1) par-
+ticipants underestimating their own performance calibrated their
+self-assessment, the difference is significant (𝑇=229.0, 𝑝=0.002); (2)
+participants overestimating their own performance calibrated their
+self-assessment, the difference is significant (𝑇=381.5, 𝑝=0.012). The
+detailed analysis of participants with different types of miscalibra-
+tion also supports H2.
+To further explore the effect of logic units-based explanation on
+calibrating self-assessment, we conducted a Kruskal-Wallis H-test
+(among these participants) by considering whether the explanation
+is provided. We found no significant results, which indicates that
+logic units-based explanations cannot amplify the effect of the
+tutorial intervention (i.e., calibrating self-assessment).
+5.2.3
+H3: effect of the tutorial on appropriate reliance.
+Similar to the analysis for H2, we only considered the participants
+who showed miscalibration in the first batch of tasks. Overall, there
+is no significant difference in reliance and performance measures
+when we compare the participants’ performance before and af-
+ter receiving the tutorial. To further check how our tutorial in-
+tervention will affect participants with different miscalibration of
+self-assessment, we conducted analysis for participants with under-
+estimation and overestimation separately. The results of Wilcoxon
+signed rank tests corresponding to each of the reliance measures
+are shown in Table 4. Both participants with underestimation and
+overestimation did not show any significant difference in reliance
+measures (i.e., Agreement Fraction and Switch Fraction). For
+participants who underestimated their performance in the first
+batch of tasks, they showed significantly worse performance and
+appropriate reliance after receiving the tutorial. In contrast, we
+found some improvement of Accuracy and appropriate reliance
+measures (i.e., Accuracy-wid, RAIR, RSR) for participants who
+overestimated their performance in the first batch of tasks. How-
+ever, the improvement is non-significant at the level of 0.0125. Thus,
+on the whole, we find partial support for H3.
+Meanwhile, to check how the tutorial intervention affects the
+participants with initial accurate self-assessment, we also conducted
+Wilcoxon signed rank tests for their performance before and after
+the tutorial intervention. No significant difference is found. Com-
+bined with the findings from participants with initial miscalibration,
+we found that: (1) the designed tutorial intervention does not show
+much impact on participants with accurate self-assessment, (2) the
+designed tutorial intervention has positive impact on appropri-
+ate reliance for participants who initially overestimate themselves,
+while negative impact on participants with initial underestimation
+of their performance.
+Relation Between Self-assessment Calibration and the Change
+in Reliance. To further explore the relationship between the change
+in self-assessment and change with (appropriate) reliance, we con-
+ducted the Spearman rank-order test separately for participants
+
+CHI ’23, April 23–28, 2023, Hamburg, Germany
+Gaole He, Lucie Kuiper, Ujwal Gadiraju
+with overestimation and underestimation in the first batch of tasks.
+As the impact of tutorial intervention on Agreement Fraction
+and Switch Fraction is insignificant, we ignore the two metrics
+in calculating the correlation. The results are shown in Table 5.
+We found a strong negative monotonic relationship between the
+two variables in participants with overestimation. Thus, in logical
+reasoning tasks, the calibration effect in self-assessment accounted
+for 59.3% of the improved Accuracy (𝜌2 = 0.593, 𝑝 < 0.001), 55.5%
+of the improved Accuracy-wid (𝜌2 = 0.555, 𝑝 < 0.001), 32.0% of
+the improved RAIR (𝜌2 = 0.320, 𝑝 < 0.001), and 12.9% of the im-
+proved RSR (𝜌2 = 0.129, 𝑝 = 0.005). Similarly, the calibration of
+self-assessment also accounted for 26.2% of the decreased Accu-
+racy (𝜌2 = 0.262, 𝑝 = 0.001), 14.8% of the decreased Accuracy-wid
+(𝜌2 = 0.148, 𝑝 = 0.009) for participants with underestimation.
+Table 5: Correlation of self-assessment change and reliance
+change. “††” indicates the effect of variable is significant at
+the level of 0.0125. “†” indicates the effect of variable is sig-
+nificant at the level of 0.05.
+Participants
+Underestimation
+Overestimation
+Dependent Variables
+𝜌
+𝑝
+𝜌
+𝑝
+Accuracy
+-0.512
+.001††
+-0.770
+.000††
+Accuracy-wid
+-0.385
+.009††
+-0.745
+.000††
+RAIR
+-0.293
+.039†
+-0.566
+.000††
+RSR
+-0.349
+.068
+-0.359
+.005††
+In general, for all participants with miscalibrated self-assessment,
+the difference in self-assessment shows strong negative correlation
+with the difference in performance and appropriate reliance. In
+other words, the increase in self-assessment (trend to overestima-
+tion) will lead to decrease in performance and appropriate reliance,
+which is consistent with our findings in H1. While the signifi-
+cant negative correlation exists for performance measures in all
+participants with miscalibrated self-assessment, only participants
+with overestimation showed significant correlation (in the level
+of 0.0125) with RAIR and RSR. The difference indicates that the
+change of self-assessment can hardly explain why participants with
+underestimation showed worse appropriate reliance.
+To further explore the impact of logic units-based explanations
+on performance improvement (the difference between performance
+metrics from the second batch of tasks and those from the first
+batch of tasks), we conducted a Kruskal-Wallis H-test (among these
+participants) by considering whether explanations are provided.
+Overall, no significant difference is found for all behavior-based
+dependent variables considering all 87 participants who showed
+miscalibration in the first batch and then received the tutorial inter-
+vention. We further check the logic units-based explanation impact
+according to participants with underestimation (37 participants)
+and overestimation (50 participants) respectively (cf. Table 6). No
+significant difference is found for all behavior-based dependent
+variables. Although participants with explanations show better per-
+formance improvement in RSR, such difference is not significant.
+5.2.4
+H4: Two-factor analysis for final performance.
+To verify H4, we conducted a two-way ANOVA to compare the
+performance and (appropriate) reliance measures of participants
+under the effect of providing tutorial intervention and logic units-
+based explanations. In this analysis, only the second batch of tasks
+are taken into consideration, as the performance of the first batch
+of tasks is not affected by the tutorial intervention. According to
+the test results shown in Table 7, no significant impact (in the
+significance level of 0.0125) is found for tutorial intervention, logic
+units-based explanations and their interaction effect. Thus, H4 is
+not supported.
+According to the results of H3, the tutorial intervention shows
+positive impact on participants with initial overestimation, no sig-
+nificant effect on participants with accurate self-assessment, and
+negative impact on participants with initial underestimation. As
+indicated by Figure 4, the participants show compatible distribu-
+tion in the three groups with different initial self-assessment. The
+contradicting effects on the participants with miscalibrated self-
+assessment get canceled. That may explain why the tutorial in-
+tervention does not show significant impact across experimental
+conditions. On the other hand, we did not find any support for
+effectiveness of logic units-based explanations in reliving DKE or
+facilitating appropriate reliance in analysis of H1 - H3.
+5.3
+Further Analysis On the DKE
+According to Dunning and Kruger [43], participants demonstrating
+the DKE are less competent and overestimate their performance.
+For further analysis of DKE in our study, we follow the method in
+the original study as well as consequent replications [29, 43], to split
+the participants in all conditions into performance-based quartiles.
+The top-quartile corresponds to those demonstrating high perfor-
+mance (top 25%), the bottom quartile corresponds to those with low
+performance (bottom 25%), and we combine the two quartiles in
+the middle comprising of participants with a medium level of per-
+formance in the first batch of tasks. As our tutorial is demonstrated
+to be effective in calibrating self-assessment, we do not take the
+second batch of tasks into consideration. In total, 101 participants
+among 249 participants showed an overestimation of performance
+in the first batch of tasks. In high accuracy group (63 participants),
+35 participants showed underestimation of their own performance,
+and 21 participants demonstrated accurate self-assessment, while
+only 7 participants (11.1%) show overestimation of performance
+in the first batch of tasks. In comparison, 46 participants (73.0%)
+in low accuracy group (63 participants) show an overestimation
+of performance in the first batch of tasks, while only 6 partici-
+pants and 11 participants showed underestimation of their perfor-
+mance and demonstrated accurate self-assessment, respectively.
+This aligns with the observation of Dunning and Kruger [16, 18]:
+top-performance group shows the tendency to underestimate their
+performance, while low-performance group shows tendency to
+overestimate their performance. With this observation, we can
+take low accuracy group as a representative group of participants
+with DKE, and take high accuracy group as a representative group
+of participants without DKE. This aligns with and validates our
+motivation to design a tutorial intervention to mitigate DKE, and
+improve self-assessment and appropriate reliance on AI systems.
+The impact of DKE on Reliance. To further analyze how the
+DKE affects user reliance on AI systems, we compared the reliance-
+based measures of high accuracy group and low accuracy group
+
+Knowing About Knowing: An Illusion of Human Competence Can Hinder Appropriate Reliance on AI Systems
+CHI ’23, April 23–28, 2023, Hamburg, Germany
+Table 6: Kruskal-Wallis H-test results for logic units-based explanations on performance improvement of reliance-based de-
+pendent variables.
+Participants
+Underestimation
+Overestimation
+Dependent Variables
+𝐻
+𝑝
+𝑀 ± 𝑆𝐷(Exp)
+𝑀 ± 𝑆𝐷(No Exp)
+𝐻
+𝑝
+𝑀 ± 𝑆𝐷(Exp)
+𝑀 ± 𝑆𝐷(No Exp)
+Accuracy
+0.00
+.963
+−0.19 ± 0.15
+−0.18 ± 0.24
+1.38
+.241
+0.10 ± 0.27
+0.00 ± 0.30
+Agreement Fraction
+0.00
+.963
+0.01 ± 0.25
+0.04 ± 0.32
+0.88
+.349
+0.01 ± 0.38
+−0.06 ± 0.28
+Switch Fraction
+0.04
+.843
+−0.03 ± 0.39
+0.04 ± 0.41
+0.02
+.884
+0.06 ± 0.47
+0.05 ± 0.33
+Accuracy-wid
+0.00
+.951
+−0.25 ± 0.30
+−0.22 ± 0.31
+0.50
+.478
+0.16 ± 0.36
+0.11 ± 0.39
+RAIR
+0.02
+.878
+−0.23 ± 0.48
+−0.24 ± 0.57
+0.00
+.968
+0.11 ± 0.46
+0.14 ± 0.46
+RSR
+0.96
+.327
+−0.33 ± 0.50
+−0.50 ± 0.51
+1.84
+.175
+0.35 ± 0.72
+0.10 ± 0.66
+Table 7: ANOVA test results for H4 on behavior-based dependent variables in the second batch of tasks.
+Dependent Variables
+Accuracy
+Agreement Fraction
+Switch Fraction
+Accuracy-wid
+RAIR
+RSR
+Variables
+𝐹
+𝑝
+𝐹
+𝑝
+𝐹
+𝑝
+𝐹
+𝑝
+𝐹
+𝑝
+𝐹
+𝑝
+Tutorial
+2.41
+.122
+3.74
+.054
+3.87
+.050
+1.63
+.203
+4.70
+.031
+0.20
+.652
+XAI
+2.10
+.148
+0.30
+.587
+1.00
+.319
+3.35
+.068
+2.05
+.153
+0.23
+.632
+Tutorial × XAI
+0.05
+.824
+0.00
+.990
+0.00
+.956
+0.10
+.746
+0.00
+.923
+0.05
+.832
+Table 8: Kruskal-Wallis H-test results for reliance-based
+measures on high accuracy group and low accuracy group.
+“††” indicates the effect of variable is significant at the level
+of 0.0125.
+Dependent Variables
+𝐻
+𝑝
+𝑀 ± 𝑆𝐷(High)
+𝑀 ± 𝑆𝐷(Low)
+Agreement Fraction
+54.68
+<.001††
+0.75 ± 0.15
+0.46 ± 0.18
+Switch Fraction
+13.09
+<.001††
+0.46 ± 0.32
+0.27 ± 0.21
+Accuracy-wid
+81.00
+<.001††
+0.74 ± 0.24
+0.21 ± 0.15
+RAIR
+25.71
+<.001††
+0.64 ± 0.45
+0.21 ± 0.21
+RSR
+46.41
+<.001††
+0.76 ± 0.39
+0.18 ± 0.37
+using a Kruskal-Wallis H-test. The results are shown in Table 8.
+Post-hoc Mann-Whitney tests using a Bonferroni-adjusted alpha
+level of 0.0125 ( 0.05
+4 ) also confirmed the significant difference. As
+we can see, participants in the low accuracy group (representative
+for participants with DKE) achieve a relatively poorer appropriate
+reliance than participants in the high accuracy group. Participants
+in the low accuracy group demonstrate significantly less reliance
+and appropriate reliance on AI systems, which also reflects that
+under-reliance is to blame for their low performance. We also com-
+pared the time spent by participants in the high accuracy group
+with participants in low accuracy group through a Kruskal-Wallis H-
+test. The difference of time spent on tasks between the two groups
+is non-significant (𝑝 = 0.018, borderline significance in Kruskal-
+Wallis H-test). On average, the high accuracy group spent around
+30 minutes (SD=12 minutes), while the low accuracy group spent
+around 34 minutes (SD=13 minutes). Interestingly, despite the fact
+that participants in the low accuracy group spent longer time on
+the task they still relied poorly on the AI system. This is consistent
+with what has been widely understood as an impact of the DKE
+metacognitive bias.
+5.4
+Further Analysis of Trust
+In addition to the behavior-based reliance measures, we also as-
+sessed the subjective trust of participants in AI systems. In this
+subsection, we explore the impact of our tutorial intervention and
+logic units-based explanation on user trust in the AI system.
+The effect of tutorial intervention on trust. To explore whether
+our tutorial intervention had any effect on user trust in AI system,
+we conducted Wilcoxon signed ranks test comparing the trust
+before and after the tutorial. On average, participants’ trust in
+the AI system does not show significant difference after the tutorial
+intervention (increased from 2.996 to 3.016; 𝑇 = 1063.5, 𝑝 = 0.952).
+This suggests that the main impact of the tutorial was on helping
+users calibrate their competence (i.e., their self-assessment) without
+directly shaping their trust in the AI system.
+Table 9: ANCOVA test results on trust-related dependent
+variables. With different self-assessmnet patterns, we divide
+all participants into three groups. “††” indicates the effect of
+variable is significant at the level of 0.0125.
+Variables
+𝐹
+𝑝
+𝜂2
+Group
+1.15
+.318
+.009
+ATI
+1.22
+.271
+.004
+TiA-PtT
+10.21
+.002††
+.040
+To further analyze how other covariates shape user trust in AI
+system, we decided to conduct AN(C)OVAs despite the anticipation
+that our data may not be normally distributed because these analy-
+ses have been shown to be robust to Likert-type ordinal data [60]. As
+no significant difference is found between the trust before and after
+the tutorial, we aggregated the trust across the two batches of tasks
+as users’ trust in the AI system. Considering our main hypothesis,
+we aimed to explore whether overestimation of performance and
+accurate self-assessment shape user trust in the AI system. For that
+purpose, we consider the three groups of participants (based on self-
+assessment, the same criteria in H1) with different self-assessment
+patterns. The results are shown in Table 9. As we can see, propensity
+to trust was the only user factor which corresponded to a significant
+impact on TiA-Trust. In a further Spearman rank-order test, we
+
+CHI ’23, April 23–28, 2023, Hamburg, Germany
+Gaole He, Lucie Kuiper, Ujwal Gadiraju
+observed that there is a significant positive correlation between
+TiA-PtT and TiA-Trust, 𝜌(249) = 0.22, 𝑝 < .001; suggesting a
+weak linear relationship between users’ propensity to trust an AI
+system and the subjective trust measured with respect to the AI sys-
+tem in our study. We also conducted the Spearman rank-order tests
+with TiA-PtT and other reliance-based variables. No significant
+correlation was found between TiA-PtT and reliance measures.
+6
+DISCUSSION
+6.1
+Key Findings
+Our analysis of the impact of miscalibrated self-assessment on re-
+liance suggests that participants with DKE tend to overestimate
+their own competence and rely less on AI systems, which results in
+under-reliance and much worse performance. To mitigate such cog-
+nitive bias, we introduced a tutorial intervention including perfor-
+mance feedback on tasks, alongside manually crafted explanations
+to contrast the correct answer with the users’ mistakes. Experi-
+mental results indicate that such an intervention is highly effective
+in calibrating self-assessment (significant improvement), and has
+some positive effect on mitigating under-reliance and promoting ap-
+propriate reliance (non-significant results). We also note that after
+making participants who overestimated their performance aware of
+their miscalibrated self-assessment, participants tend to rely more
+(appropriately) on the AI system (i.e., increased Switch Fraction
+and appropriate reliance measures, non-significant results, from
+Table 4) and achieve a higher performance improvement when
+logic units-based explanations are provided (insignificant results
+from Table 6). However, we did not find any significant evidence
+to support that the logic units-based explanations can amplify the
+effect of the tutorial intervention in calibrating self-assessment, or
+relieving the impact of DKE.
+The tutorial and calibrated self-assessment demonstrate a posi-
+tive impact in facilitating appropriate reliance for participants who
+overestimated themselves, but an opposite trend was observed on
+participants who underestimated themselves. We found such dif-
+ference can be explained partially by the change of self-assessment.
+The calibration of overestimation can bring positive impact, while
+the calibration of underestimation may also turn into overestima-
+tion or algorithm aversion, which may explain the decrease in
+performance and appropriate reliance. The tutorial was initially de-
+signed to reveal the shortcomings of participants with DKE. While
+for participants without DKE, there is a risk that some participants
+did not get exposed to their shortcomings in this tutorial and only
+found the AI system also made mistakes, which in turn even caused
+overestimation of themselves. An alternative explanation is that the
+performance feedback in tutorial intervention showed one mistake
+from the AI system, which led to algorithm aversion. As pointed out
+by [12]: “people more quickly lose confidence in algorithmic than
+human forecasters after seeing them make the same mistake.” These
+findings advance our current understanding of human-AI decision
+making, and provide useful insights that can drive guidelines for
+designing interventions to promote appropriate reliance.
+Positioning in Existing Literature. In our study, we found that
+DKE can have a negative impact on user reliance on the AI system
+and our proposed tutorial intervention can mitigate such an impact.
+In the context of human-AI decision making, DKE is closely relevant
+to a popular stream of research around user confidence[10, 33]. For
+the participants who overestimated their performance, the designed
+tutorial intervention calibrated their self-confidence (as reflected in
+their self-assessment) and facilitated appropriate reliance. In con-
+trast, the negative impact on participants who underestimated their
+performance can be explained by: (1) the calibrated self-assessment
+which can also bring over-confidence, or (2) their confidence/trust
+in the AI system being eroded by the observed mistake(s) of the AI
+system [3, 76]. The latter is consistent with findings in the literature
+on algorithm aversion [12]. More empirical studies are required
+to confirm and explain these observations, breeding promising
+grounds for future research.
+The participants with DKE show under-reliance on AI systems,
+which also aligns with the finding from Schaffer et al. [65]. Authors
+found that participants who reported higher familiarity with the
+task domain relied less on the intelligent assistant. The effective-
+ness of our tutorial intervention to calibrate self-assessment and
+mitigate under-reliance is also consistent with existing work using
+user tutorial / education interventions to mitigate unexpected and
+undesirable reliance patterns. All these tutorial interventions share
+a common objective of changing the mindset of users. For example,
+Chiang et al. [8] reported that user tutorials such as machine learn-
+ing literacy interventions can effectively help high-performance
+individuals to reduce over-reliance without affecting the reliance
+of low-performance individuals. Similarly, Chiang et al. [9] showed
+that a brief education session about the possible performance dis-
+parity of an ML model (on data with different distribution) can
+effectively reduce over-reliance on such cases. While their work
+focused more on changing human understanding of AI systems
+(performance, uncertainty, etc.), our work aims to help users cali-
+brate their competence (i.e., their self-assessment) on specific tasks.
+As a result, their main objective was to realize when AI systems are
+not reliable to reduce over-reliance, while we attempt to mitigate
+under-reliance for participants who overestimate themselves.
+Logic Units-based Explanations Do Not Have the Expected
+Effect. In our study, the logic units-based explanations did not aid
+in further amplifying the calibration effect of the tutorial interven-
+tion. This is in line with the findings of Wang et al. [79] and Schaffer
+et al. [65]. With a comparative study about four types of different
+explanations, authors found that “on decision making tasks that
+people are more knowledgeable, explanation that is considered to
+resemble how humans explain decisions (i.e., counterfactual expla-
+nation) does not seem to improve calibrated trust.” One potential ex-
+planation is that such explanations do not fulfill the three desiderata
+of AI explanations [79] (refer to section 2.1): the logic units-based
+explanations may help participants understand the AI, but fail to
+help them recognize the uncertainty underlying the AI or calibrate
+their trust in the AI in AI-assisted decision making. Another poten-
+tial cause is such explanations may introduce automation bias [65],
+which will cause over-reliance. Our results suggest that logic units-
+based explanations may still be hard to follow, because participants
+still need to connect and interpret the logic units by themselves.
+A limitation of our current work is that we did not gather explicit
+input from participants on their perceived understanding of the
+explanations. One further step to ground such logic units into read-
+able logical claims may work better for users. However, we do not
+
+Knowing About Knowing: An Illusion of Human Competence Can Hinder Appropriate Reliance on AI Systems
+CHI ’23, April 23–28, 2023, Hamburg, Germany
+deny the prospect that some XAI methods may have the potential
+to help mitigate DKE and calibrate user confidence in human-AI
+decision making. For example, contrastive explanations may work
+in the context of human-AI decision making [51, 59].
+6.2
+Implications
+As our findings suggest that participants with DKE tend to rely
+less on AI systems, it implies that future work should look more
+closely at the effects of self-assessment in human-AI collaboration.
+Although our tutorial intervention shows significant improvement
+in calibrating self-assessment, the improvement in appropriate re-
+liance is still limited (with borderline significance). Meanwhile, such
+calibration of self-assessment may even hurt the team performance
+for participants with initial underestimation of their performance.
+For these participants, the tutorial calibrated their underestimation,
+which may also lead to illusion of superior performance (overes-
+timation of themselves). In order to further promote appropriate
+reliance in human-AI collaboration, we need to develop more effec-
+tive human-centered tutorials. Meanwhile, participants who show
+lower performance in our scenario have significantly higher proba-
+bility to overestimate their performance, which aligns with DKE
+properties. Thus, we can leverage overestimation of individual per-
+formance as an indicator of such a meta-cognitive bias and further
+mitigate it with personalized or appropriate interventions.
+Guidelines for Tutorial Designs to Promote Appropriate Re-
+liance. While our tutorial intervention proved to be effective in
+helping users calibrate their self-assessment, accurate self-assessment
+does not necessarily translate to optimal appropriate reliance. Com-
+pared with participants with accurate self-assessment, the partici-
+pants with underestimation showed a significantly better perfor-
+mance in RSR (see Table 3), and calibrating such underestimation
+may even lead to decreased appropriate reliance (see Table 4), which
+indicates accurate self-assessment does not necessarily lead to op-
+timal appropriate reliance. One possible cause is that while the
+tutorial makes such users aware that they underestimated them-
+selves and they can make correct decisions when the AI system is
+wrong in the task, users may have an illusion of superior capability
+than the AI system. As a result, on some tasks where AI systems are
+more capable, users make mistakes by exhibiting under-reliance
+on the AI system due to recalibrated overestimation of their own
+competence. Our findings suggest that we should pay attention to
+avoiding such side effects of making users overestimate themselves
+in comparison to the AI system. To avoid such side effects, tutori-
+als designed to mitigate a specific kind of bias should be carefully
+checked before subjecting them to broad participant pools. This also
+implies that tutorials designed for promoting appropriate reliance
+should not only reveal the shortcomings of users or AI systems
+(i.e., when they are less capable of making the right decision), but
+also their strengths (i.e., when they are capable or more capable).
+This has useful implications for the future design of interventions
+to mitigate cognitive biases in human-AI decision making.
+In previous work on mitigating over-reliance with a tutorial
+intervention, researchers focused on revealing the AI systems’ brit-
+tleness [8, 9]. Combined with their findings, we argue that a more
+effective tutorial to promote appropriate reliance can be one that
+helps users understand both themselves and AI systems, and not
+only revealing the weakness but also showing the strengths of each.
+With such a comprehensive understanding, human decision mak-
+ers can potentially have a better chance to understand when they
+should rely on AI systems, and when they should rely on them-
+selves, ultimately leading to (more) appropriate reliance. More work
+is required to understand whether and how explanations can medi-
+ate this process of creating a better understanding among users of
+AI system capabilities in comparison to their own. This resonates
+with recent work exploring human-AI complementarity [3, 44, 52].
+6.3
+Caveats and Limitations
+Potential Biases. Our research questions focused on DKE and re-
+liance and how to mitigate such impact. As we cannot pre-identify
+which participants have DKE, we recruit the participants and deter-
+mine it with performance assessment. However, such assessment
+may be affected by other factors, which can lead to biased results.
+For example, although we relied on a pilot study to inform our
+task selection while creating two batches of tasks with comparable
+difficulty levels, we cannot be certain that they would be perceived
+the same way on average across the participants.
+As pointed out by Draws et al. [15], cognitive biases introduced
+by task design and workflow may have a negative impact on crowd-
+sourcing experiments. With the help of Cognitive Biases Checklist
+introduced [15], we analyzed potential bias in our study. Self-interest
+bias is possible, because crowd workers we recruited from the Pro-
+lific platform are motivated by monetary compensation. To alleviate
+any participants with low effort results, we put attention checks to
+remove ineligible participants from our study. As the question and
+context in Reclor dataset may be something participants familiar
+with, familiarity bias and availability bias can also affect our results.
+Transferability Concern. In our study, all analyses are based on
+the logical reasoning task, which most laypeople are capable of
+dealing with. However, in practice, the application scenarios may be
+affected by more factors (like user expertise, familiarity, and input
+modality). This gap can be a potential threat to the transferability of
+our findings and implications. However, Dunning and Kruger [43]
+showed that participants suffer from DKE across multiple scenarios:
+“participants scoring in the bottom quartile on tests of humor, gram-
+mar, and logic grossly overestimated their test performance and
+ability.” These effects were replicated in a number of other tasks,
+like human-AI collaboration [65] and crowdsourcing [63, 76]. Our
+findings are therefore highly relevant and can play an important
+role in informing the design for appropriate reliance in the context
+of human-AI interaction, collaboration, and teaming.
+7
+CONCLUSIONS AND FUTURE WORK
+In this paper, we present a quantitative study to understand the
+impact of the Dunning-Kruger effect (DKE) on reliance behavior of
+participants in a human-AI decision making context. We propose a
+tutorial intervention and explore its effectiveness in mitigating such
+an effect. Our results suggest that participants who overestimate
+their own performance tend to rely less on the AI system. Com-
+bined with the findings that participants with DKE show a much
+higher probability of overestimating their performance, we con-
+clude that participants with DKE rely less on AI systems, and such
+
+CHI ’23, April 23–28, 2023, Hamburg, Germany
+Gaole He, Lucie Kuiper, Ujwal Gadiraju
+under-reliance hinders them in achieving better performance on
+average (RQ1). Through a rigorous experimental setup and statisti-
+cal analysis, we found the effectiveness of our tutorial intervention
+in mitigating DKE (RQ2). However, we found that the tutorial may
+mislead some participants (i.e., participants who underestimated
+themselves) to overestimate their performance or exhibit algorithm
+aversion, which in turn harms their appropriate reliance on the AI
+system. Our findings suggest that, to fully mitigate the negative im-
+pact of the Dunning-Kruger effect and achieve appropriate reliance,
+more comprehensive, insightful, and personalized user tutorials
+are required. We reflected on guidelines for better tutorial designs
+based on our key findings.
+We found that our tutorial intervention failed to make a differ-
+ence in participants’ subjective trust in the AI systems. Instead, we
+found that users’ general propensity to trust has a significant im-
+pact on shaping their subjective trust in the AI system. Future work
+can further look into how user trust can be reshaped with different
+interventions or by using more effective explanations (e.g., con-
+trastive explanations or logical explanations in natural language).
+We hope the key findings and implications reported in this work
+will inspire further research on promoting appropriate reliance.
+ACKNOWLEDGMENTS
+This work was partially supported by the TU Delft Design@Scale AI
+Lab and the 4TU.CEE UNCAGE project. This work used the Dutch
+national e-infrastructure with the support of the SURF Cooperative
+using grant no. EINF-3888. We thank all participants from Prolific.
+REFERENCES
+[1] Ricardo Baeza-Yates. 2018. Bias on the web. Commun. ACM 61, 6 (2018), 54–61.
+[2] Gagan Bansal, Besmira Nushi, Ece Kamar, Walter S Lasecki, Daniel S Weld, and
+Eric Horvitz. 2019. Beyond accuracy: The role of mental models in human-AI
+team performance. In Proceedings of the AAAI Conference on Human Computation
+and Crowdsourcing, Vol. 7. 2–11.
+[3] Gagan Bansal, Tongshuang Wu, Joyce Zhou, Raymond Fok, Besmira Nushi, Ece
+Kamar, Marco Tulio Ribeiro, and Daniel Weld. 2021. Does the whole exceed
+its parts? the effect of ai explanations on complementary team performance. In
+Proceedings of the 2021 CHI Conference on Human Factors in Computing Systems.
+1–16.
+[4] Cynthia Sherraden Bradley, Kristina Thomas Dreifuerst, Brandon Kyle Johnson,
+and Ann Loomis. 2022. More than a Meme: The Dunning-Kruger Effect as an
+Opportunity for Positive Change in Nursing Education. Clinical Simulation in
+Nursing 66 (2022), 58–65.
+[5] Zana Buçinca, Maja Barbara Malaya, and Krzysztof Z Gajos. 2021. To trust or to
+think: cognitive forcing functions can reduce overreliance on AI in AI-assisted
+decision-making. Proceedings of the ACM on Human-Computer Interaction 5,
+CSCW1 (2021), 1–21.
+[6] Jason W Burton, Mari-Klara Stein, and Tina Blegind Jensen. 2020. A systematic
+review of algorithm aversion in augmented decision making. Journal of Behavioral
+Decision Making 33, 2 (2020), 220–239.
+[7] Noah Castelo, Maarten W Bos, and Donald R Lehmann. 2019. Task-dependent
+algorithm aversion. Journal of Marketing Research 56, 5 (2019), 809–825.
+[8] Chun-Wei Chiang and Ming Yin. 2022. Exploring the Effects of Machine Learning
+Literacy Interventions on Laypeople’s Reliance on Machine Learning Models.
+In IUI 2022: 27th International Conference on Intelligent User Interfaces, Helsinki,
+Finland, March 22 - 25, 2022, Giulio Jacucci, Samuel Kaski, Cristina Conati, Simone
+Stumpf, Tuukka Ruotsalo, and Krzysztof Gajos (Eds.). ACM, 148–161.
+[9] Chun-Wei Chiang and Ming Yin. 2021. You’d Better Stop! Understanding Human
+Reliance on Machine Learning Models under Covariate Shift. In 13th ACM Web
+Science Conference 2021. 120–129.
+[10] Leah Chong, Guanglu Zhang, Kosa Goucher-Lambert, Kenneth Kotovsky, and
+Jonathan Cagan. 2022. Human confidence in artificial intelligence and in them-
+selves: The evolution and impact of confidence on adoption of AI advice. Com-
+puters in Human Behavior 127 (2022), 107018.
+[11] Michael Chromik, Malin Eiband, Felicitas Buchner, Adrian Krüger, and Andreas
+Butz. 2021. I think i get your point, AI! the illusion of explanatory depth in
+explainable AI. In 26th International Conference on Intelligent User Interfaces.
+307–317.
+[12] Berkeley J Dietvorst, Joseph P Simmons, and Cade Massey. 2015. Algorithm
+aversion: people erroneously avoid algorithms after seeing them err. Journal of
+Experimental Psychology: General 144, 1 (2015), 114.
+[13] Berkeley J Dietvorst, Joseph P Simmons, and Cade Massey. 2018. Overcoming
+algorithm aversion: People will use imperfect algorithms if they can (even slightly)
+modify them. Management Science 64, 3 (2018), 1155–1170.
+[14] Nicole Dillen, Marko Ilievski, Edith Law, Lennart E Nacke, Krzysztof Czarnecki,
+and Oliver Schneider. 2020. Keep calm and ride along: Passenger comfort and
+anxiety as physiological responses to autonomous driving styles. In Proceedings
+of the 2020 CHI conference on human factors in computing systems. 1–13.
+[15] Tim Draws, Alisa Rieger, Oana Inel, Ujwal Gadiraju, and Nava Tintarev. 2021.
+A checklist to combat cognitive biases in crowdsourcing. In Proceedings of the
+AAAI Conference on Human Computation and Crowdsourcing, Vol. 9. 48–59.
+[16] David Dunning. 2011. The Dunning–Kruger effect: On being ignorant of one’s
+own ignorance. In Advances in experimental social psychology. Vol. 44. Elsevier,
+247–296.
+[17] David Dunning, Chip Heath, and Jerry M Suls. 2004. Flawed self-assessment:
+Implications for health, education, and the workplace. Psychological science in
+the public interest 5, 3 (2004), 69–106.
+[18] Joyce Ehrlinger, Kerri Johnson, Matthew Banner, David Dunning, and Justin
+Kruger. 2008. Why the unskilled are unaware: Further explorations of (absent)
+self-insight among the incompetent. Organizational behavior and human decision
+processes 105, 1 (2008), 98–121.
+[19] Upol Ehsan, Q Vera Liao, Michael Muller, Mark O Riedl, and Justin D Weisz.
+2021. Expanding explainability: Towards social transparency in ai systems. In
+Proceedings of the 2021 CHI Conference on Human Factors in Computing Systems.
+1–19.
+[20] Upol Ehsan and Mark O Riedl. 2020. Human-centered explainable ai: towards a re-
+flective sociotechnical approach. In International Conference on Human-Computer
+Interaction. Springer, 449–466.
+[21] Upol Ehsan, Philipp Wintersberger, Q Vera Liao, Martina Mara, Marc Streit,
+Sandra Wachter, Andreas Riener, and Mark O Riedl. 2021. Operationalizing
+Human-Centered Perspectives in Explainable AI. In Extended Abstracts of the
+2021 CHI Conference on Human Factors in Computing Systems. 1–6.
+[22] Upol Ehsan, Philipp Wintersberger, Q Vera Liao, Elizabeth Anne Watkins, Carina
+Manger, Hal Daumé III, Andreas Riener, and Mark O Riedl. 2022. Human-Centered
+Explainable AI (HCXAI): beyond opening the black-box of AI. In CHI Conference
+on Human Factors in Computing Systems Extended Abstracts. 1–7.
+[23] Alexander Erlei, Richeek Das, Lukas Meub, Avishek Anand, and Ujwal Gadiraju.
+2022. For What It’s Worth: Humans Overwrite Their Economic Self-interest
+to Avoid Bargaining With AI Systems. In CHI Conference on Human Factors in
+Computing Systems. 1–18.
+[24] Alexander Erlei, Franck Nekdem, Lukas Meub, Avishek Anand, and Ujwal Gadi-
+raju. 2020. Impact of algorithmic decision making on human behavior: Evidence
+from ultimatum bargaining. In Proceedings of the AAAI conference on human
+computation and crowdsourcing, Vol. 8. 43–52.
+[25] Franz Faul, Edgar Erdfelder, Axel Buchner, and Albert-Georg Lang. 2009. Sta-
+tistical power analyses using G* Power 3.1: Tests for correlation and regression
+analyses. Behavior research methods 41, 4 (2009), 1149–1160.
+[26] Jennifer Fereday and Eimear Muir-Cochrane. 2006. The role of performance
+feedback in the self-assessment of competence: a research study with nursing
+clinicians. Collegian 13, 1 (2006), 10–15.
+[27] Riccardo Fogliato, Alexandra Chouldechova, and Zachary Lipton. 2021. The
+impact of algorithmic risk assessments on human predictions and its analysis via
+crowdsourcing studies. Proceedings of the ACM on Human-Computer Interaction
+5, CSCW2 (2021), 1–24.
+[28] Thomas Franke, Christiane Attig, and Daniel Wessel. 2019. A personal resource
+for technology interaction: development and validation of the affinity for technol-
+ogy interaction (ATI) scale. International Journal of Human–Computer Interaction
+35, 6 (2019), 456–467.
+[29] Ujwal Gadiraju, Besnik Fetahu, Ricardo Kawase, Patrick Siehndel, and Stefan
+Dietze. 2017. Using worker self-assessments for competence-based pre-selection
+in crowdsourcing microtasks. ACM Transactions on Computer-Human Interaction
+(TOCHI) 24, 4 (2017), 1–26.
+[30] Ujwal Gadiraju, Ricardo Kawase, Stefan Dietze, and Gianluca Demartini. 2015.
+Understanding malicious behavior in crowdsourcing platforms: The case of online
+surveys. In Proceedings of the 33rd Annual ACM Conference on Human Factors in
+Computing Systems. 1631–1640.
+[31] Jan Gogoll and Matthias Uhl. 2018. Rage against the machine: Automation in
+the moral domain. Journal of Behavioral and Experimental Economics 74 (2018),
+97–103.
+[32] Ben Green and Yiling Chen. 2019. Disparate interactions: An algorithm-in-the-
+loop analysis of fairness in risk assessments. In Proceedings of the conference on
+fairness, accountability, and transparency. 90–99.
+[33] Ben Green and Yiling Chen. 2019. The principles and limits of algorithm-in-the-
+loop decision making. Proceedings of the ACM on Human-Computer Interaction 3,
+
+Knowing About Knowing: An Illusion of Human Competence Can Hinder Appropriate Reliance on AI Systems
+CHI ’23, April 23–28, 2023, Hamburg, Germany
+CSCW (2019), 1–24.
+[34] Ben Green and Yiling Chen. 2020. Algorithmic risk assessments can alter human
+decision-making processes in high-stakes government contexts. arXiv preprint
+arXiv:2012.05370 (2020).
+[35] Gaole He, Agathe Balayn, Stefan Buijsman, Jie Yang, and Ujwal Gadiraju. 2022.
+It Is Like Finding a Polar Bear in the Savannah! Concept-Level AI Explanations
+with Analogical Inference from Commonsense Knowledge. In Proceedings of the
+AAAI Conference on Human Computation and Crowdsourcing, Vol. 10. 89–101.
+[36] Robert R Hoffman, Shane T Mueller, Gary Klein, and Jordan Litman. 2018. Metrics
+for explainable AI: Challenges and prospects. arXiv preprint arXiv:1812.04608
+(2018).
+[37] Yoyo Tsung-Yu Hou and Malte F Jung. 2021. Who is the expert? Reconciling
+algorithm aversion and algorithm appreciation in AI-supported decision making.
+Proceedings of the ACM on Human-Computer Interaction 5, CSCW2 (2021), 1–25.
+[38] Christoph Hube, Besnik Fetahu, and Ujwal Gadiraju. 2019. Understanding and
+mitigating worker biases in the crowdsourced collection of subjective judgments.
+In Proceedings of the 2019 CHI Conference on Human Factors in Computing Systems.
+1–12.
+[39] Rachel A Jansen, Anna N Rafferty, and Thomas L Griffiths. 2021. A rational
+model of the Dunning–Kruger effect supports insensitivity to evidence in low
+performers. Nature Human Behaviour 5, 6 (2021), 756–763.
+[40] Ekaterina Jussupow, Izak Benbasat, and Armin Heinzl. 2020. Why are we averse
+towards Algorithms? A comprehensive literature Review on Algorithm aversion.
+In 28th European Conference on Information Systems - Liberty, Equality, and Fra-
+ternity in a Digitizing World, ECIS 2020, Marrakech, Morocco, June 15-17, 2020,
+Frantz Rowe, Redouane El Amrani, Moez Limayem, Sue Newell, Nancy Pouloudi,
+Eric van Heck, and Ali El Quammah (Eds.).
+[41] Moritz Körber. 2018. Theoretical considerations and development of a question-
+naire to measure trust in automation. In Congress of the International Ergonomics
+Association. Springer, 13–30.
+[42] Max F Kramer, Jana Schaich Borg, Vincent Conitzer, and Walter Sinnott-
+Armstrong. 2018. When do people want AI to make decisions?. In Proceedings of
+the 2018 AAAI/ACM Conference on AI, Ethics, and Society. 204–209.
+[43] Justin Kruger and David Dunning. 1999. Unskilled and unaware of it: how diffi-
+culties in recognizing one’s own incompetence lead to inflated self-assessments.
+Journal of personality and social psychology 77, 6 (1999), 1121.
+[44] Vivian Lai, Chacha Chen, Q Vera Liao, Alison Smith-Renner, and Chenhao Tan.
+2021. Towards a science of human-ai decision making: a survey of empirical
+studies. arXiv preprint arXiv:2112.11471 (2021).
+[45] Vivian Lai, Han Liu, and Chenhao Tan. 2020. "Why is ’Chicago’ deceptive?"
+Towards Building Model-Driven Tutorials for Humans. In CHI ’20: CHI Confer-
+ence on Human Factors in Computing Systems, Honolulu, HI, USA, April 25-30,
+2020, Regina Bernhaupt, Florian ’Floyd’ Mueller, David Verweij, Josh Andres,
+Joanna McGrenere, Andy Cockburn, Ignacio Avellino, Alix Goguey, Pernille Bjøn,
+Shengdong Zhao, Briane Paul Samson, and Rafal Kocielnik (Eds.). ACM, 1–13.
+[46] Vivian Lai and Chenhao Tan. 2019. On human predictions with explanations and
+predictions of machine learning models: A case study on deception detection. In
+Proceedings of the conference on fairness, accountability, and transparency. 29–38.
+[47] John D Lee and Katrina A See. 2004. Trust in automation: Designing for appro-
+priate reliance. Human factors 46, 1 (2004), 50–80.
+[48] Min Hun Lee, Daniel P Siewiorek, Asim Smailagic, Alexandre Bernardino, and
+Sergi Bermúdez i Badia. 2021. A human-ai collaborative approach for clinical
+decision making on rehabilitation assessment. In Proceedings of the 2021 CHI
+Conference on Human Factors in Computing Systems. 1–14.
+[49] Mengyao Li, Brittany E Holthausen, Rachel E Stuck, and Bruce N Walker. 2019.
+No risk no trust: Investigating perceived risk in highly automated driving. In
+Proceedings of the 11th International Conference on Automotive User Interfaces and
+Interactive Vehicular Applications. 177–185.
+[50] Q Vera Liao and Kush R Varshney. 2021. Human-Centered Explainable AI (XAI):
+From Algorithms to User Experiences. arXiv preprint arXiv:2110.10790 (2021).
+[51] Peter Lipton. 1990. Contrastive explanation. Royal Institute of Philosophy Supple-
+ments 27 (1990), 247–266.
+[52] Han Liu, Vivian Lai, and Chenhao Tan. 2021. Understanding the Effect of Out-
+of-distribution Examples and Interactive Explanations on Human-AI Decision
+Making. Proc. ACM Hum. Comput. Interact. 5, CSCW2 (2021), 1–45.
+[53] Jennifer M Logg, Julia A Minson, and Don A Moore. 2019. Algorithm appreciation:
+People prefer algorithmic to human judgment. Organizational Behavior and
+Human Decision Processes 151 (2019), 90–103.
+[54] Chiara Longoni, Andrea Bonezzi, and Carey K Morewedge. 2019. Resistance to
+medical artificial intelligence. Journal of Consumer Research 46, 4 (2019), 629–650.
+[55] Zhuoran Lu and Ming Yin. 2021. Human Reliance on Machine Learning Models
+When Performance Feedback is Limited: Heuristics and Risks. In CHI ’21: CHI
+Conference on Human Factors in Computing Systems, Virtual Event / Yokohama,
+Japan, May 8-13, 2021, Yoshifumi Kitamura, Aaron Quigley, Katherine Isbister,
+Takeo Igarashi, Pernille Bjørn, and Steven Mark Drucker (Eds.). ACM, 78:1–78:16.
+[56] Catherine C Marshall and Frank M Shipman. 2013. Experiences surveying the
+crowd: Reflections on methods, participation, and reliability. In Proceedings of
+the 5th Annual ACM Web Science Conference. 234–243.
+[57] Conor Thomas McKevitt. 2016. Engaging students with self-assessment and tutor
+feedback to improve performance and support assessment capacity. Journal of
+University Teaching & Learning Practice 13, 1 (2016), 2.
+[58] Scott Mayer McKinney, Marcin Sieniek, Varun Godbole, Jonathan Godwin,
+Natasha Antropova, Hutan Ashrafian, Trevor Back, Mary Chesus, Greg S Cor-
+rado, Ara Darzi, et al. 2020. International evaluation of an AI system for breast
+cancer screening. Nature 577, 7788 (2020), 89–94.
+[59] Tim Miller. 2021. Contrastive explanation: A structural-model approach. The
+Knowledge Engineering Review 36 (2021).
+[60] Geoff Norman. 2010. Likert scales, levels of measurement and the “laws” of
+statistics. Advances in health sciences education 15, 5 (2010), 625–632.
+[61] Amy Rechkemmer and Ming Yin. 2022. When Confidence Meets Accuracy:
+Exploring the Effects of Multiple Performance Indicators on Trust in Machine
+Learning Models. In CHI ’22: CHI Conference on Human Factors in Computing
+Systems, New Orleans, LA, USA, 29 April 2022 - 5 May 2022, Simone D. J. Barbosa,
+Cliff Lampe, Caroline Appert, David A. Shamma, Steven Mark Drucker, Julie R.
+Williamson, and Koji Yatani (Eds.). ACM, 535:1–535:14.
+[62] Vincent Robbemond, Oana Inel, and Ujwal Gadiraju. 2022. Understanding the
+Role of Explanation Modality in AI-assisted Decision-making. In Proceedings
+of the 30th ACM Conference on User Modeling, Adaptation and Personalization.
+223–233.
+[63] Ioannis Petros Samiotis, Sihang Qiu, Christoph Lofi, Jie Yang, Ujwal Gadiraju,
+and Alessandro Bozzon. 2021. Exploring the Music Perception Skills of Crowd
+Workers. In Proceedings of the AAAI Conference on Human Computation and
+Crowdsourcing, Vol. 9. 108–119.
+[64] James Sawler. 2021. Economics 101-ism and the Dunning-Kruger effect: Reducing
+overconfidence among introductory macroeconomics students. International
+Review of Economics Education 36 (2021), 100208.
+[65] James Schaffer, John O’Donovan, James Michaelis, Adrienne Raglin, and Tobias
+Höllerer. 2019. I Can Do Better than Your AI: Expertise and Explanations. In
+Proceedings of the 24th International Conference on Intelligent User Interfaces
+(Marina del Ray, California) (IUI ’19). Association for Computing Machinery, New
+York, NY, USA, 240–251.
+[66] Max Schemmer, Patrick Hemmer, Niklas Kühl, Carina Benz, and Gerhard Satzger.
+2022. Should I Follow AI-based Advice? Measuring Appropriate Reliance in
+Human-AI Decision-Making. In ACM Conference on Human Factors in Computing
+Systems (CHI’22), Workshop on Trust and Reliance in AI-Human Teams (trAIt).
+[67] Patrick Schramowski, Wolfgang Stammer, Stefano Teso, Anna Brugger, Franziska
+Herbert, Xiaoting Shao, Hans-Georg Luigs, Anne-Katrin Mahlein, and Kristian
+Kersting. 2020. Making deep neural networks right for the right scientific reasons
+by interacting with their explanations. Nature Machine Intelligence 2, 8 (2020),
+476–486.
+[68] Andrew Selbst and Julia Powles. 2018. "Meaningful Information" and the Right
+to Explanation. In Conference on Fairness, Accountability and Transparency, FAT
+2018, 23-24 February 2018, New York, NY, USA (Proceedings of Machine Learning
+Research, Vol. 81), Sorelle A. Friedler and Christo Wilson (Eds.). PMLR, 48.
+[69] Amit Sheth, Manas Gaur, Kaushik Roy, and Keyur Faldu. 2021. Knowledge-
+intensive language understanding for explainable AI. IEEE Internet Computing
+25, 5 (2021), 19–24.
+[70] Donghee Shin. 2022. Expanding the role of trust in the experience of algorith-
+mic journalism: User sensemaking of algorithmic heuristics in Korean users.
+Journalism Practice 16, 6 (2022), 1168–1191.
+[71] Donghee Shin. 2022. How do people judge the credibility of algorithmic sources?
+Ai & Society 37, 1 (2022), 81–96.
+[72] Donghee Shin, Kerk F Kee, and Emily Y Shin. 2022. Algorithm awareness: Why
+user awareness is critical for personal privacy in the adoption of algorithmic
+platforms? International Journal of Information Management 65 (2022), 102494.
+[73] Donghee Shin, Azmat Rasul, and Anestis Fotiadis. 2021. Why am I seeing this?
+Deconstructing algorithm literacy through the lens of users. Internet Research
+(2021).
+[74] Donghee Shin, Bouziane Zaid, Frank Biocca, and Azmat Rasul. 2022. In Platforms
+We Trust? Unlocking the Black-Box of News Algorithms through Interpretable
+AI. Journal of Broadcasting & Electronic Media (2022), 1–22.
+[75] Donghee Shin, Bouziane Zaid, and Mohammed Ibahrine. 2020. Algorithm appreci-
+ation: Algorithmic performance, developmental processes, and user interactions.
+In 2020 International Conference on Communications, Computing, Cybersecurity,
+and Informatics (CCCI). IEEE, 1–5.
+[76] Suzanne Tolmeijer, Ujwal Gadiraju, Ramya Ghantasala, Akshit Gupta, and Abra-
+ham Bernstein. 2021. Second Chance for a First Impression? Trust Development
+in Intelligent System Interaction. In Proceedings of the 29th ACM Conference on
+User Modeling, Adaptation and Personalization, UMAP 2021, Utrecht, The Nether-
+lands, June, 21-25, 2021, Judith Masthoff, Eelco Herder, Nava Tintarev, and Marko
+Tkalcic (Eds.). ACM, 77–87.
+[77] Richard Tomsett, Alun Preece, Dave Braines, Federico Cerutti, Supriyo
+Chakraborty, Mani Srivastava, Gavin Pearson, and Lance Kaplan. 2020. Rapid
+trust calibration through interpretable and uncertainty-aware AI. Patterns 1, 4
+(2020), 100049.
+
+CHI ’23, April 23–28, 2023, Hamburg, Germany
+Gaole He, Lucie Kuiper, Ujwal Gadiraju
+[78] Danding Wang, Qian Yang, Ashraf Abdul, and Brian Y Lim. 2019. Designing
+theory-driven user-centric explainable AI. In Proceedings of the 2019 CHI confer-
+ence on human factors in computing systems. 1–15.
+[79] Xinru Wang and Ming Yin. 2021. Are Explanations Helpful? A Comparative
+Study of the Effects of Explanations in AI-Assisted Decision-Making. In 26th
+International Conference on Intelligent User Interfaces. 318–328.
+[80] Fangzhi Xu, Jun Liu, Qika Lin, Yudai Pan, and Lingling Zhang. 2022. Logiformer:
+A Two-Branch Graph Transformer Network for Interpretable Logical Reasoning.
+In SIGIR ’22: The 45th International ACM SIGIR Conference on Research and Devel-
+opment in Information Retrieval, Madrid, Spain, July 11 - 15, 2022, Enrique Amigó,
+Pablo Castells, Julio Gonzalo, Ben Carterette, J. Shane Culpepper, and Gabriella
+Kazai (Eds.). ACM, 1055–1065.
+[81] Hanqi Yan, Lin Gui, and Yulan He. 2022. Hierarchical Interpretation of Neural
+Text Classification. arXiv preprint arXiv:2202.09792 (2022).
+[82] Ilan Yaniv and Eli Kleinberger. 2000. Advice taking in decision making: Egocentric
+discounting and reputation formation. Organizational behavior and human
+decision processes 83, 2 (2000), 260–281.
+[83] Ming Yin, Jennifer Wortman Vaughan, and Hanna Wallach. 2019. Understanding
+the effect of accuracy on trust in machine learning models. In Proceedings of the
+2019 chi conference on human factors in computing systems. 1–12.
+[84] Sangseok You, Cathy Liu Yang, and Xitong Li. 2022. Algorithmic versus Hu-
+man Advice: Does Presenting Prediction Performance Matter for Algorithm
+Appreciation? Journal of Management Information Systems 39, 2 (2022), 336–365.
+[85] Weihao Yu, Zihang Jiang, Yanfei Dong, and Jiashi Feng. 2020. ReClor: A Reading
+Comprehension Dataset Requiring Logical Reasoning. In International Conference
+on Learning Representations (ICLR).
+[86] Muhammad Bilal Zafar, Philipp Schmidt, Michele Donini, Cédric Archambeau,
+Felix Biessmann, Sanjiv Ranjan Das, and Krishnaram Kenthapadi. 2021. More
+Than Words: Towards Better Quality Interpretations of Text Classifiers. arXiv
+preprint arXiv:2112.12444 (2021).
+[87] Yunfeng Zhang, Q. Vera Liao, and Rachel K. E. Bellamy. 2020. Effect of confidence
+and explanation on accuracy and trust calibration in AI-assisted decision making.
+In FAT* ’20: Conference on Fairness, Accountability, and Transparency, Barcelona,
+Spain, January 27-30, 2020, Mireille Hildebrandt, Carlos Castillo, L. Elisa Celis,
+Salvatore Ruggieri, Linnet Taylor, and Gabriela Zanfir-Fortuna (Eds.). ACM, 295–
+305.
+
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+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf,len=1580
+page_content='Knowing About Knowing: An Illusion of Human Competence  Can Hinder Appropriate Reliance on AI Systems  Gaole He  Delft University of Technology  Delft, The Netherlands  g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='he@tudelft.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='nl  Lucie Kuiper  Delft University of Technology  Delft, The Netherlands  lucieakuiper@gmail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='com  Ujwal Gadiraju  Delft University of Technology  Delft, The Netherlands  u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='gadiraju@tudelft.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='nl  ABSTRACT  The dazzling promises of AI systems to augment humans in various  tasks hinge on whether humans can appropriately rely on them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  Recent research has shown that appropriate reliance is the key to  achieving complementary team performance in AI-assisted deci-  sion making.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' This paper addresses an under-explored problem of  whether the Dunning-Kruger Effect (DKE) among people can hinder  their appropriate reliance on AI systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' DKE is a metacognitive  bias due to which less-competent individuals overestimate their  own skill and performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Through an empirical study (𝑁 = 249),  we explored the impact of DKE on human reliance on an AI sys-  tem, and whether such effects can be mitigated using a tutorial  intervention that reveals the fallibility of AI advice, and exploiting  logic units-based explanations to improve user understanding of AI  advice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' We found that participants who overestimate their perfor-  mance tend to exhibit under-reliance on AI systems, which hinders  optimal team performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Logic units-based explanations did not  help users in either improving the calibration of their competence  or facilitating appropriate reliance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' While the tutorial intervention  was highly effective in helping users calibrate their self-assessment  and facilitating appropriate reliance among participants with over-  estimated self-assessment, we found that it can potentially hurt  the appropriate reliance of participants with underestimated self-  assessment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Our work has broad implications on the design of  methods to tackle user cognitive biases while facilitating appro-  priate reliance on AI systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Our findings advance the current  understanding of the role of self-assessment in shaping trust and  reliance in human-AI decision making.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' This lays out promising  future directions for relevant HCI research in this community.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  CCS CONCEPTS  Human-centered computing → Empirical studies in HCI;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  Computing methodologies → Artificial intelligence;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' • Ap-  plied computing → Law, social and behavioral sciences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  KEYWORDS  Human-AI Decision Making, Appropriate Reliance, XAI, Dunning-  Kruger Effect  Permission to make digital or hard copies of part or all of this work for personal or  classroom use is granted without fee provided that copies are not made or distributed  for profit or commercial advantage and that copies bear this notice and the full citation  on the first page.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Copyrights for third-party components of this work must be honored.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  For all other uses, contact the owner/author(s).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  CHI ’23, April 23–28, 2023, Hamburg, Germany  © 2023 Copyright held by the owner/author(s).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  ACM ISBN 978-1-4503-9421-5/23/04.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='1145/3544548.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='3581025  ACM Reference Format:  Gaole He, Lucie Kuiper, and Ujwal Gadiraju.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' 2023.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Knowing About Knowing:  An Illusion of Human Competence Can Hinder Appropriate Reliance on  AI Systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' In Proceedings of the 2023 CHI Conference on Human Factors in  Computing Systems (CHI ’23), April 23–28, 2023, Hamburg, Germany.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' ACM,  New York, NY, USA, 18 pages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='1145/3544548.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='3581025  1  INTRODUCTION  In the last decade, powerful AI systems (especially deep learning  systems) have shown better performance than human experts on  many tasks, sometimes outperforming humans by a large mar-  gin [58, 87].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Attracted by the predictive capability of such AI sys-  tems, researchers and practitioners have started to adopt such sys-  tems to support human decision makers in critical domains (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=', fi-  nancial [33], medical domains [48]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' With the wish of complemen-  tary team performance, one goal of such human-AI collaboration is  appropriate reliance: human decision makers rely on an AI system  when it is accurate (or perhaps more precisely, when it is more  accurate than humans) and do not rely on it when the system is  inaccurate (or, ideally, whenever it is wrong).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' In such a collabo-  rative decision process, human factors (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=', knowledge, mindset,  cognitive bias) and the explanations for AI advice are important  for trust in the AI system and for human reliance on the system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  Several prior works have carried out empirical studies within this  context of human-AI decision making, to explore the effectiveness  of different kinds of explanations and the role of human factors in  shaping such collaboration [3, 8, 24, 33, 52, 62, 79, 87].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  In recent literature exploring human-AI interaction, researchers  have shown a great interest in understanding what shapes user trust  and reliance on AI systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' They found that factors like first impres-  sion [76], AI literacy [8], risk perception [33, 34], and performance  feedback [55, 61] among others, play important roles in shaping  human trust and reliance on AI systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Explanations (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=', feature  attribution of input) have been found to be useful in promoting hu-  man understanding and adoption of AI advice [3, 52, 79, 87] and He  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' [35] recently proposed analogies as an instrument to increase  the intelligibility of explanations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' However, prior studies observed  improvements in performance in the presence of explanations only  when the AI system outperformed both the human and the best  team [3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' One reason for such phenomenon is under-reliance, which  indicates humans do not rely on accurate AI predictions as of-  ten as it is ideal to [23, 79, 82].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' In this work, we explore whether  Dunning-Kruger effect (DKE) [43] – a metacognitive bias due to  which individuals overestimate their competence and performance  – affects user reliance on AI systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' This a particularly important  metacognitive bias to understand in the context of human-AI de-  cision making, since one can intuitively understand how inflated  self-assessments and illusory superiority over an AI system can  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='11333v1  [cs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='HC]  25 Jan 2023  CHI ’23, April 23–28, 2023, Hamburg, Germany  Gaole He, Lucie Kuiper, Ujwal Gadiraju  result in overly relying on oneself or exhibiting under-reliance  on AI advice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' This can cloud human behavior in their interaction  with AI systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' However, to the best of our knowledge no prior  work has addressed this.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' In addition, DKE is closely related to user  confidence in decision making, which has been identified as an  important user factor and has been recently explored in the con-  text of human-AI decision making [10, 33].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' To achieve the goal  of appropriate reliance, users are expected to adequately calibrate  their self-confidence and their confidence in the AI system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Our  work can lead to fundamental HCI insights that can help facilitate  appropriate reliance of humans on AI systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  To explore the impact of DKE on user reliance, we need to first  identify participants who demonstrate the DKE (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=', participants  who perform relatively poorly but overestimate their performance).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  According to existing research on the DKE [16, 18], the participants  representing the bottom performance quartile tend to overestimate  their skill and depict an illusory superiority, while those in the  top performance quartile do not exhibit such a trend.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Researchers  have also operationalized self-assessments to serve as indicators of  competence in different online tasks [29].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Informed by such prior  work, we consider overestimated self-assessments in the context of  human-AI decision making as an indicator of the DKE and explore  it further.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Through an explicit analysis of participants’ performance  in the bottom quartile, we verified that the overestimation in their  performance is highly indicative of DKE in our study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' In this scope,  we explore whether we can design interventions to help users  improve their own calibration of their skills in the task at hand.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  Inspired by existing work in mitigating cognitive biases such  as the DKE [43] and promoting appropriate reliance [8, 45, 79],  we propose to leverage tutorials to calibrate their self-assessment  through revealing the actual performance level of participants with  performance feedback.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' In such a tutorial, after the initial decision  making, participants are provided with correct answers and expla-  nations to contrast with their final choice (if they make a wrong  choice).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' As pointed out by existing research [17], one cause of DKE  can be that people place too much confidence in the insightfulness  of their judgments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' When the correct answer differs from their  own choice, they may refrain from trusting such ground truth in  the absence of additional rationale.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' To ensure the effectiveness of  revealing users’ shortcomings, we provide them with contrastive  explanations which point out not only the reason for correct an-  swers, but also why their choice was incorrect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Based on prior work,  we expect such a training session to help users realize their errors  and calibrate their self-assessment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Furthermore, they become more  skillful at the task, which is also highlighted by Kruger et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' [43]  in mitigating DKE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  When AI advice disagrees with human decisions, the lack of ra-  tionales may be a reason not to adopt AI advice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' To help participants  interpret the AI advice, we leverage logic units-based explanations  which reveal the AI system’s internal states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' When users recognize  that an explanation provides reasonable evidence for supporting AI  advice, it is much easier for them to resolve disagreement in their  decision making.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' As a result, participants have a better opportunity  to know and understand when they “should” in fact rely on AI  systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' From this standpoint, effective explanations alongside the  tutorial may help mitigate the impact of the Dunning-Kruger Effect  on user reliance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' To analyze the impact of DKE on user reliance on  AI systems in this paper, we aim to find answers for the following  two research questions:  RQ1: How does the Dunning-Kruger Effect shape reliance  on AI systems?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  RQ2: How can the Dunning-Kruger Effect be mitigated in  human-AI decision making tasks?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  To answer these questions, and based on existing literature, we  proposed four hypotheses considering the effect of the overesti-  mation of performance on (appropriate) reliance, the effect of the  tutorial intervention on self-assessment calibration and reliance  for participants with miscalibrated self-assessment, the effect of  logic units-based explanations and tutorial intervention on reliance  and team performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' We tested these hypotheses in an empirical  study (𝑁 = 249) of human-AI collaborative decision making in a  logical reasoning task (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=', multi-choice logical question answer-  ing based on a context paragraph).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' We found a negative impact  of the DKE on human reliance behavior, where participants with  DKE relied significantly less on the AI system than their counter-  parts without DKE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' To mitigate such effects, we designed a tutorial  intervention for making users aware of their miscalibrated self-  assessment and provided logic units-based explanations to help  explain AI advice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Although we found that the intervention tutorial  was highly effective in improving participants’ self-assessments,  their improvement in appropriate reliance and performance is lim-  ited (statistically non-significant).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Moreover, no obvious benefits  were found with introducing logic units-based explanations in the  logical reasoning task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  Our results highlight that the overestimation of performance will  result in under-reliance, and such miscalibrated self-assessment can  be improved with our proposed tutorial intervention.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' We also found  that participants who overestimated their performance demon-  strated an increased appropriate reliance, which the calibration of  self-assessment can partially explain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' However, this was in contrast  to participants who initially underestimated their performance –  while they calibrated their self-assessment, they achieved signifi-  cantly worse appropriate reliance and performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' One potential  cause is that such tutorials help them recognize their actual per-  formance but also cause the illusion of superiority to AI systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  Such finding is also in line with algorithm aversion [12], where  users are less tolerant of the mistakes made by AI systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' In ad-  dition, we found that the users’ general propensity to trust goes  a long way in shaping trust in AI systems, despite our tutorial  not having an effect in reshaping subjective trust.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Based on the  results from our empirical study, we provide guidelines for design-  ing more comprehensive user tutorials and point out promising  future directions for further research around self-assessments in  the context of human-AI decision making.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Although we found that  miscalibrated self-assessments may hinder appropriate reliance  (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=', participants with DKE relied less on AI systems), the par-  ticipants with accurate self-assessment did not necessarily show  optimal appropriate reliance (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=', we found that participants with  underestimation showed better appropriate reliance and perfor-  mance).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' This interplay between self-assessment and reliance on AI  Knowing About Knowing: An Illusion of Human Competence Can Hinder Appropriate Reliance on AI Systems  CHI ’23, April 23–28, 2023, Hamburg, Germany  systems is potentially more complex than what can be explained  by a linear relationship and, therefore, deserves further research.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  In summary, we explored the effectiveness of a tutorial inter-  vention to mitigate the DKE and, in turn, facilitate appropriate  reliance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' We found evidence suggesting its effectiveness through an  empirical study in a logical reasoning task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Our work has important  implications for HCI research in the realm of human-AI interaction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  Our findings indicate that incorrect self-assessments and a preva-  lent meta-cognitive bias can affect user objective reliance on the AI  system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Thus, while designing for optimal human-AI interaction, it  is important to consider the extent to which users are aware of their  own abilities and that of the AI system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Our work is an important  first step towards furthering our understanding of how cognitive  biases shape human reliance on AI systems, an understudied aspect  in this quickly evolving realm of research.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Considering the unique  and evolving landscape of AI systems, the associated metaphors,  and end-user expectations that are mediated through abstractions  and their own experiences, we believe that studying the role of  the DKE in the human-AI decision making context is a timely and  unique contribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' We hope that our work can inform future  research on designing human-AI interactions that can facilitate  appropriate reliance on AI systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  2  BACKGROUND AND RELATED WORK  This paper contributes to the growing literature on human-AI  interaction, collaboration, and teaming, by exploring how the  Dunning-Kruger Effect shapes user reliance on AI systems  and whether such effect can be mitigated with a user tutorial  that highlights the fallibility of AI advice and logic units-  based explanation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Thus, we position our work in different strands  of related literature: the general literature on AI-assisted decision  making and what roles explanations play in such collaboration (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='1),  more specific literature on promoting appropriate reliance (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='2),  the contradicting literature on algorithm aversion and algorithm  appreciation (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='3), and finally the literature on self-assessments,  which has been explored in both psychology and other HCI studies  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='1  Human-AI Collaborative Decision Making  In recent years, AI-assisted decision making has received more and  more attention.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' In such collaboration, user factors and interaction  with AI systems are observed to be of much impact on final user be-  haviors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Among these work, most researchers are interested in how  users shape their trust in AI systems and how user behaviors will  be affected by AI systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Topics like performance feedback [2, 55],  risk perception [27, 34], uncertainty [77] and confidence [10, 79, 87]  of machine learning models, impact of explanations [3, 46] have  been extensively studied in human-AI decision making.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Meanwhile,  fairness, accountability, and transparency of incorporating AI sys-  tems for collaborative decision making received more and more  attention from a wide range of stakeholders [19, 21].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' For a more  comprehensive survey of existing work on Human-AI decision  making, readers can refer to [44].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  According to GDPR, the users of AI systems should have the  right to access meaningful explanations of model predictions [68].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  Under this perspective, more and more researchers have started to  provide human-centered explainable AI (XAI) solutions to promote  human-AI collaboration [20–22, 50, 78].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Up to now, the benefits  of incorporating XAI methods in human-AI collaboration are still  limited [3, 44].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' As reported by most existing work, though XAI  methods can aid understanding of AI advice, such effect does not  necessarily lead to clear performance improvement [3, 52].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' For in-  stance, Liu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' [52] observed that interactive explanations may  “reinforce human biases and lead to limited performance improve-  ment”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Based on a comprehensive literature review, Wang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' [79]  proposed three desiderata of AI explanations to promote appropri-  ate reliance: (1) critical for people to understand the AI, (2) recognize  the uncertainty underlying the AI, and (3) calibrate their trust in  the AI in AI-assisted decision making.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' With such ideal properties,  effective explanations may also potentially help participant realize  their weakness and mistake when they disagree with AI advice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  Under this perspective, we also explored whether logic units-based  explanations can help participants calibrate their self-assessment  and promote appropriate reliance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='2  Empirical Studies on Appropriate Reliance  AI systems and human decision makers are supposed to achieve  complementary team performance through taking advantage of  both powerful predictive capability of AI systems and flexibility of  human users to handle complex decision tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' However, existing  literature still struggles to find such complementary team perfor-  mance — in most empirical studies, AI alone performs much better  than human-AI team [44, 52].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' With further analysis, researchers  point out two main causes: (1) under-reliance, users fail to fully take  advantage of powerful AI systems, and (2) over-reliance, users fail  to rely on themselves when they actually outperform AI systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  To promote appropriate reliance, existing research mainly fo-  cused on mitigating under-reliance and over-reliance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Different in-  terventions like cognitive forcing functions [5], user tutorial [8, 9]  and explanations [79] are proved to be highly effective in mitigating  such unexpected reliance patterns.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Buçinca et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' [5] introduced  three types of cognitive functions to mitigate over-reliance: show  AI advice on demand, update decision with AI advice after the  initial decision, and keep participants waiting for a while before  providing advice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Their experimental results indicate that such cog-  nitive forcing functions are even more effective than simple XAI  methods in mitigating over-reliance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' With a comparative study  of four types of different explanations, Wang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' [79] reported  that feature importance and feature contribution explanations can  promote appropriate reliance with mitigating under-reliance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  “User tutorials, when presented in appropriate forms, can help  some people rely on ML models more appropriately” [8].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Another  important branch is educating users with user tutorials, which  stands out in recent years.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' On one hand, such user tutorials make  users aware of the weakness of AI systems, which further calibrate  user trust and reliance on AI systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' For example, Chiang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' [9]  found that a brief education session (to increase people’s awareness  of the machine learning model’s possible performance disparity  on different data) can effectively reduce over-reliance on out-of-  distribution data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' On the other hand, such a system can educate  participants with domain-specific knowledge extracted from an  AI system, which further improves users’ capability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' As a typical  CHI ’23, April 23–28, 2023, Hamburg, Germany  Gaole He, Lucie Kuiper, Ujwal Gadiraju  example, Lai et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' [45] proposed model-driven tutorials to help  humans understand patterns learned by models in a training phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  Inspired by this series of research, we also explored whether DKE  can be mitigated with user tutorial.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' For the purpose of calibrating  self-assessment, we include performance feedback and explanations  to contrast wrong user choice with correct answers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='3  Algorithm Aversion and Algorithm  Appreciation  In the face of intelligent predictive agents, which may outperform  human experts, people show two contradicting altitudes: Algo-  rithm Aversion and Algorithm Appreciation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Compared to human  forecasters, people more quickly lose confidence in AI systems af-  ter seeing them make the same mistakes [12].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Thus, some users  are reluctant to use superior but imperfect algorithms [6].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Such a  phenomenon is called “Algorithm Aversion,” which has been ob-  served across multiple domains, like moral decision making [31],  economic bargains [23], medical diagnosis [54], and autonomous  driving [14].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Burton et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' [6] summarized the cause and solution  of algorithm aversion with five aspects: expectations and exper-  tise, decision autonomy, incentivization, cognitive compatibility,  and divergent rationalities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Meanwhile, Dietvorst et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' [13] found  that such algorithm aversion can be overcome with the chance to  modify algorithm advice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Readers can refer to two recent survey  papers [6, 40] for a comprehensive literature review.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' In contrast,  Logg et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' [53] found that users were influenced more by the algo-  rithmic decision instead of human decision, and they first coined  the notion of “Algorithm Appreciation” to describe such a phenom-  enon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Others revealed similar findings in contexts where tasks are  perceived as being more objective [7], machines share rationale  with humans [75] or with prior exposure to similar systems [42].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  Besides contradicting attitudes towards the use of AI systems,  prior work has shown how different human factors such as algorith-  mic literacy [72], expertise [53], and cognitive load [84] can affect  users’ final adoption of algorithmic advice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' For example, users’  algorithmic literacy [71–73] about fairness, accountability, trans-  parency, and explainability is found to greatly affect their trust and  privacy concern in adopting the advice from AI systems [70, 74].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  Logg et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' [53] found that experts may even show more tendency  to discount algorithmic advice when compared to laypeople.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Fur-  thermore, these factors can also affect the extent to which users  show algorithm aversion or algorithm appreciation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' For instance,  You et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' [84] argue that algorithm appreciation declines when the  transparency of the advice source’s prediction performance further  increases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' In their study, they used a series of numbers instead of  aggregated average performance, which increases the transparency  of prediction performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' But they observed a decrease in algo-  rithm appreciation, which was explained by the greater cognitive  load imposed by the elaborated format.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' A recent work [37] found  that the choice of framings of human agents and algorithmic agents  may affect user perception of agent competence (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=', expert power),  which further affects user behavior and cause inconsistent obser-  vations of algorithm aversion and algorithm appreciation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' In this  work, since we explore means to facilitate appropriate reliance of  humans on AI systems, we position our findings in the context of  the research breaching algorithm aversion and appreciation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Future  work can further explore the role of algorithmic aversion and ap-  preciation in the context of interventions to facilitate appropriate  reliance on AI systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='4  Self-assessment in HCI Studies  Evaluating one’s own performance on a task, typically known as  “self-assessment”, is perceived as a fundamental skill, but people  appear to calibrate their abilities [39] poorly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' In general, most people  tend to overestimate their own abilities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' The cause of such an effect  is multi-fold, like people tend to think they are above average and  people place too much confidence in the insightfulness of their  judgments [17].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' With self-assessment, existing HCI research has  explored using it as a measure for different purposes: Gadiraju et  al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' [29] used self-assessment for competence-based pre-selection  in crowdsourcing marketplaces, Green et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' [33] measured users’  risk assessment with comparing self-reported confidence with their  actual performance, and Chromik et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' [11] compared perceived  understanding of XAI methods with their actual understanding to  reveal users’ illusion of explanatory depth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  Dunning-Kruger effect (DKE) [43] described the dual burden the  unskilled suffer from, besides the low performance, the unskilled  will also lack the skill to estimate their own ability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Kruger et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  also found that a training session to increase the skills of partic-  ipants is highly successful in mitigating such effect [43].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' It had  some positive effects and showed that by increasing knowledge, the  overestimation could also be reduced.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Further work also proved the  effectiveness of such training in different domains like medicine [4]  and economics [64].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  Besides the popularity in psychology research, Dunning-Kruger  effect was also studied in human-computer interaction field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' In a  recent study, Schaffer et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' [65] conducted a user study based on  Diner’s Dilemma game.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' They found that participants who consid-  ered themselves very familiar with the task domain showed more  trust in an intelligent assistant but relied less on it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Presenting ex-  planations was not as effective as expected, and sometimes even  resulted in automation bias.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Using logical reasoning tasks with  varying difficulty levels, Gadiraju et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' [29] showed that online  crowd workers also fall prey to the DKE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' The authors proposed  the use of self-assessments in a pre-selection strategy to improve  quality-related outcomes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Informed by prior literature, we selected  logical reasoning tasks as the exploratory lens to address our re-  search questions since the tasks themselves are straightforward to  understand for laypeople, but with increasing difficulty, they also  create room for inviting AI advice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' This serves suitably to study the  DKE in the context of human-AI decision making.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  3  METHOD AND HYPOTHESIS  In this section, we describe the logical reasoning task (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=', multi-  choice logical question answering based on a context paragraph)  and present our hypotheses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='1  Logical Reasoning Task  Prior work in the human-AI decision making context has explored  how one can reliably study human behavior in proxy tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' These  work has established the importance of designing tasks, where  users can find that there is a need to rely on AI (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=', owing to the  Knowing About Knowing: An Illusion of Human Competence Can Hinder Appropriate Reliance on AI Systems  CHI ’23, April 23–28, 2023, Hamburg, Germany  Figure 1: An example of a logical reasoning task used to  obtain an initial human decision in the two-stage decision  making process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  task difficulty or a perceivable benefit) and where there is a risk  associated with such reliance (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=', dealing with an imperfect AI  system) [5, 76].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' This follows from the work of Lee and See [47]  who defined trust in the Human-AI interaction context as “the  attitude that an agent will help achieve an individual’s goals in a  situation characterized by uncertainty and vulnerability.” The basis  for our experimental setup is a task where participants are asked  to choose an option in a multi-choice setting based on a paragraph  of context presented to them (an example of the interface page  is shown in Figure 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' We use the publicly available Reclor1 [85]  dataset to this end.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' The dataset corresponds to characteristically  high difficulty of logical reasoning tasks and has been used in prior  work exploring Human-AI team performance [3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' This task was  chosen as a realistic scenario for human-AI collaboration, where  humans incentivized to complete the task accurately, may have the  capability to reason accurately and find the right answer, but may  also evidently perceive a benefit in adopting AI advice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' In addition,  the Dunning-Kruger Effect which has been widely replicated in a  variety of contexts has been shown to be prevalent in the domain  of logical reasoning as well [16, 43].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  In the basic setting of the task, participants are presented with  three snippets of information: (1) a context paragraph, (2) a question  related to this context, and (3) four different options corresponding  to the question.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Among the four options, a single option is deemed  to be the best match to the question (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=', ground truth).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Participants  are asked to first go through the context paragraph, and then make  a choice based on the question.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' This simulates a realistic scenario  where participants make decisions in a reading comprehension set-  ting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' While humans are capable of handling such tasks, AI systems  may outperform them by extracting useful information and dealing  1https://whyu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='me/reclor/  with complex reasoning structures which require a larger working  memory capacity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' The task interface is shown in Figure 2(a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  Two-stage Decision Making.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' To analyze human reliance on AI  systems, all participants in our study worked on tasks with a two-  stage decision making process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' In the first stage, only task informa-  tion was provided, and participants were asked to make decisions  themselves (example shown in Figure 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' After that, we showed  the same task with AI advice (and explanations depending on the  experimental condition) and provided an opportunity for the par-  ticipants to alter their initial choice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' An example of second stage is  shown in Figure 2(a), where “Your choice” shows the initial decision  participants made in the first stage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' This setup of an initial unaided  decision and the presentation of advice from an AI system in order  to make a second and final choice is similar to the update condition  in [33], and in line with findings that people first make a decision  on their own and only then decide whether to incorporate system  advice [32].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' It also fits with the research of Dietvorst et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' [13] on  trust in two-stage decision making.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  Quality Control.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' To ensure participant reliability and that partici-  pants worked on the logical reasoning tasks genuinely (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=', read  the context paragraph and question carefully), we employed three  attention check questions during the study process [56].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' For this  purpose, we embedded explicit instructions asking participants to  select a specific option either in the context paragraph (once) or  the question (twice).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' For example, we embedded the instruction,  “Confirm that you have read the context by selecting answer B.” into  a context paragraph on the task interface (which looks nearly iden-  tical to other tasks).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' A conservative estimate through trial runs  reflected that participants would take at least 1 minute to complete  each task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' As a further quality control measure, we deactivated the  submit button corresponding to each task page (including tasks in  tutorial phase) for 30 seconds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Since attention check pages do not  require deliberation, we reduced that time to 5 seconds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='2  Logic Units-based Explanations  In natural language processing tasks, feature attribution methods  (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=', text highlights on input) are the most popular in existing  literature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' However, multiple pieces of research work point out that  such token-level highlights are still hard to interpret [69, 81, 86].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  Meanwhile, since logical reasoning tasks highlight the potential for  logical reasoning congruent to human understanding, explanations  based on logic units (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=', text spans) may be a better choice to reveal  how AI systems reach their final decision.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' With this perspective,  we drew inspiration from LogiFormer, proposed by Xu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' [80],  who conducted logical reasoning with logic units based on pre-  trained language models to generate such explanations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' LogiFormer  adopted a graph transformer network for logical reasoning of logic  units, where the logic units are text spans connected with causal  relations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Following this interpretability design,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' we also relied on  the self-attention matrix A ∈ R𝑛×𝑛 (n indicates the number of logic  units) from the last layer of the graph transformer network and  identified the important logic units with the following formula:  𝐸 = 𝐴𝑟𝑔𝑚𝑎𝑥𝑘 (  𝑗=𝑛  ∑︁  𝑗=1  A𝑖𝑗),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  (1)  Tasks  Context  Physician: In comparing our country with two other countries of roughly the same population size,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  I found that even though we face the same dietary,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' bacterial,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' and stress-related causes of ulcers as  they do,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' prescriptions for ulcer medicines in all socioeconomic strata are much rarer here than in  those two countries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=" It's clear that we suffer significantly fewer ulcers, per capita, than they do." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content="  Task 1/16  Which one of the following, if true, most strengthens the physician's argument?" metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content="  The two countries that were compared  The physician's country has a much better  with the physician's country had  system for reporting the number of  approximately the same ulcer rates as  prescriptions of a given type that are  each other." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  obtained each year than is present in  either of the other two countries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content="  A person in the physician's country who is  Several other countries not covered in the  suffering from ulcers is just as likely to  physician's comparisons have more  obtain a prescription for the ailment as is  prescriptions for ulcer medication than  a person suffering from ulcers in one of  does the physician's country." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  the other two countries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  Confirm and continueCHI ’23, April 23–28, 2023, Hamburg, Germany  Gaole He, Lucie Kuiper, Ujwal Gadiraju  (a) Logical question answering page with AI advice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  (b) Tutorial page with manual explanation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  Figure 2: Screenshots of the task interface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' In panel (a), the logic units-based explanations are highlighted with a light blue  background color in the context paragraph and the option suggested by the AI system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' In panel (b), we show the rationale of  correct answers in contrast with users’ final choice at the bottom (when users do not select the correct answer in the decision  making stage) at the bottom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  where 𝐸 is the top-𝑘 logic units which receive most attention  from other logic units (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=', we calculated it with the sum along  each column of the self-attention matrix).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' One example of such  explanation is shown in figure 2(a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  Our implementation and extracted logic units-based explana-  tions can be found in Github repo.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='2 To generate the explanations  described above, we first trained the LogiFormer model on the Re-  clor dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' With the trained model, we generated logic units-based  explanations according to Equation 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' In this study, we specify𝑘 = 5  to highlight the most important logic units for each task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Notice  that, such explanations are generated for each option, and the spans  are only extracted from the context paragraph and each option.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' For  more details about the LogiFormer model, we refer readers to the  original paper [80] and the corresponding implementation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='3  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='3  Proposing a Tutorial Intervention to Help  Users Calibrate Their Skills  To answer RQ2, we need to verify whether our proposed interven-  tion can help mitigate the DKE among the same participants who  demonstrated it in the absence of the intervention.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' This requires  two batches of tasks that can facilitate comparative performance  2https://github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='com/RichardHGL/CHI2023_DKE  3https://github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='com/xufangzhi/Logiformer  assessment and on which participants can be asked to self-assess  their performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Based on the effectiveness of tutorials as inter-  ventions in previous HCI literature [8, 9, 45], we designed a tutorial  as a means to shed light on the fallibility of AI advice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' In our pa-  per, we, therefore, considered the tutorial as an intervention and  analyzed its effectiveness by comparing participants’ reliance and  self-assessment before and after the tutorial was delivered.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Inspired  by existing work to mitigate different kinds of cognitive biases  through revealing such biases to users [1, 38], we decided to adopt  a tutorial to help users calibrate their skills through self-assessment  on logical reasoning tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' To this end, we designed a tutorial with  the aim of revealing to users that they may not be as capable in such  tasks as they may believe.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Furthermore, to ensure the effectiveness  of revealing their mistakes, we designed persuasive explanations  for users.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' To achieve that goal, we chose to provide contrastive  explanations which point out not only the reason for correct an-  swers but also the reason to reject users’ wrong choices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' As none  of the existing off-the-shelf toolkits can be used to obtain such  strongly persuasive explanations, we manually created explana-  tions for each option in the four tasks considered in the tutorial  phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' These explanations corresponding to each task have also  been made available on the Open Science Framework companion  page.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' An example of such performance feedback and contrastive  explanation can be found in Figure 2(b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' On this page,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=" we showed  Tasks  Context  A study of young children's ability to learn foreign languages found that those with  parents who read them more than one book per week in their native language were  75% more proficient in the foreign languages that they learned than children whose  that children's ability to remember new vocabulary in a second language drops off  sharply after the age of 6," metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' when it becomes 75% more difficult to retain new words  learned in the second language  Task 2/16  Assuming the statements above are true,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' which of the following can be inferred from  them?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  A  The ease of learning a second  Students whose parents enter  B  language depends almost  them in early education and who  exclusively on environmental  read to them frequently are more  Al advice  factors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  likely to have extra income and  more free time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  D  Students who begin studying a  Proficient speakers of a second  language later in life would have  languagearelikelyto havebegur  Your choice  had an easier time learning some  learning it before the age of 6  aspects of that language if they  D  had begun studying it as a young  child.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  Confirm and continueTasks  Context  When doctors vaccinate a patient, their intention is to expose him or her to a  Correct  weakened form of a disease-causing pathogen and thus to make the patient better  answer  able to resist the pathogen and less likely to develop a severe form of that disease  later.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  D  Task 8/16  Which one of the following best illustrates the principle that the passage illustrates?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  A In some circumstances, firefighters B Some police departments  use fire to fight fire by creating an  energetically pursue those who  Al advice  intense explosion very close to an  commit minor crimes;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' in doing so  uncontrollable blaze that they wish  they intend to provide examples to  A  to extinguish, thus momentarily  deter people who might be  depriving it of the oxygen it needs  tempted to commit more-serious  to continue burning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  crimes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  Your choice  C In some cases, a business will  Some parents read their children  close down some of its operations,  fairy tales containing allegorical  its intention being to position the  treatments of treachery and  company to be more profitable  cruelty, with the intention of  later even though this involves  making them less emotionally  expenses in the current period.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  vulnerable to these phenomena  when they encounter them later in  life.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  The answer is D rather than C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' In answer C the problem is solved by cutting down profit in the  beginning but growing it later on.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' However, in this context, the problem is solved by giving exposure  to a weakened version.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' In answer D the fairy tales also act as a weakened version of treachery and  cruelty to which the children are exposed, thus making the principles align.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  Confirm and continueKnowing About Knowing: An Illusion of Human Competence Can Hinder Appropriate Reliance on AI Systems  CHI ’23, April 23–28, 2023, Hamburg, Germany  the correct answer in a box with light blue background color.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' The  final decision of the participant after receiving AI advice, and the AI  advice itself are shown in boxes with a dark blue background color.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  The contrastive explanation is shown at the bottom of this page.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  Through such a performance feedback intervention, we hope that  users with inflated self-assessments can realize their true capability  with respect to the tasks and recalibrate their self-assessment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Such  an intervention can potentially help users improve their reliance  on AI systems [36].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='4  Pilot Study for Task Selection  To answer our research questions, we need to analyze the impact  of the Dunning-Kruger effect on reliance measures and the effec-  tiveness of the proposed intervention to mitigate such an effect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  Note that the Dunning-Kruger effect corresponds to one’s skills in a  given task [16].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' To operationalize this, we need two batches of tasks  with similar difficulty levels, through which we can verify the effec-  tiveness of the intervention by comparing performance before and  after the intervention.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Meanwhile, for the tutorial tasks, we need  tasks that may trigger the Dunning-Kruger effect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' In other words,  tasks that participants may make mistakes on with high confidence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  For these purposes, we conducted a pilot study with 10 participants  from the Prolific crowdsourcing platform.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='4 In the pilot study, each  participant worked on 30 questions randomly sampled from the  validation set of the Reclor dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' We collected their choice and  confidence level for each task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' With six participants who passed all  the attention checks, we assessed the difficulty of each task based  on the number of participants who answered the task correctly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  Considering that most participants spend around 1 minute to fully  understand a task and make a decision, we considered the batch  size to be six.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' We collected two batches of tasks which are of similar  difficulty (informed by the average accuracy on the tasks in the  pilot study).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' To make the tutorial effective but not cumbersome, we  selected four tasks for the tutorial.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' The tasks for the tutorial were  selected in a similar fashion as the other batches, as the tutorial  only has four questions instead of six, the tasks with the lowest and  highest accuracy were removed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Such selection strategy creates  a batch similar in difficulty to the other batches.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Among the four  tasks, we configured the AI advice to be correct on two of them and  misleading on the other two.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' All participants were rewarded with  hourly wage of £7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='5 (estimated completion time was 33 minutes),  and extra bonus of £0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='05 for each correct decision.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='5  Hypotheses  Our experiment was designed to answer questions surrounding the  impact of Dunning-Kruger effect on user reliance on AI systems,  and how to mitigate such potentially undesirable impact.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' People  who are less competent in a task struggle more with estimating their  own performance in the task, compared to the more competent  counterparts [43].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Impacted by DKE, users with the option to rely  on AI advice may overestimate their own performance in a task and  tend to rely on themselves when they are actually less capable than  the AI systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Apart from them, some users can exhibit accurate  self-assessment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Such accurate self-assessments can be indicative  of a good understanding of the task difficulty and personal skills,  4https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='prolific.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='co/  which may help these users rely on AI systems more appropriately.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  Meanwhile, effective explanations may amplify such an effect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Thus,  we hypothesize that:  (H1) Users overestimating their own performance will  demonstrate relatively less reliance on AI systems than users  demonstrating accurate self-assessment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  According to previous work [26, 57], interventions that provide  users with feedback on their performance may help improve their  self-assessment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' By providing users with an opportunity to reflect  on their skills and recalibrate their skills on the given task, we  argue that the impact of the DKE can be mitigated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' As a result of an  improved calibration of oneself, such users are better suited to rely  on AI systems appropriately when making decisions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Therefore, we  hypothesize that:  (H2) Making users aware of their miscalibrated self-  assessment, will help them improve their self-assessment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  (H3) Making users aware of their miscalibrated self-  assessment will result in relatively more appropriate reliance  on AI systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  Performance feedback can potentially help participants improve  their self-assessment, which may facilitate appropriate reliance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  At the same time, explanations have been shown to improve the  human understanding and interpretation of AI advice [3, 52, 79],  which can also potentially contribute to appropriate reliance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Thus,  we hypothesize to observe the following in a human-AI decision  making context:  (H4) Providing performance feedback and meaningful ex-  planations can facilitate appropriate reliance on the AI system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  4  STUDY DESIGN  This section describes our experimental conditions, variables, sta-  tistical analysis, procedure, and participants in our main study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='1  Experimental Conditions  In our study, all participants worked on logical reasoning tasks  with two-stage decision making process (described in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' The  only difference is whether tutorial is presented and whether ex-  planations are provided along with AI advice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' To comprehensively  study the effect of each factor and their interaction effect, we con-  sidered a 2 × 2 factorial design with four experimental conditions:  (1) no tutorial, no XAI (represented as × Tutorial,× XAI), (2)  with tutorial, no XAI (represented as ✓ Tutorial,× XAI), (3) no  tutorial, with XAI (represented as × Tutorial,✓ XAI), (4) with  tutorial, with XAI (represented as ✓ Tutorial,✓ XAI).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' In condi-  tions with tutorial, participants were presented with four selected  tasks with performance feedback and contrastive explanation for  correct answers against wrong choice (when participants missed  the wrong answer).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' While in conditions without tutorial, the four  CHI ’23, April 23–28, 2023, Hamburg, Germany  Gaole He, Lucie Kuiper, Ujwal Gadiraju  Table 1: The different appropriate reliance patterns consid-  ered in [66].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' 𝑑𝑖 is initial human decision, while 𝑑𝑓 is the final  decision after AI advice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  𝑑𝑖  AI advice  𝑑𝑓  Reliance  Incorrect  Correct  Correct  Positive AI reliance  Incorrect  Correct  Incorrect  Negative self-reliance  Correct  Incorrect  Correct  Positive self-reliance  Correct  Incorrect  Incorrect  Negative AI reliance  tasks selected are presented as normal tasks without any perfor-  mance feedback or explanation for correct answers, to prevent any  learning effect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' In conditions with XAI, the top-5 most important  logic units are highlighted as an explanation for AI advice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  For each batch of six tasks, the AI system was configured to  provide correct advice on four of them and misleading advice on  two tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' So the accuracy of AI systems is around 66.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='7%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' To avoid  any ordering effect, we randomly assign one batch of tasks as first  batch of tasks for each participant and further shuffled the order of  tasks within each batch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='2  Measures and Variables  We measure the reliance of participants on the AI system via two  metrics: the Agreement Fraction and the Switch Fraction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' These  look at the degree to which participants are in agreement with AI  advice, and how often they adopt AI advice in cases of initial dis-  agreement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' They are commonly used in the literature, for example  in [83, 87].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' In addition, we consider the accuracy in batches to  measure participants’ performance with AI assistance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Since cases  without initial disagreement do not clearly signal reliance on the  system we restrict the scope of the appropriate reliance measure to  accurately understand how participants handle divergent system  advice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Max et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' [66] presented four conditions of appropriate  reliance patterns (see Table 1) when the disagreement exists and  correct answer exists in human initial decision or AI advice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' We  followed them to adopt Relative positive AI reliance (RAIR) and Rel-  ative positive self-reliance (RSR) as appropriate reliance measures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  The two measures assessed users’ appropriate reliance from two  dimensions, which can help analyze the dynamics of reliance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' To  provide an overview of participants’ appropriate reliance under  initial disagreement, we considered Accuracy-wid (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=', accuracy  with initial disagreement).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' These measures are computed as follows:  Agreement Fraction = Number of decisions same as the system  Total number of decisions  ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  Switch Fraction = Number of decisions user switched to agree with the system  Total number of decisions with initial disagreement  ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  Accuracy = Number of correct final decisions  Total number of decisions  ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  Accuracy-wid = Number of correct final decisions with initial disagreement  Total number of decisions with initial disagreement  ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  RAIR =  Positive AI reliance  Positive AI reliance + Negative self-reliance,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  RSR =  Positive self-reliance  Positive self-reliance + Negative AI reliance .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  To measure the self-assessment of users, we gathered responses on  the following question after each batch of tasks – “From the previ-  ous 6 questions, how many questions do you estimate to have been  answered correctly?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' (after receiving AI advice)”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Comparing that es-  timation with the actual correct number, we can calculate the degree  of miscalibration and self-assessment as: Degree of Miscalibra-  tion = |Estimated correct number - Actual correct number|, Self-  assessment = Estimated correct number - Actual correct number.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  Meanwhile, for conditions with explanations, we also assessed the  helpfulness of explanations with the question, “To what extent  was the explanation (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=', the highlighted words/phrases) helpful in  making your final decision?”' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Responses were gathered on a 5-point  Likert scale from 1 to 5 corresponding to the labels not helpful, very  slightly helpful, slightly helpful, helpful, very helpful.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  For a deeper analysis of our results, a number of additional  measures were considered based on observations from existing  literature [49, 67, 76]:  Trust in Automation (TiA) questionnaire [41], a validated  instrument to measure (subjective) trust [76].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' In this study  we adopted two subscales: Propensity to Trust (TiA-PtT),  Trust in Automation (TiA-Trust).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Thus, we consider possible  effects of trust on reliance, in accordance with Lee et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' [47].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  Affinity for Technology Interaction Scale (ATI) [28], admin-  istered in the pre-task questionnaire.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Thus, we account for  the effect of participants’ affinity with technology on their  reliance on systems [76].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  Table 2 presents an overview of all the variables considered in  our study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='3  Participants  Sample Size Estimation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Before recruiting participants, we com-  puted the required sample size in a power analysis for the 2 × 2  factorial design using G*Power [25].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' To correct for error-inflation as  a result of testing multiple hypotheses, we applied a Bonferroni cor-  rection so that the significance threshold decreased to 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='05  4  = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='0125.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  We specified the default effect size 𝑓 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='25 (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=', indicating a mod-  erate effect), a significance threshold 𝛼 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='0125 (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=', due to testing  multiple hypotheses), a statistical power of (1 − 𝛽) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='8, and the  consideration of 4 different experimental conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' This resulted  in a required sample size of 244 participants.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' We thereby recruited  314 participants from the crowdsourcing platform Prolific5, in order  to accommodate potential exclusion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  Compensation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' All participants were rewarded with £2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='5, amount-  ing to an hourly wage of £7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='5 (estimated completion time was 20  minutes).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' We rewarded participants with extra bonuses of £0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='1 for  every correct decision in the 16 trial cases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' By incentivizing partici-  pants to reach a correct decision, we operationalize the concomitant  "vulnerability" discussed by Lee and See [47] as a contextual re-  quirement to encourage appropriate system reliance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  Filter Criteria.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' All participants were proficient English speakers  above the age of 18 and they had an approval rate of at least 90% on  the Prolific platform.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' We excluded participants from our analysis  if they failed at least one attention check (65 participants).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' The  resulting sample of 249 participants had an average age of 38 (𝑆𝐷 =  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='8) and a gender distribution (48.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='6% female, 51.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='4% male).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  5https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='prolific.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='co  Knowing About Knowing: An Illusion of Human Competence Can Hinder Appropriate Reliance on AI Systems  CHI ’23, April 23–28, 2023, Hamburg, Germany  Table 2: The different variables considered in our experimental study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' “DV” refers to the dependent variable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' RAIR, RSR, and  Accuracy-wid are indicators of appropriate reliance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  Variable Type  Variable Name  Value Type  Value Scale  Performance (DV)  Accuracy  Continuous, Interval  [0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='0, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='0]  Accuracy-wid  Continuous  [0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='0, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='0]  Reliance (DV)  Agreement Fraction  Continuous, Interval  [0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='0, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='0]  Switch Fraction  Continuous  [0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='0, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='0]  RAIR  Continuous  [0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='0, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='0]  RSR  Continuous  [0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='0, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='0]  Assessment (DV)  Degree of Miscalibration  Continuous, Interval  [0,6]  Self-assessment  Continuous, Interval  [-6,6]  Trust (DV)  TiA-Trust  Likert  5-point, 1:strong distrust, 5: strong trust  Covariates  ATI  Likert  6-point, 1: low, 6: high  TiA-PtT  Likert  5-point, 1: tend to distrust, 5: tend to trust  Other  Helpfulness of Explanation  Likert  5-point, 1: not helpful, 5: very helpful  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='4  Procedure  The full procedure that participants followed in our study is illus-  trated in Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' All participants first read the same basic instruc-  tions on the logical reasoning task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Next, participants were asked  to complete a pre-task questionnaire to measure their propensity  to trust and affinity for technology interaction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  Instructions  Pre-task  Questionnaire  Task Batch 1  Tutorial Batch  Task Batch 2  Post-task  Questionnaire  ATI, TiA-PtT  Post-task  Questionnaire  Done  Start  Self-assessment,  TiA-trust  Self-assessment, TiA-  trust, helpfulness of  explanations  6 trial cases  4 trial cases,  Performance feedback  6 trial cases  Figure 3: Illustration of the procedure participants followed  within our study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' This flow chart describes the experimen-  tal condition ✓ Tutorial,✓ XAI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Blue boxes represent the  questionnaire phase, orange boxes represent the task phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  Participants were then assigned to one experimental condition,  which differed in whether or not tutorial feedback is provided and  the system’s prediction is supplemented with explanation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' In ×  Tutorial,× XAI and × Tutorial,✓ XAI conditions, participants  worked on the four trial cases without any difference with the task  batch, no extra information was provided.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' After that, participants  will work on 16 tasks (two task phases with six tasks, and one  tutorial phase with four tasks).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Selection of these cases is described  in section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' After each task phase, post-task questionnaires were  adopted to assess their self-assessment and trust in AI systems (TiA-  trust).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Participants in the × Tutorial,✓ XAI and ✓ Tutorial,✓  XAI conditions were additionally asked for their perceived help-  fulness of the explanations they were presented with.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' To further  ensure the reliability of responses gathered in the questionnaire and  the task phases, we added four attention check questions spread  out at random through the different stages of the procedure [30].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  5  RESULTS  In this section, we present the results of our study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' We discuss  descriptive statistics, the outcomes of the hypothesis tests we con-  ducted, and our exploratory findings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Our code and data can be  found on Github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='6  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='1  Descriptive Statistics  In our analysis, we only kept participants who passed all atten-  tion checks, which deemed to be more reliable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Participants were  distributed in a balanced fashion over the four experimental condi-  tions as follows: 63 (× Tutorial,× XAI), 62 (✓ Tutorial,× XAI),  62 (× Tutorial,✓ XAI), 62 (✓ Tutorial,✓ XAI).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' On average,  participants spend around 32 minutes (𝑆𝐷 = 11 minutes) in our  study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' We found no significant difference in the time spent across  the four experimental conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  Figure 4: Distribution of participants with underestimated,  accurate, and overestimated self-assessment across all ex-  perimental conditions in the first batch of tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  Distribution of Covariates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' The covariates’ distribution is as fol-  lows: ATI (𝑀 = 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='73, 𝑆𝐷 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='99, 6-point Likert scale, and 1: low, 6:  6https://github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='com/RichardHGL/CHI2023_DKE  Under  25  Accurate  Over  20  15  10  5  NoTutorial.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  With Tutorial.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  NoTutorial  WithTutorial.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  No XAI  No XAI  WithXAI  WithXAI  ConditionCHI ’23, April 23–28, 2023, Hamburg, Germany  Gaole He, Lucie Kuiper, Ujwal Gadiraju  Table 3: Kruskal-Wallis H-test results for inflated self-assessments (H1) on reliance-based dependent variables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' “††” indicates  the effect of variable is significant at the level of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='0125.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' “Under”, “Accurate”, abd “Over” refers to participants who underesti-  mated , accurately estimated, and overestimated their performance on the first batch of tasks, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  Dependent Variables  𝐻  𝑝  𝑀 ± 𝑆𝐷(Under)  𝑀 ± 𝑆𝐷(Accurate)  𝑀 ± 𝑆𝐷(Over)  Post-hoc results  Accuracy  74.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='06  <.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='001††  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='72 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='16  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='61 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='15  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='45 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='19  Under > Accurate > Over  Agreement Fraction  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='87  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='004††  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='70 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='18  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='69 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='21  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='59 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='24  Under, Accurate > Over  Switch Fraction  23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='31  <.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='001††  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='50 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='28  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='53 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='31  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='32 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='32  Under, Accurate > Over  Accuracy-wid  87.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='94  <.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='001††  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='65 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='21  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='53 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='27  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='28 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='22  Under > Accurate > Over  RAIR  46.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='91  <.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='001††  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='65 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='36  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='58 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='37  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='27 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='33  Under, Accurate > Over  RSR  30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='23  <.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='001††  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='67 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='44  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='41 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='47  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='27 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='43  Under > Accurate, Over  high), TiA-Propensity to Trust (𝑀 = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='95, 𝑆𝐷 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='60, 5-point Likert  scale, 1: tend to distrust, 5: tend to trust).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  Distribution of Participants.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Among 249 participants, we identi-  fied the participants who underestimated their performance (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=', Self-  assessment < 0), those with an accurate self-assessment (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=', Self-  assessment = 0), and those with overestimation of their perfor-  mance (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=', Self-assessment > 0) according to their performance in  the first batch of tasks (shown in Figure 4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' In general, participants  showed relatively balanced distribution into the three types of self-  assessment across conditions: (1) the number of participants with  underestimated self-assessment lies in the range of 15 ∼ 20, (2) the  number of participants with accurate self-assessment lies in the  range of 15 ∼ 25, (3) the number of participants with overestimated  self-assessment was in the range of 20 ∼ 30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' We also compared  the time spent by participants with different self-assessment and  participants with different experimental conditions, and found no  statistically significant difference with Kruskal-Wallis H-tests.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  Figure 5: Distribution of participants with perceived helpful-  ness of logic units-based explanations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  For participants in conditions with explanation (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=', [× Tutorial,  ✓ XAI] and [✓ Tutorial,✓ XAI]), we assessed the helpfulness of  logic units-based explanations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' The ratios of perceived helpfulness  are illustrated with Figure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' As we can see, most people (57.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='2%)  think it slightly or very slightly helpful, while only 28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='3% partici-  pants show positive feedback to the logic units-based explanations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  Performance Overview.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' On average across all conditions, par-  ticipants achieved an accuracy of 56.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='9% (𝑆𝐷 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='16) over the two  batches of tasks, still lower than the aforementioned AI accuracy  of 66.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='7%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' The agreement fraction is 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='665 (𝑆𝐷 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='17) while the  switching fraction is 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='453 (𝑆𝐷 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='27).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' With these measures, we  confirm that when disagreement appears participants in our study  did not always switch to AI advice or blindly rely on the AI system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  As all dependent variables are not normally distributed, we used  non-parametric statistical tests to verify our hypotheses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='2  Hypothesis Tests  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='1  H1: effect of inflated self-assessments on AI system reliance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  To analyze the main effect of participants’ inflated self-assessment  (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=', overestimation of performance) on their reliance on the AI  system, we conducted Kruskal-Wallis H-tests by considering how  participants varied in their self-assessment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' We categorize all partic-  ipants into three groups according to the self-assessment: (1) partic-  ipants who underestimated their performance (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=', Self-assessment  < 0), (2) participants with accurate performance self-assessment  (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=', Self-assessment = 0), and (3) participants who overestimated  their performance (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=', Self-assessment > 0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' For this analysis, we  considered all participants across the four experimental conditions,  and the performance metrics are calculated based on the first batch  of tasks (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=', 6 tasks).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' The results are shown in Table 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  Effect of Overestimated Self-Assessments on Objective Re-  liance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' For all reliance-based measures, we found a statistically  significant difference between the performance of the participants  who overestimated their performance and those with accurate  self-assessment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Post-hoc Mann-Whitney tests using a Bonferroni-  adjusted alpha level of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='0125 ( 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='05  4 ) were used to make pairwise  comparisons of performance, revealing that participants who did  not overestimate their performance in fact performed significantly  better than those who did (The only exception is on metric RSR).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  Overall, participants with accurate self-assessment and underes-  timation of their own performance performed much better than  participants who overestimated their own performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' The main  reason is that they showed more reliance on the AI system and  achieved better appropriate reliance when their initial decision dis-  agreed with AI advice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' The results indicate that participants who  overestimate their own performance rely significantly less on AI  systems compared to those who do not.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Due to such under-reliance  and inappropriate reliance when initial disagreement exists, they  achieved a significantly lower accuracy on average.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Thus, we find  support for hypothesis H1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  We also found that participants who underestimated their per-  formance achieved significantly higher Accuracy, Accuracy-wid,  Very Slightly Helpful  39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='5%  Not Helpful  14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='5%  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='5%  Very Helpful  17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='7%  21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='8%  Slightly Helpful  HelpfulKnowing About Knowing: An Illusion of Human Competence Can Hinder Appropriate Reliance on AI Systems  CHI ’23, April 23–28, 2023, Hamburg, Germany  Table 4: Wilcoxon signed ranks test results for H3 on reliance-based dependent variables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' For participants with initial underes-  timation, we report results with one-sided hypothesis that the performance / reliance decrease after tutorial.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' For participants  with initial overestimation, we report results with one-sided hypothesis that the performance / reliance increase after tutorial.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  “†” and “††” indicates the effect of variable is significant at the level of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='05 and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='0125, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  Participants  Underestimation  Overestimation  Dependent Variables  𝑇  𝑝  𝑀 ± 𝑆𝐷(first)  𝑀 ± 𝑆𝐷(second)  Trend  𝑇  𝑝  𝑀 ± 𝑆𝐷(first)  𝑀 ± 𝑆𝐷(second)  Trend  Accuracy  407.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='5  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='000††  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='73 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='17  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='55 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='21  ↓  303.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='0  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='075  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='46 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='18  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='51 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='22 Agreement Fraction  212.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='5  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='543  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='68 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='20  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='70 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='23 451.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='0  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='605  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='60 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='23  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='57 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='23 Switch Fraction  267.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='5  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='592  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='47 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='29  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='48 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='36 367.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='5  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='147  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='31 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='33  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='36 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='31 Accuracy-wid  418.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='0  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='000††  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='68 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='22  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='44 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='29  ↓  338.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='0  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='013†  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='27 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='20  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='41 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='28  ↑  RAIR  313.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='0  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='006††  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='68 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='37  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='45 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='38  ↓  194.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='0  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='038†  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='24 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='32  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='36 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='36  ↑  RSR  204.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='0  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='000††  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='72 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='43  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='30 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='44  ↓  151.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='0  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='020†  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='29 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='45  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='52 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='48  ↑  and RSR than participants demonstrating accurate self-assessment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  Since they showed similar degrees of reliance (Agreement Frac-  tion and Switch Fraction) on the AI system, the improvement of  overall accuracy is mainly due to appropriate reliance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' In general,  they showed significantly better RSR, which indicates that they  have a better chance to rely on themselves to make correct decisions  when they initially disagree with misleading AI advice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  In the first batch of tasks, we found no difference (with Kruskal-  Wallis H-tests) in reliance and accuracy metrics when comparing  participants in XAI conditions (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=', × Tutorial,✓ XAI and ✓  Tutorial,✓ XAI) with participants in non-XAI (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=', × Tutorial,×  XAI and ✓ Tutorial,× XAI).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' To verify how the provided logic  units-based explanations affect participants with different self-  assessments, we compared the performance and reliance measures  of participants with XAI and without XAI in underestimation, ac-  curate self-assessment, and overestimation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' No significant effects  were found from the logic units-based explanation on performance  and reliance for participants with overestimated self-assessment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='2  H2: effect of the tutorial on self-assessment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  To verify H2, we used Wilcoxon signed rank tests to compare  the performance of participants before and after the tutorial.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' We  considered participants who are provided with the tutorial for self-  assessment calibration (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=', ✓ Tutorial,× XAI and ✓ Tutorial,✓  XAI).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Meanwhile, we exclude participants who have accurate as-  sessment on the first batch of tasks from this analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Finally, we  have 87 participants reserved for analysis of H2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' On average, the  participants’ self-assessment get improved after receiving the tuto-  rial (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=', decreased Degree of Miscalibration, 𝑀 ±𝑆𝐷(first) = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='67  ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='91, 𝑀 ±𝑆𝐷(second) = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='14 ± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='04;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' a smaller value indicates more  accurate self-assessment).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' A Wilcoxon signed rank test indicated  that the difference was statistically significant, 𝑇=1175.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='0, 𝑝<0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='001,  which supports H2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' To further check how the tutorial intervention  has an impact on participants with different types of miscalibration,  we separately conducted Wilcoxon signed rank tests on partici-  pants underestimating their own performance and overestimating  their own performance separately.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' The results indicate that: (1) par-  ticipants underestimating their own performance calibrated their  self-assessment, the difference is significant (𝑇=229.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='0, 𝑝=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='002);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' (2)  participants overestimating their own performance calibrated their  self-assessment, the difference is significant (𝑇=381.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='5, 𝑝=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' The  detailed analysis of participants with different types of miscalibra-  tion also supports H2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  To further explore the effect of logic units-based explanation on  calibrating self-assessment, we conducted a Kruskal-Wallis H-test  (among these participants) by considering whether the explanation  is provided.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' We found no significant results, which indicates that  logic units-based explanations cannot amplify the effect of the  tutorial intervention (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=', calibrating self-assessment).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='3  H3: effect of the tutorial on appropriate reliance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  Similar to the analysis for H2, we only considered the participants  who showed miscalibration in the first batch of tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Overall, there  is no significant difference in reliance and performance measures  when we compare the participants’ performance before and af-  ter receiving the tutorial.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' To further check how our tutorial in-  tervention will affect participants with different miscalibration of  self-assessment, we conducted analysis for participants with under-  estimation and overestimation separately.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' The results of Wilcoxon  signed rank tests corresponding to each of the reliance measures  are shown in Table 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Both participants with underestimation and  overestimation did not show any significant difference in reliance  measures (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=', Agreement Fraction and Switch Fraction).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' For  participants who underestimated their performance in the first  batch of tasks, they showed significantly worse performance and  appropriate reliance after receiving the tutorial.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' In contrast, we  found some improvement of Accuracy and appropriate reliance  measures (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=', Accuracy-wid, RAIR, RSR) for participants who  overestimated their performance in the first batch of tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' How-  ever, the improvement is non-significant at the level of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='0125.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Thus,  on the whole, we find partial support for H3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  Meanwhile, to check how the tutorial intervention affects the  participants with initial accurate self-assessment, we also conducted  Wilcoxon signed rank tests for their performance before and after  the tutorial intervention.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' No significant difference is found.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Com-  bined with the findings from participants with initial miscalibration,  we found that: (1) the designed tutorial intervention does not show  much impact on participants with accurate self-assessment, (2) the  designed tutorial intervention has positive impact on appropri-  ate reliance for participants who initially overestimate themselves,  while negative impact on participants with initial underestimation  of their performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  Relation Between Self-assessment Calibration and the Change  in Reliance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' To further explore the relationship between the change  in self-assessment and change with (appropriate) reliance, we con-  ducted the Spearman rank-order test separately for participants  CHI ’23, April 23–28, 2023, Hamburg, Germany  Gaole He, Lucie Kuiper, Ujwal Gadiraju  with overestimation and underestimation in the first batch of tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  As the impact of tutorial intervention on Agreement Fraction  and Switch Fraction is insignificant, we ignore the two metrics  in calculating the correlation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' The results are shown in Table 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  We found a strong negative monotonic relationship between the  two variables in participants with overestimation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Thus, in logical  reasoning tasks, the calibration effect in self-assessment accounted  for 59.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='3% of the improved Accuracy (𝜌2 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='593, 𝑝 < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='001), 55.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='5%  of the improved Accuracy-wid (𝜌2 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='555, 𝑝 < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='001), 32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='0% of  the improved RAIR (𝜌2 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='320, 𝑝 < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='001), and 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='9% of the im-  proved RSR (𝜌2 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='129, 𝑝 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='005).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Similarly, the calibration of  self-assessment also accounted for 26.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='2% of the decreased Accu-  racy (𝜌2 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='262, 𝑝 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='001), 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='8% of the decreased Accuracy-wid  (𝜌2 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='148, 𝑝 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='009) for participants with underestimation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  Table 5: Correlation of self-assessment change and reliance  change.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' “††” indicates the effect of variable is significant at  the level of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='0125.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' “†” indicates the effect of variable is sig-  nificant at the level of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='05.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  Participants  Underestimation  Overestimation  Dependent Variables  𝜌  𝑝  𝜌  𝑝  Accuracy  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='512  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='001††  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='770  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='000††  Accuracy-wid  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='385  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='009††  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='745  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='000††  RAIR  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='293  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='039†  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='566  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='000††  RSR  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='349  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='068  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='359  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='005††  In general, for all participants with miscalibrated self-assessment,  the difference in self-assessment shows strong negative correlation  with the difference in performance and appropriate reliance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' In  other words, the increase in self-assessment (trend to overestima-  tion) will lead to decrease in performance and appropriate reliance,  which is consistent with our findings in H1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' While the signifi-  cant negative correlation exists for performance measures in all  participants with miscalibrated self-assessment, only participants  with overestimation showed significant correlation (in the level  of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='0125) with RAIR and RSR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' The difference indicates that the  change of self-assessment can hardly explain why participants with  underestimation showed worse appropriate reliance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  To further explore the impact of logic units-based explanations  on performance improvement (the difference between performance  metrics from the second batch of tasks and those from the first  batch of tasks), we conducted a Kruskal-Wallis H-test (among these  participants) by considering whether explanations are provided.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  Overall, no significant difference is found for all behavior-based  dependent variables considering all 87 participants who showed  miscalibration in the first batch and then received the tutorial inter-  vention.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' We further check the logic units-based explanation impact  according to participants with underestimation (37 participants)  and overestimation (50 participants) respectively (cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Table 6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' No  significant difference is found for all behavior-based dependent  variables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Although participants with explanations show better per-  formance improvement in RSR, such difference is not significant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='4  H4: Two-factor analysis for final performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  To verify H4, we conducted a two-way ANOVA to compare the  performance and (appropriate) reliance measures of participants  under the effect of providing tutorial intervention and logic units-  based explanations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' In this analysis, only the second batch of tasks  are taken into consideration, as the performance of the first batch  of tasks is not affected by the tutorial intervention.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' According to  the test results shown in Table 7, no significant impact (in the  significance level of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='0125) is found for tutorial intervention, logic  units-based explanations and their interaction effect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Thus, H4 is  not supported.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  According to the results of H3, the tutorial intervention shows  positive impact on participants with initial overestimation, no sig-  nificant effect on participants with accurate self-assessment, and  negative impact on participants with initial underestimation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' As  indicated by Figure 4, the participants show compatible distribu-  tion in the three groups with different initial self-assessment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' The  contradicting effects on the participants with miscalibrated self-  assessment get canceled.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' That may explain why the tutorial in-  tervention does not show significant impact across experimental  conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' On the other hand, we did not find any support for  effectiveness of logic units-based explanations in reliving DKE or  facilitating appropriate reliance in analysis of H1 - H3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='3  Further Analysis On the DKE  According to Dunning and Kruger [43], participants demonstrating  the DKE are less competent and overestimate their performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  For further analysis of DKE in our study, we follow the method in  the original study as well as consequent replications [29, 43], to split  the participants in all conditions into performance-based quartiles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  The top-quartile corresponds to those demonstrating high perfor-  mance (top 25%), the bottom quartile corresponds to those with low  performance (bottom 25%), and we combine the two quartiles in  the middle comprising of participants with a medium level of per-  formance in the first batch of tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' As our tutorial is demonstrated  to be effective in calibrating self-assessment, we do not take the  second batch of tasks into consideration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' In total, 101 participants  among 249 participants showed an overestimation of performance  in the first batch of tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' In high accuracy group (63 participants),  35 participants showed underestimation of their own performance,  and 21 participants demonstrated accurate self-assessment, while  only 7 participants (11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='1%) show overestimation of performance  in the first batch of tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' In comparison, 46 participants (73.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='0%)  in low accuracy group (63 participants) show an overestimation  of performance in the first batch of tasks, while only 6 partici-  pants and 11 participants showed underestimation of their perfor-  mance and demonstrated accurate self-assessment, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  This aligns with the observation of Dunning and Kruger [16, 18]:  top-performance group shows the tendency to underestimate their  performance, while low-performance group shows tendency to  overestimate their performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' With this observation, we can  take low accuracy group as a representative group of participants  with DKE, and take high accuracy group as a representative group  of participants without DKE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' This aligns with and validates our  motivation to design a tutorial intervention to mitigate DKE, and  improve self-assessment and appropriate reliance on AI systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  The impact of DKE on Reliance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' To further analyze how the  DKE affects user reliance on AI systems, we compared the reliance-  based measures of high accuracy group and low accuracy group  Knowing About Knowing: An Illusion of Human Competence Can Hinder Appropriate Reliance on AI Systems  CHI ’23, April 23–28, 2023, Hamburg, Germany  Table 6: Kruskal-Wallis H-test results for logic units-based explanations on performance improvement of reliance-based de-  pendent variables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  Participants  Underestimation  Overestimation  Dependent Variables  𝐻  𝑝  𝑀 ± 𝑆𝐷(Exp)  𝑀 ± 𝑆𝐷(No Exp)  𝐻  𝑝  𝑀 ± 𝑆𝐷(Exp)  𝑀 ± 𝑆𝐷(No Exp)  Accuracy  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='00  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='963  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='19 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='15  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='18 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='24  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='38  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='241  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='10 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='27  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='00 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='30  Agreement Fraction  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='00  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='963  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='01 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='25  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='04 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='32  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='88  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
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+page_content='01 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='38  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='06 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='28  Switch Fraction  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='04  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='843  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='03 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='39  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='04 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='41  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='02  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='884  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='06 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='47  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='05 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='33  Accuracy-wid  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='00  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='951  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='25 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='30  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='22 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='31  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='50  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='478  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='16 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='36  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='11 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='39  RAIR  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='02  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='878  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='23 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='48  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='24 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='57  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='00  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='968  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='11 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='46  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='14 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='46  RSR  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='96  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='327  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='33 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='50  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='50 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='51  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
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+page_content='35 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='72  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='10 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='66  Table 7: ANOVA test results for H4 on behavior-based dependent variables in the second batch of tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  Dependent Variables  Accuracy  Agreement Fraction  Switch Fraction  Accuracy-wid  RAIR  RSR  Variables  𝐹  𝑝  𝐹  𝑝  𝐹  𝑝  𝐹  𝑝  𝐹  𝑝  𝐹  𝑝  Tutorial  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='41  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
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+page_content='652  XAI  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='10  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
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+page_content='632  Tutorial × XAI  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='05  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
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+page_content='956  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='10  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='746  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='00  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='923  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
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+page_content='832  Table 8: Kruskal-Wallis H-test results for reliance-based  measures on high accuracy group and low accuracy group.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  “††” indicates the effect of variable is significant at the level  of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='0125.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  Dependent Variables  𝐻  𝑝  𝑀 ± 𝑆𝐷(High)  𝑀 ± 𝑆𝐷(Low)  Agreement Fraction  54.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='68  <.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='001††  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='75 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='15  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='46 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='18  Switch Fraction  13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='09  <.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='001††  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='46 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='32  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='27 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='21  Accuracy-wid  81.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='00  <.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='001††  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='74 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='24  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='21 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='15  RAIR  25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='71  <.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='001††  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='64 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='45  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='21 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='21  RSR  46.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='41  <.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='001††  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='76 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='39  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='18 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='37  using a Kruskal-Wallis H-test.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' The results are shown in Table 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  Post-hoc Mann-Whitney tests using a Bonferroni-adjusted alpha  level of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='0125 ( 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='05  4 ) also confirmed the significant difference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' As  we can see, participants in the low accuracy group (representative  for participants with DKE) achieve a relatively poorer appropriate  reliance than participants in the high accuracy group.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Participants  in the low accuracy group demonstrate significantly less reliance  and appropriate reliance on AI systems, which also reflects that  under-reliance is to blame for their low performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' We also com-  pared the time spent by participants in the high accuracy group  with participants in low accuracy group through a Kruskal-Wallis H-  test.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' The difference of time spent on tasks between the two groups  is non-significant (𝑝 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='018, borderline significance in Kruskal-  Wallis H-test).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' On average, the high accuracy group spent around  30 minutes (SD=12 minutes), while the low accuracy group spent  around 34 minutes (SD=13 minutes).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Interestingly, despite the fact  that participants in the low accuracy group spent longer time on  the task they still relied poorly on the AI system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' This is consistent  with what has been widely understood as an impact of the DKE  metacognitive bias.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='4  Further Analysis of Trust  In addition to the behavior-based reliance measures, we also as-  sessed the subjective trust of participants in AI systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' In this  subsection, we explore the impact of our tutorial intervention and  logic units-based explanation on user trust in the AI system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  The effect of tutorial intervention on trust.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' To explore whether  our tutorial intervention had any effect on user trust in AI system,  we conducted Wilcoxon signed ranks test comparing the trust  before and after the tutorial.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' On average, participants’ trust in  the AI system does not show significant difference after the tutorial  intervention (increased from 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='996 to 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='016;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' 𝑇 = 1063.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='5, 𝑝 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='952).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  This suggests that the main impact of the tutorial was on helping  users calibrate their competence (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=', their self-assessment) without  directly shaping their trust in the AI system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  Table 9: ANCOVA test results on trust-related dependent  variables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' With different self-assessmnet patterns, we divide  all participants into three groups.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' “††” indicates the effect of  variable is significant at the level of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='0125.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  Variables  𝐹  𝑝  𝜂2  Group  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='15  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='318  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='009  ATI  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='22  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='271  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='004  TiA-PtT  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='21  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='002††  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='040  To further analyze how other covariates shape user trust in AI  system, we decided to conduct AN(C)OVAs despite the anticipation  that our data may not be normally distributed because these analy-  ses have been shown to be robust to Likert-type ordinal data [60].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' As  no significant difference is found between the trust before and after  the tutorial, we aggregated the trust across the two batches of tasks  as users’ trust in the AI system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Considering our main hypothesis,  we aimed to explore whether overestimation of performance and  accurate self-assessment shape user trust in the AI system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' For that  purpose, we consider the three groups of participants (based on self-  assessment, the same criteria in H1) with different self-assessment  patterns.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' The results are shown in Table 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' As we can see, propensity  to trust was the only user factor which corresponded to a significant  impact on TiA-Trust.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' In a further Spearman rank-order test, we  CHI ’23, April 23–28, 2023, Hamburg, Germany  Gaole He, Lucie Kuiper, Ujwal Gadiraju  observed that there is a significant positive correlation between  TiA-PtT and TiA-Trust, 𝜌(249) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='22, 𝑝 < .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='001;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' suggesting a  weak linear relationship between users’ propensity to trust an AI  system and the subjective trust measured with respect to the AI sys-  tem in our study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' We also conducted the Spearman rank-order tests  with TiA-PtT and other reliance-based variables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' No significant  correlation was found between TiA-PtT and reliance measures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  6  DISCUSSION  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='1  Key Findings  Our analysis of the impact of miscalibrated self-assessment on re-  liance suggests that participants with DKE tend to overestimate  their own competence and rely less on AI systems, which results in  under-reliance and much worse performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' To mitigate such cog-  nitive bias, we introduced a tutorial intervention including perfor-  mance feedback on tasks, alongside manually crafted explanations  to contrast the correct answer with the users’ mistakes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Experi-  mental results indicate that such an intervention is highly effective  in calibrating self-assessment (significant improvement), and has  some positive effect on mitigating under-reliance and promoting ap-  propriate reliance (non-significant results).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' We also note that after  making participants who overestimated their performance aware of  their miscalibrated self-assessment, participants tend to rely more  (appropriately) on the AI system (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=', increased Switch Fraction  and appropriate reliance measures, non-significant results, from  Table 4) and achieve a higher performance improvement when  logic units-based explanations are provided (insignificant results  from Table 6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' However, we did not find any significant evidence  to support that the logic units-based explanations can amplify the  effect of the tutorial intervention in calibrating self-assessment, or  relieving the impact of DKE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  The tutorial and calibrated self-assessment demonstrate a posi-  tive impact in facilitating appropriate reliance for participants who  overestimated themselves, but an opposite trend was observed on  participants who underestimated themselves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' We found such dif-  ference can be explained partially by the change of self-assessment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  The calibration of overestimation can bring positive impact, while  the calibration of underestimation may also turn into overestima-  tion or algorithm aversion, which may explain the decrease in  performance and appropriate reliance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' The tutorial was initially de-  signed to reveal the shortcomings of participants with DKE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' While  for participants without DKE, there is a risk that some participants  did not get exposed to their shortcomings in this tutorial and only  found the AI system also made mistakes, which in turn even caused  overestimation of themselves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' An alternative explanation is that the  performance feedback in tutorial intervention showed one mistake  from the AI system, which led to algorithm aversion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' As pointed out  by [12]: “people more quickly lose confidence in algorithmic than  human forecasters after seeing them make the same mistake.” These  findings advance our current understanding of human-AI decision  making, and provide useful insights that can drive guidelines for  designing interventions to promote appropriate reliance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  Positioning in Existing Literature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' In our study, we found that  DKE can have a negative impact on user reliance on the AI system  and our proposed tutorial intervention can mitigate such an impact.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  In the context of human-AI decision making, DKE is closely relevant  to a popular stream of research around user confidence[10, 33].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' For  the participants who overestimated their performance, the designed  tutorial intervention calibrated their self-confidence (as reflected in  their self-assessment) and facilitated appropriate reliance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' In con-  trast, the negative impact on participants who underestimated their  performance can be explained by: (1) the calibrated self-assessment  which can also bring over-confidence, or (2) their confidence/trust  in the AI system being eroded by the observed mistake(s) of the AI  system [3, 76].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' The latter is consistent with findings in the literature  on algorithm aversion [12].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' More empirical studies are required  to confirm and explain these observations, breeding promising  grounds for future research.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  The participants with DKE show under-reliance on AI systems,  which also aligns with the finding from Schaffer et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' [65].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Authors  found that participants who reported higher familiarity with the  task domain relied less on the intelligent assistant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' The effective-  ness of our tutorial intervention to calibrate self-assessment and  mitigate under-reliance is also consistent with existing work using  user tutorial / education interventions to mitigate unexpected and  undesirable reliance patterns.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' All these tutorial interventions share  a common objective of changing the mindset of users.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' For example,  Chiang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' [8] reported that user tutorials such as machine learn-  ing literacy interventions can effectively help high-performance  individuals to reduce over-reliance without affecting the reliance  of low-performance individuals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Similarly, Chiang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' [9] showed  that a brief education session about the possible performance dis-  parity of an ML model (on data with different distribution) can  effectively reduce over-reliance on such cases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' While their work  focused more on changing human understanding of AI systems  (performance, uncertainty, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' ), our work aims to help users cali-  brate their competence (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=', their self-assessment) on specific tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  As a result, their main objective was to realize when AI systems are  not reliable to reduce over-reliance, while we attempt to mitigate  under-reliance for participants who overestimate themselves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  Logic Units-based Explanations Do Not Have the Expected  Effect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' In our study, the logic units-based explanations did not aid  in further amplifying the calibration effect of the tutorial interven-  tion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' This is in line with the findings of Wang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' [79] and Schaffer  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' [65].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' With a comparative study about four types of different  explanations, authors found that “on decision making tasks that  people are more knowledgeable, explanation that is considered to  resemble how humans explain decisions (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=', counterfactual expla-  nation) does not seem to improve calibrated trust.” One potential ex-  planation is that such explanations do not fulfill the three desiderata  of AI explanations [79] (refer to section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='1): the logic units-based  explanations may help participants understand the AI, but fail to  help them recognize the uncertainty underlying the AI or calibrate  their trust in the AI in AI-assisted decision making.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Another poten-  tial cause is such explanations may introduce automation bias [65],  which will cause over-reliance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Our results suggest that logic units-  based explanations may still be hard to follow, because participants  still need to connect and interpret the logic units by themselves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  A limitation of our current work is that we did not gather explicit  input from participants on their perceived understanding of the  explanations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' One further step to ground such logic units into read-  able logical claims may work better for users.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' However, we do not  Knowing About Knowing: An Illusion of Human Competence Can Hinder Appropriate Reliance on AI Systems  CHI ’23, April 23–28, 2023, Hamburg, Germany  deny the prospect that some XAI methods may have the potential  to help mitigate DKE and calibrate user confidence in human-AI  decision making.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' For example, contrastive explanations may work  in the context of human-AI decision making [51, 59].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='2  Implications  As our findings suggest that participants with DKE tend to rely  less on AI systems, it implies that future work should look more  closely at the effects of self-assessment in human-AI collaboration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  Although our tutorial intervention shows significant improvement  in calibrating self-assessment, the improvement in appropriate re-  liance is still limited (with borderline significance).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Meanwhile, such  calibration of self-assessment may even hurt the team performance  for participants with initial underestimation of their performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  For these participants, the tutorial calibrated their underestimation,  which may also lead to illusion of superior performance (overes-  timation of themselves).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' In order to further promote appropriate  reliance in human-AI collaboration, we need to develop more effec-  tive human-centered tutorials.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Meanwhile, participants who show  lower performance in our scenario have significantly higher proba-  bility to overestimate their performance, which aligns with DKE  properties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Thus, we can leverage overestimation of individual per-  formance as an indicator of such a meta-cognitive bias and further  mitigate it with personalized or appropriate interventions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  Guidelines for Tutorial Designs to Promote Appropriate Re-  liance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' While our tutorial intervention proved to be effective in  helping users calibrate their self-assessment, accurate self-assessment  does not necessarily translate to optimal appropriate reliance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Com-  pared with participants with accurate self-assessment, the partici-  pants with underestimation showed a significantly better perfor-  mance in RSR (see Table 3), and calibrating such underestimation  may even lead to decreased appropriate reliance (see Table 4), which  indicates accurate self-assessment does not necessarily lead to op-  timal appropriate reliance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' One possible cause is that while the  tutorial makes such users aware that they underestimated them-  selves and they can make correct decisions when the AI system is  wrong in the task, users may have an illusion of superior capability  than the AI system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' As a result, on some tasks where AI systems are  more capable, users make mistakes by exhibiting under-reliance  on the AI system due to recalibrated overestimation of their own  competence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Our findings suggest that we should pay attention to  avoiding such side effects of making users overestimate themselves  in comparison to the AI system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' To avoid such side effects, tutori-  als designed to mitigate a specific kind of bias should be carefully  checked before subjecting them to broad participant pools.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' This also  implies that tutorials designed for promoting appropriate reliance  should not only reveal the shortcomings of users or AI systems  (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=', when they are less capable of making the right decision), but  also their strengths (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=', when they are capable or more capable).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  This has useful implications for the future design of interventions  to mitigate cognitive biases in human-AI decision making.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  In previous work on mitigating over-reliance with a tutorial  intervention, researchers focused on revealing the AI systems’ brit-  tleness [8, 9].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Combined with their findings, we argue that a more  effective tutorial to promote appropriate reliance can be one that  helps users understand both themselves and AI systems, and not  only revealing the weakness but also showing the strengths of each.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  With such a comprehensive understanding, human decision mak-  ers can potentially have a better chance to understand when they  should rely on AI systems, and when they should rely on them-  selves, ultimately leading to (more) appropriate reliance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' More work  is required to understand whether and how explanations can medi-  ate this process of creating a better understanding among users of  AI system capabilities in comparison to their own.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' This resonates  with recent work exploring human-AI complementarity [3, 44, 52].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='3  Caveats and Limitations  Potential Biases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Our research questions focused on DKE and re-  liance and how to mitigate such impact.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' As we cannot pre-identify  which participants have DKE, we recruit the participants and deter-  mine it with performance assessment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' However, such assessment  may be affected by other factors, which can lead to biased results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  For example, although we relied on a pilot study to inform our  task selection while creating two batches of tasks with comparable  difficulty levels, we cannot be certain that they would be perceived  the same way on average across the participants.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  As pointed out by Draws et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' [15], cognitive biases introduced  by task design and workflow may have a negative impact on crowd-  sourcing experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' With the help of Cognitive Biases Checklist  introduced [15], we analyzed potential bias in our study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Self-interest  bias is possible, because crowd workers we recruited from the Pro-  lific platform are motivated by monetary compensation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' To alleviate  any participants with low effort results, we put attention checks to  remove ineligible participants from our study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' As the question and  context in Reclor dataset may be something participants familiar  with, familiarity bias and availability bias can also affect our results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  Transferability Concern.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' In our study, all analyses are based on  the logical reasoning task, which most laypeople are capable of  dealing with.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' However, in practice, the application scenarios may be  affected by more factors (like user expertise, familiarity, and input  modality).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' This gap can be a potential threat to the transferability of  our findings and implications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' However, Dunning and Kruger [43]  showed that participants suffer from DKE across multiple scenarios:  “participants scoring in the bottom quartile on tests of humor, gram-  mar, and logic grossly overestimated their test performance and  ability.” These effects were replicated in a number of other tasks,  like human-AI collaboration [65] and crowdsourcing [63, 76].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Our  findings are therefore highly relevant and can play an important  role in informing the design for appropriate reliance in the context  of human-AI interaction, collaboration, and teaming.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  7  CONCLUSIONS AND FUTURE WORK  In this paper, we present a quantitative study to understand the  impact of the Dunning-Kruger effect (DKE) on reliance behavior of  participants in a human-AI decision making context.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' We propose a  tutorial intervention and explore its effectiveness in mitigating such  an effect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Our results suggest that participants who overestimate  their own performance tend to rely less on the AI system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Com-  bined with the findings that participants with DKE show a much  higher probability of overestimating their performance, we con-  clude that participants with DKE rely less on AI systems, and such  CHI ’23, April 23–28, 2023, Hamburg, Germany  Gaole He, Lucie Kuiper, Ujwal Gadiraju  under-reliance hinders them in achieving better performance on  average (RQ1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Through a rigorous experimental setup and statisti-  cal analysis, we found the effectiveness of our tutorial intervention  in mitigating DKE (RQ2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' However, we found that the tutorial may  mislead some participants (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=', participants who underestimated  themselves) to overestimate their performance or exhibit algorithm  aversion, which in turn harms their appropriate reliance on the AI  system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Our findings suggest that, to fully mitigate the negative im-  pact of the Dunning-Kruger effect and achieve appropriate reliance,  more comprehensive, insightful, and personalized user tutorials  are required.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' We reflected on guidelines for better tutorial designs  based on our key findings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  We found that our tutorial intervention failed to make a differ-  ence in participants’ subjective trust in the AI systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Instead, we  found that users’ general propensity to trust has a significant im-  pact on shaping their subjective trust in the AI system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Future work  can further look into how user trust can be reshaped with different  interventions or by using more effective explanations (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=', con-  trastive explanations or logical explanations in natural language).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  We hope the key findings and implications reported in this work  will inspire further research on promoting appropriate reliance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  ACKNOWLEDGMENTS  This work was partially supported by the TU Delft Design@Scale AI  Lab and the 4TU.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='CEE UNCAGE project.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' This work used the Dutch  national e-infrastructure with the support of the SURF Cooperative  using grant no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' EINF-3888.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' We thank all participants from Prolific.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  REFERENCES  [1] Ricardo Baeza-Yates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Bias on the web.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' ACM 61, 6 (2018), 54–61.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  [2] Gagan Bansal, Besmira Nushi, Ece Kamar, Walter S Lasecki, Daniel S Weld, and  Eric Horvitz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Beyond accuracy: The role of mental models in human-AI  team performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' In Proceedings of the AAAI Conference on Human Computation  and Crowdsourcing, Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' 2–11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  [3] Gagan Bansal, Tongshuang Wu, Joyce Zhou, Raymond Fok, Besmira Nushi, Ece  Kamar, Marco Tulio Ribeiro, and Daniel Weld.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Does the whole exceed  its parts?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' the effect of ai explanations on complementary team performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' In  Proceedings of the 2021 CHI Conference on Human Factors in Computing Systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  1–16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  [4] Cynthia Sherraden Bradley, Kristina Thomas Dreifuerst, Brandon Kyle Johnson,  and Ann Loomis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' More than a Meme: The Dunning-Kruger Effect as an  Opportunity for Positive Change in Nursing Education.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Clinical Simulation in  Nursing 66 (2022), 58–65.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  [5] Zana Buçinca, Maja Barbara Malaya, and Krzysztof Z Gajos.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' To trust or to  think: cognitive forcing functions can reduce overreliance on AI in AI-assisted  decision-making.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Proceedings of the ACM on Human-Computer Interaction 5,  CSCW1 (2021), 1–21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  [6] Jason W Burton, Mari-Klara Stein, and Tina Blegind Jensen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' A systematic  review of algorithm aversion in augmented decision making.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Journal of Behavioral  Decision Making 33, 2 (2020), 220–239.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  [7] Noah Castelo, Maarten W Bos, and Donald R Lehmann.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Task-dependent  algorithm aversion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Journal of Marketing Research 56, 5 (2019), 809–825.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  [8] Chun-Wei Chiang and Ming Yin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Exploring the Effects of Machine Learning  Literacy Interventions on Laypeople’s Reliance on Machine Learning Models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  In IUI 2022: 27th International Conference on Intelligent User Interfaces, Helsinki,  Finland, March 22 - 25, 2022, Giulio Jacucci, Samuel Kaski, Cristina Conati, Simone  Stumpf, Tuukka Ruotsalo, and Krzysztof Gajos (Eds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=').' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' ACM, 148–161.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  [9] Chun-Wei Chiang and Ming Yin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' You’d Better Stop!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Understanding Human  Reliance on Machine Learning Models under Covariate Shift.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' In 13th ACM Web  Science Conference 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' 120–129.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  [10] Leah Chong, Guanglu Zhang, Kosa Goucher-Lambert, Kenneth Kotovsky, and  Jonathan Cagan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Human confidence in artificial intelligence and in them-  selves: The evolution and impact of confidence on adoption of AI advice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Com-  puters in Human Behavior 127 (2022), 107018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  [11] Michael Chromik, Malin Eiband, Felicitas Buchner, Adrian Krüger, and Andreas  Butz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' I think i get your point, AI!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' the illusion of explanatory depth in  explainable AI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' In 26th International Conference on Intelligent User Interfaces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  307–317.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  [12] Berkeley J Dietvorst, Joseph P Simmons, and Cade Massey.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Algorithm  aversion: people erroneously avoid algorithms after seeing them err.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Journal of  Experimental Psychology: General 144, 1 (2015), 114.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  [13] Berkeley J Dietvorst, Joseph P Simmons, and Cade Massey.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Overcoming  algorithm aversion: People will use imperfect algorithms if they can (even slightly)  modify them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Management Science 64, 3 (2018), 1155–1170.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  [14] Nicole Dillen, Marko Ilievski, Edith Law, Lennart E Nacke, Krzysztof Czarnecki,  and Oliver Schneider.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Keep calm and ride along: Passenger comfort and  anxiety as physiological responses to autonomous driving styles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' In Proceedings  of the 2020 CHI conference on human factors in computing systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' 1–13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  [15] Tim Draws, Alisa Rieger, Oana Inel, Ujwal Gadiraju, and Nava Tintarev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  A checklist to combat cognitive biases in crowdsourcing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' In Proceedings of the  AAAI Conference on Human Computation and Crowdsourcing, Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' 48–59.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  [16] David Dunning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' 2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' The Dunning–Kruger effect: On being ignorant of one’s  own ignorance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' In Advances in experimental social psychology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' 44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Elsevier,  247–296.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  [17] David Dunning, Chip Heath, and Jerry M Suls.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' 2004.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Flawed self-assessment:  Implications for health, education, and the workplace.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Psychological science in  the public interest 5, 3 (2004), 69–106.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  [18] Joyce Ehrlinger, Kerri Johnson, Matthew Banner, David Dunning, and Justin  Kruger.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' 2008.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Why the unskilled are unaware: Further explorations of (absent)  self-insight among the incompetent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Organizational behavior and human decision  processes 105, 1 (2008), 98–121.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  [19] Upol Ehsan, Q Vera Liao, Michael Muller, Mark O Riedl, and Justin D Weisz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Expanding explainability: Towards social transparency in ai systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' In  Proceedings of the 2021 CHI Conference on Human Factors in Computing Systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  1–19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  [20] Upol Ehsan and Mark O Riedl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Human-centered explainable ai: towards a re-  flective sociotechnical approach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' In International Conference on Human-Computer  Interaction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Springer, 449–466.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  [21] Upol Ehsan, Philipp Wintersberger, Q Vera Liao, Martina Mara, Marc Streit,  Sandra Wachter, Andreas Riener, and Mark O Riedl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Operationalizing  Human-Centered Perspectives in Explainable AI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' In Extended Abstracts of the  2021 CHI Conference on Human Factors in Computing Systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' 1–6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  [22] Upol Ehsan, Philipp Wintersberger, Q Vera Liao, Elizabeth Anne Watkins, Carina  Manger, Hal Daumé III, Andreas Riener, and Mark O Riedl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Human-Centered  Explainable AI (HCXAI): beyond opening the black-box of AI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' In CHI Conference  on Human Factors in Computing Systems Extended Abstracts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' 1–7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  [23] Alexander Erlei, Richeek Das, Lukas Meub, Avishek Anand, and Ujwal Gadiraju.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' For What It’s Worth: Humans Overwrite Their Economic Self-interest  to Avoid Bargaining With AI Systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' In CHI Conference on Human Factors in  Computing Systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' 1–18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  [24] Alexander Erlei, Franck Nekdem, Lukas Meub, Avishek Anand, and Ujwal Gadi-  raju.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Impact of algorithmic decision making on human behavior: Evidence  from ultimatum bargaining.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' In Proceedings of the AAAI conference on human  computation and crowdsourcing, Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' 43–52.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  [25] Franz Faul, Edgar Erdfelder, Axel Buchner, and Albert-Georg Lang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' 2009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Sta-  tistical power analyses using G* Power 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='1: Tests for correlation and regression  analyses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Behavior research methods 41, 4 (2009), 1149–1160.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  [26] Jennifer Fereday and Eimear Muir-Cochrane.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' 2006.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' The role of performance  feedback in the self-assessment of competence: a research study with nursing  clinicians.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Collegian 13, 1 (2006), 10–15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  [27] Riccardo Fogliato, Alexandra Chouldechova, and Zachary Lipton.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' The  impact of algorithmic risk assessments on human predictions and its analysis via  crowdsourcing studies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Proceedings of the ACM on Human-Computer Interaction  5, CSCW2 (2021), 1–24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  [28] Thomas Franke, Christiane Attig, and Daniel Wessel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' A personal resource  for technology interaction: development and validation of the affinity for technol-  ogy interaction (ATI) scale.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' International Journal of Human–Computer Interaction  35, 6 (2019), 456–467.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  [29] Ujwal Gadiraju, Besnik Fetahu, Ricardo Kawase, Patrick Siehndel, and Stefan  Dietze.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Using worker self-assessments for competence-based pre-selection  in crowdsourcing microtasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' ACM Transactions on Computer-Human Interaction  (TOCHI) 24, 4 (2017), 1–26.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  [30] Ujwal Gadiraju, Ricardo Kawase, Stefan Dietze, and Gianluca Demartini.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  Understanding malicious behavior in crowdsourcing platforms: The case of online  surveys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' In Proceedings of the 33rd Annual ACM Conference on Human Factors in  Computing Systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' 1631–1640.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  [31] Jan Gogoll and Matthias Uhl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Rage against the machine: Automation in  the moral domain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Journal of Behavioral and Experimental Economics 74 (2018),  97–103.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  [32] Ben Green and Yiling Chen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Disparate interactions: An algorithm-in-the-  loop analysis of fairness in risk assessments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' In Proceedings of the conference on  fairness, accountability, and transparency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' 90–99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  [33] Ben Green and Yiling Chen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' The principles and limits of algorithm-in-the-  loop decision making.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Proceedings of the ACM on Human-Computer Interaction 3,  Knowing About Knowing: An Illusion of Human Competence Can Hinder Appropriate Reliance on AI Systems  CHI ’23, April 23–28, 2023, Hamburg, Germany  CSCW (2019), 1–24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  [34] Ben Green and Yiling Chen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Algorithmic risk assessments can alter human  decision-making processes in high-stakes government contexts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' arXiv preprint  arXiv:2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='05370 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  [35] Gaole He, Agathe Balayn, Stefan Buijsman, Jie Yang, and Ujwal Gadiraju.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  It Is Like Finding a Polar Bear in the Savannah!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Concept-Level AI Explanations  with Analogical Inference from Commonsense Knowledge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' In Proceedings of the  AAAI Conference on Human Computation and Crowdsourcing, Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' 89–101.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  [36] Robert R Hoffman, Shane T Mueller, Gary Klein, and Jordan Litman.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Metrics  for explainable AI: Challenges and prospects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' arXiv preprint arXiv:1812.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='04608  (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  [37] Yoyo Tsung-Yu Hou and Malte F Jung.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Who is the expert?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Reconciling  algorithm aversion and algorithm appreciation in AI-supported decision making.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  Proceedings of the ACM on Human-Computer Interaction 5, CSCW2 (2021), 1–25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  [38] Christoph Hube, Besnik Fetahu, and Ujwal Gadiraju.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Understanding and  mitigating worker biases in the crowdsourced collection of subjective judgments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  In Proceedings of the 2019 CHI Conference on Human Factors in Computing Systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  1–12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  [39] Rachel A Jansen, Anna N Rafferty, and Thomas L Griffiths.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' A rational  model of the Dunning–Kruger effect supports insensitivity to evidence in low  performers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Nature Human Behaviour 5, 6 (2021), 756–763.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  [40] Ekaterina Jussupow, Izak Benbasat, and Armin Heinzl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Why are we averse  towards Algorithms?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' A comprehensive literature Review on Algorithm aversion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  In 28th European Conference on Information Systems - Liberty, Equality, and Fra-  ternity in a Digitizing World, ECIS 2020, Marrakech, Morocco, June 15-17, 2020,  Frantz Rowe, Redouane El Amrani, Moez Limayem, Sue Newell, Nancy Pouloudi,  Eric van Heck, and Ali El Quammah (Eds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  [41] Moritz Körber.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Theoretical considerations and development of a question-  naire to measure trust in automation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' In Congress of the International Ergonomics  Association.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Springer, 13–30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  [42] Max F Kramer, Jana Schaich Borg, Vincent Conitzer, and Walter Sinnott-  Armstrong.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' When do people want AI to make decisions?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='. In Proceedings of  the 2018 AAAI/ACM Conference on AI, Ethics, and Society.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' 204–209.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  [43] Justin Kruger and David Dunning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' 1999.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Unskilled and unaware of it: how diffi-  culties in recognizing one’s own incompetence lead to inflated self-assessments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  Journal of personality and social psychology 77, 6 (1999), 1121.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  [44] Vivian Lai, Chacha Chen, Q Vera Liao, Alison Smith-Renner, and Chenhao Tan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Towards a science of human-ai decision making: a survey of empirical  studies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' arXiv preprint arXiv:2112.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='11471 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  [45] Vivian Lai, Han Liu, and Chenhao Tan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' "Why is ’Chicago’ deceptive?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='"  Towards Building Model-Driven Tutorials for Humans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' In CHI ’20: CHI Confer-  ence on Human Factors in Computing Systems, Honolulu, HI, USA, April 25-30,  2020, Regina Bernhaupt, Florian ’Floyd’ Mueller, David Verweij, Josh Andres,  Joanna McGrenere, Andy Cockburn, Ignacio Avellino, Alix Goguey, Pernille Bjøn,  Shengdong Zhao, Briane Paul Samson, and Rafal Kocielnik (Eds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=').' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' ACM, 1–13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  [46] Vivian Lai and Chenhao Tan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' On human predictions with explanations and  predictions of machine learning models: A case study on deception detection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' In  Proceedings of the conference on fairness, accountability, and transparency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' 29–38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  [47] John D Lee and Katrina A See.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' 2004.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Trust in automation: Designing for appro-  priate reliance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Human factors 46, 1 (2004), 50–80.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  [48] Min Hun Lee, Daniel P Siewiorek, Asim Smailagic, Alexandre Bernardino, and  Sergi Bermúdez i Badia.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' A human-ai collaborative approach for clinical  decision making on rehabilitation assessment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' In Proceedings of the 2021 CHI  Conference on Human Factors in Computing Systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' 1–14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  [49] Mengyao Li, Brittany E Holthausen, Rachel E Stuck, and Bruce N Walker.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  No risk no trust: Investigating perceived risk in highly automated driving.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' In  Proceedings of the 11th International Conference on Automotive User Interfaces and  Interactive Vehicular Applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' 177–185.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  [50] Q Vera Liao and Kush R Varshney.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Human-Centered Explainable AI (XAI):  From Algorithms to User Experiences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' arXiv preprint arXiv:2110.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='10790 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  [51] Peter Lipton.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' 1990.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Contrastive explanation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Royal Institute of Philosophy Supple-  ments 27 (1990), 247–266.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  [52] Han Liu, Vivian Lai, and Chenhao Tan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Understanding the Effect of Out-  of-distribution Examples and Interactive Explanations on Human-AI Decision  Making.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' ACM Hum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Comput.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Interact.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' 5, CSCW2 (2021), 1–45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  [53] Jennifer M Logg, Julia A Minson, and Don A Moore.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Algorithm appreciation:  People prefer algorithmic to human judgment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Organizational Behavior and  Human Decision Processes 151 (2019), 90–103.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  [54] Chiara Longoni, Andrea Bonezzi, and Carey K Morewedge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Resistance to  medical artificial intelligence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Journal of Consumer Research 46, 4 (2019), 629–650.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  [55] Zhuoran Lu and Ming Yin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Human Reliance on Machine Learning Models  When Performance Feedback is Limited: Heuristics and Risks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' In CHI ’21: CHI  Conference on Human Factors in Computing Systems, Virtual Event / Yokohama,  Japan, May 8-13, 2021, Yoshifumi Kitamura, Aaron Quigley, Katherine Isbister,  Takeo Igarashi, Pernille Bjørn, and Steven Mark Drucker (Eds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=').' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' ACM, 78:1–78:16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  [56] Catherine C Marshall and Frank M Shipman.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Experiences surveying the  crowd: Reflections on methods, participation, and reliability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' In Proceedings of  the 5th Annual ACM Web Science Conference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' 234–243.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  [57] Conor Thomas McKevitt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Engaging students with self-assessment and tutor  feedback to improve performance and support assessment capacity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Journal of  University Teaching & Learning Practice 13, 1 (2016), 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  [58] Scott Mayer McKinney, Marcin Sieniek, Varun Godbole, Jonathan Godwin,  Natasha Antropova, Hutan Ashrafian, Trevor Back, Mary Chesus, Greg S Cor-  rado, Ara Darzi, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' International evaluation of an AI system for breast  cancer screening.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Nature 577, 7788 (2020), 89–94.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  [59] Tim Miller.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Contrastive explanation: A structural-model approach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' The  Knowledge Engineering Review 36 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  [60] Geoff Norman.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' 2010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Likert scales, levels of measurement and the “laws” of  statistics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Advances in health sciences education 15, 5 (2010), 625–632.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  [61] Amy Rechkemmer and Ming Yin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' When Confidence Meets Accuracy:  Exploring the Effects of Multiple Performance Indicators on Trust in Machine  Learning Models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' In CHI ’22: CHI Conference on Human Factors in Computing  Systems, New Orleans, LA, USA, 29 April 2022 - 5 May 2022, Simone D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Barbosa,  Cliff Lampe, Caroline Appert, David A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Shamma, Steven Mark Drucker, Julie R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  Williamson, and Koji Yatani (Eds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=').' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' ACM, 535:1–535:14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  [62] Vincent Robbemond, Oana Inel, and Ujwal Gadiraju.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Understanding the  Role of Explanation Modality in AI-assisted Decision-making.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' In Proceedings  of the 30th ACM Conference on User Modeling, Adaptation and Personalization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  223–233.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  [63] Ioannis Petros Samiotis, Sihang Qiu, Christoph Lofi, Jie Yang, Ujwal Gadiraju,  and Alessandro Bozzon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Exploring the Music Perception Skills of Crowd  Workers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' In Proceedings of the AAAI Conference on Human Computation and  Crowdsourcing, Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' 108–119.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  [64] James Sawler.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Economics 101-ism and the Dunning-Kruger effect: Reducing  overconfidence among introductory macroeconomics students.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' International  Review of Economics Education 36 (2021), 100208.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  [65] James Schaffer, John O’Donovan, James Michaelis, Adrienne Raglin, and Tobias  Höllerer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' I Can Do Better than Your AI: Expertise and Explanations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' In  Proceedings of the 24th International Conference on Intelligent User Interfaces  (Marina del Ray, California) (IUI ’19).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Association for Computing Machinery, New  York, NY, USA, 240–251.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  [66] Max Schemmer, Patrick Hemmer, Niklas Kühl, Carina Benz, and Gerhard Satzger.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Should I Follow AI-based Advice?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Measuring Appropriate Reliance in  Human-AI Decision-Making.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' In ACM Conference on Human Factors in Computing  Systems (CHI’22), Workshop on Trust and Reliance in AI-Human Teams (trAIt).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  [67] Patrick Schramowski, Wolfgang Stammer, Stefano Teso, Anna Brugger, Franziska  Herbert, Xiaoting Shao, Hans-Georg Luigs, Anne-Katrin Mahlein, and Kristian  Kersting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Making deep neural networks right for the right scientific reasons  by interacting with their explanations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Nature Machine Intelligence 2, 8 (2020),  476–486.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  [68] Andrew Selbst and Julia Powles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' "Meaningful Information" and the Right  to Explanation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' In Conference on Fairness, Accountability and Transparency, FAT  2018, 23-24 February 2018, New York, NY, USA (Proceedings of Machine Learning  Research, Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' 81), Sorelle A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Friedler and Christo Wilson (Eds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=').' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' PMLR, 48.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  [69] Amit Sheth, Manas Gaur, Kaushik Roy, and Keyur Faldu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Knowledge-  intensive language understanding for explainable AI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' IEEE Internet Computing  25, 5 (2021), 19–24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  [70] Donghee Shin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Expanding the role of trust in the experience of algorith-  mic journalism: User sensemaking of algorithmic heuristics in Korean users.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  Journalism Practice 16, 6 (2022), 1168–1191.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  [71] Donghee Shin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' How do people judge the credibility of algorithmic sources?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  Ai & Society 37, 1 (2022), 81–96.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  [72] Donghee Shin, Kerk F Kee, and Emily Y Shin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Algorithm awareness: Why  user awareness is critical for personal privacy in the adoption of algorithmic  platforms?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' International Journal of Information Management 65 (2022), 102494.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  [73] Donghee Shin, Azmat Rasul, and Anestis Fotiadis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Why am I seeing this?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  Deconstructing algorithm literacy through the lens of users.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Internet Research  (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  [74] Donghee Shin, Bouziane Zaid, Frank Biocca, and Azmat Rasul.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' In Platforms  We Trust?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Unlocking the Black-Box of News Algorithms through Interpretable  AI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Journal of Broadcasting & Electronic Media (2022), 1–22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  [75] Donghee Shin, Bouziane Zaid, and Mohammed Ibahrine.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Algorithm appreci-  ation: Algorithmic performance, developmental processes, and user interactions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  In 2020 International Conference on Communications, Computing, Cybersecurity,  and Informatics (CCCI).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' IEEE, 1–5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  [76] Suzanne Tolmeijer, Ujwal Gadiraju, Ramya Ghantasala, Akshit Gupta, and Abra-  ham Bernstein.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Second Chance for a First Impression?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Trust Development  in Intelligent System Interaction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' In Proceedings of the 29th ACM Conference on  User Modeling, Adaptation and Personalization, UMAP 2021, Utrecht, The Nether-  lands, June, 21-25, 2021, Judith Masthoff, Eelco Herder, Nava Tintarev, and Marko  Tkalcic (Eds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=').' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' ACM, 77–87.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  [77] Richard Tomsett, Alun Preece, Dave Braines, Federico Cerutti, Supriyo  Chakraborty, Mani Srivastava, Gavin Pearson, and Lance Kaplan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Rapid  trust calibration through interpretable and uncertainty-aware AI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Patterns 1, 4  (2020), 100049.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  CHI ’23, April 23–28, 2023, Hamburg, Germany  Gaole He, Lucie Kuiper, Ujwal Gadiraju  [78] Danding Wang, Qian Yang, Ashraf Abdul, and Brian Y Lim.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Designing  theory-driven user-centric explainable AI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' In Proceedings of the 2019 CHI confer-  ence on human factors in computing systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' 1–15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  [79] Xinru Wang and Ming Yin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Are Explanations Helpful?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' A Comparative  Study of the Effects of Explanations in AI-Assisted Decision-Making.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' In 26th  International Conference on Intelligent User Interfaces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' 318–328.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  [80] Fangzhi Xu, Jun Liu, Qika Lin, Yudai Pan, and Lingling Zhang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Logiformer:  A Two-Branch Graph Transformer Network for Interpretable Logical Reasoning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  In SIGIR ’22: The 45th International ACM SIGIR Conference on Research and Devel-  opment in Information Retrieval, Madrid, Spain, July 11 - 15, 2022, Enrique Amigó,  Pablo Castells, Julio Gonzalo, Ben Carterette, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Shane Culpepper, and Gabriella  Kazai (Eds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=').' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' ACM, 1055–1065.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  [81] Hanqi Yan, Lin Gui, and Yulan He.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Hierarchical Interpretation of Neural  Text Classification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' arXiv preprint arXiv:2202.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='09792 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  [82] Ilan Yaniv and Eli Kleinberger.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' 2000.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Advice taking in decision making: Egocentric  discounting and reputation formation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Organizational behavior and human  decision processes 83, 2 (2000), 260–281.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  [83] Ming Yin, Jennifer Wortman Vaughan, and Hanna Wallach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Understanding  the effect of accuracy on trust in machine learning models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' In Proceedings of the  2019 chi conference on human factors in computing systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' 1–12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  [84] Sangseok You, Cathy Liu Yang, and Xitong Li.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Algorithmic versus Hu-  man Advice: Does Presenting Prediction Performance Matter for Algorithm  Appreciation?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Journal of Management Information Systems 39, 2 (2022), 336–365.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  [85] Weihao Yu, Zihang Jiang, Yanfei Dong, and Jiashi Feng.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' ReClor: A Reading  Comprehension Dataset Requiring Logical Reasoning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' In International Conference  on Learning Representations (ICLR).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  [86] Muhammad Bilal Zafar, Philipp Schmidt, Michele Donini, Cédric Archambeau,  Felix Biessmann, Sanjiv Ranjan Das, and Krishnaram Kenthapadi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' More  Than Words: Towards Better Quality Interpretations of Text Classifiers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' arXiv  preprint arXiv:2112.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='12444 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  [87] Yunfeng Zhang, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Vera Liao, and Rachel K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Bellamy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Effect of confidence  and explanation on accuracy and trust calibration in AI-assisted decision making.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content='  In FAT* ’20: Conference on Fairness, Accountability, and Transparency, Barcelona,  Spain, January 27-30, 2020, Mireille Hildebrandt, Carlos Castillo, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' Elisa Celis,  Salvatore Ruggieri, Linnet Taylor, and Gabriela Zanfir-Fortuna (Eds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=').' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
+page_content=' ACM, 295–  305.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/lNFIT4oBgHgl3EQfryt6/content/2301.11333v1.pdf'}
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+How Do Constraints of Nuclear Symmetry Energy Reconcile with Diﬀerent Models?
+Yingxun Zhang,1, 2, ∗ Yangyang Liu,1, † Yongjia Wang,3, ‡ Qingfeng Li,3, 4, § and Zhuxia Li1
+1China Institute of Atomic Energy, Beijing 102413, China
+2Guangxi Key Laboratory of Nuclear Physics and Technology,
+Guangxi Normal University, Guilin, 541004, China
+3School of Science, Huzhou University, Huzhou 313000, China
+4Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, China
+(Dated: January 3, 2023)
+By simultaneously describing the data of isospin sensitive nucleonic ﬂow and pion observables,
+such as vn
+2 /vch
+2
+and π−/π+, with ultra-relativistic quantum molecular dynamics (UrQMD) model,
+we got the symmetry energy at ﬂow and pion characteristic densities which are S(1.2ρ0) = 34 ± 4
+MeV and S(1.5ρ0) = 36 ± 8 MeV. Within the uncertainties, the constraints of symmetry energy
+at characteristic densities are consistent with the previous constraints by using other transport
+models.
+The consistency suggests that the reliable constraints on symmetry energy should be
+presented at the characteristic density of isospin sensitive observables. By using the constraints of
+symmetry energy at two diﬀerent characteristic densities, the extrapolated value of L is provided.
+Within 2σ uncertainty, the extrapolated value of L is in 5 − 70 MeV which is consistent with the
+recent combination analysis from PREX-II and astrophyiscs data. Further, the calculations with
+the constrained parameter sets can describe the data of charged pion multiplicities from SπRIT
+collaboration.
+Knowledge of the symmetry energy is crucial for un-
+derstanding the isospin asymmetric objects, such as
+the structure of neutron-rich nuclei, the mechanism of
+neutron-rich heavy ion collisions, and the properties of
+neutron stars[1, 2]. However, theoretical predictions on
+the symmetry energy away from the normal density show
+larger uncertainty, and it leads that the constraint of
+symmetry energy becomes one of the important goals in
+nuclear physics[3, 4].
+For probing the symmetry energy at suprasaturation
+density, the isospin-sensitive observables in heavy ion col-
+lisions (HICs), such as the ratio of elliptic ﬂow of neutron
+to charged particle, hydrogen isotopes or proton (vn
+2 /vch
+2 ,
+vn
+2 /vH
+2 or vn
+2 /vp
+2)[5–9] and the yield ratios of charged pi-
+ons (i.e., M(π−)/M(π+) or named as π−/π+)[10–20],
+were frequently used.
+By comparing the transverse-
+momentum-dependent or integrated FOPI/LAND ellip-
+tic ﬂow data of nucleons and hydrogen isotopes with
+UrQMD[5, 7] and T¨uQMD models[6], a moderately soft
+to linear symmetry energy is obtained[8]. Usually, the
+constraints of symmetry energy were presented by the
+symmetry energy coeﬃcient S0 and the slope of symme-
+try energy L at normal density.
+The lower limit of L
+obtained with the ﬂow ratio data is 60 MeV[21], which
+overlaps with the upper limits of the constraints from the
+nuclear structure and isospin diﬀusion, i.e., L ≈ 60 ± 20
+MeV[22–24].
+The deduced L from FOPI π−/π+ data
+show strong model dependence[12–18, 25], which ranges
+from 12 MeV to 144 MeV.
+To reduce the model dependence on the constraints of
+symmetry energy, especially at suprasaturation densities,
+∗ zhyx@ciae.ac.cn
+† liuyangyang@ciae.ac.cn
+‡ wangyongjia@zjhu.edu.cn
+§ liqf@zjhu.edu.cn
+the transport model evaluation project was performed
+among the transport model community since 2009. Up
+to now, the transport model evaluation project has made
+important progress on the reduction of model depen-
+dence of transport model by benchmarking the treatment
+of particle-particle collision[26, 27] and nucleonic mean
+ﬁeld potential[28] in both Boltzmann-Uehling-Uhlenbeck
+(BUU) type and Quantum molecular dynamics (QMD)
+type models. However, the recent works on SπRIT pion
+data [20] for Sn+Sn collision system at 0.27A GeV have
+also shown the model dependence after comparing the
+pion production with seven updated transport models.
+It hints the model dependence of the inferred L by using
+ﬂow or pion observables may come from the extrapolation
+of symmetry energy from the probed density to normal
+density.
+To verify this issue, one has to know which density is
+probed by ﬂow and pion observables. The named char-
+acteristic density was proposed in Refs. [18, 24, 29, 30],
+which is used to quantitatively describe the density
+probed by the ﬂow or pion observables.
+After know-
+ing the characteristic density, the consistency or incon-
+sistency of symmetry energy constraints can be further
+understood. In this work, we simultaneously investigate
+the ﬂow and pion observables within the framework of
+UrQMD model. By comparing the calculation to ASY-
+EOS and FOPI data, the data favored parameter sets
+are obtained and a remarkable consistency is found at
+both ﬂow and pion characteristic densities among diﬀer-
+ent transport models.
+The version of UrQMD model we used is the same as
+that in Ref.[18] but the momentum dependent interaction
+and the cross sections of NN → N∆ near the threshold
+energy are reﬁned, more details are in Ref. [31].
+The
+nucleonic potential energy U is calculated from the po-
+tential energy density, i.e., U =
+�
+ud3r.
+The u reads
+arXiv:2301.00212v1  [nucl-th]  31 Dec 2022
+
+2
+as
+u = α
+2
+ρ2
+ρ0
++
+β
+η + 1
+ρη+1
+ρη
+0
+(1)
++gsur
+2ρ0
+(∇ρ)2 + gsur,iso
+ρ0
+[∇(ρn − ρp)]2
++umd + usym.
+The parameters α, β, and η are related to the two, three-
+body interaction term. The third and fourth terms are
+isospin independent and isospin dependent surface term,
+respectively. The umd is from the momentum dependent
+interaction (MDI) term, which is calculated according to
+the following relationship,
+umd =
+�
+N1,N2=n,p
+�
+d3p1d3p2fN1 (r, ⃗p1) fN2 (r, ⃗p2)
+vmd(∆p12).
+(2)
+fNi(r, ⃗p) is the phase space density of particle Ni. The
+form of MDI, i.e., vmd(∆p12), is assumed as,
+vmd(∆p12) = t4 ln2(1 + t5∆p2
+12) + c,
+(3)
+where ∆p12 = |p1 − p2|, and the parameters t4, t5 and c
+are obtained by reproducing the real part of the optical
+potential of Hama’s data by using Eq.(3) and
+Vmd(p1) =
+�
+p2<pF
+vmd(p1 − p2)d3p2/
+�
+p2<pF
+d3p2,
+(4)
+within the kinetic energy Ekin ≈ 750 MeV. The method
+we used is as same as in Ref.[32]. With the consideration
+of MDI, the parameter α, β, and η are readjusted to keep
+the incompressibility of symmetric nuclear matter K0 =
+231 MeV. The values of parameters and corresponding
+eﬀective mass are listed in Table I.
+TABLE I. Parameters used in this work. t4, c, α, β and K0
+are in MeV. t5 is in MeV−2. η and m∗/m are dimensionless.
+Para.
+t4
+t5
+c
+α
+β
+η
+K0 m∗/m
+vHama
+md
+3.058 5×10−4 -86 -335 253 1.16 231 0.635
+For the potential energy density of symmetry energy
+part, i.e., usym, we take two forms in the calculations.
+One is the Skyrme-type polynomial form (form (a) in
+Eq. (5)) and another is the density power law form (form
+(b) in Eq. (5)). It reads,
+usym = Spot
+sym(ρ)ρδ2
+(5)
+=
+�
+(A( ρ
+ρ0 ) + B( ρ
+ρ0 )γs + C( ρ
+ρ0 )5/3)ρδ2, (a)
+Cs
+2 ( ρ
+ρ0 )γiρδ2.
+(b)
+In the following calculations, S0 varies from 30 to 34 MeV
+and L varies from 5 to 144 MeV. The corresponding pa-
+rameters in Eq.(5) are determined with the relationship
+in Ref.[24, 33].
+The calculations of Au+Au at 0.4A GeV and Sn+Sn at
+0.27 A GeV are performed with 200,000 events. Since the
+collision centrality is determined by the Zbound or Zrat
+in the Ref. [8] and the detected charged particle multi-
+plicity [25] or the ratio of total transverse to longitudinal
+kinetic energies in the center-of-mass (c.m.) system in
+Ref. [34], the corresponding impact parameter b will be
+in a wide range and the weight of b is a Gaussian shape
+rather than a triangular shape. This impact smearing
+eﬀect [8, 35–37] is also considered in calculations. In Ta-
+ble.II, we list the experimental sixteen observables we
+investigated.
+TABLE II. Sixteen experimental observables and the corre-
+sponding averaged impact parameters (in fm) analyzed in this
+work.
+Obsevable
+< b >
+system
+Exp.
+vn
+1 (pt/A)
+5.69
+Au+Au
+ASY-EOS [8]
+vch
+1 (pt/A)
+5.69
+Au+Au
+ASY-EOS [8]
+vn
+2 (pt/A)
+5.69
+Au+Au
+ASY-EOS [8]
+vch
+2 (pt/A)
+5.69
+Au+Au
+ASY-EOS [8]
+vn
+2 /vch
+2 (pt/A)
+5.69
+Au+Au
+ASY-EOS [8]
+M(π)
+<2a
+Au+Au
+FOPI [34]
+π−/π+
+<2a.
+Au+Au
+FOPI [34]
+Y (π−)
+3
+108Sn+112Sn
+SπRIT [25]
+Y (π−)
+3
+112Sn+124Sn
+SπRIT [25]
+Y (π−)
+3
+132Sn+124Sn
+SπRIT [25]
+Y (π+)
+3
+108Sn+112Sn
+SπRIT [25]
+Y (π+)
+3
+112Sn+124Sn
+SπRIT [25]
+Y (π+)
+3
+132Sn+124Sn
+SπRIT [25]
+π−/π+
+3
+108Sn+112Sn
+SπRIT [25]
+π−/π+
+3
+112Sn+124Sn
+SπRIT [25]
+π−/π+
+3
+132Sn+124Sn
+SπRIT [25]
+a We did not put the average b value here since experimental
+paper only provides b/bmax < 0.15, which is obtained by
+estimating the impact parameter b from the measured
+diﬀerential cross sections for the ERAT under a geometrical
+sharp-cut approximation.
+Fig.1 illustrates the UrQMD model calculations and
+the measured data for the directed (v1) and the el-
+liptic ﬂow (v2) of neutrons and charged particles as a
+function of the transverse momentum per nucleon pt/A.
+The intervals of the polar angle and rapidity are cho-
+sen to be the same as in the ASY-EOS analysis, i.e.,
+37◦ < θlab < 53◦ and −0.5 < y0 < 0.5. As an exam-
+ple, we present the results obtained with L = 35 MeV
+(dashed lines) and L = 144 MeV (solid lines) at S0 = 30
+MeV. The symbols are the ASY-EOS data from Ref.[8].
+As shown in panels (a) and (b), the calculations with dif-
+ferent L fall in the data region. But the results calculated
+with L = 35 MeV and L = 144 MeV sets are overlapping
+each other, which indicates v1 in the plotted intervals has
+no sensitivity to the nuclear symmetry energy, due to the
+spectator matter blocking eﬀect.
+For the elliptic ﬂow, the eﬀects of symmetry energy
+
+3
+-0.2
+0.0
+0.2
+0.2
+0.4
+0.6
+-0.1
+0.0
+0.2
+0.4
+0.6
+0.8
+ASY-EOS
+ 
+v1
+neutron
+(c)
+  L35
+  L144
+(a)
+ 
+ 
+v2
+pt/A (GeV/c)
+ 
+(d)
+Au+Au Ebeam=0.4A GeV
+Charged particles
+(b)
+ 
+pt/A (GeV/c)
+FIG. 1. The directed ﬂow v1 (upper panels) and elliptic ﬂow
+v2 (lower panels) of free neutrons (left panels) and charged
+particles (right panels). The dash and solid lines represent
+the results with L = 35 MeV and L = 144 MeV, respectively.
+The ASY-EOS data of collective ﬂow for neutron and charged
+particles are shown as circle and triangle symbols[8].
+on v2 of both free neutrons and charged particles can
+be clearly observed as in Fig.1 (c) and (d).
+Both the
+vn
+2 and vch
+2
+have negative values and decrease with pt/A
+increasing, which means a preference for particle emis-
+sion out of the reaction plane, towards 90◦ and 270◦. As
+shown in Fig.1 (c), the values of vn
+2 obtained with stiﬀ
+symmetry energy case are lower than that with soft sym-
+metry energy case. The reason is that the stiﬀ symmetry
+energy provides a stronger repulsive force on neutrons
+at suprasaturation density than that for soft symmetry
+energy cases. For charged particles, as shown in panel
+(d), vch
+2
+obtained with the stiﬀ symmetry energy case
+are higher than that with the soft symmetry energy case.
+This is because the emitted charged particles are mainly
+composed of free protons, which feel stronger attractive
+interaction for the stiﬀ symmetry energy case than that
+for the soft symmetry energy case at suprasaturation den-
+sity. Consequently, vch
+2
+obtained with the stiﬀ symmetry
+energy case is higher than that with the soft symmetry
+energy case, which has also been discussed in Refs. [5–
+7, 38]. However, vn
+2 or vch
+2
+cannot be used individually
+to constrain the symmetry energy, because both vn
+2 or
+vch
+2
+not only depend on the symmetry energy but also on
+the MDI and incompressibility. For example, the calcula-
+tions with diﬀerent incompressibility can lead to diﬀerent
+results on the elliptic ﬂow[39].
+To isolate the contributions from the isocalar poten-
+tial, vn
+2 /vch
+2
+ratio was proposed to probe symmetry en-
+ergy and several analysis have been performed by using
+the UrQMD model or T¨uQMD model[8, 17]. In Fig.2 (a),
+we present the calculated results for vn
+2 /vch
+2 as a function
+of pt/A obtained with L = 35 MeV and 144 MeV sets at
+S0 = 30, 32.5 and 34 MeV. The symbols are the ASY-
+EOS data points. The calculations show that vn
+2 /vch
+2
+is
+sensitive to L, especially at the low pt region in which
+the mean-ﬁeld play more important role. The values of
+vn
+2 /vch
+2
+obtained with L = 144 MeV sets are larger than
+that with L = 35 MeV sets. This behavior can be un-
+derstood from Fig.1 (c) and (d). By comparing the cal-
+culations of vn
+2 /vch
+2
+to ASY-EOS experimental data and
+doing a χ2 analysis, one draw the conclusion on the slope
+of symmetry energy is 5-67 MeV for S0 = 32.5 MeV case.
+After considering the uncertainties of S0, the constraints
+on the L extend to 5-70 MeV which are presented in panel
+(b).
+FIG. 2. Panel (a) vn
+2 /vch
+2
+as a function of pt/A for L = 35
+MeV and L = 144 MeV with S0 in the range from 30 MeV to
+34 MeV; (b) χ2 as a function of L for S0=30 (blue lines) and
+34 MeV (red lines). Panel (c) and (d) are M(π)/Apart. and
+π−/π+ ratio as a function of L with S0 = 30 and 34 MeV,
+respectively. Panel (e) and (f) are the multiplicity of charged
+pion and its ratio as a function of N/Z of the system. The
+black symbols represent the ASY-EOS experimental data[8],
+the cyan-shaded region is the FOPI data and the blue symbols
+are the SπRIT data.
+Fig.2 (c) and (d) show the calculated Mπ and π−/π+
+for Au+Au as a function of L (shaded region with diﬀer-
+ent color boundary) and the FOPI data (cyan shaded re-
+gion). The width of the red-shaded region represents the
+results obtained with S0 from 30 to 34 MeV. M(π) cal-
+culated with diﬀerent S0 and L falls into the data region,
+and suggest that M(π) can not be used to distinguish
+
+2
+20
+ASY-EOS
+1 . 0.4A GeV
+L=144MeV
+S=30 MeV
+W2
+10
+S,=34 MeV
+L=35 MeV
+(a)
+(b)
+0.30
+1
+0.45
+0.60
+0
+50
+100
+150
+p/A (GeV/c)
+L(MeV)
+0.020
+3.5
+part
+FOPI
+2.
+A
+M
+3.0
+0.015
+S,=30. MeV
+[(c)
+(d)
+S.=34 MeV
+2.5
+0
+50
+100
+0
+50
+100
+150
+L(MeV)
+L(MeV)
+0.8
+S元RIT
+0.27A
+JGeV. Sn+Sn
+5.0
+元
+元
+S,=30 MeV, L=5 MeV
+元
+M
+0.4
+允*
+2.5
+(e)
+(f)
+S,=34 MeV, L=84 MeV
+0.0
+1.2
+1.4
+1.61.2
+1.4
+1.6
+N/Z
+N/Z4
+L. The π−/π+ ratios obtained with UrQMD model are
+sensitive to L, and it decreases with the increase of L.
+Comparing the calculated results of π−/π+ to the FOPI
+experimental data, the parameter sets with L=5-70 MeV
+are favored.
+To test the validation of obtained parameter sets, we
+also perform the calculations of Sn+Sn and compare the
+pion production results to SπRIT data (black symbols).
+Fig.2 (e) and (f) show the charged pion multiplicities
+and its ratio as a function of N/Z of system. Two ex-
+treme values of L are used in the validation. One is for
+S0 = 30 MeV and L = 5 MeV and another is S0 = 34
+MeV and L = 84 MeV. The testing calculations demon-
+strate that the calculation with L = 5 MeV set can de-
+scribe the M(π−) and M(π+) for three reaction system,
+108Sn+112Sn, 112Sn+124Sn and 132Sn+124Sn, within the
+experimental uncertainties. For π−/π+ ratios, the calcu-
+lations can reproduce the data for the 108Sn+112Sn and
+112Sn+124Sn system, but underestimate the data for very
+neutron rich system 132Sn+124Sn. The discrepancy is re-
+lated to the subthreshold pion production mechanism,
+where the threshold eﬀects[40–42] and isospin-dependent
+medium correction on NN → N∆ cross section[43, 44]
+become important.
+Although the data favored parameter sets are pre-
+sented with L value at normal density, one should keep
+in mind that the isospin observables vn
+2 /vch
+2
+and π−/π+
+probe the symmetry energy information at suprasatura-
+tion density region rather than at normal density. The in-
+teresting point is what density is probed by ﬂow and pion
+observables? Here, we use the named characteristic den-
+sity to quantitatively describe them. For pion observable,
+the characteristic density is obtained by averaging the
+compressed density with pion production rate in spatio-
+temporal domain [18], and the calculations show that
+the characteristic density of pion observable is around
+1.5 times normal density.
+For collective ﬂow, the idea of calculating characteristic
+density is as same as pion characteristic density[18, 30],
+but the weight is replaced by the momentum change of
+nucleons which reﬂects strength of driven force for the
+collective motion of emitted particles. With this weight
+deﬁnition, the more momentum change during the time
+evolution is, the more weight on the collective motion
+of nucleon is. Finally, the characteristic density for the
+collective ﬂow are obtained, and it is 1.2 ± 0.6ρ0. It is
+consistent with the characteristic density obtained in the
+Ref.[30], but is smaller than the characteristic density
+obtained with pion observable.
+Now, let’s illustrate the constraints of symmetry en-
+ergy at ﬂow and pion characteristic densities, i.e., at
+1.2ρ0 and 1.5ρ0.
+In Fig.3(a), we present the values
+of the symmetry energy at ﬂow characteristic density
+1.2ρ0 and pion characteristic density 1.5ρ0. The black
+square symbols are the results obtained in this work,
+and the values of them are S(1.2ρ0) = 34 ± 4 MeV and
+S(1.5ρ0) = 36 ± 8 MeV. The constraints of S(ρ) at ﬂow
+characteristic density, i.e., at 1.2ρ0, are consistent with
+the analysis of elliptic ﬂow ratios or elliptic ﬂow diﬀer-
+ence by UrQMD[7] or T¨uQMD calculations[6, 9] (which
+are presented by blue symbols) within statistical uncer-
+tainties. The constraints of S(ρ) at pion characteristic
+density, i.e., at 1.5ρ0, is also consistent with our previous
+analysis and constraints from SπRIT[25], T¨uQMD[17],
+dcQMD[20] and IBUU[12, 19] within statistical uncer-
+tainties, except the constraints obtained by LQMD[13].
+Our constraint is also consistent with the recent incli-
+nation analyses by Lynch and Betty [29] (pink shaded
+region) and ab initial theoretical predictions by chiral ef-
+fective ﬁeld theory (χEFT) [45] (orange region).
+Another interesting and important question is what are
+the extrapolated values of symmetry energy at normal
+density, i.e., S0 and L? Fig. 3 (b) shows the extrapo-
+lated values of S0 and L at ρ0 by using both vn
+2 /vch
+2
+and
+π−/π+ in this work (black symbols). The extrapolated
+S0 and L are in 30 − 34 MeV and 5 − 70 MeV, respec-
+tively. The blue symbols are the results from the elliptic
+ﬂow ratios, such as vn
+2 /vp
+2, vn
+2 /vH
+2 and vn
+2 /vch
+2 [5–9], or el-
+liptic ﬂow diﬀerence, such as vn
+2 −vp
+2 and vn
+2 −vH
+2 [6, 7], and
+dark green symbols are the results from π−/π+ ratios[12–
+14, 17–20]. Diﬀerent than the consistency at 1.2ρ0 and
+1.5ρ0 by using ﬂow observables and pion observables, us-
+ing one observable to extrapolate constraints on S0 and L
+leads to an obvious model dependence. For example, the
+extrapolated L by UrQMD, T¨uQMD, dcQMD, IBUU04
+and IBL models with only isospin sensitive pion or ﬂow
+observable are diﬀerent, even within the same transport
+model. Consequently, describing the constraints of sym-
+metry energy at their characteristic density is more reli-
+able than only giving the extrapolated values of S0 and
+L.
+Furthermore, we also compare the extrapolated S0
+and L with the recent constraints by analyzing neu-
+tron skin [46–49], isospin degree of freedom [50], com-
+bined analysis of neutron skin, isospin diﬀusion and neu-
+tron stars [24], and combined analysis from neutron skin
+and astrophysics [51].
+Our result is below the con-
+straints with a speciﬁc class of relativistic energy density
+functional[52], but it is consistent with the one from the
+combining astrophysical data with PREX-II and chiral
+eﬀective ﬁeld theory, L = 53+14
+−15 MeV[48], and it is also
+well consistent with the constraints extracted from the
+charge radius of 54Ni, where they deduced 21 < L < 88
+MeV[47], and very recent Bayesian analysis of charge-
+weak form factor diﬀerence ∆FCW in 48Ca and 208Pb by
+the CREX and PREX-2 collaborations, where they in-
+fer −26 < L < 62 Mev[49]. The consistency with the
+analysis of the isospin degree of freedom (IDOF) and
+isospin diﬀusion with ImQMD model[24, 50], and in the
+ab initial calculations with chiral eﬀective ﬁeld theory
+(χEFT) [45] and relativistic Brueckner-Hartree-Fock the-
+ory (RBHF) [53] is also observed.
+Even the ﬂow and pion observables can not directly
+give the constraints of symmetry energy at subsatura-
+tion density, we also plot the extrapolated symmetry en-
+ergy at subsaturation density with the dashed lines for
+
+5
+FIG. 3. Panel(a): The constrains of the density dependence of symmetry energy at the collective ﬂow characteristic density
+1.2ρ0 and the π−/π+ characteristic density 1.5ρ0. Panel(b): The constraints on S0 and L by using elliptic ﬂow diﬀerence,
+elliptic ﬂow ratio and π−/π+ in this work (green symbols).
+understanding its validity at subsaturation density. The
+uncertainty of extrapolated form of symmetry energy is
+large, but it is still in the reasonable region and covers
+constraints of symmetry energy from the HIC(n/p)[54],
+isospin diﬀusion in HIC(isodiﬀ)[55], mass calculated by
+the eﬀective Skyrme interaction[56] and DFT theory[57],
+Isospin analog state (IAS)[58], electric dipole polarization
+(αD)[59] at their sensitive density, which are decoded in
+Ref.[29].
+In summary, we have investigated the inﬂuence of sym-
+metry energy on nucleonic and pion observable, such as
+vn
+1 , vch
+1 , vn
+2 , vch
+2 , vn
+2 /vch
+2 , M(π) and π−/π+, with UrQMD
+model for Au+Au at the beam energy of 0.4A GeV. To
+constrain the symmetry energy at suprasaturation den-
+sity with the ﬂow and pion observables, the characteristic
+densities obtained with ﬂow and pion observables are dis-
+cussed. Our analysis found that the ﬂow characteristic
+density is around 1.2ρ0 and pion characteristic density is
+around 1.5ρ0. By simultaneously describing the data of
+vn
+2 /vch
+2
+and π−/π+, we got the S(1.2ρ0) = 34 ± 4 MeV
+and S(1.2ρ0) = 36 ± 8 MeV. The constrained symmetry
+energy at characteristic densities are consistent with pre-
+vious analysis by using pion and ﬂow observables with
+diﬀerent transport models, and suggest that the reliable
+constraints on symmetry energy should be presented at
+the characteristic density of isospin sensitive observables.
+Further, the obtained parameter sets are also tested by
+simulating the pion production for Sn+Sn at 0.27A GeV.
+Our validated calculations show that the favored param-
+eter sets can describe the charged pion multiplicity for
+three Sn+Sn reaction systems. The underestimation of
+π−/π+ for 132Sn+124Sn is observed in our calculations,
+which may be attributed to the isospin dependent thresh-
+old eﬀects and isospin dependent in-medium NN → N∆
+cross sections. The line of this work is in progress.
+The inconsistent results on the value of L do not ex-
+actly reﬂect the debates, since the value of L at normal
+density is usually extrapolated from the symmetry en-
+ergy at characteristic density. To enhance the reliability
+of extrapolation of S0 and L, one can expect to use more
+than one isospin sensitive observables which will have the
+information of symmetry energy at diﬀerent characteris-
+tic densities. The extrapolated values of L in this work
+are in 5−70 MeV within 2σ uncertainty for S0 = 30−34
+MeV, which is below the analysis of PREX-II results with
+a speciﬁc class of relativistic energy density functional,
+but is consistent with the constraints from charged ra-
+dius of 54Ni, from the combining astrophysical data with
+PREX-II and chiral eﬀective ﬁeld theory.
+ACKNOWLEDGEMENTS
+The authors thank the discussions on the trans-
+port model and symmetry energy constraints at TMEP
+weekly meeting. This work was supported by the Na-
+tional Key R&D Program of China under Grant No.
+2018 YFA0404404, the National Natural Science Foun-
+dation of China Nos.11875323, 12275359, 12205377,
+11875125, U2032145, 11790320, 11790323, 11790325, and
+11961141003, the Continuous Basic Scientiﬁc Research
+Project (No. WDJC-2019-13), the Continuous Basic Sci-
+entiﬁc Research Project (No. WDJC-2019-13), and the
+funding of China Institute of Atomic Energy, and the
+Leading Innovation Project of the CNNC under Grant
+No.
+LC192209000701, No.
+LC202309000201.
+We ac-
+
+200
+v/ , Russotto
+★ HIC (n/p
+☆ HIC (isodim) 
+■
+ This work
+ v,/,, Wang
+Mass (skyrme
+ IAS
+ vi/vs, Cozma
+Mass (DFT)
+O v/2, Wang
+(MeV)
+(Mev)
+PREX-II
+v-v , Cozma
+60 FZZ
+xEFT
+V v'-v, Wang
+100
+ v,/veh , Russotto
+(d)s
+++++++++ otj ot
++v-v, Wang
+L
+DOF
+,ch, Cozma
+STRIT
+20 
+@ Zhan
+元 / t, Xiao
+/元t, Fel
+XEF
+ 元/nt, Xie
+元/t,Cozma
+chiral EFT
+元 /元t, Liu
+(b)
+0.0
+0.5
+1.0
+1.5
+32
+36
+40
+元 /元t, Yong
+plpo
+_ 元 /nt, Estee
+S. (MeV)6
+knowledge support by the computing server C3S2 in
+Huzhou University.
+[1] B. A. Li, L. W. Chen, and C. M. Ko, Phys. Rept. 464,
+113 (2008).
+[2] C. J. Horowitz, E. F. Brown, Y. Kim, W. G. Lynch,
+R. Michaels, A. Ono, J. Piekarewicz, M. B. Tsang, and
+H. H. Wolter, Journal of Physics G: Nuclear and Particle
+Physics 41, 093001 (2014), URL https://dx.doi.org/
+10.1088/0954-3899/41/9/093001.
+[3] J. Carlson, M. P. Carpenter, R. Casten, C. Elster,
+P. Fallon,
+A. Gade,
+C. Gross,
+G. Hagen,
+A. C.
+Hayes, D. W. Higinbotham, et al., Progress in Par-
+ticle and Nuclear Physics 94, 68 (2017), ISSN 0146-
+6410, URL https://www.sciencedirect.com/science/
+article/pii/S0146641016300722.
+[4] A. Bracco, Europhysics News 48, 21 (2017).
+[5] P. Russotto, P. Wu, M. Zoric, M. Chartier, Y. Leifels,
+R. Lemmon, Q. Li, J. Lukasik, A. Pagano, P. Pawlowski,
+et al., Physics Letters B 697, 471 (2011), ISSN 0370-
+2693, URL https://www.sciencedirect.com/science/
+article/pii/S037026931100178X.
+[6] M. D. Cozma, Y. Leifels, W. Trautmann, Q. Li, and
+P. Russotto, Phys. Rev. C 88, 044912 (2013).
+[7] Y. J. Wang, C. C. Guo, Q. F. Li, H. F. Zhang, Y. Leifels,
+and W. Trautmann, Phys. Rev. C 89, 044603 (2014).
+[8] P. Russotto, S. Gannon, S. Kupny, P. Lasko, L. Acosta,
+M. Adamczyk, A. Al-Ajlan, M. Al-Garawi, and e. a. Al-
+Homaidhi, Phys. Rev. C 94, 034608 (2016), URL https:
+//link.aps.org/doi/10.1103/PhysRevC.94.034608.
+[9] M. D. Cozma, Eur. Phys. J. A 54, 40 (2018).
+[10] B. A. Li, Phys. Rev. Lett. 88, 192701 (2002).
+[11] B. A. Li, Nucl. Phys. A 708, 365 (2002).
+[12] Z. G. Xiao, B. A. Li, L. W. Chen, G. C. Yong, and
+M. Zhang, Phys. Rev. Lett. 102, 062502 (2009).
+[13] Z. Q. Feng and G. M. Jin, Phys. Lett. B 683, 140 (2010).
+[14] W. J. Xie, J. Su, L. Zhu, and F. S. Zhang, Phys. Lett. B
+718, 1510 (2013).
+[15] J. Hong and P. Danielewicz, Phys. Rev. C 90, 024605
+(2014).
+[16] T. Song and C. M. Ko, Phys. Rev. C 91, 014901 (2015).
+[17] M. D. Cozma, Phys. Lett. B 753, 166 (2016).
+[18] Y. Y. Liu, Y. J. Wang, Y. Cui, C. J. Xia, Z. X. Li, Y. J.
+Chen, Q. F. Li, and Y. X. Zhang, Phys. Rev. C 103,
+014616 (2021).
+[19] G. C. Yong, Phys. Rev. C 104, 014613 (2021).
+[20] J. Estee, W. G. Lynch, C. Y. Tsang, J. Barney, G. Jhang,
+M. B. Tsang, R. Wang, M. Kaneko, J. W. Lee, T. Isobe,
+et al. (SπRIT Collaboration), Phys. Rev. Lett. 126,
+162701 (2021), URL https://link.aps.org/doi/10.
+1103/PhysRevLett.126.162701.
+[21] Y. J. Wang and Q. F. Li, Front. Phys. (Beijing) 15, 44302
+(2020).
+[22] B. A. Li and X. Han, Phys. Lett. B 727, 276 (2013).
+[23] M. Oertel, M. Hempel, T. Kl¨ahn, and S. Typel, Rev.
+Mod. Phys. 89, 015007 (2017).
+[24] Y. X. Zhang, M. Liu, C. J. Xia, Z. X. Li, and S. K.
+Biswal, Phys. Rev. C 101, 034303 (2020).
+[25] G.
+Jhang,
+J.
+Estee,
+J.
+Barney,
+G.
+Cerizza,
+M. Kaneko, J. Lee, W. Lynch, T. Isobe, M. Kurata-
+Nishimura,
+T.
+Murakami,
+et
+al.,
+Physics
+Letters
+B
+813,
+136016
+(2021),
+ISSN
+0370-2693,
+URL
+https://www.sciencedirect.com/science/article/
+pii/S0370269320308194.
+[26] Y.-X. Zhang, Y.-J. Wang, M. Colonna, P. Danielewicz,
+A.
+Ono,
+M.
+B.
+Tsang,
+H.
+Wolter,
+J.
+Xu,
+L.-
+W.
+Chen,
+D.
+Cozma,
+et
+al.,
+Phys.
+Rev.
+C
+97,
+034625 (2018), URL https://link.aps.org/doi/10.
+1103/PhysRevC.97.034625.
+[27] A. Ono, J. Xu, M. Colonna, P. Danielewicz, C. M.
+Ko,
+M.
+B.
+Tsang,
+Y.-J.
+Wang,
+H.
+Wolter,
+Y.-
+X. Zhang, L.-W. Chen, et al., Phys. Rev. C 100,
+044617 (2019), URL https://link.aps.org/doi/10.
+1103/PhysRevC.100.044617.
+[28] M. Colonna, Y.-X. Zhang, Y.-J. Wang, D. Cozma,
+P. Danielewicz, C. M. Ko, A. Ono, M. B. Tsang,
+R. Wang,
+H. Wolter,
+et al.,
+Phys. Rev. C 104,
+024603 (2021), URL https://link.aps.org/doi/10.
+1103/PhysRevC.104.024603.
+[29] W. G. Lynch and M. B. Tsang, Phys. Lett. B 830, 137098
+(2022).
+[30] A. Le F`evre, Y. Leifels, W. Reisdorf, J. Aichelin, and
+C. Hartnack, Nucl. Phys. A 945, 112 (2016).
+[31] Y. Liu, Y. Zhang, J. Yang, Y. Wang, Q. Li, and Z. Li, in
+preparation (2022).
+[32] C. Hartnack and J. Aichelin, Phys. Rev. C 49, 2801
+(1994).
+[33] Y. Zhang, N. Wang, Q.-F. Li, L. Ou, J.-L. Tian, M. Liu,
+K. Zhao, X.-Z. Wu, and Z.-X. Li, Front. Phys. (Beijing)
+15, 54301 (2020).
+[34] W. Reisdorf, A. Andronic, R. Averbeck, M. Benabder-
+rahmane,
+O. Hartmann,
+N. Herrmann,
+K. Hilden-
+brand,
+T.
+Kang,
+Y.
+Kim,
+and
+et.
+al.,
+Nuclear
+Physics A 848,
+366 (2010),
+ISSN 0375-9474,
+URL
+https://www.sciencedirect.com/science/article/
+pii/S0375947410006810.
+[35] J. D. Frankland, D. Gruyer, E. Bonnet, B. Borderie,
+R. Bougault, A. Chbihi, J. E. Ducret, D. Durand, Q. Fa-
+ble, M. Henri, et al. (INDRA Collaboration), Phys. Rev.
+C 104, 034609 (2021), URL https://link.aps.org/
+doi/10.1103/PhysRevC.104.034609.
+[36] L. Li, Y. Zhang, Z. Li, N. Wang, Y. Cui, and J. Winkel-
+bauer, Phys. Rev. C 97, 044606 (2018).
+[37] L. Li, X. Chen, Y. Cui, Z. Li, and Y. Zhang (2022),
+2201.12586.
+[38] Y. Wang, Q. Li, Y. Leifels, and A. Le F`evre, Phys. Lett.
+B 802, 135249 (2020).
+[39] Y. Wang, C. Guo, Q. Li, A. Le F`evre, Y. Leifels, and
+W. Trautmann, Phys. Lett. B 778, 207 (2018).
+[40] G. Ferini, M. Colonna, T. Gaitanos, and M. Di Toro,
+Nucl. Phys. A 762, 147 (2005).
+[41] T. Song and C. M. Ko, Phys. Rev. C 91, 014901 (2015).
+[42] Z. Zhang and C. M. Ko, Phys. Rev. C 95, 064604 (2017).
+[43] Q. Li and Z. Li, Phys. Lett. B 773, 557 (2017).
+[44] Y. Cui, Y. Zhang, and Z. Li, Phys. Rev. C 98, 054605
+(2018).
+[45] C. Drischler, R. J. Furnstahl, J. A. Melendez, and D. R.
+Phillips, Phys. Rev. Lett. 125, 202702 (2020).
+
+7
+[46] B. T. Reed,
+F. J. Fattoyev,
+C. J. Horowitz,
+and
+J. Piekarewicz, Phys. Rev. Lett. 126, 172503 (2021).
+[47] S. V. Pineda et al., Phys. Rev. Lett. 127, 182503 (2021).
+[48] R. Essick, I. Tews, P. Landry, and A. Schwenk, Phys.
+Rev. Lett. 127, 192701 (2021).
+[49] Z. Zhang and L.-W. Chen (2022), 2207.03328.
+[50] Y. Zhang, J. Tian, W. Cheng, F. Guan, Y. Huang, H. Li,
+L. L¨u, R. Wang, Y. Wang, Q. Wu, et al., Phys. Rev.
+C 95, 041602 (2017), URL https://link.aps.org/doi/
+10.1103/PhysRevC.95.041602.
+[51] R. Essick, P. Landry, A. Schwenk, and I. Tews, Phys.
+Rev. C 104, 065804 (2021).
+[52] R. Essick, I. Tews, P. Landry, and A. Schwenk, Phys.
+Rev. Lett. 127, 192701 (2021), 2102.10074.
+[53] S. Wang, H. Tong, Q. Zhao, C. Wang, P. Ring, and
+J. Meng, Phys. Rev. C 106, L021305 (2022).
+[54] P. Morfouace et al., Phys. Lett. B 799, 135045 (2019).
+[55] M. B. Tsang, Y. Zhang, P. Danielewicz, M. Famiano,
+Z. Li, W. G. Lynch, and A. W. Steiner, Phys. Rev. Lett.
+102, 122701 (2009).
+[56] B. A. Brown, Phys. Rev. Lett. 111, 232502 (2013).
+[57] M. Kortelainen, J. McDonnell, W. Nazarewicz, P. G.
+Reinhard, J. Sarich, N. Schunck, M. V. Stoitsov, and
+S. M. Wild, Phys. Rev. C 85, 024304 (2012).
+[58] P. Danielewicz, P. Singh, and J. Lee, Nucl. Phys. A 958,
+147 (2017).
+[59] Z. Zhang and L.-W. Chen, Phys. Rev. C 92, 031301
+(2015).
+
diff --git a/ntAyT4oBgHgl3EQfY_cD/content/tmp_files/load_file.txt b/ntAyT4oBgHgl3EQfY_cD/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..9989696dbb045b67c6a0fdb3f1251d0098396900
--- /dev/null
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+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf,len=927
+page_content='How Do Constraints of Nuclear Symmetry Energy Reconcile with Diﬀerent Models?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='  Yingxun Zhang,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' 2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' ∗ Yangyang Liu,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' † Yongjia Wang,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='3,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' ‡ Qingfeng Li,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='3,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' 4,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' § and Zhuxia Li1  1China Institute of Atomic Energy,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Beijing 102413,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' China  2Guangxi Key Laboratory of Nuclear Physics and Technology,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='  Guangxi Normal University,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Guilin,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' 541004,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' China  3School of Science,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Huzhou University,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Huzhou 313000,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' China  4Institute of Modern Physics,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Chinese Academy of Sciences,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Lanzhou 730000,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' China  (Dated: January 3,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' 2023)  By simultaneously describing the data of isospin sensitive nucleonic ﬂow and pion observables,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='  such as vn  2 /vch  2  and π−/π+,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' with ultra-relativistic quantum molecular dynamics (UrQMD) model,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='  we got the symmetry energy at ﬂow and pion characteristic densities which are S(1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='2ρ0) = 34 ± 4  MeV and S(1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='5ρ0) = 36 ± 8 MeV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Within the uncertainties, the constraints of symmetry energy  at characteristic densities are consistent with the previous constraints by using other transport  models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='  The consistency suggests that the reliable constraints on symmetry energy should be  presented at the characteristic density of isospin sensitive observables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' By using the constraints of  symmetry energy at two diﬀerent characteristic densities, the extrapolated value of L is provided.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='  Within 2σ uncertainty, the extrapolated value of L is in 5 − 70 MeV which is consistent with the  recent combination analysis from PREX-II and astrophyiscs data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Further, the calculations with  the constrained parameter sets can describe the data of charged pion multiplicities from SπRIT  collaboration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='  Knowledge of the symmetry energy is crucial for un-  derstanding the isospin asymmetric objects, such as  the structure of neutron-rich nuclei, the mechanism of  neutron-rich heavy ion collisions, and the properties of  neutron stars[1, 2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' However, theoretical predictions on  the symmetry energy away from the normal density show  larger uncertainty, and it leads that the constraint of  symmetry energy becomes one of the important goals in  nuclear physics[3, 4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='  For probing the symmetry energy at suprasaturation  density, the isospin-sensitive observables in heavy ion col-  lisions (HICs), such as the ratio of elliptic ﬂow of neutron  to charged particle, hydrogen isotopes or proton (vn  2 /vch  2 ,  vn  2 /vH  2 or vn  2 /vp  2)[5–9] and the yield ratios of charged pi-  ons (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=', M(π−)/M(π+) or named as π−/π+)[10–20],  were frequently used.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='  By comparing the transverse-  momentum-dependent or integrated FOPI/LAND ellip-  tic ﬂow data of nucleons and hydrogen isotopes with  UrQMD[5, 7] and T¨uQMD models[6], a moderately soft  to linear symmetry energy is obtained[8].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Usually, the  constraints of symmetry energy were presented by the  symmetry energy coeﬃcient S0 and the slope of symme-  try energy L at normal density.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='  The lower limit of L  obtained with the ﬂow ratio data is 60 MeV[21], which  overlaps with the upper limits of the constraints from the  nuclear structure and isospin diﬀusion, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=', L ≈ 60 ± 20  MeV[22–24].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='  The deduced L from FOPI π−/π+ data  show strong model dependence[12–18, 25], which ranges  from 12 MeV to 144 MeV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='  To reduce the model dependence on the constraints of  symmetry energy, especially at suprasaturation densities,  ∗ zhyx@ciae.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='ac.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='cn  † liuyangyang@ciae.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='ac.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='cn  ‡ wangyongjia@zjhu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='edu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='cn  § liqf@zjhu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='edu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='cn  the transport model evaluation project was performed  among the transport model community since 2009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Up  to now, the transport model evaluation project has made  important progress on the reduction of model depen-  dence of transport model by benchmarking the treatment  of particle-particle collision[26, 27] and nucleonic mean  ﬁeld potential[28] in both Boltzmann-Uehling-Uhlenbeck  (BUU) type and Quantum molecular dynamics (QMD)  type models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' However, the recent works on SπRIT pion  data [20] for Sn+Sn collision system at 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='27A GeV have  also shown the model dependence after comparing the  pion production with seven updated transport models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='  It hints the model dependence of the inferred L by using  ﬂow or pion observables may come from the extrapolation  of symmetry energy from the probed density to normal  density.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='  To verify this issue, one has to know which density is  probed by ﬂow and pion observables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' The named char-  acteristic density was proposed in Refs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' [18, 24, 29, 30],  which is used to quantitatively describe the density  probed by the ﬂow or pion observables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='  After know-  ing the characteristic density, the consistency or incon-  sistency of symmetry energy constraints can be further  understood.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' In this work, we simultaneously investigate  the ﬂow and pion observables within the framework of  UrQMD model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' By comparing the calculation to ASY-  EOS and FOPI data, the data favored parameter sets  are obtained and a remarkable consistency is found at  both ﬂow and pion characteristic densities among diﬀer-  ent transport models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='  The version of UrQMD model we used is the same as  that in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' [18] but the momentum dependent interaction  and the cross sections of NN → N∆ near the threshold  energy are reﬁned, more details are in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' [31].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='  The  nucleonic potential energy U is calculated from the po-  tential energy density, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=', U =  �  ud3r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='  The u reads  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='00212v1  [nucl-th]  31 Dec 2022  2  as  u = α  2  ρ2  ρ0  +  β  η + 1  ρη+1  ρη  0  (1)  +gsur  2ρ0  (∇ρ)2 + gsur,iso  ρ0  [∇(ρn − ρp)]2  +umd + usym.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='  The parameters α, β, and η are related to the two, three-  body interaction term.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' The third and fourth terms are  isospin independent and isospin dependent surface term,  respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' The umd is from the momentum dependent  interaction (MDI) term, which is calculated according to  the following relationship,  umd =  �  N1,N2=n,p  �  d3p1d3p2fN1 (r, ⃗p1) fN2 (r, ⃗p2)  vmd(∆p12).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='  (2)  fNi(r, ⃗p) is the phase space density of particle Ni.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' The  form of MDI, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=', vmd(∆p12), is assumed as,  vmd(∆p12) = t4 ln2(1 + t5∆p2  12) + c,  (3)  where ∆p12 = |p1 − p2|, and the parameters t4, t5 and c  are obtained by reproducing the real part of the optical  potential of Hama’s data by using Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' (3) and  Vmd(p1) =  �  p2<pF  vmd(p1 − p2)d3p2/  �  p2<pF  d3p2,  (4)  within the kinetic energy Ekin ≈ 750 MeV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' The method  we used is as same as in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='[32].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' With the consideration  of MDI, the parameter α, β, and η are readjusted to keep  the incompressibility of symmetric nuclear matter K0 =  231 MeV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' The values of parameters and corresponding  eﬀective mass are listed in Table I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='  TABLE I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Parameters used in this work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' t4, c, α, β and K0  are in MeV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' t5 is in MeV−2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' η and m∗/m are dimensionless.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='  Para.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='  t4  t5  c  α  β  η  K0 m∗/m  vHama  md  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='058 5×10−4 -86 -335 253 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='16 231 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='635  For the potential energy density of symmetry energy  part, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=', usym, we take two forms in the calculations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='  One is the Skyrme-type polynomial form (form (a) in  Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' (5)) and another is the density power law form (form  (b) in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' (5)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' It reads,  usym = Spot  sym(ρ)ρδ2  (5)  =  �  (A( ρ  ρ0 ) + B( ρ  ρ0 )γs + C( ρ  ρ0 )5/3)ρδ2, (a)  Cs  2 ( ρ  ρ0 )γiρδ2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='  (b)  In the following calculations, S0 varies from 30 to 34 MeV  and L varies from 5 to 144 MeV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' The corresponding pa-  rameters in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' (5) are determined with the relationship  in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' [24, 33].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='  The calculations of Au+Au at 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='4A GeV and Sn+Sn at  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='27 A GeV are performed with 200,000 events.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Since the  collision centrality is determined by the Zbound or Zrat  in the Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' [8] and the detected charged particle multi-  plicity [25] or the ratio of total transverse to longitudinal  kinetic energies in the center-of-mass (c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=') system in  Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' [34], the corresponding impact parameter b will be  in a wide range and the weight of b is a Gaussian shape  rather than a triangular shape.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' This impact smearing  eﬀect [8, 35–37] is also considered in calculations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' In Ta-  ble.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='II, we list the experimental sixteen observables we  investigated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='  TABLE II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Sixteen experimental observables and the corre-  sponding averaged impact parameters (in fm) analyzed in this  work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='  Obsevable  < b >  system  Exp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='  vn  1 (pt/A)  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='69  Au+Au  ASY-EOS [8]  vch  1 (pt/A)  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='69  Au+Au  ASY-EOS [8]  vn  2 (pt/A)  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='69  Au+Au  ASY-EOS [8]  vch  2 (pt/A)  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='69  Au+Au  ASY-EOS [8]  vn  2 /vch  2 (pt/A)  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='69  Au+Au  ASY-EOS [8]  M(π)  <2a  Au+Au  FOPI [34]  π−/π+  <2a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='  Au+Au  FOPI [34]  Y (π−)  3  108Sn+112Sn  SπRIT [25]  Y (π−)  3  112Sn+124Sn  SπRIT [25]  Y (π−)  3  132Sn+124Sn  SπRIT [25]  Y (π+)  3  108Sn+112Sn  SπRIT [25]  Y (π+)  3  112Sn+124Sn  SπRIT [25]  Y (π+)  3  132Sn+124Sn  SπRIT [25]  π−/π+  3  108Sn+112Sn  SπRIT [25]  π−/π+  3  112Sn+124Sn  SπRIT [25]  π−/π+  3  132Sn+124Sn  SπRIT [25]  a We did not put the average b value here since experimental  paper only provides b/bmax < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='15, which is obtained by  estimating the impact parameter b from the measured  diﬀerential cross sections for the ERAT under a geometrical  sharp-cut approximation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='1 illustrates the UrQMD model calculations and  the measured data for the directed (v1) and the el-  liptic ﬂow (v2) of neutrons and charged particles as a  function of the transverse momentum per nucleon pt/A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='  The intervals of the polar angle and rapidity are cho-  sen to be the same as in the ASY-EOS analysis, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=',  37◦ < θlab < 53◦ and −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='5 < y0 < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' As an exam-  ple, we present the results obtained with L = 35 MeV  (dashed lines) and L = 144 MeV (solid lines) at S0 = 30  MeV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' The symbols are the ASY-EOS data from Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' [8].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='  As shown in panels (a) and (b), the calculations with dif-  ferent L fall in the data region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' But the results calculated  with L = 35 MeV and L = 144 MeV sets are overlapping  each other, which indicates v1 in the plotted intervals has  no sensitivity to the nuclear symmetry energy, due to the  spectator matter blocking eﬀect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='  For the elliptic ﬂow, the eﬀects of symmetry energy  3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='8  ASY-EOS  v1  neutron  (c)  L35  L144  (a)  v2  pt/A (GeV/c)  (d)  Au+Au Ebeam=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='4A GeV  Charged particles  (b)  pt/A (GeV/c)  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' The directed ﬂow v1 (upper panels) and elliptic ﬂow  v2 (lower panels) of free neutrons (left panels) and charged  particles (right panels).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' The dash and solid lines represent  the results with L = 35 MeV and L = 144 MeV, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='  The ASY-EOS data of collective ﬂow for neutron and charged  particles are shown as circle and triangle symbols[8].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='  on v2 of both free neutrons and charged particles can  be clearly observed as in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='1 (c) and (d).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='  Both the  vn  2 and vch  2  have negative values and decrease with pt/A  increasing, which means a preference for particle emis-  sion out of the reaction plane, towards 90◦ and 270◦.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' As  shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='1 (c), the values of vn  2 obtained with stiﬀ  symmetry energy case are lower than that with soft sym-  metry energy case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' The reason is that the stiﬀ symmetry  energy provides a stronger repulsive force on neutrons  at suprasaturation density than that for soft symmetry  energy cases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' For charged particles, as shown in panel  (d), vch  2  obtained with the stiﬀ symmetry energy case  are higher than that with the soft symmetry energy case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='  This is because the emitted charged particles are mainly  composed of free protons, which feel stronger attractive  interaction for the stiﬀ symmetry energy case than that  for the soft symmetry energy case at suprasaturation den-  sity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Consequently, vch  2  obtained with the stiﬀ symmetry  energy case is higher than that with the soft symmetry  energy case, which has also been discussed in Refs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' [5–  7, 38].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' However, vn  2 or vch  2  cannot be used individually  to constrain the symmetry energy, because both vn  2 or  vch  2  not only depend on the symmetry energy but also on  the MDI and incompressibility.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' For example, the calcula-  tions with diﬀerent incompressibility can lead to diﬀerent  results on the elliptic ﬂow[39].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='  To isolate the contributions from the isocalar poten-  tial, vn  2 /vch  2  ratio was proposed to probe symmetry en-  ergy and several analysis have been performed by using  the UrQMD model or T¨uQMD model[8, 17].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='2 (a),  we present the calculated results for vn  2 /vch  2 as a function  of pt/A obtained with L = 35 MeV and 144 MeV sets at  S0 = 30, 32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='5 and 34 MeV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' The symbols are the ASY-  EOS data points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' The calculations show that vn  2 /vch  2  is  sensitive to L, especially at the low pt region in which  the mean-ﬁeld play more important role.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' The values of  vn  2 /vch  2  obtained with L = 144 MeV sets are larger than  that with L = 35 MeV sets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' This behavior can be un-  derstood from Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='1 (c) and (d).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' By comparing the cal-  culations of vn  2 /vch  2  to ASY-EOS experimental data and  doing a χ2 analysis, one draw the conclusion on the slope  of symmetry energy is 5-67 MeV for S0 = 32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='5 MeV case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='  After considering the uncertainties of S0, the constraints  on the L extend to 5-70 MeV which are presented in panel  (b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Panel (a) vn  2 /vch  2  as a function of pt/A for L = 35  MeV and L = 144 MeV with S0 in the range from 30 MeV to  34 MeV;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' (b) χ2 as a function of L for S0=30 (blue lines) and  34 MeV (red lines).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Panel (c) and (d) are M(π)/Apart.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' and  π−/π+ ratio as a function of L with S0 = 30 and 34 MeV,  respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Panel (e) and (f) are the multiplicity of charged  pion and its ratio as a function of N/Z of the system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' The  black symbols represent the ASY-EOS experimental data[8],  the cyan-shaded region is the FOPI data and the blue symbols  are the SπRIT data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='2 (c) and (d) show the calculated Mπ and π−/π+  for Au+Au as a function of L (shaded region with diﬀer-  ent color boundary) and the FOPI data (cyan shaded re-  gion).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' The width of the red-shaded region represents the  results obtained with S0 from 30 to 34 MeV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' M(π) cal-  culated with diﬀerent S0 and L falls into the data region,  and suggest that M(π) can not be used to distinguish  2  20  ASY-EOS  1 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='4A GeV  L=144MeV  S=30 MeV  W2  10  S,=34 MeV  L=35 MeV  (a)  (b)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='30  1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='45  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='60  0  50  100  150  p/A (GeV/c)  L(MeV)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='020  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='5  part  FOPI  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='  A  M  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='015  S,=30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' MeV  [(c)  (d)  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='=34 MeV  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='5  0  50  100  0  50  100  150  L(MeV)  L(MeV)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='8  S元RIT  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='27A  JGeV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Sn+Sn  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='0  元  元  S,=30 MeV, L=5 MeV  元  M  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='4  允*  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='5  (e)  (f)  S,=34 MeV, L=84 MeV  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='2  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='4  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='61.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='2  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='4  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='6  N/Z  N/Z4  L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' The π−/π+ ratios obtained with UrQMD model are  sensitive to L, and it decreases with the increase of L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='  Comparing the calculated results of π−/π+ to the FOPI  experimental data, the parameter sets with L=5-70 MeV  are favored.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='  To test the validation of obtained parameter sets, we  also perform the calculations of Sn+Sn and compare the  pion production results to SπRIT data (black symbols).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='2 (e) and (f) show the charged pion multiplicities  and its ratio as a function of N/Z of system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Two ex-  treme values of L are used in the validation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' One is for  S0 = 30 MeV and L = 5 MeV and another is S0 = 34  MeV and L = 84 MeV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' The testing calculations demon-  strate that the calculation with L = 5 MeV set can de-  scribe the M(π−) and M(π+) for three reaction system,  108Sn+112Sn, 112Sn+124Sn and 132Sn+124Sn, within the  experimental uncertainties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' For π−/π+ ratios, the calcu-  lations can reproduce the data for the 108Sn+112Sn and  112Sn+124Sn system, but underestimate the data for very  neutron rich system 132Sn+124Sn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' The discrepancy is re-  lated to the subthreshold pion production mechanism,  where the threshold eﬀects[40–42] and isospin-dependent  medium correction on NN → N∆ cross section[43, 44]  become important.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='  Although the data favored parameter sets are pre-  sented with L value at normal density, one should keep  in mind that the isospin observables vn  2 /vch  2  and π−/π+  probe the symmetry energy information at suprasatura-  tion density region rather than at normal density.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' The in-  teresting point is what density is probed by ﬂow and pion  observables?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Here, we use the named characteristic den-  sity to quantitatively describe them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' For pion observable,  the characteristic density is obtained by averaging the  compressed density with pion production rate in spatio-  temporal domain [18], and the calculations show that  the characteristic density of pion observable is around  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='5 times normal density.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='  For collective ﬂow, the idea of calculating characteristic  density is as same as pion characteristic density[18, 30],  but the weight is replaced by the momentum change of  nucleons which reﬂects strength of driven force for the  collective motion of emitted particles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' With this weight  deﬁnition, the more momentum change during the time  evolution is, the more weight on the collective motion  of nucleon is.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Finally, the characteristic density for the  collective ﬂow are obtained, and it is 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='2 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='6ρ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' It is  consistent with the characteristic density obtained in the  Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' [30], but is smaller than the characteristic density  obtained with pion observable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='  Now, let’s illustrate the constraints of symmetry en-  ergy at ﬂow and pion characteristic densities, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=', at  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='2ρ0 and 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='5ρ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='  In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='3(a), we present the values  of the symmetry energy at ﬂow characteristic density  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='2ρ0 and pion characteristic density 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='5ρ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' The black  square symbols are the results obtained in this work,  and the values of them are S(1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='2ρ0) = 34 ± 4 MeV and  S(1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='5ρ0) = 36 ± 8 MeV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' The constraints of S(ρ) at ﬂow  characteristic density, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=', at 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='2ρ0, are consistent with  the analysis of elliptic ﬂow ratios or elliptic ﬂow diﬀer-  ence by UrQMD[7] or T¨uQMD calculations[6, 9] (which  are presented by blue symbols) within statistical uncer-  tainties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' The constraints of S(ρ) at pion characteristic  density, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=', at 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='5ρ0, is also consistent with our previous  analysis and constraints from SπRIT[25], T¨uQMD[17],  dcQMD[20] and IBUU[12, 19] within statistical uncer-  tainties, except the constraints obtained by LQMD[13].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='  Our constraint is also consistent with the recent incli-  nation analyses by Lynch and Betty [29] (pink shaded  region) and ab initial theoretical predictions by chiral ef-  fective ﬁeld theory (χEFT) [45] (orange region).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='  Another interesting and important question is what are  the extrapolated values of symmetry energy at normal  density, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=', S0 and L?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' 3 (b) shows the extrapo-  lated values of S0 and L at ρ0 by using both vn  2 /vch  2  and  π−/π+ in this work (black symbols).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' The extrapolated  S0 and L are in 30 − 34 MeV and 5 − 70 MeV, respec-  tively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' The blue symbols are the results from the elliptic  ﬂow ratios, such as vn  2 /vp  2, vn  2 /vH  2 and vn  2 /vch  2 [5–9], or el-  liptic ﬂow diﬀerence, such as vn  2 −vp  2 and vn  2 −vH  2 [6, 7], and  dark green symbols are the results from π−/π+ ratios[12–  14, 17–20].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Diﬀerent than the consistency at 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='2ρ0 and  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='5ρ0 by using ﬂow observables and pion observables, us-  ing one observable to extrapolate constraints on S0 and L  leads to an obvious model dependence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' For example, the  extrapolated L by UrQMD, T¨uQMD, dcQMD, IBUU04  and IBL models with only isospin sensitive pion or ﬂow  observable are diﬀerent, even within the same transport  model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Consequently, describing the constraints of sym-  metry energy at their characteristic density is more reli-  able than only giving the extrapolated values of S0 and  L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='  Furthermore, we also compare the extrapolated S0  and L with the recent constraints by analyzing neu-  tron skin [46–49], isospin degree of freedom [50], com-  bined analysis of neutron skin, isospin diﬀusion and neu-  tron stars [24], and combined analysis from neutron skin  and astrophysics [51].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='  Our result is below the con-  straints with a speciﬁc class of relativistic energy density  functional[52],' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' but it is consistent with the one from the  combining astrophysical data with PREX-II and chiral  eﬀective ﬁeld theory,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' L = 53+14  −15 MeV[48],' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' and it is also  well consistent with the constraints extracted from the  charge radius of 54Ni,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' where they deduced 21 < L < 88  MeV[47],' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' and very recent Bayesian analysis of charge-  weak form factor diﬀerence ∆FCW in 48Ca and 208Pb by  the CREX and PREX-2 collaborations,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' where they in-  fer −26 < L < 62 Mev[49].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' The consistency with the  analysis of the isospin degree of freedom (IDOF) and  isospin diﬀusion with ImQMD model[24, 50], and in the  ab initial calculations with chiral eﬀective ﬁeld theory  (χEFT) [45] and relativistic Brueckner-Hartree-Fock the-  ory (RBHF) [53] is also observed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='  Even the ﬂow and pion observables can not directly  give the constraints of symmetry energy at subsatura-  tion density, we also plot the extrapolated symmetry en-  ergy at subsaturation density with the dashed lines for  5  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Panel(a): The constrains of the density dependence of symmetry energy at the collective ﬂow characteristic density  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='2ρ0 and the π−/π+ characteristic density 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='5ρ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Panel(b): The constraints on S0 and L by using elliptic ﬂow diﬀerence,  elliptic ﬂow ratio and π−/π+ in this work (green symbols).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='  understanding its validity at subsaturation density.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' The  uncertainty of extrapolated form of symmetry energy is  large, but it is still in the reasonable region and covers  constraints of symmetry energy from the HIC(n/p)[54],  isospin diﬀusion in HIC(isodiﬀ)[55], mass calculated by  the eﬀective Skyrme interaction[56] and DFT theory[57],  Isospin analog state (IAS)[58], electric dipole polarization  (αD)[59] at their sensitive density, which are decoded in  Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' [29].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='  In summary, we have investigated the inﬂuence of sym-  metry energy on nucleonic and pion observable, such as  vn  1 , vch  1 , vn  2 , vch  2 , vn  2 /vch  2 , M(π) and π−/π+, with UrQMD  model for Au+Au at the beam energy of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='4A GeV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' To  constrain the symmetry energy at suprasaturation den-  sity with the ﬂow and pion observables, the characteristic  densities obtained with ﬂow and pion observables are dis-  cussed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Our analysis found that the ﬂow characteristic  density is around 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='2ρ0 and pion characteristic density is  around 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='5ρ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' By simultaneously describing the data of  vn  2 /vch  2  and π−/π+, we got the S(1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='2ρ0) = 34 ± 4 MeV  and S(1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='2ρ0) = 36 ± 8 MeV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' The constrained symmetry  energy at characteristic densities are consistent with pre-  vious analysis by using pion and ﬂow observables with  diﬀerent transport models, and suggest that the reliable  constraints on symmetry energy should be presented at  the characteristic density of isospin sensitive observables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='  Further, the obtained parameter sets are also tested by  simulating the pion production for Sn+Sn at 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='27A GeV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='  Our validated calculations show that the favored param-  eter sets can describe the charged pion multiplicity for  three Sn+Sn reaction systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' The underestimation of  π−/π+ for 132Sn+124Sn is observed in our calculations,  which may be attributed to the isospin dependent thresh-  old eﬀects and isospin dependent in-medium NN → N∆  cross sections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' The line of this work is in progress.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='  The inconsistent results on the value of L do not ex-  actly reﬂect the debates, since the value of L at normal  density is usually extrapolated from the symmetry en-  ergy at characteristic density.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' To enhance the reliability  of extrapolation of S0 and L, one can expect to use more  than one isospin sensitive observables which will have the  information of symmetry energy at diﬀerent characteris-  tic densities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' The extrapolated values of L in this work  are in 5−70 MeV within 2σ uncertainty for S0 = 30−34  MeV, which is below the analysis of PREX-II results with  a speciﬁc class of relativistic energy density functional,  but is consistent with the constraints from charged ra-  dius of 54Ni, from the combining astrophysical data with  PREX-II and chiral eﬀective ﬁeld theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='  ACKNOWLEDGEMENTS  The authors thank the discussions on the trans-  port model and symmetry energy constraints at TMEP  weekly meeting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' This work was supported by the Na-  tional Key R&D Program of China under Grant No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='  2018 YFA0404404, the National Natural Science Foun-  dation of China Nos.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='11875323, 12275359, 12205377,  11875125, U2032145, 11790320, 11790323, 11790325, and  11961141003, the Continuous Basic Scientiﬁc Research  Project (No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' WDJC-2019-13), the Continuous Basic Sci-  entiﬁc Research Project (No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' WDJC-2019-13), and the  funding of China Institute of Atomic Energy, and the  Leading Innovation Project of the CNNC under Grant  No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='  LC192209000701, No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='  LC202309000201.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content="  We ac-  200  v/ , Russotto  ★ HIC (n/p  ☆ HIC (isodim)  ■  This work  v,/,, Wang  Mass (skyrme  IAS  vi/vs, Cozma  Mass (DFT)  O v/2, Wang  (MeV)  (Mev)  PREX-II  v-v , Cozma  60 FZZ  xEFT  V v'-v, Wang  100  v,/veh , Russotto  (d)s  ++++++++ otj ot  +v-v, Wang  L  DOF  ,ch, Cozma  STRIT  20  @ Zhan  元 / t, Xiao  /元t, Fel  XEF  元/nt, Xie  元/t,Cozma  chiral EFT  元 /元t, Liu  (b)  0." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='5  32  36  40  元 /元t, Yong  plpo  _ 元 /nt, Estee  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' (MeV)6  knowledge support by the computing server C3S2 in  Huzhou University.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='  [1] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Li, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Chen, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Ko, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Rept.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' 464,  113 (2008).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='  [2] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Horowitz, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Brown, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Kim, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Lynch,  R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Michaels, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Ono, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Piekarewicz, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Tsang, and  H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Wolter, Journal of Physics G: Nuclear and Particle  Physics 41, 093001 (2014), URL https://dx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='org/  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='1088/0954-3899/41/9/093001.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='  [3] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Carlson, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Carpenter, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Casten, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Elster,  P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Fallon,  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Gade,  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Gross,  G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Hagen,  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='  Hayes, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Higinbotham, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=', Progress in Par-  ticle and Nuclear Physics 94, 68 (2017), ISSN 0146-  6410, URL https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
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+page_content='  [4] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Bracco, Europhysics News 48, 21 (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='  [5] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Russotto, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Wu, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Zoric, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Chartier, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Leifels,  R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Lemmon, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Li, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Lukasik, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Pagano, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Pawlowski,  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=', Physics Letters B 697, 471 (2011), ISSN 0370-  2693, URL https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
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+page_content='  [6] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Cozma, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Leifels, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Trautmann, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Li, and  P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Russotto, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' C 88, 044912 (2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='  [7] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Wang, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Guo, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Li, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Zhang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Leifels,  and W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Trautmann, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' C 89, 044603 (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='  [8] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Russotto, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Gannon, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Kupny, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Lasko, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Acosta,  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Adamczyk, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Al-Ajlan, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Al-Garawi, and e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Al-  Homaidhi, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' C 94, 034608 (2016), URL https:  //link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='aps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='1103/PhysRevC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='94.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='034608.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='  [9] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Cozma, Eur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' A 54, 40 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='  [10] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Li, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' 88, 192701 (2002).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='  [11] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Li, Nucl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' A 708, 365 (2002).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='  [12] Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Xiao, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Li, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Chen, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Yong, and  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Zhang, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' 102, 062502 (2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='  [13] Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Feng and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Jin, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' B 683, 140 (2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='  [14] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Xie, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Su, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Zhu, and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Zhang, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' B  718, 1510 (2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='  [15] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Hong and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Danielewicz, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' C 90, 024605  (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='  [16] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Song and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Ko, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' C 91, 014901 (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='  [17] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Cozma, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' B 753, 166 (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='  [18] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Liu, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Wang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
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+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Xia, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
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+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
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+page_content=' C 103,  014616 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
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+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
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+page_content=' C 104, 014613 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='  [20] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
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+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
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+page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
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+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
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+page_content=' Wang, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
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+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Lee, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
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+page_content=' (SπRIT Collaboration), Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' 126,  162701 (2021), URL https://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
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+page_content='  [21] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Wang and Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Li, Front.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' (Beijing) 15, 44302  (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='  [22] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Li and X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
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+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' B 727, 276 (2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='  [23] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Oertel, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Hempel, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Kl¨ahn, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Typel, Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='  Mod.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' 89, 015007 (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='  [24] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Zhang, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Liu, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Xia, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
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+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
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+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' C 101, 034303 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='  [25] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='  Jhang,  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
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+page_content='  Cerizza,  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
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+page_content=' Lee, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Lynch, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
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+page_content=' Kurata-  Nishimura,  T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='  Murakami,  et  al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=',  Physics  Letters  B  813,  136016  (2021),  ISSN  0370-2693,  URL  https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
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+page_content='  [26] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='-X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Zhang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='-J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Wang, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Colonna, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Danielewicz,  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='  Ono,  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='  Tsang,  H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='  Wolter,  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='  Xu,  L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='-  W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='  Chen,  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
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+page_content='  Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='  C  97,  034625 (2018), URL https://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='aps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='  1103/PhysRevC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='97.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='034625.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='  [27] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Ono, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Xu, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Colonna, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Danielewicz, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='  Ko,  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='  Tsang,  Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='-J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='  Wang,  H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
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+page_content='-W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
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+page_content=' C 100,  044617 (2019), URL https://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
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+page_content='-X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
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+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Ko, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
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+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
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+page_content=' B 830, 137098  (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
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+page_content=' Le F`evre, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Leifels, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
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+page_content=' Aichelin, and  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
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+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' A 945, 112 (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='  [31] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Liu, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
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+page_content=' Hartnack and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
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+page_content=' C 49, 2801  (1994).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='  [33] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Zhang, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
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+page_content='-F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
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+page_content=' Ou, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='-L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Tian, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
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+page_content='-Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
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+page_content='-X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
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+page_content='  [34] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Reisdorf, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
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+page_content=' Benabder-  rahmane,  O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
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+page_content='  al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
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+page_content='  [35] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Frankland, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
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+page_content=' Borderie,  R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
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+page_content=' Chbihi, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Ducret, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
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+page_content='  C 104, 034609 (2021), URL https://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
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+page_content='  [36] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Li, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Zhang, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Li, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Wang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Cui, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Winkel-  bauer, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' C 97, 044606 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='  [37] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Li, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Chen, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Cui, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Li, and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Zhang (2022),  2201.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='12586.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='  [38] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Wang, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Li, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Leifels, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Le F`evre, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='  B 802, 135249 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='  [39] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Wang, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Guo, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Li, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Le F`evre, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Leifels, and  W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Trautmann, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' B 778, 207 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='  [40] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Ferini, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Colonna, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Gaitanos, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Di Toro,  Nucl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' A 762, 147 (2005).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='  [41] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Song and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Ko, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' C 91, 014901 (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='  [42] Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Zhang and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Ko, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' C 95, 064604 (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='  [43] Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Li and Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Li, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' B 773, 557 (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='  [44] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Cui, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Zhang, and Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Li, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' C 98, 054605  (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='  [45] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Drischler, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Furnstahl, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Melendez, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='  Phillips, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' 125, 202702 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='  7  [46] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Reed,  F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Fattoyev,  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Horowitz,  and  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Piekarewicz, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' 126, 172503 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='  [47] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Pineda et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=', Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' 127, 182503 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='  [48] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Essick, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Tews, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Landry, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Schwenk, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='  Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' 127, 192701 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='  [49] Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Zhang and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='-W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Chen (2022), 2207.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='03328.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='  [50] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Zhang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Tian, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Cheng, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Guan, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Huang, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Li,  L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' L¨u, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Wang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Wang, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Wu, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=', Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='  C 95, 041602 (2017), URL https://link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='aps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='org/doi/  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='1103/PhysRevC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='95.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='041602.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='  [51] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Essick, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Landry, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Schwenk, and I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Tews, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='  Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' C 104, 065804 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='  [52] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Essick, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Tews, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Landry, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Schwenk, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='  Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' 127, 192701 (2021), 2102.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='10074.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='  [53] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Wang, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Tong, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Zhao, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Wang, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Ring, and  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Meng, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' C 106, L021305 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='  [54] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Morfouace et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=', Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' B 799, 135045 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='  [55] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Tsang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Zhang, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Danielewicz, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Famiano,  Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Li, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Lynch, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Steiner, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='  102, 122701 (2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='  [56] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Brown, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' 111, 232502 (2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='  [57] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Kortelainen, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' McDonnell, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Nazarewicz, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='  Reinhard, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Sarich, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Schunck, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Stoitsov, and  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Wild, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' C 85, 024304 (2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='  [58] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Danielewicz, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Singh, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Lee, Nucl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' A 958,  147 (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='  [59] Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Zhang and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content='-W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Chen, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
+page_content=' C 92, 031301  (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntAyT4oBgHgl3EQfY_cD/content/2301.00212v1.pdf'}
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+Multimodal Inverse Cloze Task for
+Knowledge-based Visual Question Answering⋆
+Paul Lerner1, Olivier Ferret2, and Camille Guinaudeau1
+1 Universit´e Paris-Saclay, CNRS, LISN, 91400, Orsay, France
+{paul.lerner,camille.guinaudeau}@lisn.upsaclay.fr
+2 Universit´e Paris-Saclay, CEA, List, F-91120, Palaiseau, France
+olivier.ferret@cea.fr
+Abstract. We present a new pre-training method, Multimodal Inverse
+Cloze Task, for Knowledge-based Visual Question Answering about nam-
+ed Entities (KVQAE). KVQAE is a recently introduced task that consists
+in answering questions about named entities grounded in a visual context
+using a Knowledge Base. Therefore, the interaction between the modal-
+ities is paramount to retrieve information and must be captured with
+complex fusion models. As these models require a lot of training data,
+we design this pre-training task from existing work in textual Question
+Answering. It consists in considering a sentence as a pseudo-question and
+its context as a pseudo-relevant passage and is extended by considering
+images near texts in multimodal documents. Our method is applicable to
+diﬀerent neural network architectures and leads to a 9% relative-MRR
+and 15% relative-F1 gain for retrieval and reading comprehension, re-
+spectively, over a no-pre-training baseline.
+Keywords: Visual Question Answering · Pre-training · Multimodal Fu-
+sion.
+1
+Introduction
+Knowledge-based Visual Question Answering about named Entities (KVQAE) is
+a challenging task recently introduced in [50]. It consists in answering questions
+about named entities grounded in a visual context using a Knowledge Base
+(KB). Figure 1 provides two examples of visual questions along with relevant
+visual passages from a KB. To address the task, one must thus retrieve relevant
+information from a KB. This contrasts with standard Visual Question Answering
+(VQA, [1]), where questions target the content of the image (e.g. the color of an
+object or the number of objects) or Knowledge-based VQA (about coarse-grained
+object categories) [40], where one can rely on oﬀ-the-shelf object detection [17]. In
+⋆ This work was supported by the ANR-19-CE23-0028 MEERQAT project. This work
+was granted access to the HPC resources of IDRIS under the allocation 2021-
+AD011012846 made by GENCI.
+arXiv:2301.04366v1  [cs.CL]  11 Jan 2023
+
+2
+P. Lerner et al.
+Visual Question (input)
+Relevant visual passage in the Knowledge Base
+“Which constituency
+did this man repre-
+sent
+when
+he
+was
+Prime Minister?”
+“Macmillan indeed lost Stockton in the landslide
+Labour victory of 1945, but returned to Parlia-
+ment in the November 1945 by-election in Brom-
+ley.”
+“In
+which
+year
+did
+this ocean liner make
+her maiden voyage?”
+“Queen Elizabeth 2, often referred to simply as
+QE2, is a ﬂoating hotel and retired ocean liner
+built for the Cunard Line which was operated by
+Cunard as both a transatlantic liner and a cruise
+ship from 1969 to 2008.”
+Fig. 1: Example of visual questions about named entities from the ViQuAE
+dataset along with relevant visual passages from its Knowledge Base [32].
+KVQAE, both text and image modalities bring useful information that must be
+combined. Therefore, the task is more broadly related to Multimodal Information
+Retrieval (IR) and Multimodal Fusion.
+There are two paradigms for multimodal IR and for multimodal learning
+more generally: early fusion (data- and feature-level) and late fusion (score-
+and decision-level) [30]. On the one hand, late fusion is more straightforward
+as both Natural Language Processing and Computer Vision techniques can be
+applied independently, but it neglects interaction between the modalities. On
+the other hand, the richness of early fusion often comes at the cost of increasing
+complexity and model parameters. This adds an extra challenge for KVQAE
+where the two existing datasets are either small (ViQuAE [32]) or generated
+automatically (KVQA [50]). To overcome this challenge, we propose to pre-train
+our fusion model using a multimodal Inverse Cloze Task (ICT). ICT has been
+introduced in [31] to pre-train a neural retriever for textual Question Answering
+(QA). It consists in considering a sentence as a pseudo-question and its context
+as a pseudo-relevant passage. It can be seen as a generalization of the skip-gram
+objective [41]. We extend it by considering images near texts in multimodal
+documents.
+Our main contributions are: (i) Multimodal ICT, a new pre-training method
+that allows tackling small KVQAE datasets such as ViQuAE; (ii) a multimodal
+IR framework for KVQAE; (iii) experiments with diﬀerent neural network ar-
+chitectures, including recently proposed multimodal BERTs.
+2
+Related Work
+Dense Retrieval. Dense Retrieval is a rapidly evolving ﬁeld, surveyed in
+[36,11], with new pre-training tasks, optimizing methods, and variants of the
+Transformer architecture emerging [47,23,15,14]. [31] were the ﬁrst to outperform
+sparse bag-of-words representations such as BM25 with dense representations for
+QA. Their approach relies on three components: (i) pre-trained language mod-
+els such as BERT [10], which allow to encode the semantic of a sentence in a
+
+CUNARDMultimodal Inverse Cloze Task for KVQAE
+3
+dense vector; (ii) a contrastive learning objective that optimizes the similarities
+between questions’ and text passages’ embeddings (see Section 3); (iii) an un-
+supervised training task, ICT (see Section 1). [27] criticize the latter for being
+computationally intensive3 and argue that regular sentences are not good surro-
+gates of questions. Instead, they propose DPR, which takes advantage of (i) the
+heuristic of whether the passage contains the answer to the question to deem it
+relevant; (ii) unsupervised IR methods such as BM25 to mine hard negatives ex-
+amples, which proved to be the key of their method’s success. We aim at taking
+advantage of both approaches by (i) pre-training our model on text QA datasets
+like DPR; (ii) incorporating multimodality into this hopefully-well-initialized
+model by adapting the ICT of [31] to multimodal documents.
+Multimodal Fusion and Pre-Training. The success of BERT in NLP [10],
+which relies on the easily-parallelizable Transformer architecture [58], an unsu-
+pervised training objective, and a task-agnostic architecture, has concurrently in-
+spired many works in the VQA and cross-modal retrieval ﬁelds [57,38,35,56,34,7].
+These models are uniﬁed under a single framework in [5] and partly reviewed
+in [28]. All of these models rely on the Transformer architecture, often initialized
+with a pre-trained BERT, in order to fuse image and text. The training is weakly
+supervised, based upon image caption datasets such as COCO [37] or Concep-
+tual Captions [51], and pre-trained object detectors like Faster R-CNN [48].
+[22] show that these models learn nontrivial interactions between the modali-
+ties for VQA. Multimodal BERTs can be broadly categorized into single-stream
+and multi-stream. Single-stream models feed both text tokens’ embeddings and
+image regions’ embeddings to the same Transformer model, relying on the self-
+attention mechanism to fuse them. Instead, in the multi-stream architecture,
+text and image are ﬁrst processed by two independent Transformers before us-
+ing cross-attention to fuse the modalities. Both architectures have been shown
+to perform equally well in [5]. In this work, we use a single-stream model to
+take advantage of pre-training on text-only (on QA datasets). Also note that,
+while inspired by these work, we do not use the same training objectives or data,
+which are arguably unsuited for named entities’ representations, as explained in
+the next section.
+Multimodal Information Retrieval and KVQAE. Multimodal IR has
+largely been addressed using late fusion techniques (see [9] for a survey) but
+we are mostly interested in early fusion techniques in this work.
+[9] review ﬁrst attempts at early fusion. It was then systematically done by
+concatenating the features of both modalities in a single vector, with a focus
+on the feature weighting scheme. Concatenation is confronted with the curse of
+dimensionality as the resulting feature space equals the sum of the dimensions
+of each modality’s features.
+[44] and [39] concurrently proposed an approach quite similar to ours for
+Knowledge-based VQA. They adapt DPR [27] by replacing the question encoder
+3 [31] use a batch size of over 4K questions.
+
+4
+P. Lerner et al.
+with LXMERT [57], which allows to fuse the question and image. However, un-
+like us, they keep the passage encoder based on text-only and use the same
+pre-training objectives as [57], namely Masked Language Modeling, Masked Re-
+gion Modeling, and Image-Text Matching. We expect that these objectives are
+suited to learn representations of coarse-grained object categories but not named
+entities. In other words, they are suited for standard VQA but not KVQAE. For
+example, Masked Region Modeling relies on an object detector, which is not
+applicable to KVQAE. While both [44] and [39] experiment on OK-VQA [40],
+their results are inconsistent: [44] show that their model is competitive with a
+BM25 baseline that takes as input the question and the human-written cap-
+tion of the image while the model of [39] is outperformed by BM25 with an
+automatically-generated caption. The discrepancies between these works can be
+explained because they use neither the same KB nor the same evaluation metrics.
+[19] also experiment with diﬀerent multimodal BERTs but dispense passage-level
+annotation for an end-to-end training of the retriever and answer classiﬁer4.
+Although they experiment with KVQA [50], we do not consider the work
+of [52,16,21] as their systems take a human-written caption as input, which
+makes the role of the image content unclear. [50] follow a late fusion approach
+at the decision-level. First, they detect and disambiguate the named entity men-
+tions in the question. Then, they rely on a face recognition step as their dataset,
+KVQA, is restricted to questions about person named entities. Facts from both
+textually- and visually-detected entities are retrieved from Wikidata5 and pro-
+cessed by a memory network [60]. In contrast, our work is in line with [32], who
+use unstructured text from Wikipedia as KB. Unlike [32], who follow a late fu-
+sion approach, searching the question and the image independently, we aim at
+a uniﬁed representation of the text and image, both on the visual question and
+KB sides.
+3
+Methods
+In this section, we ﬁrst formalize our KVQAE framework, then describe the
+models before diving into the three training stages: (i) DPR for textual Ques-
+tion Answering; (ii) Multimodal Inverse Cloze Task, our main contribution; (iii)
+Fine-tuning for KVQAE. Finally, we discuss the inference mechanism and im-
+plementation details.
+3.1
+Information Retrieval Framework
+In our multimodal setting, both visual questions (from the dataset) and visual
+passages (from the KB) consist of a text-image pair (t, i), as in Figure 1. Our goal
+is to ﬁnd the optimal model E to encode adequate representations q = E(tq, iq)
+and p = E(tp, ip) such that they are close if (tp, ip) is relevant for (tq, iq) (denoted
+4 Standard (Knowledge-based) VQA is often treated as a classiﬁcation task.
+5 https://www.wikidata.org/
+
+Multimodal Inverse Cloze Task for KVQAE
+5
+with the superscripts (+) and (−)). Search then boils down to retrieving the K
+closest visual passages to the visual question. When computing the similarity
+between two vectors, here with the dot product, the objective used throughout
+all the training stages (§3.3) is to minimize the following negative log-likelihood
+loss for all visual questions in the dataset [31,27]: − log
+exp (q·p+)
+exp (q·p+)+�
+j exp (q·p−
+j ).
+This contrastive objective allows to eﬃciently utilize passages relevant to other
+questions in the batch as in-batch negatives, since computing the similarity be-
+tween two vectors is rather inexpensive compared to the forward pass of the
+whole model. We present two diﬀerent models E in the next section according
+to their fusion mechanism.
+3.2
+Models
+All of our models take advantage of BERT6 [10] and CLIP7 [46] as building blocks
+to represent text and image, respectively. BERT is trained for masked language
+modeling and next sentence prediction on Wikipedia and BooksCorpus [62].
+CLIP has been trained with a contrastive objective in a weakly-supervised man-
+ner over 400M image and caption pairs. It has demonstrated better generalization
+capacities than fully-supervised models and is eﬃcient for KVQAE, as empiri-
+cally demonstrated in [32]. We experiment with two diﬀerent fusion techniques:
+ECA and ILF.
+Early Cross-Attention fusion (ECA) is carried out by a single-stream Trans-
+former model like the multimodal BERTs described above (e.g. UNITER [7]).
+However, instead of relying on a ﬁxed object detector such as Faster R-CNN, we
+take advantage of CLIP, as motivated above. To enable early fusion, the visual
+embedding produced by CLIP is projected in the same space as the text using a
+linear layer with Wc ∈ Rc×d parameters trained from scratch: ec = CLIP(i)·Wc.
+The resulting embedding is then concatenated with the word embeddings in the
+sequence dimension, acting as a “visual token”. Those embeddings are then fed
+to the Transformer model, where the attention mechanism should enable inter-
+action between the modalities. The ﬁnal embedding corresponds to the special
+[CLS] token: ECA(t, i) = BERT([t; ec])[CLS]. The Transformer model is ﬁrst
+initialized from BERT.
+Intermediate Linear Fusion (ILF) introduces an additional Wt ∈ Rd×d pa-
+rameters trained from scratch used to simply project the representation of the
+[CLS] token in the same space as the CLIP embedding before summing the two8:
+ILF(t, i) = BERT(t)[CLS] · Wt + ec.
+Because both ECA and ILF produce multimodal representations q and p,
+ranking is done directly using their similarity q·p. As baseline, we follow [32] and
+linearly combine text and image similarities after zero-mean and unit-variance
+6 Uncased “base” 12-layers version available at https://huggingface.co.
+7 With a ResNet-50 backbone [20].
+8 Note
+that
+this
+is
+equivalent
+to
+concatenating
+both
+before
+projecting
+like
+[BERT(t)[CLS]; CLIP(i)] · [Wt; Wc].
+
+6
+P. Lerner et al.
+Barack Obama
+…
+…
+U.S. Senate (2005-2008)
+A sentence about Obama being senator.
+In the context we find related sentences.
+Believed to be relevant.
+Fig. 2: Overview of Multimodal Inverse Cloze Task via Wikipedia/WIT.
+normalization (omitted in the following equation):
+α × BERT(tq)[CLS] · BERT(tp)[CLS] + (1 − α) × cos(CLIP(iq), CLIP(ip))
+(1)
+The interpolation hyperparameter α is optimized on the validation set using
+grid search to maximize Mean Reciprocal Rank. The left term (text similarity)
+is referred to as DPR in the rest of the paper.
+3.3
+Training stages
+The models are trained sequentially in three stages:
+Stage 1: DPR for textual Question Answering. Leaving visual represen-
+tations aside, a DPR model is trained starting from the BERT initialization [27].
+DPR consists of two BERT encoders: one for the question tq and one for the
+text passage tp. We use the model pre-trained by [32] on TriviaQA, ﬁltered of all
+questions used in their dataset, ViQuAE. They use the KILT [43] version of Triv-
+iaQA and Wikipedia, which serves as KB in this stage. Each article is then split
+into disjoint passages of 100 words for text retrieval, while preserving sentence
+boundaries, and the title of the article is appended to the beginning of each pas-
+sage. This yields 32M passages, that is ≈ 5.4 passages per article. Following [27],
+irrelevant passages (i.e. hard negatives) are mined using BM25 [49].
+Stage 2: Multimodal Inverse Cloze Task. This is the main contribution of
+the paper. We propose to extend the ICT of [31] to multimodal documents. ICT
+consists in considering a sentence as a pseudo-question tq and its context as a
+pseudo-relevant passage t+
+p . Note that the title of the article is appended to the
+beginning of each passage tp (as in Stage 1). We extend it using the contextual
+images of Wikipedia paragraphs for the pseudo-question and the infobox image
+for the passage (see Figure 2). [31] empirically demonstrated that a key success
+of their approach was to leave the pseudo-question in the relevant passage in 10%
+of the training samples so that the model will learn to perform word matching,
+as lexical overlap is ultimately a very useful feature for retrieval. In our case,
+
+祖
+WIKIPEDIAMultimodal Inverse Cloze Task for KVQAE
+7
+however, we argue that it is neither necessary, as the model should be strongly
+initialized from Stage 1 training on TriviaQA, nor beneﬁcial, as the model could
+then ignore the image modality. Question and passage encoders pre-trained in
+Stage 1 are used to initialize the visual question and visual passage encoders,
+respectively.
+The process is eased thanks to the WIT dataset [54]. WIT consists of millions
+of images with associated text from Wikipedia and Wikimedia Commons in 108
+diﬀerent languages. We are, however, only interested in English for this work.
+While [54] have multiple strategies to ﬁnd text related to a given Wikipedia
+image, such as its Commons’ caption, we use only the contextual paragraph as
+text source in order to mimic the downstream KVQAE setting. The resulting
+English subset of WIT yields 400K infobox images/articles that correspond to
+1.2M paragraphs/images. Those 1.2M paragraphs consist of 13.6M sentences,
+i.e. potential pseudo-questions, which are 26 words long on average. Therefore,
+to stick as close as possible to stages 1 and 3, where passages are up to 100
+words long, passages consist of four sentences. This slightly diﬀers from [31]
+who consider passages of up to 288 wordpieces, prior to the pseudo-question
+masking.
+Because both ViQuAE and WIT images are taken from Wikimedia Com-
+mons9, we can estimate from the image URLs that 14% of ViQuAE images
+overlap with WIT. This might lead to a bias that we analyze in Section 4.1.
+Inspired by [2], to prevent catastrophic forgetting and enforce a modality-
+invariant representation of the entities, the last l layers of BERT are frozen
+during this stage. In this way, we tune only the ﬁrst, modality-speciﬁc layers
+of ECA, the intuition being to “replace” the text-named entities learned during
+Stage 1 with the “visual” entities present in the images. ILF fully freezes BERT
+during this stage, relying only on the Wt parameters to tune the text represen-
+tation. Furthermore, CLIP is systematically frozen throughout all stages.
+We do not have a straightforward way of mining irrelevant visual passages
+in this stage. In early experiments, we tried to synthesize them by permuting
+images in the batch: (t+
+p , i+
+p ) ← (t+
+p , i−
+p ), but it did not improve the results.
+After ﬁltering corrupted images or images with inappropriate image formats
+(e.g. .svg) and paragraphs with a single sentence, we end up with 975K para-
+graphs/images. We refer to it as WIT in the rest of the paper. It is split into
+train (878K), validation (48K, to tune hyperparameters), and test (48K, as a
+sanity check) subsets such that there is no overlap between articles.
+Stage 3: Knowledge-based Visual Question Answering about Named
+Entities. This stage consists in ﬁne-tuning the model on a downstream KVQAE
+dataset, which provides visual questions (tq, iq) and relevant visual passages
+(t+
+p , i+
+p ). Following [2], all layers of the model are tuned during this stage.
+A subtlety of this stage is the selection of irrelevant visual passages (t−
+p , i−
+p ).
+As mentioned in Section 2, it was shown to be essential to DPR [27], and it is
+more generally important for contrastive learning [26]. In [32], irrelevant passages
+9 https://commons.wikimedia.org/
+
+8
+P. Lerner et al.
+are mined with BM25 to train DPR. However, we suppose that this is suboptimal
+for ECA and ILF as BM25 will only mine textually-plausible passages but not
+visually-plausible ones. Therefore, we use the system provided by [32] to mine
+irrelevant passages. It is a late-fusion of DPR, ArcFace [8], CLIP, and ImageNet-
+ResNet [20]. This leads to diﬀerent training setups between DPR (used as a
+baseline) and our models. However, we have experimented both for DPR and
+found no signiﬁcant diﬀerences10.
+We use the same KB as [32], which is based upon KILT’s Wikipedia and
+Wikidata images of the corresponding entities. It consists of 1.5M articles (thus
+images/entities) split into 12M passages of at most 100 words as in Stage 1.
+Visual questions in ViQuAE are split into train (1,190), validation (1,250),
+and test (1,257) without overlap between images’ URLs [32]. We do not experi-
+ment with KVQA [50] for the following reasons: (i) it is generated automatically
+from Wikidata so our text-based KB has a poor coverage of the answers; (ii)
+it comprises yes/no questions for which passage relevance cannot be assessed
+automatically.
+3.4
+Inference
+For eﬃcient retrieval, every passage in the KB is embedded along with its cor-
+responding image by the visual passage encoder beforehand. Given a question
+grounded in an image, both are embedded by the visual question encoder. Search
+is then carried out with maximum inner product search using Faiss [25].
+3.5
+Implementation Details
+Our code is built upon PyTorch [42], Hugging Face’s transformers [61] and
+datasets [33] (itself wrapping Faiss). It is freely available along with the data
+and trained models11.
+To train ECA, we use the same hyperparameters as [32] for DPR, them-
+selves based upon [27]. In particular, we use a learning rate of 2 × 10−5 along
+with the Adam optimizer [29]. It is scheduled linearly with 100 and 4 warm-up
+steps for stages 2 and 3, respectively. However, for ILF, we found, based on the
+validation set, that it converged faster with a learning rate of 2 × 10−3 and a
+constant scheduler during Stage 2. We believe this is because ILF fully freezes
+BERT in Stage 2, so it does not require careful scheduling or a small learn-
+ing rate. Dropout [55] is applied in BERT and after projecting embedding with
+Wc and Wt with a probability of 0.1 (as in the standard BERT conﬁguration).
+Likewise, layer normalization [3] is applied in BERT and after summing the two
+embeddings in ILF. Gradients’ norms are clipped at 2.
+Models in stages 2 and 3 are trained with a batch size of 512 and 298 visual
+questions, respectively. The success of contrastive learning partly relies on a large
+number of in-batch negatives and, therefore, a large batch size [45]. We found
+10 Evaluation methods are detailed in Section 4
+11 https://github.com/PaulLerner/ViQuAE
+
+Multimodal Inverse Cloze Task for KVQAE
+9
+Table 1: IR evaluation on ViQuAE. l: Number of frozen layers during Multimodal
+ICT. Superscripts denote signiﬁcant diﬀerences in Fisher’s randomization test
+with p ≤ 0.01. Hits@1 is omitted as it is equivalent to P@1.
+# Model
+Multimodal ICT MRR@100 P@1
+P@20
+Hits@20
+a DPR
+NA
+32.8
+22.8
+16.4
+61.2
+b DPR + CLIP
+NA
+34.5a
+24.8a
+15.8
+61.8
+c
+ECA
+
+34.6
+25.9a
+17.2ab
+61.6
+d ECA (l = 6)
+
+37.8abce
+26.7a
+19.5abce
+67.6abce
+e
+ECA (l = 0)
+
+35.1
+24.7
+17.6b
+63.7
+f
+ILF (l = 12)
+
+37.3a
+26.8a
+19.1abce
+66.9abc
+that gradient checkpointing [6] enables the use of much larger batch sizes for
+ECA12. Instead of [32] who use four NVIDIA V100 GPUs with 32GB of RAM
+each for a total batch size of 128 questions, we are able to ﬁt a batch of 298
+questions (as stated above) in a single V100 GPU. Stage 2 takes most of the
+compute budget, with most models converging after ≈ 8K steps, which takes
+around three days13. Checkpoint selection is made based on the validation in-
+batch Mean Reciprocal Rank, for all stages. In-batch means that only the other
+visual passages in the batch are ranked and that each visual question is paired
+with only one relevant visual passage (as during training).
+4
+Results
+The retrieval models are evaluated in two diﬀerent ways: (i) by computing stan-
+dard IR metrics on visual passage retrieval; (ii) by feeding retrieved visual pas-
+sages to a reader module that is tasked with extracting the concise answer to
+the question, thus achieving KVQAE. Put diﬀerently, either evaluate whether
+the system is able to retrieve a relevant passage for the question or whether it is
+able to answer the question. We ﬁnd both metrics to correlate. Ablation studies
+are carried out with IR metrics.
+ViQuAE is based upon TriviaQA, so it is only distantly supervised: the an-
+swer is considered correct if it string-matches the ground truth and, likewise, a
+passage is deemed relevant if it contains the ground truth14. Moreover, Wikipedia
+aliases of the ground truth are considered to be valid answers.
+4.1
+Information Retrieval
+Because of the setting of ViQuAE, it is impossible to get complete coverage of
+relevant passages. Therefore we do not use any metric based on recall (e.g. R-
+12 It is not necessary for ILF that fully freezes BERT.
+13 Jean Zay GPUs consume 0.482kW (or 0.259kW after heat recovery) in France, which
+has an average grid emission factor of 0.0569 kgCO2e/kWh according to https:
+//bilans-ges.ademe.fr/en.
+14 After standard preprocessing (lowercasing, stripping articles, and punctuation).
+
+10
+P. Lerner et al.
+Visual Question
+ECA top-1
+DPR + CLIP top-1
+“In which English palace was
+this man born?”
+“Who designed this cathedral?”
+He was appointed
+[...] Surveyor of the
+Fabric of St Paul's
+Cathedral, 
+where
+he was responsible
+for maintaining the
+building designed
+by Sir Christopher
+Wren.
+Sir George Gilbert
+Scott 
+led 
+the
+restoration 
+of
+Salisbury Cathedral
+between 
+1863 
+–
+1878. It was during
+this 
+time 
+that
+Skidmore 
+created
+the cathedral's choir
+screen. 
+Blenheim Palace was the birthplace of
+the 1st Duke's famous descendant,
+Winston Churchill [...] 
+In 
+1762, 
+George
+purchased Buckingham
+House (on the site now
+occupied 
+by
+Buckingham 
+Palace)
+for use as a family
+retreat. 
+His 
+other
+residences were Kew  
+and Windsor Castle. St James's Palace was
+retained for official use. 
+Fig. 3: Qualitative examples where ECA (l = 6) ﬁnds a relevant visual passage
+in top-1 but late fusion falls behind.
+Precision, mAP, etc.). Instead, we evaluate the models with Precision@K (P@K),
+Mean Reciprocal Rank (MRR), and Hits@K. Hits@K is the proportion of ques-
+tions for which IR retrieves at least one relevant passage in top-K. Statistical
+signiﬁcance tests are conducted using Fisher’s randomization test [12,53]. Met-
+rics and statistical tests are computed with ranx [4] and are reported in Table 1.
+The best models pre-trained with Multimodal ICT (d and f) outperform the
+text-only (a) and late-fusion (b) baselines on all metrics. Some qualitative exam-
+ples are shown in Figure 3. In the ﬁrst row, we can see evidence of cross-modal
+interaction between the image depicting Winston Churchill and the passage that
+mentions him (while being illustrated by a totally diﬀerent image). In contrast,
+the late fusion baseline exhibits textual bias by returning a passage that men-
+tions several English palaces (highlighted in red). The same observation can be
+made for the second row, where St Paul’s Cathedral is only mentioned in the
+relevant passage but not depicted in the contextual image. Cross-modal interac-
+tions prove useful in this case because of the heterogeneity of visual depictions:
+Winston Churchill is depicted by a statue in the visual question but by a pho-
+tograph in the KB.
+We can see that Multimodal ICT is essential to ECA (c vs. d). Without it,
+it performs on par with late fusion. We believe this is because of overﬁtting on
+the small training set of ViQuAE. However, we ﬁnd that ﬁne-tuning on ViQuAE
+is also essential to ECA, which exhibits catastrophic forgetting because of the
+sequential learning setup: indeed, after Stage 2, it falls behind DPR. We see
+that the freezing technique of [2] helps to prevent catastrophic forgetting to
+some extent (d vs. e). It is also visible in the upstream WIT pre-training where
+
+Multimodal Inverse Cloze Task for KVQAE
+11
+Table 2: Reading Comprehension evaluation on ViQuAE, averaged over 5 runs
+of the reader. l: Number of frozen layers during Multimodal ICT.
+#
+IR Model
+Multimodal ICT Exact Match
+F1
+a
+DPR
+NA
+16.9 ± 0.4
+20.1 ± 0.5
+b DPR + CLIP
+NA
+19.0 ± 0.4
+22.3 ± 0.4
+c
+ECA
+
+17.7 ± 0.6
+21.2 ± 0.8
+d
+ECA (l = 6)
+
+20.6 ± 0.3
+24.4 ± 0.2
+e
+ECA (l = 0)
+
+20.8 ± 0.8
+24.3 ± 0.9
+f
+ILF (l = 12)
+
+21.3 ± 0.6
+25.4 ± 0.3
+ECA achieves 91.6 and 92.9 in-batch MRR on WIT’s test set with l = 6 and
+l = 0, respectively: ﬁtting WIT better leads to further forgetting.
+Unlike what is suggested by related work (§2), we ﬁnd that the linear fusion
+model performs on par with the more early, cross-attention based, fusion model
+(f vs. d). This suggests that the improvement over the late fusion baseline indeed
+comes from the Multimodal ICT pre-training, which is not very sensitive to the
+model’s architecture. Moreover, the architecture of ILF allows to fully freeze
+BERT during Stage 2, which circumvents catastrophic forgetting15. We leave
+other training strategies (e.g. multi-tasking, using adapters [24]) for future work.
+Nothing suggests that ECA is better on the 14% of ViQuAE images that
+overlap with WIT. ECA is better on the out-of-WIT subset (38.0 vs. 36.5 MRR),
+but it is the other way around for DPR and late fusion.
+4.2
+Reading Comprehension
+To extract the answers from the retrieved passages, we keep the same model
+as [32]. It uses the Multi-passage BERT architecture [59] and is thus based on
+text only because once the relevant passage has been retrieved, the question may
+be answered without looking at the image. To limit the variations due to training
+and the number of experiments, we use the model trained by [32] oﬀ-the-shelf
+and simply change its input passages. It takes the top-24 passages as input. The
+model was ﬁrst trained on TriviaQA (ﬁltered of all questions used in ViQuAE),
+then ﬁne-tuned on ViQuAE, much like stages 1 and 3. The authors provide ﬁve
+diﬀerent versions of the model that correspond to diﬀerent random seeds.
+We use Exact Match and F1-score (at the bag-of-words level) to evaluate the
+extracted answers. In Table 2 we can verify that more relevant passages indeed
+lead to better downstream answers. The only diﬀerence with the IR evaluation
+is the role of the freezing technique of [2] (d vs. e), which is less clear here.
+15 ILF only achieves 87.1 in-batch MRR on WIT’s test set because of the freezing.
+
+12
+P. Lerner et al.
+5
+Generic vs. Specialized Image Representations
+Numbers reported in the previous section are actually on par with the best results
+of [32]. This is because the latter is based on ArcFace and ImageNet-ResNet,
+in addition to DPR and CLIP. In particular, [32] have a heuristic for taking
+advantage of the face representations provided by ArcFace: they use ArcFace if
+faces are detected and a combination of CLIP and ImageNet-ResNet otherwise.
+They show that this method improves retrieval precision for questions about
+persons (for which face representations are relevant). However, this approach
+is not scalable for two reasons: (i) there are near 1,000 diﬀerent entity types
+in ViQuAE (according to Wikidata’s ontology), and not all can beneﬁt from
+specialized representations; (ii) combining several representations (e.g. CLIP and
+ImageNet-ResNet) for the same entity type is computationally expensive and
+quickly saturates. To provide a comparable system to the late fusion of [32], we
+have tried integrating ArcFace and ImageNet-ResNet in ECA. However, we have
+failed to outperform the CLIP-only version of ECA. Intuitively, we think that
+ECA dilutes the specialized representations of ArcFace and is unable to preserve
+them throughout all twelve layers of BERT. Therefore, in this setting, ECA is
+overall on par with late fusion (37.7 vs. 37.9 MRR, not signiﬁcant) but better
+on questions about non-persons (39.3 vs. 35.7 MRR), which again suggests that
+it is unable to exploit ArcFace’s representations.
+6
+Conclusion and Perspectives
+We have presented a new pre-training method, Multimodal Inverse Cloze Task,
+for Knowledge-based Visual Question Answering about Named Entities. Multi-
+modal ICT leverages contextual images in multimodal documents to generate
+pseudo-visual questions. It enables the use of more complex multimodal fusion
+models than previously proposed late fusion methods. Consequently, our method
+improves retrieval accuracy over the latter by 10% relative-MRR, leading to a
+9% relative-F1 improvement in downstream reading comprehension (i.e. answer
+extraction), on the recently introduced ViQuAE dataset. We believe it is thanks
+to cross-modal interactions, which are prohibited by late fusion. More precisely,
+we qualitatively observed that these interactions occurred between the image of
+the visual question and the text of the KB, which counteracts the heterogeneity
+of visual depictions.
+We have experimented our pre-training method with two diﬀerent neural
+networks architectures: (i) ECA, which follows recently proposed Multimodal
+BERTs by fusing modalities Early via Cross-Attention; (ii) ILF, a more standard
+model that fuses modalities through a linear projection. We found that both
+perform equally well, unlike in standard VQA and cross-modal retrieval. We
+argue that it might be because of their diﬀerence in training settings, which leads
+ECA to catastrophic forgetting. However, further investigations are required.
+While aiming for generic multimodal representations of named entities, we
+found that integrating specialized representations in our models, such as ArcFace
+
+Multimodal Inverse Cloze Task for KVQAE
+13
+for faces, was not beneﬁcial. We hypothesize that the studied architectures may
+be inappropriate but we leave this issue for future studies.
+For future work, we think that generalizing Multimodal ICT for re-ranking
+(processing (tq, iq) and (tp, ip) simultaneously) and reading comprehension (gen-
+erating or extracting the answer from (tp, ip)) is an exciting research lead. Indeed,
+there is evidence that sharing the same model for IR and reading comprehen-
+sion, or IR and re-ranking, is beneﬁcial for textual QA [13] and cross-modal
+retrieval [18], respectively: two tasks that closely relate to KVQAE.
+References
+1. Antol, S., Agrawal, A., Lu, J., Mitchell, M., Batra, D., Zitnick, C.L., Parikh,
+D.: VQA: Visual Question Answering. In: 2015 IEEE International Confer-
+ence on Computer Vision (ICCV). pp. 2425–2433. IEEE, Santiago, Chile
+(Dec 2015). https://doi.org/10.1109/ICCV.2015.279, http://ieeexplore.ieee.org/
+document/7410636/
+2. Aytar, Y., Castrejon, L., Vondrick, C., Pirsiavash, H., Torralba, A.: Cross-modal
+scene networks. IEEE transactions on pattern analysis and machine intelligence
+40(10), 2303–2314 (2017), publisher: IEEE
+3. Ba, J.L., Kiros, J.R., Hinton, G.E.: Layer Normalization. arXiv:1607.06450 [cs,
+stat] (Jul 2016), http://arxiv.org/abs/1607.06450, arXiv: 1607.06450
+4. Bassani, E.: ranx: A Blazing-Fast Python Library for Ranking Evaluation
+and Comparison. In: Hagen, M., Verberne, S., Macdonald, C., Seifert, C., Balog, K.,
+Nørv˚ag, K., Setty, V. (eds.) Advances in Information Retrieval. pp. 259–264. Lec-
+ture Notes in Computer Science, Springer International Publishing, Cham (2022).
+https://doi.org/10.1007/978-3-030-99739-7 30
+5. Bugliarello, E., Cotterell, R., Okazaki, N., Elliott, D.: Multimodal Pretraining
+Unmasked: A Meta-Analysis and a Uniﬁed Framework of Vision-and-Language
+BERTs. Transactions of the Association for Computational Linguistics 9, 978–
+994 (Sep 2021). https://doi.org/10.1162/tacl a 00408, https://doi.org/10.1162/
+tacl a 00408
+6. Chen, T., Xu, B., Zhang, C., Guestrin, C.: Training Deep Nets with Sublin-
+ear Memory Cost (Apr 2016). https://doi.org/10.48550/arXiv.1604.06174, http:
+//arxiv.org/abs/1604.06174, number: arXiv:1604.06174 arXiv:1604.06174 [cs]
+7. Chen, Y.C., Li, L., Yu, L., El Kholy, A., Ahmed, F., Gan, Z., Cheng, Y., Liu, J.:
+Uniter: Universal image-text representation learning. In: European Conference on
+Computer Vision. pp. 104–120. Springer (2020)
+8. Deng, J., Guo, J., Xue, N., Zafeiriou, S.: Arcface: Additive angular margin
+loss for deep face recognition. In: Proceedings of the IEEE/CVF Conference
+on Computer Vision and Pattern Recognition (CVPR) (June 2019), https:
+//openaccess.thecvf.com/content CVPR 2019/html/Deng ArcFace Additive
+Angular Margin Loss for Deep Face Recognition CVPR 2019 paper.html
+9. Depeursinge, A., M¨uller, H.: Fusion Techniques for Combining Textual and
+Visual Information Retrieval. In: M¨uller, H., Clough, P., Deselaers, T., Ca-
+puto, B. (eds.) ImageCLEF: Experimental Evaluation in Visual Information
+Retrieval, pp. 95–114. The Information Retrieval Series, Springer, Berlin, Hei-
+delberg (2010). https://doi.org/10.1007/978-3-642-15181-1 6, https://doi.org/10.
+1007/978-3-642-15181-1 6
+
+14
+P. Lerner et al.
+10. Devlin, J., Chang, M.W., Lee, K., Toutanova, K.: BERT: Pre-training of deep
+bidirectional transformers for language understanding. In: Proceedings of the 2019
+Conference of the North American Chapter of the Association for Computational
+Linguistics: Human Language Technologies, Volume 1 (Long and Short Papers).
+pp. 4171–4186. Association for Computational Linguistics, Minneapolis, Min-
+nesota (Jun 2019). https://doi.org/10.18653/v1/N19-1423, https://aclanthology.
+org/N19-1423
+11. Fan, Y., Xie, X., Cai, Y., Chen, J., Ma, X., Li, X., Zhang, R., Guo, J., Liu, Y.:
+Pre-training Methods in Information Retrieval. arXiv:2111.13853 [cs] (Nov 2021),
+http://arxiv.org/abs/2111.13853, arXiv: 2111.13853
+12. Fisher, R.A.: The design of experiments. The design of experiments. (2nd
+Ed)
+(1937),
+https://www.cabdirect.org/cabdirect/abstract/19371601600,
+pub-
+lisher: Oliver & Boyd, Edinburgh & London.
+13. Fun, H., Gandhi, S., Ravi, S.: Eﬃcient Retrieval Optimized Multi-task Learn-
+ing. arXiv:2104.10129 [cs] (Apr 2021), http://arxiv.org/abs/2104.10129, arXiv:
+2104.10129
+14. Gao, L., Callan, J.: Condenser: a Pre-training Architecture for Dense Retrieval.
+In: Proceedings of the 2021 Conference on Empirical Methods in Natural Lan-
+guage Processing. pp. 981–993. Association for Computational Linguistics, Online
+and Punta Cana, Dominican Republic (Nov 2021), https://aclanthology.org/2021.
+emnlp-main.75
+15. Gao, L., Callan, J.: Unsupervised corpus aware language model pre-training
+for dense passage retrieval. In: Proceedings of the 60th Annual Meeting of
+the Association for Computational Linguistics (Volume 1: Long Papers). pp.
+2843–2853. Association for Computational Linguistics, Dublin, Ireland (May
+2022). https://doi.org/10.18653/v1/2022.acl-long.203, https://aclanthology.org/
+2022.acl-long.203
+16. Garcia-Olano,
+D.,
+Onoe,
+Y.,
+Ghosh,
+J.:
+Improving
+and
+diagnosing
+knowledge-based
+visual
+question
+answering
+via
+entity
+enhanced
+knowl-
+edge
+injection.
+In:
+Companion
+Proceedings
+of
+the
+Web
+Conference
+2022.
+p.
+705–715.
+WWW
+’22,
+Association
+for
+Computing
+Machinery,
+New
+York,
+NY,
+USA
+(2022).
+https://doi.org/10.1145/3487553.3524648,
+https://doi.org/10.1145/3487553.3524648
+17. Gard`eres, F., Ziaeefard, M.: ConceptBert: Concept-Aware Representation for Vi-
+sual Question Answering. Findings of the Association for Computational Linguis-
+tics: EMNLP 2020 p. 10 (2020), https://aclanthology.org/2020.ﬁndings-emnlp.44/
+18. Geigle, G., Pfeiﬀer, J., Reimers, N., Vuli´c, I., Gurevych, I.: Retrieve Fast, Rerank
+Smart: Cooperative and Joint Approaches for Improved Cross-Modal Retrieval.
+Transactions of the Association for Computational Linguistics 10, 503–521 (05
+2022). https://doi.org/10.1162/tacl a 00473, https://doi.org/10.1162/tacl a 00473
+19. Guo, Y., Nie, L., Wong, Y., Liu, Y., Cheng, Z., Kankanhalli, M.: A Uniﬁed End-
+to-End Retriever-Reader Framework for Knowledge-based VQA (Jun 2022), http:
+//arxiv.org/abs/2206.14989, number: arXiv:2206.14989 arXiv:2206.14989 [cs]
+20. He, K., Zhang, X., Ren, S., Sun, J.: Deep residual learning for image recognition. In:
+Proceedings of the IEEE conference on computer vision and pattern recognition.
+pp. 770–778 (2016), https://openaccess.thecvf.com/content cvpr 2016/papers/He
+Deep Residual Learning CVPR 2016 paper.pdf
+21. Heo, Y.J., Kim, E.S., Choi, W.S., Zhang, B.T.: Hypergraph Transformer: Weakly-
+supervised multi-hop reasoning for knowledge-based visual question answering. In:
+Proceedings of the 60th Annual Meeting of the Association for Computational
+
+Multimodal Inverse Cloze Task for KVQAE
+15
+Linguistics (Volume 1: Long Papers). pp. 373–390. Association for Computational
+Linguistics, Dublin, Ireland (May 2022). https://doi.org/10.18653/v1/2022.acl-
+long.29, https://aclanthology.org/2022.acl-long.29
+22. Hessel, J., Lee, L.: Does my multimodal model learn cross-modal interac-
+tions? it’s harder to tell than you might think! In: Proceedings of the 2020
+Conference on Empirical Methods in Natural Language Processing (EMNLP).
+pp. 861–877. Association for Computational Linguistics, Online (Nov 2020).
+https://doi.org/10.18653/v1/2020.emnlp-main.62, https://aclanthology.org/2020.
+emnlp-main.62
+23. Hofst¨atter, S., Lin, S.C., Yang, J.H., Lin, J., Hanbury, A.: Eﬃciently teaching
+an eﬀective dense retriever with balanced topic aware sampling. In: Proceedings
+of the 44th International ACM SIGIR Conference on Research and Development
+in Information Retrieval. p. 113–122. SIGIR ’21, Association for Computing Ma-
+chinery, New York, NY, USA (2021). https://doi.org/10.1145/3404835.3462891,
+https://doi.org/10.1145/3404835.3462891
+24. Houlsby, N., Giurgiu, A., Jastrzebski, S., Morrone, B., Laroussilhe, Q.D., Ges-
+mundo, A., Attariyan, M., Gelly, S.: Parameter-Eﬃcient Transfer Learning
+for NLP. In: Proceedings of the 36th International Conference on Machine
+Learning. pp. 2790–2799. PMLR (May 2019), https://proceedings.mlr.press/v97/
+houlsby19a.html, iSSN: 2640-3498
+25. Johnson,
+J.,
+Douze,
+M.,
+J´egou,
+H.:
+Billion-scale
+similarity
+search
+with
+GPUs.
+IEEE
+Transactions
+on
+Big
+Data
+7(3),
+535–547
+(2019).
+https://doi.org/10.1109/TBDATA.2019.2921572
+26. Kalantidis,
+Y.,
+Sariyildiz,
+M.B.,
+Pion,
+N.,
+Weinzaepfel,
+P.,
+Larlus,
+D.:
+Hard
+Negative
+Mixing
+for
+Contrastive
+Learning.
+In:
+Advances
+in
+Neu-
+ral
+Information
+Processing
+Systems.
+vol.
+33,
+pp.
+21798–21809.
+Curran
+Associates,
+Inc.
+(2020),
+https://proceedings.neurips.cc/paper/2020/hash/
+f7cade80b7cc92b991cf4d2806d6bd78-Abstract.html
+27. Karpukhin, V., Oguz, B., Min, S., Lewis, P., Wu, L., Edunov, S., Chen, D., Yih,
+W.t.: Dense passage retrieval for open-domain question answering. In: Proceedings
+of the 2020 Conference on Empirical Methods in Natural Language Processing
+(EMNLP). pp. 6769–6781. Association for Computational Linguistics, Online (Nov
+2020), https://www.aclweb.org/anthology/2020.emnlp-main.550
+28. Khan,
+S.,
+Naseer,
+M.,
+Hayat,
+M.,
+Zamir,
+S.W.,
+Khan,
+F.S.,
+Shah,
+M.:
+Transformers
+in
+vision:
+A
+survey.
+ACM
+Comput.
+Surv.
+(dec
+2021).
+https://doi.org/10.1145/3505244, https://doi.org/10.1145/3505244, just Accepted
+29. Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. In: Proceed-
+ings of the 3rd International Conference for Learning Representations (Jan 2015),
+http://arxiv.org/abs/1412.6980
+30. Kludas, J., Bruno, E., Marchand-Maillet, S.: Information fusion in multimedia in-
+formation retrieval. In: International Workshop on Adaptive Multimedia Retrieval.
+pp. 147–159. Springer (2007)
+31. Lee, K., Chang, M.W., Toutanova, K.: Latent Retrieval for Weakly Super-
+vised Open Domain Question Answering. In: Proceedings of the 57th An-
+nual Meeting of the Association for Computational Linguistics. pp. 6086–
+6096. Association for Computational Linguistics, Florence, Italy (Jul 2019).
+https://doi.org/10.18653/v1/P19-1612, https://aclanthology.org/P19-1612
+32. Lerner, P., Ferret, O., Guinaudeau, C., Le Borgne, H., Besan¸con, R., Moreno,
+J.G., Lov´on Melgarejo, J.: ViQuAE, a dataset for knowledge-based visual ques-
+tion answering about named entities. In: Proceedings of The 45th Interna-
+
+16
+P. Lerner et al.
+tional ACM SIGIR Conference on Research and Development in Information Re-
+trieval. SIGIR’22, Association for Computing Machinery, New York, NY, USA
+(2022). https://doi.org/10.1145/3477495.3531753, https://hal.archives-ouvertes.
+fr/hal-03650618
+33. Lhoest, Q., Villanova del Moral, A., Jernite, Y., Thakur, A., von Platen, P., Patil,
+S., Chaumond, J., Drame, M., Plu, J., Tunstall, L., Davison, J., ˇSaˇsko, M., Chh-
+ablani, G., Malik, B., Brandeis, S., Le Scao, T., Sanh, V., Xu, C., Patry, N.,
+McMillan-Major, A., Schmid, P., Gugger, S., Delangue, C., Matussi`ere, T., De-
+but, L., Bekman, S., Cistac, P., Goehringer, T., Mustar, V., Lagunas, F., Rush,
+A., Wolf, T.: Datasets: A Community Library for Natural Language Processing.
+In: Proceedings of the 2021 Conference on Empirical Methods in Natural Lan-
+guage Processing: System Demonstrations. pp. 175–184. Association for Compu-
+tational Linguistics, Online and Punta Cana, Dominican Republic (Nov 2021),
+https://aclanthology.org/2021.emnlp-demo.21
+34. Li, G., Duan, N., Fang, Y., Gong, M., Jiang, D.: Unicoder-VL: A Universal
+Encoder for Vision and Language by Cross-Modal Pre-Training. Proceedings of
+the AAAI Conference on Artiﬁcial Intelligence 34(07), 11336–11344 (Apr 2020).
+https://doi.org/10.1609/aaai.v34i07.6795, https://ojs.aaai.org/index.php/AAAI/
+article/view/6795, number: 07
+35. Li, L.H., Yatskar, M., Yin, D., Hsieh, C.J., Chang, K.W.: VisualBERT: A Simple
+and Performant Baseline for Vision and Language (Jan 2019), https://openreview.
+net/forum?id=OiixWIb7JpAg
+36. Lin, J., Nogueira, R., Yates, A.: Pretrained transformers for text ranking: Bert
+and beyond. Synthesis Lectures on Human Language Technologies 14(4), 1–325
+(2021). https://doi.org/10.2200/S01123ED1V01Y202108HLT053
+37. Lin, T.Y., Maire, M., Belongie, S., Hays, J., Perona, P., Ramanan, D., Doll´ar,
+P., Zitnick, C.L.: Microsoft COCO: Common Objects in Context. In: Fleet, D.,
+Pajdla, T., Schiele, B., Tuytelaars, T. (eds.) Computer Vision – ECCV 2014. pp.
+740–755. Lecture Notes in Computer Science, Springer International Publishing,
+Cham (2014). https://doi.org/10.1007/978-3-319-10602-1 48
+38. Lu, J., Batra, D., Parikh, D., Lee, S.: ViLBERT: Pretraining Task-Agnostic Vi-
+siolinguistic Representations for Vision-and-Language Tasks. Advances in Neural
+Information Processing Systems 32, 13–23 (2019), https://proceedings.neurips.cc/
+paper/2019/hash/c74d97b01eae257e44aa9d5bade97baf-Abstract.html
+39. Luo, M., Zeng, Y., Banerjee, P., Baral, C.: Weakly-supervised visual-retriever-
+reader for knowledge-based question answering. In: Proceedings of the 2021 Con-
+ference on Empirical Methods in Natural Language Processing. pp. 6417–6431.
+Association for Computational Linguistics, Online and Punta Cana, Dominican
+Republic (Nov 2021). https://doi.org/10.18653/v1/2021.emnlp-main.517, https:
+//aclanthology.org/2021.emnlp-main.517
+40. Marino, K., Rastegari, M., Farhadi, A., Mottaghi, R.: OK-VQA: A visual question
+answering benchmark requiring external knowledge. In: Proceedings of the IEEE
+Conference on Computer Vision and Pattern Recognition. pp. 3195–3204 (2019),
+https://ieeexplore.ieee.org/document/8953725/
+41. Mikolov, T., Sutskever, I., Chen, K., Corrado, G.S., Dean, J.: Distributed Repre-
+sentations of Words and Phrases and their Compositionality. Advances in Neural
+Information Processing Systems 26 (2013), https://papers.neurips.cc/paper/2013/
+hash/9aa42b31882ec039965f3c4923ce901b-Abstract.html
+42. Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T.,
+Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z.,
+
+Multimodal Inverse Cloze Task for KVQAE
+17
+Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala,
+S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library. Ad-
+vances in Neural Information Processing Systems 32 (2019), https://papers.nips.
+cc/paper/2019/hash/bdbca288fee7f92f2bfa9f7012727740-Abstract.html
+43. Petroni, F., Piktus, A., Fan, A., Lewis, P., Yazdani, M., De Cao, N., Thorne,
+J., Jernite, Y., Karpukhin, V., Maillard, J., Plachouras, V., Rockt¨aschel,
+T., Riedel, S.: KILT: a benchmark for knowledge intensive language tasks.
+In: Proceedings of the 2021 Conference of the North American Chapter of
+the Association for Computational Linguistics: Human Language Technologies.
+pp. 2523–2544. Association for Computational Linguistics, Online (Jun 2021).
+https://doi.org/10.18653/v1/2021.naacl-main.200, https://aclanthology.org/2021.
+naacl-main.200
+44. Qu, C., Zamani, H., Yang, L., Croft, W.B., Learned-Miller, E.: Passage re-
+trieval for outside-knowledge visual question answering. In: Proceedings of the
+44th International ACM SIGIR Conference on Research and Development in In-
+formation Retrieval. p. 1753–1757. SIGIR ’21, Association for Computing Ma-
+chinery, New York, NY, USA (2021). https://doi.org/10.1145/3404835.3462987,
+https://doi.org/10.1145/3404835.3462987
+45. Qu, Y., Ding, Y., Liu, J., Liu, K., Ren, R., Zhao, W.X., Dong, D., Wu, H., Wang,
+H.: RocketQA: An Optimized Training Approach to Dense Passage Retrieval for
+Open-Domain Question Answering. In: Proceedings of the 2021 Conference of
+the North American Chapter of the Association for Computational Linguistics:
+Human Language Technologies. pp. 5835–5847. Association for Computational
+Linguistics, Online (Jun 2021). https://doi.org/10.18653/v1/2021.naacl-main.466,
+https://aclanthology.org/2021.naacl-main.466
+46. Radford, A., Kim, J.W., Hallacy, C., Ramesh, A., Goh, G., Agarwal, S., Sastry, G.,
+Askell, A., Mishkin, P., Clark, J., et al.: Learning transferable visual models from
+natural language supervision. In: International Conference on Machine Learning.
+pp. 8748–8763. PMLR (2021)
+47. Ram, O., Shachaf, G., Levy, O., Berant, J., Globerson, A.: Learning to Retrieve
+Passages without Supervision. In: Proceedings of the 2022 Conference of the North
+American Chapter of the Association for Computational Linguistics: Human Lan-
+guage Technologies. pp. 2687–2700. Association for Computational Linguistics,
+Seattle, United States (Jul 2022), https://aclanthology.org/2022.naacl-main.193
+48. Ren, S., He, K., Girshick, R., Sun, J.: Faster R-CNN: Towards Real-Time Ob-
+ject Detection with Region Proposal Networks. Advances in Neural Information
+Processing Systems 28, 91–99 (2015), https://proceedings.neurips.cc/paper/2015/
+hash/14bfa6bb14875e45bba028a21ed38046-Abstract.html
+49. Robertson, S.E., Walker, S., Jones, S., Hancock-Beaulieu, M.M., Gatford, M.:
+Okapi at TREC-3. In: Harman, D.K. (ed.) Third Text REtrieval Conference
+(TREC-3). NIST Special Publication, vol. 500-225, pp. 109–126. National Insti-
+tute of Standards and Technology (NIST) (1995), https://citeseerx.ist.psu.edu/
+viewdoc/download?doi=10.1.1.32.9922&rep=rep1&type=pdf
+50. Shah, S., Mishra, A., Yadati, N., Talukdar, P.P.: KVQA: Knowledge-Aware Vi-
+sual Question Answering. In: Proceedings of the AAAI Conference on Artiﬁcial
+Intelligence. vol. 33, pp. 8876–8884 (2019), https://144.208.67.177/ojs/index.php/
+AAAI/article/view/4915
+51. Sharma, P., Ding, N., Goodman, S., Soricut, R.: Conceptual captions: A cleaned,
+hypernymed, image alt-text dataset for automatic image captioning. In: Proceed-
+
+18
+P. Lerner et al.
+ings of the 56th Annual Meeting of the Association for Computational Linguistics
+(Volume 1: Long Papers). pp. 2556–2565 (2018)
+52. Shevchenko, V., Teney, D., Dick, A., van den Hengel, A.: Reasoning over vision and
+language: Exploring the beneﬁts of supplemental knowledge. In: Proceedings of the
+Third Workshop on Beyond Vision and LANguage: inTEgrating Real-world kNowl-
+edge (LANTERN). pp. 1–18. Association for Computational Linguistics, Kyiv,
+Ukraine (Apr 2021), https://aclanthology.org/2021.lantern-1.1
+53. Smucker, M.D., Allan, J., Carterette, B.: A comparison of statistical signiﬁcance
+tests for information retrieval evaluation. In: Proceedings of the sixteenth ACM
+conference on Conference on information and knowledge management. pp. 623–
+632. CIKM ’07, Association for Computing Machinery, New York, NY, USA
+(Nov 2007). https://doi.org/10.1145/1321440.1321528, https://doi.org/10.1145/
+1321440.1321528
+54. Srinivasan,
+K.,
+Raman,
+K.,
+Chen,
+J.,
+Bendersky,
+M.,
+Najork,
+M.:
+Wit:
+Wikipedia-based
+image
+text
+dataset
+for
+multimodal
+multilingual
+ma-
+chine
+learning.
+In:
+Proceedings
+of
+the
+44th
+International
+ACM
+SI-
+GIR
+Conference
+on
+Research
+and
+Development
+in
+Information
+Re-
+trieval.
+p.
+2443–2449.
+SIGIR
+’21,
+Association
+for
+Computing
+Machinery,
+New
+York,
+NY,
+USA
+(2021).
+https://doi.org/10.1145/3404835.3463257,
+https://doi.org/10.1145/3404835.3463257
+55. Srivastava, N., Hinton, G., Krizhevsky, A., Sutskever, I., Salakhutdinov, R.:
+Dropout: a simple way to prevent neural networks from overﬁtting. The journal of
+machine learning research 15(1), 1929–1958 (2014), publisher: JMLR. org
+56. Su, W., Zhu, X., Cao, Y., Li, B., Lu, L., Wei, F., Dai, J.: VL-BERT: Pre-training
+of Generic Visual-Linguistic Representations. In: Proceedings of ICLR 2020 (Feb
+2020), http://arxiv.org/abs/1908.08530, arXiv: 1908.08530
+57. Tan, H., Bansal, M.: LXMERT: Learning Cross-Modality Encoder Repre-
+sentations from Transformers. In: Proceedings of the 2019 Conference on
+Empirical Methods in Natural Language Processing and the 9th Interna-
+tional Joint Conference on Natural Language Processing (EMNLP-IJCNLP).
+pp. 5100–5111. Association for Computational Linguistics, Hong Kong, China
+(Nov
+2019).
+https://doi.org/10.18653/v1/D19-1514,
+https://www.aclweb.org/
+anthology/D19-1514
+58. Vaswani, A., Shazeer, N., Parmar, N., Uszkoreit, J., Jones, L., Gomez, A.N., Kaiser,
+�L., Polosukhin, I.: Attention is all you need. In: Advances in neural information
+processing systems. pp. 5998–6008 (2017)
+59. Wang,
+Z.,
+Li,
+L.,
+Li,
+Q.,
+Zeng,
+D.:
+Multimodal
+Data
+Enhanced
+Rep-
+resentation
+Learning
+for
+Knowledge
+Graphs.
+In:
+2019
+International
+Joint
+Conference
+on
+Neural
+Networks
+(IJCNN).
+pp.
+1–8
+(Jul
+2019).
+https://doi.org/10.1109/IJCNN.2019.8852079, iSSN: 2161-4407
+60. Weston, J., Chopra, S., Bordes, A.: Memory networks (2015)
+61. Wolf, T., Debut, L., Sanh, V., Chaumond, J., Delangue, C., Moi, A., Cistac, P.,
+Rault, T., Louf, R., Funtowicz, M., Davison, J., Shleifer, S., von Platen, P., Ma, C.,
+Jernite, Y., Plu, J., Xu, C., Scao, T.L., Gugger, S., Drame, M., Lhoest, Q., Rush,
+A.M.: HuggingFace’s Transformers: State-of-the-art Natural Language Processing.
+arXiv:1910.03771 [cs] (Jul 2020), http://arxiv.org/abs/1910.03771
+62. Zhu, Y., Kiros, R., Zemel, R., Salakhutdinov, R., Urtasun, R., Torralba,
+A.,
+Fidler,
+S.:
+Aligning
+books
+and
+movies:
+Towards
+story-like
+visual
+ex-
+planations
+by
+watching
+movies
+and
+reading
+books.
+In:
+Proceedings
+of
+the
+IEEE
+International
+Conference
+on
+Computer
+Vision
+(ICCV)
+(Decem-
+
+Multimodal Inverse Cloze Task for KVQAE
+19
+ber 2015), https://www.cv-foundation.org/openaccess/content iccv 2015/html/
+Zhu Aligning Books and ICCV 2015 paper.html
+
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+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf,len=1315
+page_content='Multimodal Inverse Cloze Task for  Knowledge-based Visual Question Answering⋆  Paul Lerner1, Olivier Ferret2, and Camille Guinaudeau1  1 Universit´e Paris-Saclay, CNRS, LISN, 91400, Orsay, France  {paul.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='lerner,camille.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='guinaudeau}@lisn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='upsaclay.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='fr  2 Universit´e Paris-Saclay, CEA, List, F-91120, Palaiseau, France  olivier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='ferret@cea.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='fr  Abstract.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' We present a new pre-training method, Multimodal Inverse  Cloze Task, for Knowledge-based Visual Question Answering about nam-  ed Entities (KVQAE).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' KVQAE is a recently introduced task that consists  in answering questions about named entities grounded in a visual context  using a Knowledge Base.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' Therefore, the interaction between the modal-  ities is paramount to retrieve information and must be captured with  complex fusion models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' As these models require a lot of training data,  we design this pre-training task from existing work in textual Question  Answering.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' It consists in considering a sentence as a pseudo-question and  its context as a pseudo-relevant passage and is extended by considering  images near texts in multimodal documents.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' Our method is applicable to  diﬀerent neural network architectures and leads to a 9% relative-MRR  and 15% relative-F1 gain for retrieval and reading comprehension, re-  spectively, over a no-pre-training baseline.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='  Keywords: Visual Question Answering · Pre-training · Multimodal Fu-  sion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='  1  Introduction  Knowledge-based Visual Question Answering about named Entities (KVQAE) is  a challenging task recently introduced in [50].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' It consists in answering questions  about named entities grounded in a visual context using a Knowledge Base  (KB).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' Figure 1 provides two examples of visual questions along with relevant  visual passages from a KB.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' To address the task, one must thus retrieve relevant  information from a KB.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' This contrasts with standard Visual Question Answering  (VQA, [1]), where questions target the content of the image (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' the color of an  object or the number of objects) or Knowledge-based VQA (about coarse-grained  object categories) [40], where one can rely on oﬀ-the-shelf object detection [17].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' In  ⋆ This work was supported by the ANR-19-CE23-0028 MEERQAT project.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' This work  was granted access to the HPC resources of IDRIS under the allocation 2021-  AD011012846 made by GENCI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='04366v1  [cs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='CL]  11 Jan 2023  2  P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' Lerner et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='  Visual Question (input)  Relevant visual passage in the Knowledge Base  “Which constituency  did this man repre-  sent  when  he  was  Prime Minister?”' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='  “Macmillan indeed lost Stockton in the landslide  Labour victory of 1945, but returned to Parlia-  ment in the November 1945 by-election in Brom-  ley.”  “In  which  year  did  this ocean liner make  her maiden voyage?”' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='  “Queen Elizabeth 2, often referred to simply as  QE2, is a ﬂoating hotel and retired ocean liner  built for the Cunard Line which was operated by  Cunard as both a transatlantic liner and a cruise  ship from 1969 to 2008.”  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' 1: Example of visual questions about named entities from the ViQuAE  dataset along with relevant visual passages from its Knowledge Base [32].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='  KVQAE, both text and image modalities bring useful information that must be  combined.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' Therefore, the task is more broadly related to Multimodal Information  Retrieval (IR) and Multimodal Fusion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='  There are two paradigms for multimodal IR and for multimodal learning  more generally: early fusion (data- and feature-level) and late fusion (score-  and decision-level) [30].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' On the one hand, late fusion is more straightforward  as both Natural Language Processing and Computer Vision techniques can be  applied independently, but it neglects interaction between the modalities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' On  the other hand, the richness of early fusion often comes at the cost of increasing  complexity and model parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' This adds an extra challenge for KVQAE  where the two existing datasets are either small (ViQuAE [32]) or generated  automatically (KVQA [50]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' To overcome this challenge, we propose to pre-train  our fusion model using a multimodal Inverse Cloze Task (ICT).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' ICT has been  introduced in [31] to pre-train a neural retriever for textual Question Answering  (QA).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' It consists in considering a sentence as a pseudo-question and its context  as a pseudo-relevant passage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' It can be seen as a generalization of the skip-gram  objective [41].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' We extend it by considering images near texts in multimodal  documents.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='  Our main contributions are: (i) Multimodal ICT, a new pre-training method  that allows tackling small KVQAE datasets such as ViQuAE;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' (ii) a multimodal  IR framework for KVQAE;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' (iii) experiments with diﬀerent neural network ar-  chitectures, including recently proposed multimodal BERTs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='  2  Related Work  Dense Retrieval.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' Dense Retrieval is a rapidly evolving ﬁeld, surveyed in  [36,11], with new pre-training tasks, optimizing methods, and variants of the  Transformer architecture emerging [47,23,15,14].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' [31] were the ﬁrst to outperform  sparse bag-of-words representations such as BM25 with dense representations for  QA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' Their approach relies on three components: (i) pre-trained language mod-  els such as BERT [10], which allow to encode the semantic of a sentence in a  CUNARDMultimodal Inverse Cloze Task for KVQAE  3  dense vector;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' (ii) a contrastive learning objective that optimizes the similarities  between questions’ and text passages’ embeddings (see Section 3);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' (iii) an un-  supervised training task, ICT (see Section 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' [27] criticize the latter for being  computationally intensive3 and argue that regular sentences are not good surro-  gates of questions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' Instead, they propose DPR, which takes advantage of (i) the  heuristic of whether the passage contains the answer to the question to deem it  relevant;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' (ii) unsupervised IR methods such as BM25 to mine hard negatives ex-  amples, which proved to be the key of their method’s success.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' We aim at taking  advantage of both approaches by (i) pre-training our model on text QA datasets  like DPR;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' (ii) incorporating multimodality into this hopefully-well-initialized  model by adapting the ICT of [31] to multimodal documents.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='  Multimodal Fusion and Pre-Training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' The success of BERT in NLP [10],  which relies on the easily-parallelizable Transformer architecture [58], an unsu-  pervised training objective, and a task-agnostic architecture, has concurrently in-  spired many works in the VQA and cross-modal retrieval ﬁelds [57,38,35,56,34,7].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='  These models are uniﬁed under a single framework in [5] and partly reviewed  in [28].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' All of these models rely on the Transformer architecture, often initialized  with a pre-trained BERT, in order to fuse image and text.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' The training is weakly  supervised, based upon image caption datasets such as COCO [37] or Concep-  tual Captions [51], and pre-trained object detectors like Faster R-CNN [48].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='  [22] show that these models learn nontrivial interactions between the modali-  ties for VQA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' Multimodal BERTs can be broadly categorized into single-stream  and multi-stream.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' Single-stream models feed both text tokens’ embeddings and  image regions’ embeddings to the same Transformer model, relying on the self-  attention mechanism to fuse them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' Instead, in the multi-stream architecture,  text and image are ﬁrst processed by two independent Transformers before us-  ing cross-attention to fuse the modalities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' Both architectures have been shown  to perform equally well in [5].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' In this work, we use a single-stream model to  take advantage of pre-training on text-only (on QA datasets).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' Also note that,  while inspired by these work, we do not use the same training objectives or data,  which are arguably unsuited for named entities’ representations, as explained in  the next section.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='  Multimodal Information Retrieval and KVQAE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' Multimodal IR has  largely been addressed using late fusion techniques (see [9] for a survey) but  we are mostly interested in early fusion techniques in this work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='  [9] review ﬁrst attempts at early fusion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' It was then systematically done by  concatenating the features of both modalities in a single vector, with a focus  on the feature weighting scheme.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' Concatenation is confronted with the curse of  dimensionality as the resulting feature space equals the sum of the dimensions  of each modality’s features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='  [44] and [39] concurrently proposed an approach quite similar to ours for  Knowledge-based VQA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' They adapt DPR [27] by replacing the question encoder  3 [31] use a batch size of over 4K questions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='  4  P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' Lerner et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='  with LXMERT [57], which allows to fuse the question and image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' However, un-  like us, they keep the passage encoder based on text-only and use the same  pre-training objectives as [57], namely Masked Language Modeling, Masked Re-  gion Modeling, and Image-Text Matching.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' We expect that these objectives are  suited to learn representations of coarse-grained object categories but not named  entities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' In other words, they are suited for standard VQA but not KVQAE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' For  example, Masked Region Modeling relies on an object detector, which is not  applicable to KVQAE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' While both [44] and [39] experiment on OK-VQA [40],  their results are inconsistent: [44] show that their model is competitive with a  BM25 baseline that takes as input the question and the human-written cap-  tion of the image while the model of [39] is outperformed by BM25 with an  automatically-generated caption.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' The discrepancies between these works can be  explained because they use neither the same KB nor the same evaluation metrics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='  [19] also experiment with diﬀerent multimodal BERTs but dispense passage-level  annotation for an end-to-end training of the retriever and answer classiﬁer4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='  Although they experiment with KVQA [50], we do not consider the work  of [52,16,21] as their systems take a human-written caption as input, which  makes the role of the image content unclear.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' [50] follow a late fusion approach  at the decision-level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' First, they detect and disambiguate the named entity men-  tions in the question.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' Then, they rely on a face recognition step as their dataset,  KVQA, is restricted to questions about person named entities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' Facts from both  textually- and visually-detected entities are retrieved from Wikidata5 and pro-  cessed by a memory network [60].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' In contrast, our work is in line with [32], who  use unstructured text from Wikipedia as KB.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' Unlike [32], who follow a late fu-  sion approach, searching the question and the image independently, we aim at  a uniﬁed representation of the text and image, both on the visual question and  KB sides.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='  3  Methods  In this section, we ﬁrst formalize our KVQAE framework, then describe the  models before diving into the three training stages: (i) DPR for textual Ques-  tion Answering;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' (ii) Multimodal Inverse Cloze Task, our main contribution;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' (iii)  Fine-tuning for KVQAE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' Finally, we discuss the inference mechanism and im-  plementation details.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='1  Information Retrieval Framework  In our multimodal setting, both visual questions (from the dataset) and visual  passages (from the KB) consist of a text-image pair (t, i), as in Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' Our goal  is to ﬁnd the optimal model E to encode adequate representations q = E(tq, iq)  and p = E(tp, ip) such that they are close if (tp, ip) is relevant for (tq, iq) (denoted  4 Standard (Knowledge-based) VQA is often treated as a classiﬁcation task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='  5 https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='wikidata.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='org/  Multimodal Inverse Cloze Task for KVQAE  5  with the superscripts (+) and (−)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' Search then boils down to retrieving the K  closest visual passages to the visual question.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' When computing the similarity  between two vectors, here with the dot product, the objective used throughout  all the training stages (§3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='3) is to minimize the following negative log-likelihood  loss for all visual questions in the dataset [31,27]: − log  exp (q·p+)  exp (q·p+)+�  j exp (q·p−  j ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='  This contrastive objective allows to eﬃciently utilize passages relevant to other  questions in the batch as in-batch negatives, since computing the similarity be-  tween two vectors is rather inexpensive compared to the forward pass of the  whole model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' We present two diﬀerent models E in the next section according  to their fusion mechanism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='2  Models  All of our models take advantage of BERT6 [10] and CLIP7 [46] as building blocks  to represent text and image, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' BERT is trained for masked language  modeling and next sentence prediction on Wikipedia and BooksCorpus [62].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='  CLIP has been trained with a contrastive objective in a weakly-supervised man-  ner over 400M image and caption pairs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' It has demonstrated better generalization  capacities than fully-supervised models and is eﬃcient for KVQAE, as empiri-  cally demonstrated in [32].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' We experiment with two diﬀerent fusion techniques:  ECA and ILF.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='  Early Cross-Attention fusion (ECA) is carried out by a single-stream Trans-  former model like the multimodal BERTs described above (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' UNITER [7]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='  However, instead of relying on a ﬁxed object detector such as Faster R-CNN, we  take advantage of CLIP, as motivated above.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' To enable early fusion, the visual  embedding produced by CLIP is projected in the same space as the text using a  linear layer with Wc ∈ Rc×d parameters trained from scratch: ec = CLIP(i)·Wc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='  The resulting embedding is then concatenated with the word embeddings in the  sequence dimension, acting as a “visual token”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' Those embeddings are then fed  to the Transformer model, where the attention mechanism should enable inter-  action between the modalities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' The ﬁnal embedding corresponds to the special  [CLS] token: ECA(t, i) = BERT([t;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' ec])[CLS].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' The Transformer model is ﬁrst  initialized from BERT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='  Intermediate Linear Fusion (ILF) introduces an additional Wt ∈ Rd×d pa-  rameters trained from scratch used to simply project the representation of the  [CLS] token in the same space as the CLIP embedding before summing the two8:  ILF(t, i) = BERT(t)[CLS] · Wt + ec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='  Because both ECA and ILF produce multimodal representations q and p,  ranking is done directly using their similarity q·p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' As baseline, we follow [32] and  linearly combine text and image similarities after zero-mean and unit-variance  6 Uncased “base” 12-layers version available at https://huggingface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='co.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='  7 With a ResNet-50 backbone [20].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='  8 Note  that  this  is  equivalent  to  concatenating  both  before  projecting  like  [BERT(t)[CLS];' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' CLIP(i)] · [Wt;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' Wc].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='  6  P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' Lerner et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='  Barack Obama  …  …  U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' Senate (2005-2008)  A sentence about Obama being senator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='  In the context we find related sentences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='  Believed to be relevant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' 2: Overview of Multimodal Inverse Cloze Task via Wikipedia/WIT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='  normalization (omitted in the following equation):  α × BERT(tq)[CLS] · BERT(tp)[CLS] + (1 − α) × cos(CLIP(iq), CLIP(ip))  (1)  The interpolation hyperparameter α is optimized on the validation set using  grid search to maximize Mean Reciprocal Rank.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' The left term (text similarity)  is referred to as DPR in the rest of the paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='3  Training stages  The models are trained sequentially in three stages:  Stage 1: DPR for textual Question Answering.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' Leaving visual represen-  tations aside, a DPR model is trained starting from the BERT initialization [27].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='  DPR consists of two BERT encoders: one for the question tq and one for the  text passage tp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' We use the model pre-trained by [32] on TriviaQA, ﬁltered of all  questions used in their dataset, ViQuAE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' They use the KILT [43] version of Triv-  iaQA and Wikipedia, which serves as KB in this stage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' Each article is then split  into disjoint passages of 100 words for text retrieval, while preserving sentence  boundaries, and the title of the article is appended to the beginning of each pas-  sage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' This yields 32M passages, that is ≈ 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='4 passages per article.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' Following [27],  irrelevant passages (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' hard negatives) are mined using BM25 [49].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='  Stage 2: Multimodal Inverse Cloze Task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' This is the main contribution of  the paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' We propose to extend the ICT of [31] to multimodal documents.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' ICT  consists in considering a sentence as a pseudo-question tq and its context as a  pseudo-relevant passage t+  p .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' Note that the title of the article is appended to the  beginning of each passage tp (as in Stage 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' We extend it using the contextual  images of Wikipedia paragraphs for the pseudo-question and the infobox image  for the passage (see Figure 2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' [31] empirically demonstrated that a key success  of their approach was to leave the pseudo-question in the relevant passage in 10%  of the training samples so that the model will learn to perform word matching,  as lexical overlap is ultimately a very useful feature for retrieval.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' In our case,  祖  WIKIPEDIAMultimodal Inverse Cloze Task for KVQAE  7  however, we argue that it is neither necessary, as the model should be strongly  initialized from Stage 1 training on TriviaQA, nor beneﬁcial, as the model could  then ignore the image modality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' Question and passage encoders pre-trained in  Stage 1 are used to initialize the visual question and visual passage encoders,  respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='  The process is eased thanks to the WIT dataset [54].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' WIT consists of millions  of images with associated text from Wikipedia and Wikimedia Commons in 108  diﬀerent languages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' We are, however, only interested in English for this work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='  While [54] have multiple strategies to ﬁnd text related to a given Wikipedia  image, such as its Commons’ caption, we use only the contextual paragraph as  text source in order to mimic the downstream KVQAE setting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' The resulting  English subset of WIT yields 400K infobox images/articles that correspond to  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='2M paragraphs/images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' Those 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='2M paragraphs consist of 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='6M sentences,  i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' potential pseudo-questions, which are 26 words long on average.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' Therefore,  to stick as close as possible to stages 1 and 3, where passages are up to 100  words long, passages consist of four sentences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' This slightly diﬀers from [31]  who consider passages of up to 288 wordpieces, prior to the pseudo-question  masking.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='  Because both ViQuAE and WIT images are taken from Wikimedia Com-  mons9, we can estimate from the image URLs that 14% of ViQuAE images  overlap with WIT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' This might lead to a bias that we analyze in Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='  Inspired by [2], to prevent catastrophic forgetting and enforce a modality-  invariant representation of the entities, the last l layers of BERT are frozen  during this stage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' In this way, we tune only the ﬁrst, modality-speciﬁc layers  of ECA, the intuition being to “replace” the text-named entities learned during  Stage 1 with the “visual” entities present in the images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' ILF fully freezes BERT  during this stage, relying only on the Wt parameters to tune the text represen-  tation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' Furthermore, CLIP is systematically frozen throughout all stages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='  We do not have a straightforward way of mining irrelevant visual passages  in this stage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' In early experiments, we tried to synthesize them by permuting  images in the batch: (t+  p , i+  p ) ← (t+  p , i−  p ), but it did not improve the results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='  After ﬁltering corrupted images or images with inappropriate image formats  (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='svg) and paragraphs with a single sentence, we end up with 975K para-  graphs/images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' We refer to it as WIT in the rest of the paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' It is split into  train (878K), validation (48K, to tune hyperparameters), and test (48K, as a  sanity check) subsets such that there is no overlap between articles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='  Stage 3: Knowledge-based Visual Question Answering about Named  Entities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' This stage consists in ﬁne-tuning the model on a downstream KVQAE  dataset, which provides visual questions (tq, iq) and relevant visual passages  (t+  p , i+  p ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' Following [2], all layers of the model are tuned during this stage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='  A subtlety of this stage is the selection of irrelevant visual passages (t−  p , i−  p ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='  As mentioned in Section 2, it was shown to be essential to DPR [27], and it is  more generally important for contrastive learning [26].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' In [32], irrelevant passages  9 https://commons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='wikimedia.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='org/  8  P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' Lerner et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='  are mined with BM25 to train DPR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' However, we suppose that this is suboptimal  for ECA and ILF as BM25 will only mine textually-plausible passages but not  visually-plausible ones.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' Therefore, we use the system provided by [32] to mine  irrelevant passages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' It is a late-fusion of DPR, ArcFace [8], CLIP, and ImageNet-  ResNet [20].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' This leads to diﬀerent training setups between DPR (used as a  baseline) and our models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' However, we have experimented both for DPR and  found no signiﬁcant diﬀerences10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='  We use the same KB as [32], which is based upon KILT’s Wikipedia and  Wikidata images of the corresponding entities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' It consists of 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='5M articles (thus  images/entities) split into 12M passages of at most 100 words as in Stage 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='  Visual questions in ViQuAE are split into train (1,190), validation (1,250),  and test (1,257) without overlap between images’ URLs [32].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' We do not experi-  ment with KVQA [50] for the following reasons: (i) it is generated automatically  from Wikidata so our text-based KB has a poor coverage of the answers;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' (ii)  it comprises yes/no questions for which passage relevance cannot be assessed  automatically.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='4  Inference  For eﬃcient retrieval, every passage in the KB is embedded along with its cor-  responding image by the visual passage encoder beforehand.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' Given a question  grounded in an image, both are embedded by the visual question encoder.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' Search  is then carried out with maximum inner product search using Faiss [25].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='5  Implementation Details  Our code is built upon PyTorch [42], Hugging Face’s transformers [61] and  datasets [33] (itself wrapping Faiss).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' It is freely available along with the data  and trained models11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='  To train ECA, we use the same hyperparameters as [32] for DPR, them-  selves based upon [27].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' In particular, we use a learning rate of 2 × 10−5 along  with the Adam optimizer [29].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' It is scheduled linearly with 100 and 4 warm-up  steps for stages 2 and 3, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' However, for ILF, we found, based on the  validation set, that it converged faster with a learning rate of 2 × 10−3 and a  constant scheduler during Stage 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' We believe this is because ILF fully freezes  BERT in Stage 2, so it does not require careful scheduling or a small learn-  ing rate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' Dropout [55] is applied in BERT and after projecting embedding with  Wc and Wt with a probability of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='1 (as in the standard BERT conﬁguration).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='  Likewise, layer normalization [3] is applied in BERT and after summing the two  embeddings in ILF.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' Gradients’ norms are clipped at 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='  Models in stages 2 and 3 are trained with a batch size of 512 and 298 visual  questions, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' The success of contrastive learning partly relies on a large  number of in-batch negatives and, therefore, a large batch size [45].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' We found  10 Evaluation methods are detailed in Section 4  11 https://github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='com/PaulLerner/ViQuAE  Multimodal Inverse Cloze Task for KVQAE  9  Table 1: IR evaluation on ViQuAE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' l: Number of frozen layers during Multimodal  ICT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' Superscripts denote signiﬁcant diﬀerences in Fisher’s randomization test  with p ≤ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='01.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' Hits@1 is omitted as it is equivalent to P@1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='  # Model  Multimodal ICT MRR@100 P@1  P@20  Hits@20  a DPR  NA  32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='8  22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='8  16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='4  61.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='2  b DPR + CLIP  NA  34.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='5a  24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='8a  15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='8  61.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='8  c  ECA  \x17  34.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='6  25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='9a  17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='2ab  61.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='6  d ECA (l = 6)  \x13  37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='8abce  26.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='7a  19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='5abce  67.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='6abce  e  ECA (l = 0)  \x13  35.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='1  24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='7  17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='6b  63.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='7  f  ILF (l = 12)  \x13  37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='3a  26.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='8a  19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='1abce  66.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='9abc  that gradient checkpointing [6] enables the use of much larger batch sizes for  ECA12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' Instead of [32] who use four NVIDIA V100 GPUs with 32GB of RAM  each for a total batch size of 128 questions, we are able to ﬁt a batch of 298  questions (as stated above) in a single V100 GPU.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' Stage 2 takes most of the  compute budget, with most models converging after ≈ 8K steps, which takes  around three days13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' Checkpoint selection is made based on the validation in-  batch Mean Reciprocal Rank, for all stages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' In-batch means that only the other  visual passages in the batch are ranked and that each visual question is paired  with only one relevant visual passage (as during training).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='  4  Results  The retrieval models are evaluated in two diﬀerent ways: (i) by computing stan-  dard IR metrics on visual passage retrieval;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' (ii) by feeding retrieved visual pas-  sages to a reader module that is tasked with extracting the concise answer to  the question, thus achieving KVQAE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' Put diﬀerently, either evaluate whether  the system is able to retrieve a relevant passage for the question or whether it is  able to answer the question.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' We ﬁnd both metrics to correlate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' Ablation studies  are carried out with IR metrics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='  ViQuAE is based upon TriviaQA, so it is only distantly supervised: the an-  swer is considered correct if it string-matches the ground truth and, likewise, a  passage is deemed relevant if it contains the ground truth14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' Moreover, Wikipedia  aliases of the ground truth are considered to be valid answers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='1  Information Retrieval  Because of the setting of ViQuAE, it is impossible to get complete coverage of  relevant passages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' Therefore we do not use any metric based on recall (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' R-  12 It is not necessary for ILF that fully freezes BERT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='  13 Jean Zay GPUs consume 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='482kW (or 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='259kW after heat recovery) in France, which  has an average grid emission factor of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='0569 kgCO2e/kWh according to https:  //bilans-ges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='ademe.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='fr/en.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='  14 After standard preprocessing (lowercasing, stripping articles, and punctuation).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='  10  P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' Lerner et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='  Visual Question  ECA top-1  DPR + CLIP top-1  “In which English palace was  this man born?”' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='  “Who designed this cathedral?”' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='  He was appointed  [.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content="] Surveyor of the  Fabric of St Paul's  Cathedral,  where  he was responsible  for maintaining the  building designed  by Sir Christopher  Wren." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='  Sir George Gilbert  Scott  led  the  restoration  of  Salisbury Cathedral  between  1863  –  1878.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=" It was during  this  time  that  Skidmore  created  the cathedral's choir  screen." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content="  Blenheim Palace was the birthplace of  the 1st Duke's famous descendant,  Winston Churchill [." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=']  In  1762,  George  purchased Buckingham  House (on the site now  occupied  by  Buckingham  Palace)  for use as a family  retreat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='  His  other  residences were Kew  and Windsor Castle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=" St James's Palace was  retained for official use." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' 3: Qualitative examples where ECA (l = 6) ﬁnds a relevant visual passage  in top-1 but late fusion falls behind.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='  Precision, mAP, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=').' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' Instead, we evaluate the models with Precision@K (P@K),  Mean Reciprocal Rank (MRR), and Hits@K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' Hits@K is the proportion of ques-  tions for which IR retrieves at least one relevant passage in top-K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' Statistical  signiﬁcance tests are conducted using Fisher’s randomization test [12,53].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' Met-  rics and statistical tests are computed with ranx [4] and are reported in Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='  The best models pre-trained with Multimodal ICT (d and f) outperform the  text-only (a) and late-fusion (b) baselines on all metrics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' Some qualitative exam-  ples are shown in Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' In the ﬁrst row, we can see evidence of cross-modal  interaction between the image depicting Winston Churchill and the passage that  mentions him (while being illustrated by a totally diﬀerent image).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' In contrast,  the late fusion baseline exhibits textual bias by returning a passage that men-  tions several English palaces (highlighted in red).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' The same observation can be  made for the second row, where St Paul’s Cathedral is only mentioned in the  relevant passage but not depicted in the contextual image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' Cross-modal interac-  tions prove useful in this case because of the heterogeneity of visual depictions:  Winston Churchill is depicted by a statue in the visual question but by a pho-  tograph in the KB.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='  We can see that Multimodal ICT is essential to ECA (c vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' d).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' Without it,  it performs on par with late fusion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' We believe this is because of overﬁtting on  the small training set of ViQuAE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' However, we ﬁnd that ﬁne-tuning on ViQuAE  is also essential to ECA, which exhibits catastrophic forgetting because of the  sequential learning setup: indeed, after Stage 2, it falls behind DPR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' We see  that the freezing technique of [2] helps to prevent catastrophic forgetting to  some extent (d vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' e).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' It is also visible in the upstream WIT pre-training where  Multimodal Inverse Cloze Task for KVQAE  11  Table 2: Reading Comprehension evaluation on ViQuAE, averaged over 5 runs  of the reader.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' l: Number of frozen layers during Multimodal ICT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='  #  IR Model  Multimodal ICT Exact Match  F1  a  DPR  NA  16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='9 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='4  20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='1 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='5  b DPR + CLIP  NA  19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='0 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='4  22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='3 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='4  c  ECA  \x17  17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='7 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='6  21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='2 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='8  d  ECA (l = 6)  \x13  20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='6 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='3  24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='4 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='2  e  ECA (l = 0)  \x13  20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='8 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='8  24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='3 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='9  f  ILF (l = 12)  \x13  21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='3 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='6  25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='4 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='3  ECA achieves 91.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='6 and 92.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='9 in-batch MRR on WIT’s test set with l = 6 and  l = 0, respectively: ﬁtting WIT better leads to further forgetting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='  Unlike what is suggested by related work (§2), we ﬁnd that the linear fusion  model performs on par with the more early, cross-attention based, fusion model  (f vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' d).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' This suggests that the improvement over the late fusion baseline indeed  comes from the Multimodal ICT pre-training, which is not very sensitive to the  model’s architecture.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' Moreover, the architecture of ILF allows to fully freeze  BERT during Stage 2, which circumvents catastrophic forgetting15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' We leave  other training strategies (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' multi-tasking, using adapters [24]) for future work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='  Nothing suggests that ECA is better on the 14% of ViQuAE images that  overlap with WIT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' ECA is better on the out-of-WIT subset (38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='0 vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' 36.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='5 MRR),  but it is the other way around for DPR and late fusion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='2  Reading Comprehension  To extract the answers from the retrieved passages, we keep the same model  as [32].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' It uses the Multi-passage BERT architecture [59] and is thus based on  text only because once the relevant passage has been retrieved, the question may  be answered without looking at the image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' To limit the variations due to training  and the number of experiments, we use the model trained by [32] oﬀ-the-shelf  and simply change its input passages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' It takes the top-24 passages as input.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' The  model was ﬁrst trained on TriviaQA (ﬁltered of all questions used in ViQuAE),  then ﬁne-tuned on ViQuAE, much like stages 1 and 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' The authors provide ﬁve  diﬀerent versions of the model that correspond to diﬀerent random seeds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='  We use Exact Match and F1-score (at the bag-of-words level) to evaluate the  extracted answers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' In Table 2 we can verify that more relevant passages indeed  lead to better downstream answers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' The only diﬀerence with the IR evaluation  is the role of the freezing technique of [2] (d vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' e), which is less clear here.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='  15 ILF only achieves 87.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='1 in-batch MRR on WIT’s test set because of the freezing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='  12  P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' Lerner et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='  5  Generic vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' Specialized Image Representations  Numbers reported in the previous section are actually on par with the best results  of [32].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' This is because the latter is based on ArcFace and ImageNet-ResNet,  in addition to DPR and CLIP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' In particular, [32] have a heuristic for taking  advantage of the face representations provided by ArcFace: they use ArcFace if  faces are detected and a combination of CLIP and ImageNet-ResNet otherwise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='  They show that this method improves retrieval precision for questions about  persons (for which face representations are relevant).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' However, this approach  is not scalable for two reasons: (i) there are near 1,000 diﬀerent entity types  in ViQuAE (according to Wikidata’s ontology), and not all can beneﬁt from  specialized representations;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' (ii) combining several representations (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' CLIP and  ImageNet-ResNet) for the same entity type is computationally expensive and  quickly saturates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' To provide a comparable system to the late fusion of [32], we  have tried integrating ArcFace and ImageNet-ResNet in ECA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' However, we have  failed to outperform the CLIP-only version of ECA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' Intuitively, we think that  ECA dilutes the specialized representations of ArcFace and is unable to preserve  them throughout all twelve layers of BERT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' Therefore, in this setting, ECA is  overall on par with late fusion (37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='7 vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' 37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='9 MRR, not signiﬁcant) but better  on questions about non-persons (39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='3 vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' 35.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='7 MRR), which again suggests that  it is unable to exploit ArcFace’s representations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='  6  Conclusion and Perspectives  We have presented a new pre-training method, Multimodal Inverse Cloze Task,  for Knowledge-based Visual Question Answering about Named Entities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' Multi-  modal ICT leverages contextual images in multimodal documents to generate  pseudo-visual questions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' It enables the use of more complex multimodal fusion  models than previously proposed late fusion methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' Consequently, our method  improves retrieval accuracy over the latter by 10% relative-MRR, leading to a  9% relative-F1 improvement in downstream reading comprehension (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' answer  extraction), on the recently introduced ViQuAE dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' We believe it is thanks  to cross-modal interactions, which are prohibited by late fusion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' More precisely,  we qualitatively observed that these interactions occurred between the image of  the visual question and the text of the KB, which counteracts the heterogeneity  of visual depictions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='  We have experimented our pre-training method with two diﬀerent neural  networks architectures: (i) ECA, which follows recently proposed Multimodal  BERTs by fusing modalities Early via Cross-Attention;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' (ii) ILF, a more standard  model that fuses modalities through a linear projection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' We found that both  perform equally well, unlike in standard VQA and cross-modal retrieval.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' We  argue that it might be because of their diﬀerence in training settings, which leads  ECA to catastrophic forgetting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' However, further investigations are required.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='  While aiming for generic multimodal representations of named entities, we  found that integrating specialized representations in our models, such as ArcFace  Multimodal Inverse Cloze Task for KVQAE  13  for faces, was not beneﬁcial.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' We hypothesize that the studied architectures may  be inappropriate but we leave this issue for future studies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='  For future work, we think that generalizing Multimodal ICT for re-ranking  (processing (tq, iq) and (tp, ip) simultaneously) and reading comprehension (gen-  erating or extracting the answer from (tp, ip)) is an exciting research lead.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' Indeed,  there is evidence that sharing the same model for IR and reading comprehen-  sion, or IR and re-ranking, is beneﬁcial for textual QA [13] and cross-modal  retrieval [18], respectively: two tasks that closely relate to KVQAE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='  References  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' Antol, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Agrawal, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Lu, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Mitchell, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Batra, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Zitnick, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Parikh,  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=': VQA: Visual Question Answering.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' In: 2015 IEEE International Confer-  ence on Computer Vision (ICCV).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' 2425–2433.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' IEEE, Santiago, Chile  (Dec 2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='1109/ICCV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='279, http://ieeexplore.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='ieee.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='org/  document/7410636/  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' Aytar, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Castrejon, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Vondrick, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Pirsiavash, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Torralba, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=': Cross-modal  scene networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' IEEE transactions on pattern analysis and machine intelligence  40(10), 2303–2314 (2017), publisher: IEEE  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' Ba, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Kiros, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Hinton, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' : Layer Normalization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' arXiv:1607.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='06450 [cs,  stat] (Jul 2016), http://arxiv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='org/abs/1607.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='06450, arXiv: 1607.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='06450  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' Bassani, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=': ranx: A Blazing-Fast Python Library for Ranking Evaluation  and Comparison.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' In: Hagen, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Verberne, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Macdonald, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Seifert, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Balog, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=',  Nørv˚ag, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Setty, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' (eds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=') Advances in Information Retrieval.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' 259–264.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' Lec-  ture Notes in Computer Science, Springer International Publishing, Cham (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='  https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='1007/978-3-030-99739-7 30  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' Bugliarello, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Cotterell, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Okazaki, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Elliott, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=': Multimodal Pretraining  Unmasked: A Meta-Analysis and a Uniﬁed Framework of Vision-and-Language  BERTs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' Transactions of the Association for Computational Linguistics 9, 978–  994 (Sep 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='1162/tacl a 00408, https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='1162/  tacl a 00408  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' Chen, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Xu, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Zhang, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Guestrin, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=': Training Deep Nets with Sublin-  ear Memory Cost (Apr 2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='48550/arXiv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='1604.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='06174, http:  //arxiv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='org/abs/1604.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
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+page_content='C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
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+page_content=' Deng, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Guo, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Xue, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
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+page_content=', Clough, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Deselaers, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Ca-  puto, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' (eds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=') ImageCLEF: Experimental Evaluation in Visual Information  Retrieval, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
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+page_content=' The Information Retrieval Series, Springer, Berlin, Hei-  delberg (2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
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+page_content=' Lerner et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' Devlin, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Chang, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Lee, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Toutanova, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=': BERT: Pre-training of deep  bidirectional transformers for language understanding.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' In: Proceedings of the 2019  Conference of the North American Chapter of the Association for Computational  Linguistics: Human Language Technologies, Volume 1 (Long and Short Papers).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
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+page_content=' 4171–4186.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' Association for Computational Linguistics, Minneapolis, Min-  nesota (Jun 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
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+page_content=' Fan, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Xie, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Cai, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Chen, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Ma, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Li, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Zhang, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Guo, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Liu, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=':  Pre-training Methods in Information Retrieval.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
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+page_content='13853 [cs] (Nov 2021),  http://arxiv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='org/abs/2111.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='13853, arXiv: 2111.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='13853  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' Fisher, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=': The design of experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' The design of experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' (2nd  Ed)  (1937),  https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='cabdirect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='org/cabdirect/abstract/19371601600,  pub-  lisher: Oliver & Boyd, Edinburgh & London.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='  13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' Fun, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Gandhi, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Ravi, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=': Eﬃcient Retrieval Optimized Multi-task Learn-  ing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' arXiv:2104.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='10129 [cs] (Apr 2021), http://arxiv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='org/abs/2104.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='10129, arXiv:  2104.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='10129  14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' Gao, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Callan, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=': Condenser: a Pre-training Architecture for Dense Retrieval.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='  In: Proceedings of the 2021 Conference on Empirical Methods in Natural Lan-  guage Processing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
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+page_content=' 981–993.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
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+page_content=' Gao, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Callan, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
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+page_content='  2843–2853.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' Association for Computational Linguistics, Dublin, Ireland (May  2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
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+page_content='  WWW  ’22,  Association  for  Computing  Machinery,  New  York,  NY,  USA  (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
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+page_content=' Gard`eres, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Ziaeefard, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=': ConceptBert: Concept-Aware Representation for Vi-  sual Question Answering.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
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+page_content=' 10 (2020), https://aclanthology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
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+page_content='44/  18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' Geigle, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Pfeiﬀer, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Reimers, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Vuli´c, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Gurevych, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=': Retrieve Fast, Rerank  Smart: Cooperative and Joint Approaches for Improved Cross-Modal Retrieval.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='  Transactions of the Association for Computational Linguistics 10, 503–521 (05  2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
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+page_content='1162/tacl a 00473  19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' Guo, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Nie, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Wong, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Liu, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Cheng, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Kankanhalli, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=': A Uniﬁed End-  to-End Retriever-Reader Framework for Knowledge-based VQA (Jun 2022), http:  //arxiv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='org/abs/2206.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='14989, number: arXiv:2206.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='14989 arXiv:2206.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='14989 [cs]  20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' He, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Zhang, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Ren, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Sun, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=': Deep residual learning for image recognition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' In:  Proceedings of the IEEE conference on computer vision and pattern recognition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='  pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' 770–778 (2016), https://openaccess.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='thecvf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='com/content cvpr 2016/papers/He  Deep Residual Learning CVPR 2016 paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='pdf  21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' Heo, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Kim, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Choi, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Zhang, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' : Hypergraph Transformer: Weakly-  supervised multi-hop reasoning for knowledge-based visual question answering.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' In:  Proceedings of the 60th Annual Meeting of the Association for Computational  Multimodal Inverse Cloze Task for KVQAE  15  Linguistics (Volume 1: Long Papers).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' 373–390.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' Association for Computational  Linguistics, Dublin, Ireland (May 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='18653/v1/2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='acl-  long.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='29, https://aclanthology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='org/2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='acl-long.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='29  22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' Hessel, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Lee, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=': Does my multimodal model learn cross-modal interac-  tions?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' it’s harder to tell than you might think!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' In: Proceedings of the 2020  Conference on Empirical Methods in Natural Language Processing (EMNLP).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='  pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' 861–877.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' Association for Computational Linguistics, Online (Nov 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='  https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='18653/v1/2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='emnlp-main.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='62, https://aclanthology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='org/2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
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+page_content='62  23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' Hofst¨atter, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Lin, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Yang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Lin, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Hanbury, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=': Eﬃciently teaching  an eﬀective dense retriever with balanced topic aware sampling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' In: Proceedings  of the 44th International ACM SIGIR Conference on Research and Development  in Information Retrieval.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' 113–122.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' SIGIR ’21, Association for Computing Ma-  chinery, New York, NY, USA (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='1145/3404835.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='3462891,  https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='1145/3404835.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='3462891  24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' Houlsby, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Giurgiu, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Jastrzebski, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Morrone, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Laroussilhe, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
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+page_content=',  Sariyildiz,  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
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+page_content=' Karpukhin, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Oguz, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Min, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Lewis, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Wu, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Edunov, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Chen, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Yih,  W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
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+page_content=' 6769–6781.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
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+page_content=' Khan,  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=',  Naseer,  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=',  Hayat,  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=',  Zamir,  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=',  Khan,  F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=',  Shah,  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=':  Transformers  in  vision:  A  survey.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
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+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='1145/3505244, just Accepted  29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' Kingma, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Ba, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=': Adam: A Method for Stochastic Optimization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' In: Proceed-  ings of the 3rd International Conference for Learning Representations (Jan 2015),  http://arxiv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
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+page_content=' Kludas, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Bruno, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Marchand-Maillet, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=': Information fusion in multimedia in-  formation retrieval.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' In: International Workshop on Adaptive Multimedia Retrieval.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='  pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' 147–159.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' Springer (2007)  31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' Lee, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Chang, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Toutanova, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=': Latent Retrieval for Weakly Super-  vised Open Domain Question Answering.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' In: Proceedings of the 57th An-  nual Meeting of the Association for Computational Linguistics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' 6086–  6096.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' Association for Computational Linguistics, Florence, Italy (Jul 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='  https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='18653/v1/P19-1612, https://aclanthology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='org/P19-1612  32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' Lerner, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Ferret, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Guinaudeau, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Le Borgne, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Besan¸con, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Moreno,  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Lov´on Melgarejo, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=': ViQuAE, a dataset for knowledge-based visual ques-  tion answering about named entities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' In: Proceedings of The 45th Interna-  16  P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' Lerner et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='  tional ACM SIGIR Conference on Research and Development in Information Re-  trieval.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' SIGIR’22, Association for Computing Machinery, New York, NY, USA  (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
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+page_content=' Li, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Duan, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Fang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Gong, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Jiang, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
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+page_content=' Proceedings of  the AAAI Conference on Artiﬁcial Intelligence 34(07), 11336–11344 (Apr 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
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+page_content=' Li, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Yatskar, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Yin, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Hsieh, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Chang, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
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+page_content=' : VisualBERT: A Simple  and Performant Baseline for Vision and Language (Jan 2019), https://openreview.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
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+page_content=', Nogueira, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Yates, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
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+page_content=' Synthesis Lectures on Human Language Technologies 14(4), 1–325  (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
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+page_content=' Lin, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Maire, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Belongie, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Hays, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Perona, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Ramanan, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Doll´ar,  P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Zitnick, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' : Microsoft COCO: Common Objects in Context.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' In: Fleet, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=',  Pajdla, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Schiele, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Tuytelaars, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' (eds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=') Computer Vision – ECCV 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='  740–755.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' Lecture Notes in Computer Science, Springer International Publishing,  Cham (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
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+page_content=' Lu, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Batra, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Parikh, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Lee, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=': ViLBERT: Pretraining Task-Agnostic Vi-  siolinguistic Representations for Vision-and-Language Tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' Advances in Neural  Information Processing Systems 32, 13–23 (2019), https://proceedings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
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+page_content=' Luo, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Zeng, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Banerjee, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Baral, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=': Weakly-supervised visual-retriever-  reader for knowledge-based question answering.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' In: Proceedings of the 2021 Con-  ference on Empirical Methods in Natural Language Processing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
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+page_content=', Rastegari, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Farhadi, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Mottaghi, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
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+page_content=', Sutskever, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
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+page_content=', Corrado, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
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+page_content=', Antiga, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
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+page_content=', Kopf, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Yang, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
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+page_content=', Tejani, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Chilamkurthy, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Steiner, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Fang, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Bai, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
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+page_content=', Piktus, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Fan, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
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+page_content=', De Cao, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
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+page_content=', Jernite, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
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+page_content=' 2523–2544.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' Association for Computational Linguistics, Online (Jun 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='  https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
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+page_content=' Qu, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Zamani, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Yang, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Croft, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Learned-Miller, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
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+page_content=' p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' 1753–1757.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' SIGIR ’21, Association for Computing Ma-  chinery, New York, NY, USA (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='1145/3404835.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='3462987,  https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
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+page_content=' Qu, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Ding, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Liu, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Liu, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Ren, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Zhao, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Dong, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Wu, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Wang,  H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
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+page_content=' In: Proceedings of the 2021 Conference of  the North American Chapter of the Association for Computational Linguistics:  Human Language Technologies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
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+page_content=' 5835–5847.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' Association for Computational  Linguistics, Online (Jun 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
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+page_content='org/2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
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+page_content=' Radford, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Kim, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Hallacy, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Ramesh, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Goh, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Agarwal, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Sastry, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=',  Askell, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Mishkin, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Clark, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' : Learning transferable visual models from  natural language supervision.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' In: International Conference on Machine Learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='  pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' 8748–8763.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' PMLR (2021)  47.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' Ram, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Shachaf, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Levy, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Berant, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Globerson, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=': Learning to Retrieve  Passages without Supervision.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' In: Proceedings of the 2022 Conference of the North  American Chapter of the Association for Computational Linguistics: Human Lan-  guage Technologies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' 2687–2700.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' Association for Computational Linguistics,  Seattle, United States (Jul 2022), https://aclanthology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='org/2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
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+page_content='193  48.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' Ren, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', He, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Girshick, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Sun, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=': Faster R-CNN: Towards Real-Time Ob-  ject Detection with Region Proposal Networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' Advances in Neural Information  Processing Systems 28, 91–99 (2015), https://proceedings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='neurips.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='cc/paper/2015/  hash/14bfa6bb14875e45bba028a21ed38046-Abstract.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='html  49.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' Robertson, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Walker, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Jones, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Hancock-Beaulieu, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Gatford, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=':  Okapi at TREC-3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' In: Harman, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' (ed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=') Third Text REtrieval Conference  (TREC-3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' NIST Special Publication, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' 500-225, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' 109–126.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' National Insti-  tute of Standards and Technology (NIST) (1995), https://citeseerx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='ist.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='psu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='edu/  viewdoc/download?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='doi=10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='9922&rep=rep1&type=pdf  50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' Shah, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Mishra, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Yadati, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Talukdar, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' : KVQA: Knowledge-Aware Vi-  sual Question Answering.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' In: Proceedings of the AAAI Conference on Artiﬁcial  Intelligence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' 33, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' 8876–8884 (2019), https://144.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='208.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='67.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='177/ojs/index.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='php/  AAAI/article/view/4915  51.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' Sharma, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Ding, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Goodman, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Soricut, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=': Conceptual captions: A cleaned,  hypernymed, image alt-text dataset for automatic image captioning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' In: Proceed-  18  P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' Lerner et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='  ings of the 56th Annual Meeting of the Association for Computational Linguistics  (Volume 1: Long Papers).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' 2556–2565 (2018)  52.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' Shevchenko, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Teney, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Dick, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', van den Hengel, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=': Reasoning over vision and  language: Exploring the beneﬁts of supplemental knowledge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' In: Proceedings of the  Third Workshop on Beyond Vision and LANguage: inTEgrating Real-world kNowl-  edge (LANTERN).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' 1–18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' Association for Computational Linguistics, Kyiv,  Ukraine (Apr 2021), https://aclanthology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='org/2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='lantern-1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='1  53.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' Smucker, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Allan, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Carterette, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=': A comparison of statistical signiﬁcance  tests for information retrieval evaluation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' In: Proceedings of the sixteenth ACM  conference on Conference on information and knowledge management.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' 623–  632.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' CIKM ’07, Association for Computing Machinery, New York, NY, USA  (Nov 2007).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='1145/1321440.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
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+page_content=', Hinton, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Krizhevsky, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Sutskever, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Salakhutdinov, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=':  Dropout: a simple way to prevent neural networks from overﬁtting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
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+page_content=' Su, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Zhu, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Cao, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Li, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Lu, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Wei, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Dai, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=': VL-BERT: Pre-training  of Generic Visual-Linguistic Representations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
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+page_content='08530, arXiv: 1908.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='08530  57.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' Tan, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Bansal, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=': LXMERT: Learning Cross-Modality Encoder Repre-  sentations from Transformers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' In: Proceedings of the 2019 Conference on  Empirical Methods in Natural Language Processing and the 9th Interna-  tional Joint Conference on Natural Language Processing (EMNLP-IJCNLP).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='  pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' 5100–5111.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' Association for Computational Linguistics, Hong Kong, China  (Nov  2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='  https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
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+page_content='org/  anthology/D19-1514  58.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' Vaswani, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Shazeer, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Parmar, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Uszkoreit, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Jones, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Gomez, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Kaiser,  �L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Polosukhin, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=': Attention is all you need.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' In: Advances in neural information  processing systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' 5998–6008 (2017)  59.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' Wang,  Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=',  Li,  L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=',  Li,  Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=',  Zeng,  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=':  Multimodal  Data  Enhanced  Rep-  resentation  Learning  for  Knowledge  Graphs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='  In:  2019  International  Joint  Conference  on  Neural  Networks  (IJCNN).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='  pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='  1–8  (Jul  2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='  https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='1109/IJCNN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='8852079, iSSN: 2161-4407  60.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' Weston, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Chopra, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Bordes, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=': Memory networks (2015)  61.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' Wolf, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Debut, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Sanh, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Chaumond, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Delangue, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Moi, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Cistac, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=',  Rault, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Louf, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Funtowicz, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Davison, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Shleifer, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', von Platen, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Ma, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=',  Jernite, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Plu, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Xu, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Scao, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Gugger, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Drame, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Lhoest, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Rush,  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=': HuggingFace’s Transformers: State-of-the-art Natural Language Processing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='  arXiv:1910.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='03771 [cs] (Jul 2020), http://arxiv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='org/abs/1910.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content='03771  62.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=' Zhu, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Kiros, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Zemel, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
+page_content=', Salakhutdinov, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ptE3T4oBgHgl3EQfLwlT/content/2301.04366v1.pdf'}
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+Sport Task: Fine Grained Action Detection and
+Classification of Table Tennis Strokes from Videos for
+MediaEval 2022
+Pierre-Etienne Martin1, Jordan Calandre2, Boris Mansencal3, Jenny Benois-Pineau3,
+Renaud Péteri2, Laurent Mascarilla2 and Julien Morlier4
+1CCP Department, Max Planck Institute for Evolutionary Anthropology, D-04103 Leipzig, Germany
+2MIA, La Rochelle University, La Rochelle, France
+3Univ. Bordeaux, CNRS, Bordeaux INP, LaBRI, Talence, France
+4IMS, University of Bordeaux, Talence, France
+Abstract
+Sports video analysis is a widespread research topic. Its applications are very diverse, like events detection
+during a match, video summary, or fine-grained movement analysis of athletes. As part of the MediaEval
+2022 benchmarking initiative, this task aims at detecting and classifying subtle movements from sport videos.
+We focus on recordings of table tennis matches. Conducted since 2019, this task provides a classification
+challenge from untrimmed videos recorded under natural conditions with known temporal boundaries for
+each stroke. Since 2021, the task also provides a stroke detection challenge from un-annotated, untrimmed
+videos. This year, the training, validation, and test sets are enhanced to ensure that all strokes are represented
+in each dataset. The dataset is now similar to the one used in [1, 2]. This research is intended to build tools
+for coaches and athletes who want to further evaluate their sport performances.
+1. Introduction
+Action detection and classification is one of the main challenges in computer vision [3]. Throughout
+the last few years, datasets focusing on action classification have grown tremendously, along with
+their complexity [2]. There has been a significant number of studies devoted to the analysis of
+sports gestures using motion-capture systems. Nonetheless, sensors and markers attached to the
+body have the inherent tendency to interfere with the natural behaviour of the athletes. Therefore,
+this concern motivates the development of non-invasive methods using video recording from a
+camera.
+The sports video classification project was initiated by the Sports Faculty of the University of
+Bordeaux (STAPS), the computer science laboratory LaBRI, and the MIA laboratory of the University
+of La Rochelle 1. This project intends to develop artificial intelligence and multimedia indexing
+methods for table tennis stroke recognition. The ultimate goal is to evaluate the performance of
+MediaEval’22: Multimedia Evaluation Workshop, January 13–15, 2023, Bergen, Norway and Online
+� mediaeval.sport.task@diff.u-bordeaux.fr (P. Martin)
+� www.eva.mpg.de/comparative-cultural-psychology/staff/pierre-etienne-martin (P. Martin)
+� 0000-0002-9593-4580 (P. Martin)
+© 2022 Copyright for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
+CEUR
+Workshop
+Proceedings
+http://ceur-ws.org
+ISSN 1613-0073
+CEUR Workshop Proceedings (CEUR-WS.org)
+1This research is supported by the New Aquitania Region’s CRISP project - ComputeR vIsion for Sports Performance
+and the MIRES Federation.
+arXiv:2301.13576v1  [cs.AI]  31 Jan 2023
+
+individual athletes, especially students, and thereby develop optimal training strategies. For this
+purpose, we have recorded a video corpus TTStroke-21 with volunteer athletes.
+Datasets like UCF-101 [4], HMDB [5, 6], AVA [7] and Kinetics [8, 9, 10] are used in the action
+recognition field, with an increasing number of video samples and number of classes covered over
+the years. There are very few datasets available that have a focus on fine-grained classifications in
+sports, such as FineGym [11] and TTStroke21 [12].
+To address the increasing complexity of datasets, some classification methods exploit temporal
+information as much as possible. For example, [13] learns spatio-temporal dependencies from
+videos using only RGB data. Alternatively, some methods integrate other modalities extracted from
+videos, e.g., optical flow [14, 15, 16]. Moreover, in the TTStroke-21 dataset, stroke classification
+is challenging, because movements between two strokes share strong visual similarities.
+The following sections present the Sport task and its substasks for this year, along with the
+dataset and the specific terms of use when downloading the dataset. Complementary information
+on the task may be found on the dedicated page from the MediaEval website2.
+2. Task description
+The Sport task is based on the TTStroke-21 database [17, 12]. This database is a corpus of table
+tennis recordings with players performing in natural conditions. The dataset delivered through
+this task focuses on videos acquired with GoPro cameras at a recording speed of 120 frames per
+second and annotated by professional players. This task offers researchers an opportunity to solve
+a fine-grained classification problem with videos and annotations of high quality in the sports
+domain. Compared to the Sport task from MediaEval 2021’s edition [18], the dataset has been
+enriched and the data organization and distribution differ. The task has two subtasks: stroke
+classification from trimmed videos and stroke detection from untrimmed videos. Each subtask has
+its own dataset.
+Researchers can participate in one or both subtasks and submit up to five runs for each subtask.
+The participants must fill in the provided XML files dedicated to the test set of the subtask for each
+run. The content of the XML file varies according to the subtask. The runs have to be submitted in
+an archive (zip file), with each run in a different directory for each subtask. Participants should
+also submit a working notes paper, which describes their method and indicates if any external
+data, such as other datasets or pre-trained networks, was used to compute their runs. The use
+of pre-trained models on the Sport task dataset TTStroke-21 of the previous years is however
+forbidden. The task is considered fully automatic: once the videos are provided to the system,
+results should be produced without any human intervention. Participants are encouraged to
+release their code publicly with their submission. This year, similarly to the 2021 edition, a baseline
+for both subtasks is shared publicly3 [19].
+2.1. Subtask 1 - Stroke Classification
+For this subtask, the participants are required to classify a set of trimmed videos containing only
+one table tennis stroke, or possibly no stroke at all. There are 20 possible stroke classes and an
+additional non-stroke class. For this purpose, two annotated sets are provided: a training and a
+2https://multimediaeval.github.io/editions/2022/tasks/sportsvideo/
+3https://github.com/ccp-eva/SportTaskME22
+
+validation set with respectively 807 and 230 trimmed videos. A non-annotated test set comprising
+118 trimmed videos has to be classified. The trimmed videos in the different sets may have been
+retrieved from the same untrimmed videos but at different moments in time without overlapping.
+Specifically, the participants are invited to fill an XML file and replace the default label “Unknown”
+with the stroke class assigned by the participants’ method. All submissions will be evaluated in
+terms of global accuracy for ranking, and detailed with per-class accuracy.
+In last year edition, the best global accuracy reached 74.2% [20] using SWIN-Transformers, fol-
+lowed closely by ResNet-50 models (68.8%) beating by a large margin last year baseline (20.4%) [21].
+Methods effectiveness seem to be linked to the model architecture, but also the taking into account
+of both stroke class similarity and class imbalance during training. This year, the task uses the
+same split of the TTStroke-21 database as in [1, 2] allowing better comparison with previous
+works outside the MediaEval benchmark scope.
+2.2. Subtask 2 - Stroke Detection
+For this subtask, the participants are required to segment a set of untrimmed videos with the aim
+to retrieve strokes whatever the stroke class. For this purpose, two annotated sets are provided: a
+training set and a validation set, with respectively 16 and 6 untrimmed videos. A non-annotated
+test set consisting of 6 untrimmed videos has to be temporally segmented. The videos are not
+shared across the training, the validation, and test sets; however, the same player may appear in
+the different sets.
+Specifically, the participants have to fill the provided test set XML files with the stroke temporal
+boundaries (frame index of the videos). All submissions will be evaluated in terms of mean Average
+Precision (mAP) and temporal Intersection over Union (IoU). Both are usually used for image
+segmentation but are adapted for this task:
+• mAP: each stroke represents an object to be detected temporally. Detection is considered
+True when the temporal IoU between prediction and ground truth is above an IoU threshold.
+20 thresholds from 0.5 to 0.95 with a step of 0.05 are considered, similarly to the COCO
+challenge [22]. This metric will be used for the final ranking of participants.
+• IoU: the frame-wise overlap between the ground truth and the predicted strokes across all
+the videos.
+For last year’s edition, only two participants submitted runs for this difficult subtask [23, 24].
+They did not improve the baseline result in terms of mAP but [24] reached an IoU of 0.247 against
+0.144 for the baseline, using YOLOv5 model.
+3. Dataset description
+The dataset was recorded at the Sports Faculty of the University of Bordeaux. It is constituted of
+player-centred videos without markers or sensors, recorded in natural conditions using GoPro
+cameras (see Figure 1). Professional table tennis teachers designed a dedicated taxonomy to
+describe all the possible strokes. The dataset includes 20 table tennis stroke classes: 8 services, 6
+offensive strokes, and 6 defensive strokes. The strokes may also be divided in two super-classes:
+Forehand and Backhand. The dataset was annotated by professional players using a crowd-
+sourced annotation platform. Non-stroke samples are inferred from the stroke annotations.
+
+Figure 1: Key frames of a same stroke from TTStroke-21
+In order to be able to share the dataset, we blurred the faces of the players for each original
+video frame using OpenCV deep learning face detector, based on the Single Shot Detector (SSD)
+framework with a ResNet base network. A tracking method has been implemented to decrease the
+false positive rate. The detected faces are blurred, and the video is re-encoded in MPEG-4.
+Compared with last year’s edition, the classification dataset is enriched this year with new
+and more diverse video samples. The source videos were trimmed, sorted in class folders and
+distributed among train, validation and test sets. A total of 1 155 trimmed videos, representing
+more than 210 000 frames, are considered for this subtask. For the detection subtask, 100 minutes
+of table tennis games across 28 videos recorded at 120 frames per second and distributed in train,
+validation and test sets are considered. It represents more than 718 000 frames. The resolution
+of the video for both subtasks is 1920 × 1080 representing in total 46.1 GB of disk space. The
+validation set is provided for each subtask for better comparison across participants. This set may
+be used for training when submitting the test set’s results.
+4. Specific terms of use
+Although faces are automatically blurred to preserve anonymity, some faces are misdetected, and
+thus some players remain identifiable. In order to respect the personal data of the players, this
+dataset is subject to a usage agreement, referred to as Special Conditions.
+These Special Conditions apply to the use of videos in the scope of the MediaEval workshop
+task “Sport Task: Fine Grained Action Detection and Classification of Table Tennis Strokes from
+Videos.”. They correspond to the specific usage agreement referred to in the Usage agreement for
+the MediaEval 2022 Research Collections, signed between the user and the University of Delft. The
+complete acceptance of these Special Conditions is a mandatory prerequisite for the provision
+of the videos as part of the MediaEval 2022 evaluation campaign. A complete reading of these
+conditions is necessary and requires the user, for example, to obscure the faces (blurring, black
+banner) in the video before use in any publication and to destroy the data by January 30th, 2023.
+5. Discussions
+As last year, the MediaEval Sport task offers two subtasks: i) Classification and ii) Detection of
+strokes. Classification methods performance has increased since the launch of the task. We hope
+to have more participation in the detection subtask in order to also improve in the domain of
+moment of interest in sports. The participants are encouraged to share their difficulties and their
+results even if they seem not sufficiently good. All the investigations, even when not successful,
+
+may inspire future methods.
+Acknowledgment
+The authors would like to thank the players, coaches, and annotators who contributed to
+TTStroke-21.
+References
+[1] P. Martin, J. Benois-Pineau, R. Péteri, J. Morlier, 3d attention mechanisms in twin spatio-temporal convolutional
+neural networks. application to action classification in videos of table tennis games., in: ICPR, IEEE Computer
+Society, 2021.
+[2] P. Martin, Fine-Grained Action Detection and Classification from Videos with Spatio-Temporal Convolutional
+Neural Networks. Application to Table Tennis. (Détection et classification fines d’actions à partir de vidéos par
+réseaux de neurones à convolutions spatio-temporelles. Application au tennis de table), Ph.D. thesis, University of
+La Rochelle, France, 2020. URL: https://tel.archives-ouvertes.fr/tel-03128769.
+[3] P. Martin, J. Benois-Pineau, R. Péteri, A. Zemmari, J. Morlier, 3D Convolutional Networks for Action Recognition:
+Application to Sport Gesture Recognition, Springer International Publishing, 2021.
+[4] K. Soomro, A. R. Zamir, M. Shah, UCF101: A dataset of 101 human actions classes from videos in the wild, CoRR
+abs/1212.0402 (2012).
+[5] H. Kuehne, H. Jhuang, E. Garrote, T. A. Poggio, T. Serre, HMDB: A large video database for human motion
+recognition, in: ICCV, IEEE Computer Society, 2011, pp. 2556–2563.
+[6] H. Jhuang, J. Gall, S. Zuffi, C. Schmid, M. J. Black, Towards understanding action recognition, in: ICCV, IEEE
+Computer Society, 2013, pp. 3192–3199.
+[7] C. Gu, C. Sun, D. A. Ross, C. Vondrick, C. Pantofaru, Y. Li, S. Vijayanarasimhan, G. Toderici, S. Ricco, R. Sukthankar,
+C. Schmid, J. Malik, AVA: A video dataset of spatio-temporally localized atomic visual actions (2018) 6047–6056.
+[8] W. Kay, J. Carreira, K. Simonyan, B. Zhang, C. Hillier, S. Vijayanarasimhan, F. Viola, T. Green, T. Back, P. Natsev,
+M. Suleyman, A. Zisserman, The kinetics human action video dataset, CoRR abs/1705.06950 (2017).
+[9] L. Smaira, J. Carreira, E. Noland, E. Clancy, A. Wu, A. Zisserman, A short note on the kinetics-700-2020 human
+action dataset, CoRR abs/2010.10864 (2020).
+[10] A. Li, M. Thotakuri, D. A. Ross, J. Carreira, A. Vostrikov, A. Zisserman, The ava-kinetics localized human actions
+video dataset, CoRR abs/2005.00214 (2020).
+[11] D. Shao, Y. Zhao, B. Dai, D. Lin, Finegym: A hierarchical video dataset for fine-grained action understanding, in:
+CVPR, IEEE, 2020, pp. 2613–2622.
+[12] P. Martin, J. Benois-Pineau, R. Péteri, J. Morlier, Fine grained sport action recognition with twin spatio-temporal
+convolutional neural networks, Multim. Tools Appl. 79 (2020) 20429–20447.
+[13] Z. Liu, H. Hu, Spatiotemporal relation networks for video action recognition, IEEE Access 7 (2019) 14969–14976.
+[14] J. Carreira, A. Zisserman, Quo vadis, action recognition? A new model and the kinetics dataset, in: CVPR, IEEE
+Computer Society, 2017, pp. 4724–4733.
+[15] G. Varol, I. Laptev, C. Schmid, Long-term temporal convolutions for action recognition, IEEE Trans. Pattern Anal.
+Mach. Intell. 40 (2018) 1510–1517.
+[16] P. Martin, J. Benois-Pineau, R. Péteri, J. Morlier, Optimal choice of motion estimation methods for fine-grained
+action classification with 3d convolutional networks, in: ICIP, IEEE, 2019, pp. 554–558.
+[17] P. Martin, J. Benois-Pineau, R. Péteri, J. Morlier, Sport action recognition with siamese spatio-temporal cnns:
+Application to table tennis, in: CBMI, IEEE, 2018, pp. 1–6.
+[18] P. Martin, J. Calandre, B. Mansencal, J. Benois-Pineau, R. Péteri, L. Mascarilla, J. Morlier, Sports video: Fine-grained
+action detection and classification of table tennis strokes from videos for mediaeval 2021, in: [25], 2021. URL:
+http://ceur-ws.org/Vol-3181/paper3.pdf.
+[19] P. Martin, Baseline method for the sport task of mediaeval 2022 benchmark with 3d cnns using attention
+mechanism, in: MediaEval, CEUR Workshop Proceedings, CEUR-WS.org, 2022.
+[20] Y. Qian, L. Yu, W. Liu, A. Hauptmann, Learning unbiased transformer for long-tail sports action classification, in:
+[25], 2021. URL: http://ceur-ws.org/Vol-3181/paper52.pdf.
+[21] P. Martin, Spatio-temporal CNN baseline method for the sports video task of mediaeval 2021 benchmark, in: [25],
+2021. URL: http://ceur-ws.org/Vol-3181/paper13.pdf.
+
+[22] T. Lin, M. Maire, S. J. Belongie, J. Hays, P. Perona, D. Ramanan, P. Dollár, C. L. Zitnick, Microsoft COCO: common
+objects in context, in: D. J. Fleet, T. Pajdla, B. Schiele, T. Tuytelaars (Eds.), Computer Vision - ECCV 2014 - 13th
+European Conference, Zurich, Switzerland, September 6-12, 2014, Proceedings, Part V, volume 8693 of Lecture
+Notes in Computer Science, Springer, 2014, pp. 740–755.
+[23] A. Zahra, P. Martin, Two stream network for stroke detection in table tennis, in: [25], 2021. URL: http://ceur-ws.
+org/Vol-3181/paper55.pdf.
+[24] B. J, M. T. T, B. B, J. S, L. N. N, YOLOV5 for stroke detection and classification in table tennis, in: [25], 2021. URL:
+http://ceur-ws.org/Vol-3181/paper38.pdf.
+[25] S. Hicks, K. Pogorelov, A. Lommatzsch, A. G. S. de Herrera, P. Martin, S. Z. Hassan, A. Porter, A. Kasem, S. Andreadis,
+M. Lux, M. G. Ocaña, A. Liu, M. Larson (Eds.), Working Notes Proceedings of the MediaEval 2021 Workshop,
+Online, 13-15 December 2021, volume 3181 of CEUR Workshop Proceedings, CEUR-WS.org, 2022. URL: http:
+//ceur-ws.org/Vol-3181.
+
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+page_content='Sport Task: Fine Grained Action Detection and  Classification of Table Tennis Strokes from Videos for  MediaEval 2022  Pierre-Etienne Martin1, Jordan Calandre2, Boris Mansencal3, Jenny Benois-Pineau3,  Renaud Péteri2, Laurent Mascarilla2 and Julien Morlier4  1CCP Department, Max Planck Institute for Evolutionary Anthropology, D-04103 Leipzig, Germany  2MIA, La Rochelle University, La Rochelle, France  3Univ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Bordeaux, CNRS, Bordeaux INP, LaBRI, Talence, France  4IMS, University of Bordeaux, Talence, France  Abstract  Sports video analysis is a widespread research topic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Its applications are very diverse, like events detection  during a match, video summary, or fine-grained movement analysis of athletes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' As part of the MediaEval  2022 benchmarking initiative, this task aims at detecting and classifying subtle movements from sport videos.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content='  We focus on recordings of table tennis matches.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Conducted since 2019, this task provides a classification  challenge from untrimmed videos recorded under natural conditions with known temporal boundaries for  each stroke.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Since 2021, the task also provides a stroke detection challenge from un-annotated, untrimmed  videos.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' This year, the training, validation, and test sets are enhanced to ensure that all strokes are represented  in each dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' The dataset is now similar to the one used in [1, 2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' This research is intended to build tools  for coaches and athletes who want to further evaluate their sport performances.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Introduction  Action detection and classification is one of the main challenges in computer vision [3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Throughout  the last few years, datasets focusing on action classification have grown tremendously, along with  their complexity [2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' There has been a significant number of studies devoted to the analysis of  sports gestures using motion-capture systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Nonetheless, sensors and markers attached to the  body have the inherent tendency to interfere with the natural behaviour of the athletes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Therefore,  this concern motivates the development of non-invasive methods using video recording from a  camera.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content='  The sports video classification project was initiated by the Sports Faculty of the University of  Bordeaux (STAPS), the computer science laboratory LaBRI, and the MIA laboratory of the University  of La Rochelle 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' This project intends to develop artificial intelligence and multimedia indexing  methods for table tennis stroke recognition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' The ultimate goal is to evaluate the performance of  MediaEval’22: Multimedia Evaluation Workshop, January 13–15, 2023, Bergen, Norway and Online  � mediaeval.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content='sport.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content='task@diff.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content='u-bordeaux.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content='fr (P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Martin)  � www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content='eva.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content='mpg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content='de/comparative-cultural-psychology/staff/pierre-etienne-martin (P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Martin)  � 0000-0002-9593-4580 (P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Martin)  © 2022 Copyright for this paper by its authors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Use permitted under Creative Commons License Attribution 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content='0 International (CC BY 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content='0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content='  CEUR  Workshop  Proceedings  http://ceur-ws.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content='org  ISSN 1613-0073  CEUR Workshop Proceedings (CEUR-WS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content='org)  1This research is supported by the New Aquitania Region’s CRISP project - ComputeR vIsion for Sports Performance  and the MIRES Federation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content='  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content='13576v1  [cs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content='AI]  31 Jan 2023  individual athletes, especially students, and thereby develop optimal training strategies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' For this  purpose, we have recorded a video corpus TTStroke-21 with volunteer athletes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content='  Datasets like UCF-101 [4], HMDB [5, 6], AVA [7] and Kinetics [8, 9, 10] are used in the action  recognition field, with an increasing number of video samples and number of classes covered over  the years.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' There are very few datasets available that have a focus on fine-grained classifications in  sports, such as FineGym [11] and TTStroke21 [12].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content='  To address the increasing complexity of datasets, some classification methods exploit temporal  information as much as possible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' For example, [13] learns spatio-temporal dependencies from  videos using only RGB data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Alternatively, some methods integrate other modalities extracted from  videos, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=', optical flow [14, 15, 16].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Moreover, in the TTStroke-21 dataset, stroke classification  is challenging, because movements between two strokes share strong visual similarities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content='  The following sections present the Sport task and its substasks for this year, along with the  dataset and the specific terms of use when downloading the dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Complementary information  on the task may be found on the dedicated page from the MediaEval website2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Task description  The Sport task is based on the TTStroke-21 database [17, 12].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' This database is a corpus of table  tennis recordings with players performing in natural conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' The dataset delivered through  this task focuses on videos acquired with GoPro cameras at a recording speed of 120 frames per  second and annotated by professional players.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' This task offers researchers an opportunity to solve  a fine-grained classification problem with videos and annotations of high quality in the sports  domain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Compared to the Sport task from MediaEval 2021’s edition [18], the dataset has been  enriched and the data organization and distribution differ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' The task has two subtasks: stroke  classification from trimmed videos and stroke detection from untrimmed videos.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Each subtask has  its own dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content='  Researchers can participate in one or both subtasks and submit up to five runs for each subtask.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content='  The participants must fill in the provided XML files dedicated to the test set of the subtask for each  run.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' The content of the XML file varies according to the subtask.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' The runs have to be submitted in  an archive (zip file), with each run in a different directory for each subtask.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Participants should  also submit a working notes paper, which describes their method and indicates if any external  data, such as other datasets or pre-trained networks, was used to compute their runs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' The use  of pre-trained models on the Sport task dataset TTStroke-21 of the previous years is however  forbidden.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' The task is considered fully automatic: once the videos are provided to the system,  results should be produced without any human intervention.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Participants are encouraged to  release their code publicly with their submission.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' This year, similarly to the 2021 edition, a baseline  for both subtasks is shared publicly3 [19].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Subtask 1 - Stroke Classification  For this subtask, the participants are required to classify a set of trimmed videos containing only  one table tennis stroke, or possibly no stroke at all.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' There are 20 possible stroke classes and an  additional non-stroke class.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' For this purpose, two annotated sets are provided: a training and a  2https://multimediaeval.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content='github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content='io/editions/2022/tasks/sportsvideo/  3https://github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content='com/ccp-eva/SportTaskME22  validation set with respectively 807 and 230 trimmed videos.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' A non-annotated test set comprising  118 trimmed videos has to be classified.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' The trimmed videos in the different sets may have been  retrieved from the same untrimmed videos but at different moments in time without overlapping.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content='  Specifically, the participants are invited to fill an XML file and replace the default label “Unknown”  with the stroke class assigned by the participants’ method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' All submissions will be evaluated in  terms of global accuracy for ranking, and detailed with per-class accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content='  In last year edition, the best global accuracy reached 74.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content='2% [20] using SWIN-Transformers, fol-  lowed closely by ResNet-50 models (68.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content='8%) beating by a large margin last year baseline (20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content='4%) [21].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content='  Methods effectiveness seem to be linked to the model architecture, but also the taking into account  of both stroke class similarity and class imbalance during training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' This year, the task uses the  same split of the TTStroke-21 database as in [1, 2] allowing better comparison with previous  works outside the MediaEval benchmark scope.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Subtask 2 - Stroke Detection  For this subtask, the participants are required to segment a set of untrimmed videos with the aim  to retrieve strokes whatever the stroke class.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' For this purpose, two annotated sets are provided: a  training set and a validation set, with respectively 16 and 6 untrimmed videos.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' A non-annotated  test set consisting of 6 untrimmed videos has to be temporally segmented.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' The videos are not  shared across the training, the validation, and test sets;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' however, the same player may appear in  the different sets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content='  Specifically, the participants have to fill the provided test set XML files with the stroke temporal  boundaries (frame index of the videos).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' All submissions will be evaluated in terms of mean Average  Precision (mAP) and temporal Intersection over Union (IoU).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Both are usually used for image  segmentation but are adapted for this task:  mAP: each stroke represents an object to be detected temporally.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Detection is considered  True when the temporal IoU between prediction and ground truth is above an IoU threshold.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content='  20 thresholds from 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content='5 to 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content='95 with a step of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content='05 are considered, similarly to the COCO  challenge [22].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' This metric will be used for the final ranking of participants.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content='  IoU: the frame-wise overlap between the ground truth and the predicted strokes across all  the videos.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content='  For last year’s edition, only two participants submitted runs for this difficult subtask [23, 24].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content='  They did not improve the baseline result in terms of mAP but [24] reached an IoU of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content='247 against  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content='144 for the baseline, using YOLOv5 model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Dataset description  The dataset was recorded at the Sports Faculty of the University of Bordeaux.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' It is constituted of  player-centred videos without markers or sensors, recorded in natural conditions using GoPro  cameras (see Figure 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Professional table tennis teachers designed a dedicated taxonomy to  describe all the possible strokes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' The dataset includes 20 table tennis stroke classes: 8 services, 6  offensive strokes, and 6 defensive strokes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' The strokes may also be divided in two super-classes:  Forehand and Backhand.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' The dataset was annotated by professional players using a crowd-  sourced annotation platform.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Non-stroke samples are inferred from the stroke annotations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content='  Figure 1: Key frames of a same stroke from TTStroke-21  In order to be able to share the dataset, we blurred the faces of the players for each original  video frame using OpenCV deep learning face detector, based on the Single Shot Detector (SSD)  framework with a ResNet base network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' A tracking method has been implemented to decrease the  false positive rate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' The detected faces are blurred, and the video is re-encoded in MPEG-4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content='  Compared with last year’s edition, the classification dataset is enriched this year with new  and more diverse video samples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' The source videos were trimmed, sorted in class folders and  distributed among train, validation and test sets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' A total of 1 155 trimmed videos, representing  more than 210 000 frames, are considered for this subtask.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' For the detection subtask, 100 minutes  of table tennis games across 28 videos recorded at 120 frames per second and distributed in train,  validation and test sets are considered.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' It represents more than 718 000 frames.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' The resolution  of the video for both subtasks is 1920 × 1080 representing in total 46.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content='1 GB of disk space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' The  validation set is provided for each subtask for better comparison across participants.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' This set may  be used for training when submitting the test set’s results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Specific terms of use  Although faces are automatically blurred to preserve anonymity, some faces are misdetected, and  thus some players remain identifiable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' In order to respect the personal data of the players, this  dataset is subject to a usage agreement, referred to as Special Conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content='  These Special Conditions apply to the use of videos in the scope of the MediaEval workshop  task “Sport Task: Fine Grained Action Detection and Classification of Table Tennis Strokes from  Videos.”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' They correspond to the specific usage agreement referred to in the Usage agreement for  the MediaEval 2022 Research Collections, signed between the user and the University of Delft.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' The  complete acceptance of these Special Conditions is a mandatory prerequisite for the provision  of the videos as part of the MediaEval 2022 evaluation campaign.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' A complete reading of these  conditions is necessary and requires the user, for example, to obscure the faces (blurring, black  banner) in the video before use in any publication and to destroy the data by January 30th, 2023.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Discussions  As last year, the MediaEval Sport task offers two subtasks: i) Classification and ii) Detection of  strokes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Classification methods performance has increased since the launch of the task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' We hope  to have more participation in the detection subtask in order to also improve in the domain of  moment of interest in sports.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' The participants are encouraged to share their difficulties and their  results even if they seem not sufficiently good.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' All the investigations, even when not successful,  may inspire future methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content='  Acknowledgment  The authors would like to thank the players, coaches, and annotators who contributed to  TTStroke-21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content='  References  [1] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Martin, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Benois-Pineau, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Péteri, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Morlier, 3d attention mechanisms in twin spatio-temporal convolutional  neural networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' application to action classification in videos of table tennis games.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=', in: ICPR, IEEE Computer  Society, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content='  [2] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Martin, Fine-Grained Action Detection and Classification from Videos with Spatio-Temporal Convolutional  Neural Networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Application to Table Tennis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' (Détection et classification fines d’actions à partir de vidéos par  réseaux de neurones à convolutions spatio-temporelles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Application au tennis de table), Ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content='D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' thesis, University of  La Rochelle, France, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' URL: https://tel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content='archives-ouvertes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content='fr/tel-03128769.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content='  [3] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Martin, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Benois-Pineau, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Péteri, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Zemmari, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Morlier, 3D Convolutional Networks for Action Recognition:  Application to Sport Gesture Recognition, Springer International Publishing, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content='  [4] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Soomro, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Zamir, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Shah, UCF101: A dataset of 101 human actions classes from videos in the wild, CoRR  abs/1212.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content='0402 (2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content='  [5] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Kuehne, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Jhuang, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Garrote, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Poggio, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Serre, HMDB: A large video database for human motion  recognition, in: ICCV, IEEE Computer Society, 2011, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' 2556–2563.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content='  [6] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Jhuang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Gall, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Zuffi, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Schmid, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Black, Towards understanding action recognition, in: ICCV, IEEE  Computer Society, 2013, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' 3192–3199.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content='  [7] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Gu, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Sun, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Ross, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Vondrick, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Pantofaru, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Li, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Vijayanarasimhan, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Toderici, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Ricco, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Sukthankar,  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Schmid, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Malik, AVA: A video dataset of spatio-temporally localized atomic visual actions (2018) 6047–6056.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content='  [8] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Kay, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Carreira, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Simonyan, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Zhang, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Hillier, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Vijayanarasimhan, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Viola, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Green, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Back, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Natsev,  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Suleyman, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Zisserman, The kinetics human action video dataset, CoRR abs/1705.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content='06950 (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content='  [9] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Smaira, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Carreira, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Noland, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Clancy, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Wu, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Zisserman, A short note on the kinetics-700-2020 human  action dataset, CoRR abs/2010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content='10864 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content='  [10] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Li, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Thotakuri, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Ross, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Carreira, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Vostrikov, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Zisserman, The ava-kinetics localized human actions  video dataset, CoRR abs/2005.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content='00214 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content='  [11] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Shao, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Zhao, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Dai, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Lin, Finegym: A hierarchical video dataset for fine-grained action understanding, in:  CVPR, IEEE, 2020, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' 2613–2622.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content='  [12] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Martin, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Benois-Pineau, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Péteri, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Morlier, Fine grained sport action recognition with twin spatio-temporal  convolutional neural networks, Multim.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Tools Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' 79 (2020) 20429–20447.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content='  [13] Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Liu, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Hu, Spatiotemporal relation networks for video action recognition, IEEE Access 7 (2019) 14969–14976.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content='  [14] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Carreira, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Zisserman, Quo vadis, action recognition?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' A new model and the kinetics dataset, in: CVPR, IEEE  Computer Society, 2017, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' 4724–4733.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content='  [15] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Varol, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Laptev, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Schmid, Long-term temporal convolutions for action recognition, IEEE Trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Pattern Anal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content='  Mach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Intell.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' 40 (2018) 1510–1517.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content='  [16] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Martin, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Benois-Pineau, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Péteri, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Morlier, Optimal choice of motion estimation methods for fine-grained  action classification with 3d convolutional networks, in: ICIP, IEEE, 2019, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' 554–558.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content='  [17] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Martin, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Benois-Pineau, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Péteri, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Morlier, Sport action recognition with siamese spatio-temporal cnns:  Application to table tennis, in: CBMI, IEEE, 2018, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' 1–6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content='  [18] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Martin, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Calandre, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Mansencal, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Benois-Pineau, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Péteri, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Mascarilla, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Morlier, Sports video: Fine-grained  action detection and classification of table tennis strokes from videos for mediaeval 2021, in: [25], 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' URL:  http://ceur-ws.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content='org/Vol-3181/paper3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content='pdf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content='  [19] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Martin, Baseline method for the sport task of mediaeval 2022 benchmark with 3d cnns using attention  mechanism, in: MediaEval, CEUR Workshop Proceedings, CEUR-WS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content='org, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content='  [20] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Qian, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Yu, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Liu, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Hauptmann, Learning unbiased transformer for long-tail sports action classification, in:  [25], 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' URL: http://ceur-ws.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content='org/Vol-3181/paper52.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content='pdf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content='  [21] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Martin, Spatio-temporal CNN baseline method for the sports video task of mediaeval 2021 benchmark, in: [25],  2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' URL: http://ceur-ws.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content='org/Vol-3181/paper13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content='pdf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content='  [22] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Lin, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Maire, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Belongie, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Hays, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Perona, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Ramanan, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Dollár, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Zitnick, Microsoft COCO: common  objects in context, in: D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Fleet, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Pajdla, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Schiele, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Tuytelaars (Eds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' ), Computer Vision - ECCV 2014 - 13th  European Conference, Zurich, Switzerland, September 6-12, 2014, Proceedings, Part V, volume 8693 of Lecture  Notes in Computer Science, Springer, 2014, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' 740–755.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content='  [23] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Zahra, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Martin, Two stream network for stroke detection in table tennis, in: [25], 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' URL: http://ceur-ws.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content='  org/Vol-3181/paper55.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content='pdf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content='  [24] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' J, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' T, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' B, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' S, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' N, YOLOV5 for stroke detection and classification in table tennis, in: [25], 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' URL:  http://ceur-ws.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content='org/Vol-3181/paper38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content='pdf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content='  [25] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Hicks, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Pogorelov, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Lommatzsch, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' de Herrera, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Martin, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Hassan, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Porter, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Kasem, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Andreadis,  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Lux, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Ocaña, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Liu, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' Larson (Eds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
+page_content=' ), Working Notes Proceedings of the MediaEval 2021 Workshop,  Online, 13-15 December 2021, volume 3181 of CEUR Workshop Proceedings, CEUR-WS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
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+page_content='org/Vol-3181.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtFRT4oBgHgl3EQffTfy/content/2301.13576v1.pdf'}
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+arXiv:2301.03264v1  [math.RT]  9 Jan 2023
+A GENERALIZATION OF CYCLIC SHIFT CLASSES
+XUHUA HE
+Abstract. Motivated by Lusztig’s G-stable pieces, we consider
+the combinatorial pieces: the pairs (w, K) for elements w in the
+Weyl group and subsets K of simple reﬂections that are normal-
+ized by w. We generalize the notion of cyclic shift classes on the
+Weyl groups to the set of combinatorial pieces.
+We show that
+the partial cyclic shift classes of combinatorial pieces associated
+with minimal-length elements have nice representatives. As appli-
+cations, we prove the left-right symmetry and the compatibility of
+the induction functors of the parabolic character sheaves.
+Introduction
+0.1. Cyclic shifts of Weyl group elements. Let G be a connected
+reductive group over an algebraically closed ﬁeld. Let B be a Borel
+subgroup of G and W be the Weyl group of G. Then we have the
+Bruhat decomposition G = ⊔w∈WB ˙wB. A central theme in geometric
+representation theory is understanding the (many) mysterious relation-
+ships between the reductive group G and its Weyl group W (see, e.g.,
+the Kazhdan-Lusztig theory and the Springer theory).
+We are particularly interested in the conjugation action on W. Note
+that W is a Coxeter group and is generated by simple reﬂections. In
+particular, any two elements in the same conjugacy class of W are con-
+jugated by a sequence of simple reﬂections. We say that two elements
+are in the same cyclic shift class if they are conjugated by a sequence
+of simple reﬂection, and each conjugation preserves the length. This
+length-preserving condition is crucial in the connection to the conju-
+gation problems on G. If w and w′ are in the same cyclic shift class,
+then we have an isomorphism between the quotient stacks
+B ˙wB
+∆(B)
+∼= B ˙w′B
+∆(B) .
+(a)
+Here ∆(B) denotes the conjugation action. Such an isomorphism plays
+an important role in the interaction between the conjugacy classes of
+W and unipotent conjugacy classes of G (see [10]).
+2010 Mathematics Subject Classiﬁcation. 20F55, 20G40, 14F05.
+Key words and phrases. Weyl groups, cyclic shifts, parabolic character sheaves.
+1
+
+2
+XUHUA HE
+0.2. Cyclic shifts of combinatorial pieces. In this paper, we con-
+sider an analogy of (a) for parabolic subgroups. Such an isomorphism
+will play a role in the study of Lusztig’s theory of parabolic character
+sheaves, which we will discuss in §0.4.
+The object we consider is the quotient stack P ˙wP
+∆(P ), where P = LUP is
+a standard parabolic subgroup of G, and w is an element in the Weyl
+group which normalizes the standard Levi subgroup L. In fact, for the
+applications, the object we consider will be more technical than P ˙wP
+∆(P ),
+but we ignore such complexity in the introduction.
+Our ﬁrst goal is to establish isomorphisms between P ˙wP
+∆(P ) for various
+pairs (w, P). Note that the conjugation by simple reﬂections does not
+send standard Levi subgroups to Levi subgroups.
+To overcome the
+diﬃculty, we introduce combinatorial pieces. A combinatorial piece is
+a pair (w, K), where w is an element in the Weyl group, and K is
+a subset of simple reﬂections (which represents a standard parabolic
+subgroup PK of G) such that w normalizes K.
+We then introduce
+the cyclic shift classes of the combinatorial pieces in §3.2 and prove in
+Proposition 3.1 that if (w, K) and (w′, K′) are in the same cyclic shift
+class, then we have an isomorphism between the quotient stacks
+PK ˙wPK
+∆(PK)
+∼= PK′ ˙w′PK′
+∆(PK′) .
+(b)
+Note that we may regard the Weyl group W as a subset of the
+combinatorial pieces via the map w �→ (w, ∅). The combinatorial pieces
+(w, ∅) and (w′, ∅) are cyclic shift if and only if w and w′ are cyclic shift
+in the usual sense. In this case, P∅ = B. Thus (b) can be regarded as
+a generalization of (a).
+0.3. Representatives. Our next goal is to obtain nice representatives
+for certain cyclic shift classes of combinatorial pieces.
+Let J be a subset of the simple reﬂections and WJ be the standard
+parabolic subgroup of W generated by J.
+We consider the partial
+conjugacy classes on W, i.e., the orbits of the conjugation by WJ on
+W. By [5], we have the decomposition
+W
+∆(WJ) =
+�
+(w,K)
+WKw
+∆(WK),
+(c)
+where
+W
+∆(WJ) denotes the quotient stack of W by the conjugation action
+of WJ, and the right hand side runs over the pairs (w, K), where w are
+minimal length representatives in the right cosets WJ\W and K is
+the maximal subset of J such that (w, K) is a combinatorial piece.
+Moreover, if w is a minimal length element in its partial conjugacy
+class, then w is cyclic shift (via partial conjugation, i.e., a sequence of
+conjugations in WJ) to an element in WKw for some (w, K) occurring
+in the right side of (c).
+
+3
+We prove an “upgraded version” of the above statement in Theorem
+3.2. Namely, if w1 is a minimal length element in its partial conjugacy
+class and (w1, K1) is a combinatorial piece with K1 ⊂ J, then
+(w1, K1) is cyclic shift (via partial conjugation) to (w2, K2),
+(d)
+where w2 is an element in WKw for some (w, K) occurring in the right
+side of (c).
+0.4. Applications to parabolic character sheaves. Now we dis-
+cuss some applications.
+Lusztig introduced the parabolic character
+sheaves in [8]. Roughly speaking, the parabolic character sheaves are
+certain simple perverse sheaves on the quotient stack YJ =
+UPJ \G/UPJ
+∆(LJ)
+.
+The parabolic character sheaves rely on the following decomposition of
+YJ into G-stable pieces:
+YJ =
+�
+w
+YJ,w, where YJ,w“ = ”PK ˙wPK
+∆(PK) ,
+(e)
+Here w runs over the minimal length representatives in the right coset
+WJ\W. And the quotation mark means we ignore the gerbs for unipo-
+tent groups. We refer to §2.2 for the precise statement.
+It is worth pointing out that if (w, K) is conjugate to (w′, K′), then
+it is easy to construct an isomorphism
+LK ˙w
+∆(LK) ∼=
+LK′ ˙w′
+∆(LK′). However, it is
+more involved to relate PK ˙wPK
+∆(PK) for diﬀerent combinatorial pieces (w, K).
+The results (b) and (d) on the cyclic shifts of combinatorial pieces allow
+us to understand certain behavior of the sheaves associated with an
+arbitrary combinatorial piece with respect to the decomposition (e).
+We give two applications in §4.
+(1) The left-right symmetry.
+Note that in the decompositions (c) and (d), we use the right cosets
+WJ\W. One may deﬁne similar decompositions using the left cosets
+W/WJ. A priori, the decompositions obtained using the left and right
+cosets might diﬀer. However, using the cyclic shifts of combinatorial
+pieces, we show that there exists a symmetry between the left cosets
+and the right cosets such that the corresponding substacks in
+W
+∆(WJ)
+and YJ coincide.
+(2) Induction functors.
+Let J ⊂ J′.
+Lusztig deﬁned the functor f : Sh(YJ) → Sh(YJ′).
+Suppose that w (resp. w′) is the minimal length representative in its
+right coset WJ\W (resp.
+WJ′\W), w and w′ are in the same WJ′-
+conjugacy class and ℓ(w) = ℓ(w′). Then we have
+YJ,w“ = ”PK ˙wPK
+∆(PK) and YJ′,w′“ = ”PK′ ˙w′PK′
+∆(PK′) .
+
+4
+XUHUA HE
+In Theorem 4.3, we show that the restriction of the functor f to YJ,w
+and YJ′,w′ is essentially the Harish-Chandra induction functor associ-
+ated to the reductive group LK′ and its Levi subgroups. This result is
+used in the work of Li, Nadler, and Yun [11].
+Acknowledgement:
+XH is partially supported by funds connected
+with Choh-Ming Chair at CUHK, by Hong Kong RGC grant 14300221,
+and by the Xplorer prize. This paper is motivated by a question of
+Zhiwei Yun on the parabolic character sheaves, which is used in [11].
+We thank him for explaining to me the question and related materials
+in [11]. We also thank George Lusztig for the helpful discussions.
+1. Cyclic shift classes
+1.1. Conjugacy graph. Let W be a Weyl group and S be the set of
+simple reﬂections. Let ℓ be the length function on W and ⩽ be the
+Bruhat order on W. Let δ be a group automorphism on W, which
+preserves S. We consider the δ-conjugation action on W deﬁned by
+w ·δ w′ = ww′δ(w)−1.
+Following [3, §3.2], we deﬁne the δ-conjugacy graph as follows. It is
+the direct graph with vertices in W and the edges are of the form w
+s−→δ
+w′, where w, w′ ∈ W, s ∈ S such that w′ = swδ(s) and ℓ(w′) ⩽ ℓ(w).
+We denote by →δ the pre-order relation induced on W by the δ-
+conjugacy graph. In other words, for w, w′ ∈ W, w →δ w′ if there exists
+a sequence of elements w = w1, w2, . . . , wn = w and s1, . . . , sn−1 ∈ S
+such that wi
+si−→δ wi+1 for 1 ⩽ i ⩽ n − 1.
+We write w ≈δ w′ if w →δ w′ and w′ →δ w.
+It is easy to see
+that ≈δ gives an equivalence relation on W. For w ∈ W, we write
+Cycδ(w) = {w′ ∈ W; w ≈δ w′} and call it the δ-cyclic shift class of w.
+If δ is the identity map, we may ignore the subscript δ.
+Now we give an example of the conjugacy graph.
+Example 1.1. Let W = S4 be the ﬁnite Weyl group of type A3 with
+the set of simple reﬂections S = {s1, s2, s3}. We simply write sabc···
+instead of sasbsc · · · . It is easy to see that the conjugacy class of s1s2s3
+forms a connected component of the conjugacy graph. This connected
+component is listed below.
+s12132
+s2
+�✉✉✉✉✉✉✉✉✉
+s1,s3 � s23212
+s2
+�■
+■
+■
+■
+■
+■
+■
+■
+■
+�
+s123
+s1
+�
+s3
+�
+s213
+s3
+�
+s132
+�
+s1
+� s321
+�
+�
+1.2. Geometric cyclic shifts. Let G be a connected reductive group
+over an algebraically closed ﬁeld k. Let G = G(k) and B be a Borel
+subgroup of G with maximal torus T and unipotent radical U. Let R
+be the root datum of G and δ be an automorphism of R. In particular,
+
+5
+δ(B) = B. We still denote by δ for the corresponding automorphism
+on G and on its Weyl group W = NG(T)/T. For any w ∈ W, we
+choose a representative ˙w in NG(T).
+Consider the δ-conjugation action of G deﬁned by g ·δ g′ = gg′δ(g)−1.
+Let
+G
+Adδ(G) be the quotient stack.
+We have the Bruhat decomposi-
+tion G = ⊔w∈WB ˙wB.
+Each Bruhat cell B ˙wB is stable under the
+δ-conjugation action by B. Let
+B ˙wB
+Adδ(B) be the corresponding quotient
+stack and
+πw :
+B ˙wB
+Adδ(B) −→
+G
+Adδ(G)
+be the natural morphism.
+On the other hand, we have the automorphism on T deﬁned by
+t �→ ˙wδ(t) ˙w−1. Let
+T
+Ad ˙w◦δ(T) be the quotient stack and
+pw :
+B ˙wB
+Adδ(B) −→
+T
+Ad ˙w◦δ(T)
+be the natural morphism.
+We have the following (upgraded) geometric version of cyclic shifts.
+Proposition 1.2. Let w, w′ ∈ W. Suppose that w ≈δ w′. Then there
+exist isomorphisms
+B ˙wB
+Adδ(B) ∼=
+B ˙w′B
+Adδ(B) and
+T
+Ad ˙w◦δ(T) ∼=
+T
+Ad ˙w′◦δ(T) such that
+the following diagram commutes
+T
+Ad ˙w◦δ(T)
+∼
+=
+�✤
+✤
+✤
+B ˙wB
+Adδ(B)
+pw
+�
+πw �
+∼
+=
+�✤
+✤
+✤
+G
+Adδ(G)
+T
+Ad ˙w′◦δ(T)
+B ˙w′B
+Adδ(B)
+pw′
+�
+πw′ �
+G
+Adδ(G).
+Remark 1.3. (1) An isomorphism
+B ˙wB
+Adδ(B) →
+B ˙w′B
+Adδ(B) was constructed in
+[6, §3.4]. We follow the proof in loc.cit.
+(2) The isomorphisms
+B ˙wB
+Adδ(B) ∼=
+B ˙w′B
+Adδ(B) and
+T
+Ad ˙w◦δ(T) ∼=
+T
+Ad ˙w′◦δ(T) we
+construct can be regarded as the geometric lifting of the path of cyclic
+shifts w = w1
+s1
+−→ · · ·
+sn−1
+−−→ wn = w′. Such isomorphisms depend on
+the choice of such paths, and there seem to be no canonical choices of
+isomorphisms.
+Proof. It suﬃces to consider the case where w
+s−→ w′.
+In this case,
+ℓ(w′) = ℓ(w). It is easy to see that if sw > w and w(s) > w, then
+w′ = w. Without loss of generality, we may assume furthermore that
+sw < w. Set w1 = sw. Then w1δ(s) = w′. We have
+B ˙sB ×B B ˙w1B ∼= B ˙wB,
+where B acts on B ˙sB×B ˙w1B via b·(g1, g2) = (g1b−1, bg2) and B ˙sB×B
+B ˙w1B is the quotient space. Similarly, we have
+B ˙w1B ×B Bδ( ˙s)B ∼= B ˙w′B.
+
+6
+XUHUA HE
+We have a natural isomorphism
+B ˙sB × B ˙w1B ∼= B ˙w1B × Bδ( ˙s)B,
+(g1, g2) �−→ (g2, δ(g1)).
+By deﬁnition, g1g2 and g2δ(g1) are in the same δ-conjugacy class of G.
+This isomorphism induces the desired isomorphism
+B ˙wB
+Adδ(B) ∼=
+B ˙w′B
+Adδ(B).
+Note that Ad( ˙s) ◦ Ad( ˙w) ◦ δ = Ad( ˙w′) ◦ δ ◦ Ad( ˙s) on T. The de-
+sired isomorphism
+T
+Ad ˙w◦δ(T) ∼=
+T
+Ad ˙w′◦δ(T) is induced from the conjugation
+action by ˙s.
+□
+Corollary 1.4. Let w, w′ ∈ W with w ≈δ w′.
+Let f :
+T
+Ad ˙w◦δ(T) ∼=
+T
+Ad ˙w′◦δ(T) be an isomorphism in Proposition 1.2. Then we have
+(πw)!(pw)∗ = (πw′)!(pw′)∗f : Sh(
+T
+Ad ˙w◦δ(T)) −→ Sh(
+G
+Adδ(G)).
+Here Sh(−) denotes the derived category of complexes of sheaves.
+2. Parabolic character sheaves
+2.1. Partial conjugation on W. Let J ⊂ S.
+Recall that WJ is
+the subgroup of W generated by the simple reﬂections in J. Let W J
+(resp. JW) be the set of minimal coset representatives in W/WJ (resp.
+WJ\W). For J, K ⊂ S, we simply write JW K for JW ∩ W K.
+Consider the δ-conjugation action of WJ on W deﬁned by w ·δ w′ =
+ww′δ(w)−1 for w ∈ WJ and w′ ∈ W. For w ∈ W, we write Ad(w)δ(J) =
+J if for any simple reﬂection s ∈ J, there exists a simple reﬂection
+s′ ∈ J such that wδ(s)w−1 = s′. In this case, w ∈ JW if and only if
+w ∈ W δ(J).
+For any J ⊂ S and w ∈ W, we set
+I(J, w, δ) = max{K ⊂ J; Ad(w)δ(K) = K}.
+Now we recall B´edard’s description [1] of JW.
+Let T (J, δ) be the set of sequences (Jn, wn)n⩾0 with Jn ⊂ J and
+wn ∈ W such that
+(1) J0 = J;
+(2) Jn = Jn−1 ∩ Ad(wn−1)(δ(Jn−1)) for n ⩾ 1;
+(3) wn ∈ JnW δ(Jn) for n ⩾ 0;
+(4) wn ∈ WJnwn−1Wδ(Jn−1) for n ⩾ 1.
+Then for any sequence (Jn, wn)n⩾0, we have that wm = wm+1 =
+· · · and Jm = Jm+1 = · · · for m ⩾ 0. By [8, Proposition 2.5], the
+assignment (Jn, wn)n⩾0 �→ wm for m ≫ 0 deﬁnes a bijection T (J, δ) →
+JW. Moreover, wn ∈ wWδ(Jn) for all n ⩾ 0 and I(J, w, δ) = Jm for
+m ≫ 0.
+We have the following description of WI(J,w,δ).
+Lemma 2.1. Let w ∈ JW. Then WI(J,w,δ) = �
+n∈Z(Ad(w) ◦ δ)n(WJ).
+
+7
+Proof. By deﬁnition, Ad(w) ◦ δ(WI(J,w,δ)) = WI(J,w,δ) ⊂ WJ.
+Let (Jn, wn)n⩾0 be the sequence in T (J, δ) corresponding to w. Now
+we prove that ∩n∈Z(Ad(w) ◦ δ)n(WJ) ⊂ WJn for all n.
+By deﬁnition ∩n∈Z(Ad(w) ◦ δ)n(WJ) ⊂ WJ = WJ0. Assume that we
+have proved ∩n∈Z(Ad(w) ◦ δ)n(WJ) ⊂ WJi for some i. By deﬁnition,
+w = wiδ(a) for some a ∈ WJi. Hence
+∩n∈Z (Ad(w) ◦ δ)n(WJ)
+=
+�
+∩n∈Z(Ad(w) ◦ δ)n(WJ)
+�
+∩ Ad(w) ◦ δ
+�
+∩n∈Z(Ad(w) ◦ δ)n(WJ)
+�
+⊂ WJi ∩ Ad(w) ◦ δ(WJi) = WJi ∩ Ad(wi) ◦ δ(WJi)
+= WJi+1.
+This ﬁnishes the proof.
+□
+We have the following classiﬁcation of the Adδ(WJ)-orbits on W.
+Proposition 2.2. Let J ⊂ S. Then
+(1) W = �
+w∈JW WJ ·δ (WI(J,w,δ)w);
+(2) For any w ∈ JW, the embedding WI(J,w,δ) → W, u �→ uw induces
+the bijection between the quotient stacks
+WI(J,w,δ)
+Adw◦δ(WI(J,w,δ))
+∼= WJ ·δ (WI(J,w,δ)w)
+Adδ(WJ)
+.
+Proof. Part (1) and the bijection of orbits in part (2) were proved in [5,
+Corollary 2.6]. It remains to show that the bijection on the orbits also
+gives an isomorphism between the isotropy groups. In other words,
+it remains to show that if (a, b) ∈ WJ × WI(J,w,δ)w with abδ(a)−1 ∈
+WI(J,w,δ)w, then a ∈ WI(J,w,δ).
+Let (Jn, wn)n⩾0 be the element in T (J, δ) corresponding to w. We
+argue by induction that a ∈ WJn for all n.
+By deﬁnition, a ∈ WJ = WJ0. Assume that a ∈ WJi for some i.
+Then WI(J,w,δ)w ⊂ wiWδ(Ji) and abδ(a)−1 ∈ awiWδ(Ji). Thus
+a ∈ WJi ∩ wiWδ(Ji)w−1
+i
+= WJi+1.
+Hence a ∈ WJn for all n ⩾ 0. In particular, a ∈ WI(J,w,δ).
+□
+2.2. Lusztig’s variety ZJ,δ. For any J ⊂ S, let PJ ⊃ B be the stan-
+dard parabolic subgroup of type J. Let PJ = G/PJ be the partial ﬂag
+variety. We may identify PJ with the set of parabolic subgroups of
+G that are conjugate to PJ. For any parabolic subgroup P of G, we
+denote by UP its unipotent radical. For g ∈ G and H ⊂ G, we simply
+write gH for gHg−1. Following [8], we set
+ZJ,δ = {(P, P ′, gδ(UP)); P ∈ PJ, P ′ ∈ Pδ(J), g ∈ G, gδ(P) = P ′}.
+Deﬁne the action of G × G on ZJ,δ by
+(g1, g2) · (P, P ′, gδ(UP)) = (g2P, g1P ′, g1gδ(g2)−1 δ(Ug2P)).
+
+8
+XUHUA HE
+Then G × G acts transitively on ZJ,δ.
+Let hJ,δ = (PJ, Pδ(J), UPδ(J))
+be the base point. Then the isotropy group of hJ,δ is {(δ(l)u′, lu); l ∈
+LJ, u ∈ UPJ, u′ ∈ UPδ(J)}. The map G × G → G, (g, g′) �→ (g′)−1g
+induces an isomorphism of stacks
+ZJ,δ
+∆(G)
+∼= YJ,δ.
+Here
+ZJ,δ
+∆(G) is the quotient stack for the diagonal G-action on ZJ,δ and
+YJ,δ =
+UPJ \G/UPδ(J)
+Adδ(LJ)
+is the quotient stack for the δ-conjugation action of
+LJ on UPJ\G/UPδ(J).
+Now we recall the decomposition of ZJ,δ into the G-stable pieces,
+introduced by Lusztig in [8]. For w ∈ JW, we set
+ZJ,δ;w = G∆ · (B ˙w, B)hJ,δ.
+The following result is established by Lusztig in [8].
+Proposition 2.3. Let J ⊂ S. Then
+(1) ZJ,δ = �
+w∈JW ZJ,δ;w is a decomposition into smooth, locally
+closed subvarieties.
+(2) For any w ∈ JW, there is a canonical map
+πJ,δ;w : ZJ,δ;w
+∆(G) −→
+LI(J,w,δ)
+Ad ˙w◦δ(LI(J,w,δ))
+which is an iterated gerbe for unipotent groups.
+Under the isomorphism
+ZJ,δ
+∆(G) ∼= YJ,δ, we may reformulate the above
+decomposition as follows.
+For any w ∈ W, let YJ,δ;w be the image
+of B ˙wB in YJ,δ. Then for any w ∈ JW,
+ZJ,δ;w
+∆(G) ∼= YJ,δ;w and YJ,δ =
+⊔w∈JWYJ,δ;w.
+By [4, Proposition 1.10 (1)],
+ZJ,δ;w ∼= G ×PI(J,w,δ) (PI(J,w,δ) ˙w, PI(J,w,δ)) · hJ,δ,
+where PI(J,w,δ) acts on G × (PI(J,w,δ) ˙w, PI(J,w,δ)) · hJ,δ by p · (g, z) =
+(gp−1, (p, p)·z) and G×PI(J,w,δ) (PI(J,w,δ) ˙w, PI(J,w,δ))·hJ,δ is the quotient
+space. We may reformulate it as follows.
+Proposition 2.4. Let w ∈ JW. The embedding PI(J,w,δ) ˙wPδ(I(J,w,δ) →
+G induces an isomorphism
+UPJ\PI(J,w,δ) ˙wPδ(I(J,w,δ)/UPδ(J)
+Adδ(LJ ∩ PI(J,w,δ))
+∼= YJ,δ;w.
+2.3. Parabolic character sheaves. We follow [8]. For any w ∈ W,
+we consider the following diagram
+T
+Ad ˙w◦δ(T)
+B ˙wB
+Adδ(B)
+pw
+�
+πJ,w � YJ,δ.
+
+9
+A parabolic character sheaf on YJ,δ is a simple perverse sheaf that
+is a composition factor of pHi((πJ,w)!p∗
+wL) for some w ∈ W, i ∈ Z and
+L ∈ Sh(
+T
+Ad ˙w◦δ(T)).
+On the other hand, by Proposition 2.3, for any w ∈ JW, the map
+πJ,w induces an equivalence of categories
+π∗
+J,δ;w : Sh(
+LI(J,w,δ)
+Ad ˙w◦δ(LI(J,w,δ))) ∼= Sh(ZJ,δ;w
+∆(G)) = Sh(YJ,δ;w).
+Note that LI(J,w,δ) is a connected reductive group. The character
+sheaves on
+LI(J,w,δ)
+Ad ˙w◦δ(LI(J,w,δ)) is deﬁned by Lusztig in [7].
+It is proved by Lusztig in [8] that
+Theorem 2.5. Let J ⊂ S. Then
+(1) Any parabolic character sheaf on YJ,δ is the intermediate exten-
+sion of π∗
+J,δ;w(A) for a unique w ∈ JW and a character sheaf A on
+LI(J,w,δ)
+Ad ˙w◦δ(LI(J,w,δ)).
+(2) If B is a parabolic character sheaf on YJ,δ and w ∈ JW, then any
+composition factor of pHi(B |YJ,δ;w) is of the form π∗
+J,δ;w(A) for some
+character sheaf A on
+LI(J,w,δ)
+Ad ˙w◦δ(LI(J,w,δ)).
+2.4. Partial conjugation graph. Let J ⊂ S. We consider the Adδ(WJ)-
+orbits on W. The (J, δ)-conjugacy graph, by deﬁnition, is the direct
+graph with vertices in W and the edges are of the form w
+s−→δ w′ for
+w, w′ ∈ W, s ∈ J.
+We denote by →J,δ the pre-order relation induced by
+s−→δ for s ∈ J.
+We write w ≈J,δ w′ if w →J,δ w′ and w′ →J,δ w. We call the equivalece
+class ≈J,δ the (J, δ)-cyclic shift classes on W.
+We have the following result.
+Proposition 2.6. [5, Proposition 3.4] For any w ∈ W, there exists
+w′ ∈ JW and u ∈ WI(J,w′,δ) such that w →J,δ uw′.
+Moreover, if w is of minimal length in WJ ·δ w, then u is of minimal
+length in WI(J,w′,δ) ·δ′ u and w ≈J,δ uw′, where δ′ = Ad(w′) ◦ δ.
+Remark 2.7. By Proposition 2.2 (1), w′ is uniquely determined by w.
+However, u is not unique in general.
+2.5. Partial order. For any w ∈ W and w′ ∈ JW, we write w′ ⩽J,δ w
+if there exists u ∈ WJ such that uw′δ(u)−1 ⩽ w. By [5, Corollary 4.6],
+(a) The restriction of ⩽J,δ to JW gives a partial order on JW.
+It is easy to see that for w, w′ ∈ JW, w′ ⩽ w implies that w′ ⩽J,δ
+w and w′ ⩽J,δ w implies that ℓ(w′) ⩽ ℓ(w). However, the converse
+directions do not hold in general.
+Example 2.8. Let W = S4 and J = {3}. The simple reﬂections of W
+are s1, s2, s3. We simply write sabc··· instead of sasbsc · · · . In Figure 1,
+
+10
+XUHUA HE
+we draw the Hasse diagram of JW, with respect to the usual Bruhat
+order and the partial order ⩽J,id (the extra relation is in dotted line).
+Figure 1. Hasse diagram for the partial orders on JW
+s12132
+s2132
+s1213
+s123
+s121
+s213
+s12
+s21
+s23
+s1
+s2
+1
+✴✴✴✴✴✴✴✴
+✴✴✴✴✴✴✴✴
+✎✎✎✎✎✎✎✎
+✴✴✴✴✴✴✴✴
+✎✎✎✎✎✎✎✎
+⑧⑧⑧⑧⑧⑧⑧⑧⑧⑧
+❏
+❏
+❏
+❏
+❏
+❏
+❏
+❏
+❏
+❏
+❏
+❏
+✎✎✎✎✎✎✎✎
+✎✎✎✎✎✎✎✎
+✴✴✴✴✴✴✴✴
+❏
+❏
+❏
+❏
+❏
+❏
+❏
+❏
+❏
+❏
+❏
+❏
+✴✴✴✴✴✴✴✴
+✎✎✎✎✎✎✎✎
+✴✴✴✴✴✴✴✴
+⑧
+⑧
+⑧
+⑧
+⑧
+⑧
+⑧
+⑧
+⑧
+⑧
+✎✎✎✎✎✎✎✎
+t
+t
+t
+t
+t
+t
+t
+t
+t
+t
+t
+t
+By [5, Proposition 5.8], we have
+(a) Let w ∈ W. Then YJ,δ;w = �
+w′∈JW ;w′⩽J,δw YJ,δ;w′.
+Since YJ,δ;w is irreducible, there exists a unique geometric piece YJ,δ;w′
+which is dense in YJ,δ;w. Therefore we have
+(b) For any w ∈ W, the set {w′ ∈ W J; w′ ⩽J,δ w} contains a unique
+maximal element with respect to ⩽J,δ.
+We also would like to point out the special case of (a), which will be
+used in [11].
+(c) Let w ∈ W. If WJ ·δ w ∩ JW = ∅ or w is not of minimal length
+in WJ ·δ w, then YJ,δ;w ⊂ �
+w′∈JW ;ℓ(w′)<ℓ(w) YJ,δ;w′.
+3. Cyclic shifts of pieces
+3.1. Combinatorial pieces. A δ-combinatorial piece is a pair (w, K),
+where w ∈ W and K ⊂ S with w ∈ KW and Ad(w)δ(K) = K (and
+hence w ∈ W δ(K)). To each δ-combinatorial piece (w, K), we associate
+a subset WKw of W. In particular, if K = ∅, then we naturally identify
+the δ-combinatorial piece (w, ∅) with the element w of W. In this way,
+we identify W as a subset of the set of δ-combinatorial pieces.
+We say that two δ-combinatorial pieces (w, K) and (w′, K′) are δ-
+conjugated by an element x ∈ W if w′ = x−1wδ(x), and Ad(x)−1(K) =
+K′ (and hence x ∈ W K). In this case, x−1(WKw)δ(x) = WK′w′.
+
+11
+It is worth pointing out that the whole Weyl group W does not act
+on the set of δ-combinatorial pieces. The element x acts on (w, K) only
+if Ad(x)−1(K) ⊂ S.
+3.2. Cyclic shifts of pieces. The deﬁnition of cyclic shifts on W in
+§1.1 does not generalize to the set of δ-combinatorial pieces.
+However, there is an equivalent deﬁnition of cyclic shifts on W, due
+to Brou´e and Michel in [2]. The deﬁnition is as follows. Let w, w′ ∈ W.
+Then w ≈δ w′ if there exists a sequence of elements w = w1, . . . , wn =
+w′ and elements xi, yi ∈ W such that wi = xiyi, wi+1 = yiδ(xi) and
+ℓ(wi) = ℓ(xi) + ℓ(yi) = ℓ(wi+1) for all 1 ⩽ i ⩽ n − 1. See [3, Exercise
+3.7].
+Now we deﬁne cyclic shifts of the combinatorial pieces.
+Let (w, K) and (w′, K′) be δ-combinatorial pieces. We write (w, K)
+x≈δ
+(w′, K′) if (w, K) and (w′, K′) are δ-conjugated by x, and ℓ(w) =
+ℓ(x) + ℓ(x−1w) = ℓ(w′). Let ≈δ be the equivalence relation on the
+set of δ-combinatorial pieces generated by
+x≈δ for x ∈ W. We call it the
+cyclic shift relation of the δ-combinatorial pieces. When restricting to
+W, this deﬁnition coincides with the deﬁnition of Brou´e and Michel.
+Similarly, for any J ⊂ S, let ≈J,δ be the equivalence relation on the
+set of δ-combinatorial pieces generated by
+x≈δ for x ∈ WJ. In geometric
+applications, we usually consider the ≈J,δ on the set of δ-combinatorial
+pieces (w, K) with the additional assumption that K ⊂ J.
+Proposition 3.1. Let (w, K) and (w′, K′) be δ-combinatorial pieces
+with K, K′ ⊂ J. Suppose that (w, K) ≈J,δ (w′, K′). Then there exists
+isomorphisms
+UPJ \PK ˙wPδ(K)/UPδ(J)
+Ad ˙w◦δ(LJ∩PK)
+∼=
+UPJ \PK′ ˙w′Pδ(K′)/UPδ(J)
+Ad ˙w′◦δ(LJ∩PK′)
+and
+LK
+Ad ˙w◦δ(LK) ∼=
+LK′
+Ad ˙w′◦δ(LK′) such that the following diagram commutes
+LK
+Ad ˙w◦δ(LK)
+∼
+=
+�✤
+✤
+✤
+UPJ \PK ˙wPδ(K)/UPδ(J)
+Ad ˙w◦δ(LJ∩PK)
+�
+�
+∼
+=
+�✤
+✤
+✤
+YJ,δ
+LK′
+Ad ˙w′◦δ(LK′)
+UPJ \PK′ ˙w′Pδ(K′)/UPδ(J)
+Ad ˙w′◦δ(LJ∩PK′)
+�
+� YJ,δ.
+Proof. It suﬃces to consider the case where (w, K)
+x≈δ (w′, K′) for some
+x ∈ WJ. Set y = x−1w. Then w′ = yδ(x). We have
+PK ˙wPδ(K) = UPK ˙wPδ(K) ∼= (UPK ∩ ˙wU− ˙w−1) × Pδ(K).
+Moreover, UPK ∩ ˙wU− ˙w−1 = U ∩ ˙wU− ˙w−1. Note that Ad(y)δ(K) =
+Ad(x−1w)δ(K) = Ad(x)−1(K) = K′. Similarly, we have
+PK ˙xPK′ ∼= (U ∩ ˙xU− ˙x−1) × PK′;
+PK′ ˙yPδ(K) ∼= (U ∩ ˙yU− ˙y−1) × Pδ(K).
+
+12
+XUHUA HE
+Since ℓ(w) = ℓ(x) + ℓ(y), we have U ∩ ˙wU− ˙w−1 ∼= (U ∩ ˙xU− ˙x−1) ×
+(U ∩ ˙yU− ˙y−1). Hence
+PK ˙wPδ(K) ∼= U ∩ ˙wU− ˙w−1 × Pδ(K)
+∼= (U ∩ ˙xU− ˙x−1) × (U ∩ ˙yU− ˙y−1) × Pδ(K)
+∼= (U ∩ ˙xU− ˙x−1) × PK′ ˙yPδ(K)
+∼=
+�
+(U ∩ ˙xU− ˙x−1) × PK′�
+×PK′ PK′ ˙yPδ(K)
+∼= PK ˙xPK′ ×PK′ PK′ ˙yPδ(K).
+The map (g1, g2) �→ (g2, δ(g1)) gives a natural isomorphism
+f : PK ˙xPK′ ×PK′ PK′ ˙yPδ(K)
+Adδ(PK)
+∼= PK′ ˙yPδ(K) ×Pδ(K) Pδ(K)δ( ˙x)Pδ(K′)
+Adδ(PK′)
+.
+Since K, K′ ⊂ J and x ∈ WJ, we have PK ˙xPK′ ⊂ PK and hence
+the conjugation action of PK ˙xPK′ normalizes UPJ. Thus f induces the
+desired isomorphism
+UPJ \PK ˙wPδ(K)/UPδ(J)
+Adδ(LJ∩PK)
+∼=
+UPJ \PK′ ˙w′Pδ(K′)/UPδ(J)
+Adδ(LJ ∩PK′)
+.
+Note that the representative of w′ in NG(T) is unique up to right
+multiplication by T. As we consider the morphisms on the quotient
+stacks, we may assume furthermore that ˙w′ is chosen so that ˙w′ =
+˙x−1 ˙wδ( ˙x). Then Ad( ˙x)−1 ◦ Ad( ˙w) ◦ δ = Ad( ˙w′) ◦ δ ◦ Ad( ˙x)−1 on LK.
+The desired isomorphism
+LK
+Ad ˙w◦δ(LK) ∼=
+LK′
+Ad ˙w′◦δ(LK′) is induced from the
+conjugation action by ˙x−1.
+□
+Theorem 3.2. Let J ⊂ S and (w, K) be a δ-combinatorial piece. Sup-
+pose that K ⊂ J and w is of minimal length in WJ ·δ w. Then there
+exists unique w′ ∈ JW, x ∈ WJ ∩ W I(J,w′,δ), u ∈ WI(J,w′,δ) such that
+x−1wδ(x) = uw′, Ad(x)−1(K) ⊂ J and (w, K) ≈J,δ (uw′, Ad(x)−1(K)).
+Proof. By Proposition 2.2 (1), there exists a unique w′ ∈ JW such that
+w ∈ WJ ·δ WI(J,w′,δ)w′. By Proposition 2.2 (2), there exists a unique
+x ∈ WJ ∩W I(J,w′,δ) such that x−1wδ(x) ∈ WI(J,w′,δ)w′. Let u ∈ WI(J,w′,δ)
+with x−1wδ(x) = uw′.
+By Lemma 2.1,
+WI(J,w′,δ) = ∩n∈Z(Ad(w′) ◦ δ)n(WJ) = ∩n∈Z(Ad(uw′) ◦ δ)n(WJ)
+= ∩n∈Z(Ad(x)−1Ad(w) ◦ δ ◦ Ad(x))n(WJ)
+= ∩n∈ZAd(x)−1(Ad(w) ◦ δ)nAd(x)(WJ)
+= Ad(x)−1�
+∩n∈Z(Ad(w) ◦ δ)n(WJ)
+�
+⊃ Ad(x)−1(WK).
+The second equality uses the fact that (Ad(uw′) ◦ δ)n = (Ad(w′) ◦
+δ)nAd(u′) for some u′ ∈ WI(J,w′,δ).
+Therefore x−1 sends any simple root in K to a root spanned by
+I(J, w′, δ). Since x ∈ W I(J,w′,δ), we have Ad(x)−1(K) ⊂ I(J, w′, δ). Let
+
+13
+K′ = Ad(x)−1(K). Then
+Ad(uw′)δ(K′) = Ad(x)−1Ad(w)δAd(x)(K′) = Ad(x)−1Ad(w)δ(K)
+= Ad(x)−1(K) = K′.
+Thus (uw′, K′) is a δ-combinatorial piece. It remains to prove that
+(w, K) ≈J,δ (uw′, K′).
+We associate a quadruple (Jn, wn, xn, yn)n⩾0 to w.
+Here Jn ⊂ J,
+wn ∈ JnW δ(Jn), xn ∈ WJn ∩ W Jn+1 and yn ∈ WJn+1 for all n. The
+quadruple is constructed as follows.
+Set J0 = J.
+Suppose that n ⩾ 0 and (Jm, xm) are deﬁned for
+0 ⩽ m < n.
+We set w′
+n = (x0 · · · xn−1)−1wδ(x0 · · · xn−1).
+We may
+write w′
+n as w′
+n = znw′′
+n, where w′′
+n ∈ JnW and zn ∈ WJn. Set wn =
+min(w′′
+nWδ(Jn)) and Jn+1 = Jn ∩ Ad(wn)δ(Jn). We write zn as zn =
+xnyn, where xn ∈ WJn ∩ W Jn+1 and yn ∈ WJn+1.
+The quadruple
+(Jn, wn, xn, yn)n⩾0 is deﬁned inductively.
+By deﬁnition, (Jn, wn)n⩾0 ∈ T (J, δ). Then there exists m such that
+Jm = Jm+1 = · · · , wm = wm+1 = · · · . We then have xm = xm+1 =
+· · · = 1 and ym = ym+1 = · · · .
+Moreover, Jm = I(J, wm, δ).
+Set
+x′ = x0x1 · · · xm ∈ WJ ∩ W I(J,wm,δ).
+Then (x′)−1wx′ ∈ WJmwm =
+WI(J,wm,δ)wm. By Proposition 2.2, we have wm = w′ and x′ = x.
+Moreover, we have ℓ(w′
+n) = ℓ(w′′
+n) + ℓ(zn) = ℓ(w′′
+n) + ℓ(xn) + ℓ(yn) =
+ℓ(ynw′′
+n) + ℓ(xn). Thus
+ℓ(w′
+n+1) = ℓ(x−1
+n w′
+nδ(xn)) ⩽ ℓ(x−1
+n w′
+n) + ℓ(xn) = ℓ(ynw′′
+n) + ℓ(xn)
+= ℓ(w′
+n).
+In particular, we have ℓ(w) = ℓ(w′
+0) ⩾ ℓ(w′
+1) ⩾ · · · ⩾ ℓ(w′
+m) =
+ℓ(x−1wδ(x)). By our assumption, w is of minimal length in WJ ·δ w.
+Hence ℓ(w) = ℓ(w′
+1) = · · · = ℓ(w′
+m) = ℓ(x−1wδ(x)). Moreover, we have
+w = w′
+0 ≈J,δ w′
+1 ≈J,δ · · · ≈J,δ w′
+m = x−1wδ(x).
+Note that Ad(x0)−1(WK) = Ad(x1 · · ·xm)WK′ ⊂ WJ1. Since x0 ∈
+W J1, we have Ad(x0)−1(K) ⊂ J1. By the same argument, we may
+show that Ad(x0 · · · xi)−1(K) ⊂ Ji+1 for all i ⩾ 0.
+Hence we have (w, K)
+x0≈δ (w′
+1, Ad(x0)−1(K))
+x1≈δ · · ·
+xm
+≈ δ (uw′, K′).
+□
+4. Applications
+4.1. Left-right symmetry. Recall that
+W =
+�
+w∈JW
+WJ ·δ (WI(J,w,δ)w).
+By [5, §2], we have the following decomposition of W indexed by W δ(J)
+instead of JW:
+W =
+�
+w∈W δ(J)
+WJ ·δ (WI(J,w,δ)w).
+
+14
+XUHUA HE
+Now we show that there exists a natural bijection between JW and
+W δ(J) so that the corresponding subsets of W coincide.
+Proposition 4.1. Let J ⊂ S. Then there exists a unique bijection
+ι : W δ(J) → JW such that
+�
+w, I(J, w, δ)
+�
+≈J,δ
+�
+ι(w), I(J, ι(w), δ)
+�
+.
+In particular, WJ ·δ (WI(J,w,δ)w) = WJ ·δ (WI(J,ι(w),δ)ι(w)).
+Proof. Let w ∈ W δ(J) and K = I(J, w, δ). By deﬁnition, (w, K) is a
+δ-combinatorial piece. For any u ∈ WJ, we have
+ℓ(uwδ(u)−1) ⩾ ℓ(wδ(u)−1) − ℓ(u) = ℓ(w) + ℓ(δ(u)) − ℓ(u) = ℓ(w).
+Therefore w is of minimal length in WJ ·δ w. By Theorem 3.2, there
+exists unique w′ ∈ JW, x ∈ WJ ∩ W I(J,w′,δ), u ∈ WI(J,w′,δ) such that
+x−1wδ(x) = uw′, Ad(x)−1(K) ⊂ J and (w, K) ≈J,δ (uw′, Ad(x)−1(K)).
+Set K′ = Ad(x)−1(K). By Lemma 2.1, WK = ∩n∈Z(Ad(w)◦δ)n(WJ).
+Hence
+WK′ = Ad(x)−1(WK) = ∩n∈ZAd(x)−1(Ad(w) ◦ δ)n(WJ)
+= ∩n∈Z(Ad(uw′) ◦ δ)nAd(x)−1(WJ)
+= ∩n∈Z(Ad(uw′) ◦ δ)n(WJ)
+= ∩n∈Z(Ad(w′) ◦ δ)n(WJ)
+= WI(J,w′,δ).
+The second to last equality uses the fact that (Ad(uw′)◦δ)n = (Ad(w′)◦
+δ)nAd(u′) for some u′ ∈ WI(J,w′,δ).
+Therefore K′ = I(J, w′, δ). Hence xuw′ = wδ(x) ∈ W δ(I(J,w′,δ). This
+implies that u = 1.
+So (w, K) ≈J,δ (w′, K′).
+By the deﬁnition of
+cyclic shifts of combinatorial pieces, we also have WJ ·δ (WKw) = WJ ·δ
+(WK′w′).
+□
+Let w ∈ W δ(J) and w′ = ι(w) ∈ JW. Since w ≈J,δ w′, we have
+YJ,δ;w = YJ,δ;w′. Moreover, by Proposition 3.1, we have the following
+commutative diagram
+Sh(
+LI(J,w,δ)
+Ad ˙w◦δ(LI(J,w,δ)))
+Ad( ˙x)−1
+�
+∼
+=
+� Sh(YJ,δ;w)
+Sh(
+LI(J,w′,δ)
+Ad ˙w′◦δ(LI(J,w′,δ)))
+∼
+= � Sh(YJ,δ;w′),
+where x is the unique element in WJ ∩ W I(J,w′,δ) such that w′ =
+x−1wδ(x).
+Now we provide a nontrivial example of the map ι.
+Example 4.2. Let W = S5, J = {1, 3} and δ is the identity map.
+Then one may check that ι(s121324) = s213243. In particular, the map ι is
+
+15
+diﬀerent from taking inverse, and diﬀerent from the one-step operation
+xy �→ yx for x ∈ WJ and y ∈ JW.
+4.2. The functors f J
+J′. We follow [8, §6].
+Let J ⊂ J′ ⊂ S.
+Let
+π : PJ → PJ′ be the projection map. Set
+ZJ,J′,δ = {(P, P ′, gδ(Uπ(P ))); P ∈ PJ, P ′ ∈ Pδ(J), gδ(P) = P ′}.
+Deﬁne the action of G × G on ZJ,J′,δ by (g1, g2) · (P, P ′, gUπ(P )) =
+(g2P, g1P ′, g1gδ(g2)−1δ(Uπ(g2P ))). Then G×G acts transitively on ZJ,J′,δ.
+Let hJ,J′,δ = (PJ, Pδ(J), UPδ(J′)) be the base point. Then we may identify
+ZJ,J′,δ with (G × G)/(UPJ′ × UPδ(J′))Adδ(LJ′ ∩ PJ), where LJ′ ∩ PJ is a
+standard parabolic subgroup of LJ′.
+We consider the following diagram
+ZJ,δ
+ZJ,J′,δ
+c
+�
+d
+� ZJ′,δ,
+where
+c(P, P ′, gδ(Uπ(P ))) = (P, P ′, gδ(UP)),
+d(P, P ′, gδ(Uπ(P ))) = (π(P), π(P ′), gδ(Uπ(P ))).
+It is easy to see that c is a locally trivial ﬁbration with ﬁbers iso-
+morphic to an aﬃne space UPJ/UPJ′ and d is a locally trivial ﬁbration
+with ﬁbers isomorphic to the ﬂag variety LJ′/(LJ′ ∩ PJ). Set
+f J
+J′ = d!c∗ : Sh(ZJ,δ
+∆G) −→ Sh(ZJ′,δ
+∆G ).
+We may reformulate the functors as follows. Consider the following
+diagram of stacks
+YJ,δ
+YJ,J′,δ
+q
+�
+p
+� YJ′,δ
+where YJ,J′,δ =
+UPJ′ \G/UPδ(J′)
+Adδ(LJ′∩PJ)
+and q and p are natural projection maps.
+Under the isomorphism
+ZJ,δ
+∆(G) ∼= YJ,δ and
+ZJ′,δ
+∆(G) ∼= YJ′,δ, we may rewrite
+the functor f J
+J′ as
+f J
+J′ = p!q∗ : Sh(YJ,δ) −→ Sh(YJ′,δ).
+Let w ∈ JW and w′ ∈ J′W. Let iJ,δ;w : YJ,δ;w → YJ,δ and iJ′,δ;w′ :
+YJ′,δ;w′ → YJ′,δ be the embeddings. We deﬁne
+f J,w
+J′,w′ = i∗
+J′,δ;w′ p!q∗(iJ,δ;w)! : Sh(YJ,δ;w) −→ Sh(YJ′,δ;w′).
+By deﬁnition, for any w ∈ JW, p(q−1(YJ,δ;w)) = YJ′,δ;w. Hence by
+§2.5 (c), we have
+(a) Let w ∈ JW and A be a parabolic character sheaf on YJ,δ with
+support in YJ,δ;w. Assume that WJ′ ·δ w ∩ J′W = ∅ or w is not of
+minimal length in WJ′ ·δ w. Then the support of f J
+J′(A) is contained in
+⊔w′∈J′W ;ℓ(w′)<ℓ(w)YJ′,δ;w′.
+
+16
+XUHUA HE
+4.3. Induction functor. Let (w, K) be a δ-combinatorial piece. Con-
+sider the following diagram
+LK
+Ad ˙w◦δ(LK) ∼=
+LK ˙w
+Adδ(LK)
+PK ˙wPδ(K)
+Adδ(PK)
+a
+�
+b
+�
+G
+Adδ(G),
+where a is induced from the projection map PK ˙wPδ(K) → LK ˙w and b
+is induced from the embedding PK ˙wPδ(K) → G.
+Following [12, §4.1], we deﬁne
+Ind(G,δ)
+(LK, ˙w) = b!a∗ : Sh(
+LK
+Ad ˙w◦δ(LK)) −→ Sh(
+G
+Adδ(G)).
+If w = 1, then K = δ(K) and PK is a δ-stable standard parabolic
+subgroup of G. In this case, Ind is the Harish-Chandra induction func-
+tor. If K = ∅, then PK = B and Ind is the Deligne-Lusztig induction
+functor.
+Now we prove that
+Theorem 4.3. Let J ⊂ J′ ⊂ S. Let w ∈ JW such that w is of minimal
+length in WJ ·δw. Let w′ ∈ J′W, u ∈ WI(J′,w′,δ) and x ∈ WJ′∩W I(J′,w′,δ)
+such that x−1wδ(x) = uw′. Set K = I(J, w, δ), K1 = Ad(x)−1(K),
+K′ = I(J′, w′, δ) and δ′ = Ad( ˙w′) ◦ δ. Then we have the following
+commutative diagram
+Sh(
+LK
+Ad ˙w◦δ(LK))
+Ind
+(LK′ ,δ′)
+(LK1 , ˙u) ◦Ad( ˙x)−1
+�
+π∗
+J,δ;w
+∼
+=
+� Sh(YJ,δ;w)
+fJ,w
+J′,w′
+�
+Sh(
+LK′
+Ad ˙w′◦δ(LK′))
+π∗
+J′,δ;w′
+∼
+=
+� Sh(YJ′,δ;w′).
+Proof. We have the following commutative diagram
+LK
+Ad ˙w◦δ(LK)
+Ad( ˙x)−1
+∼
+=
+�
+YJ,δ;w
+πJ,δ;w
+�
+iJ,δ;w
+�
+□
+YJ,δ
+q−1(YJ,δ;w)
+q
+�
+f
+∼
+=
+�
+i
+� YJ,J′,δ
+p
+�
+q
+�
+LK1
+Ad ˙u◦δ′(LK1)
+X
+π1
+�
+(LK′∩PK1) ˙uδ′(LK′∩PK1)
+Adδ′(LK′∩PK1)
+a
+�
+b
+�
+□
+X
+π2
+�
+b′
+�
+LK′
+Adδ′(LK′)
+YJ′,δ;w′
+πJ′,δ;w′
+�
+iJ′,δ;w′ � YJ′,δ.
+
+17
+Here X =
+UPJ′ \PK1 ˙u ˙w′Pδ(K1)/UPδ(J′)
+Ad ˙u ˙w′◦δ(LJ′∩PK1)
+.
+By Proposition 2.4, YJ,δ;w ∼=
+UPJ \PK ˙wPδ(K)/UPδ(J)
+Ad ˙w◦δ(LJ∩PK)
+.
+Thus by deﬁni-
+tion q−1(YJ,δ;w) ∼=
+UPJ′ \PK ˙wPδ(K)/UPδ(J′)
+Ad ˙w◦δ(LJ′∩PK)
+. By Theorem 3.2, (w, K) ≈J,δ
+(uw′, K1). The isomorphism f : q−1(YJ,δ;w) → X1 is given in Proposi-
+tion 3.1. The map π1 : X →
+LK1
+Ad ˙u◦δ′(LK1) is induced from the projection
+map PK1 ˙u ˙w′Pδ(K1) → LK1 ˙u ˙w′. The map π2 : X →
+(LK′∩PK1) ˙uδ′(LK′∩PK1)
+Adδ′(LK′∩PK1)
+is induced from the projection
+PK1 ˙u ˙w′Pδ(K1) −→ PK1 ˙u ˙w′Pδ(K1) ∩ LK′ ˙w′ = (LK′ ∩ PK1) ˙uδ′(LK′ ∩ PK1).
+By Proposition 2.4, YJ′,δ;w′ ∼=
+UPJ′ \PK′ ˙w′Pδ(K′)/UPδ(J′)
+Ad ˙w′◦δ(LJ′∩PK′)
+. The map b′ : X →
+YJ′,δ;w′ is induced from the embedding PK1 ˙u ˙w′Pδ(K1) ⊂ PK′ ˙w′Pδ(K′).
+Thus
+f J,w
+J′,w′π∗
+J,δ;w = i∗
+J′,δ;w′p!q∗(iJ,δ;w)!π∗
+J,w,δ = i∗
+J′,δ;w′p!i!q∗π∗
+J,w,δ
+= (b′)!f!q∗π∗
+J,w,δ = (b′)!π∗
+1Ad( ˙x)−1
+= (b′)!π∗
+2a∗Ad( ˙x)−1 = π∗
+J′,δ;w′b!a∗Ad( ˙x)−1
+= π∗
+J′,δ;w′Ind
+(LK′,δ′)
+(LK1, ˙u) ◦ Ad( ˙x)−1.
+The proof is ﬁnished.
+□
+4.4. A special case. Now we discuss a special case of Theorem 4.3.
+Let J ⊂ J′ ⊂ S. Let w ∈ JW and w′ ∈ J′W such that w ∈ WJ′ ·δ w′
+and ℓ(w) = ℓ(w′). Set K = I(J, w, δ) and K′ = I(J′, w′, δ). By Theo-
+rem 3.2, there exists a unique x ∈ WJ′ ∩W K′ such that x−1wδ(x) = w′
+and (w, K) ≈J,δ (w′, K1), where K1 = Ad(x)−1(K) ⊂ K′.
+Since
+Ad(w)δ(K) = K, we have Ad(w′)δ(K1) = K1. Set δ′ = Ad( ˙w′) ◦ δ.
+Then LK1 is a δ′-stable Levi subgroup and LK′ ∩PK1 is a δ′-stable par-
+abolic subgroup of LK′. The functor Ind
+(LK′,δ′)
+(LK1, ˙u) in Theorem 4.3 in this
+case is the Harish-Chandra induction functor.
+In this case, the functors f J,w
+J′,w′ is just the Harish-Chandra induction
+functor, composed with the conjugation by ˙x−1.
+4.5. Generalization to loop groups. Theorem 3.2 holds not only
+for Weyl groups but also for arbitrary Coxeter groups. The same proof
+works in such generality. In particular, Theorem 3.2 holds for any aﬃne
+Weyl group together with a length-preserving automorphism on it.
+Let k be an algebraically closed ﬁeld and F = k((ǫ)) be the ﬁeld
+of the formal Laurent series. Let G be a connected reductive group
+over F and G = G(F). Let I be an Iwahori subgroup of G and ˜W
+be the Iwahori-Weyl group of G. Let P ⊃ I be a parahoric subgroup.
+It is a pro-algebraic group. Let UP be the pro-unipotent radical of P
+and L ∼= P/UP be its reductive quotient. In [9], Lusztig introduced
+
+18
+XUHUA HE
+the aﬃne analogy of the parabolic character sheaves. They are certain
+simple perverse sheaves on the ind-stack UP \G/UP
+∆(L)
+.
+Note that the Iwahori-Weyl group ˜W is not a Coxeter group in gen-
+eral, but a quasi-Coxeter group. Namely, let G0 be the subgroup of
+G generated by all the parahoric subgroups. The Iwahori-Weyl group
+of G0 is an aﬃne Weyl group Wa. And ˜W = Wa ⋊ Ω, where Ω is the
+subgroup of length-zero elements of ˜W. The conjugation action of any
+element in Ω on Wa is a length-preserving automorphism. We have
+UP\G/UP
+∆(L)
+=
+�
+τ∈Ω
+UP\G0 ˙τ/UP
+∆(L)
+∼=
+�
+τ∈Ω
+UP\G0/Uδ ˙τ (P )
+Adδ ˙τ(L)
+.
+Here δ ˙τ is the automorphism on G0 given by the conjugation action of
+˙τ. Now Theorem 4.3 may be applied to
+UP \G0/Uδ ˙τ (P )
+Adδ ˙τ (L)
+using Theorem 3.2
+for the pair (Wa, Ad(τ)).
+References
+[1] R. B´edard, On the Brauer liftings for modular representations, J. Algebra 93
+(2) (1985) 332–353.
+[2] M. Brou´e and J. Michel, Sur certains ´el´ements r´eguliers des groupes de Weyl
+et les vari´et´es de Deligne-Lusztig associ´ees, Finite reductive groups (Luminy,
+1994), Progr. Math. 141, 73–139, Birkh¨auser Boston, Boston, MA, 1997.
+[3] M. Geck and G. Pfeiﬀer, Characters of ﬁnite Coxeter groups and Iwahori-Hecke
+algebras, London Mathematical Society Monographs. New Series, vol. 21, The
+Clarendon Press Oxford University Press, New York, 2000.
+[4] X. He, The G-stable pieces of the wonderful compactiﬁcation, Trans. Amer.
+Math. Soc. 359 (2007), no. 7, 3005–3024.
+[5] X. He, Minimal length elements in some double cosets of Coxeter groups, Adv.
+Math. 215 (2007), 469–503.
+[6] X. He and G. Lusztig, A generalization of Steinberg’s cross-section, J. Amer.
+Math. Soc. 25 (2012), 739-757.
+[7] G. Lusztig, Character sheaves on disconnected groups, I, Represent. Theory 7
+(2003), 374–403.
+[8] G. Lusztig, Parabolic character sheaves, I, Mosc. Math. J. 4 (2004), no. 1,
+153–179.
+[9] G. Lusztig, Parabolic character sheaves, III, Mosc. Math. J. 10 (2010), no. 3,
+603–609.
+[10] G. Lusztig, From conjugacy classes in the Weyl group to unipotent classes,
+Represent. Theory 15 (2011), 494–530.
+[11] P. Li, D. Nadler and Z. Yun, Functions on the commuting stack via Langlands
+duality, arXiv:2301.02618.
+[12] T. Shoji, Character sheaves and almost characters of reductive groups, I, Adv.
+Math. 111 (1995), no. 2, 244–313.
+The Institute of Mathematical Sciences and Department of Math-
+ematics, The Chinese University of Hong Kong, Shatin, N.T., Hong
+Kong SAR, China.
+Email address: xuhuahe@math.cuhk.edu.hk
+
diff --git a/tNE1T4oBgHgl3EQfjgS9/content/tmp_files/load_file.txt b/tNE1T4oBgHgl3EQfjgS9/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..d90ebe977bddbf63b2888fd04c9ce9a0a4f339f9
--- /dev/null
+++ b/tNE1T4oBgHgl3EQfjgS9/content/tmp_files/load_file.txt
@@ -0,0 +1,722 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf,len=721
+page_content='arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='03264v1  [math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='RT]  9 Jan 2023  A GENERALIZATION OF CYCLIC SHIFT CLASSES  XUHUA HE  Abstract.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Motivated by Lusztig’s G-stable pieces, we consider  the combinatorial pieces: the pairs (w, K) for elements w in the  Weyl group and subsets K of simple reﬂections that are normal-  ized by w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' We generalize the notion of cyclic shift classes on the  Weyl groups to the set of combinatorial pieces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  We show that  the partial cyclic shift classes of combinatorial pieces associated  with minimal-length elements have nice representatives.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' As appli-  cations, we prove the left-right symmetry and the compatibility of  the induction functors of the parabolic character sheaves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  Introduction  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Cyclic shifts of Weyl group elements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Let G be a connected  reductive group over an algebraically closed ﬁeld.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Let B be a Borel  subgroup of G and W be the Weyl group of G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Then we have the  Bruhat decomposition G = ⊔w∈WB ˙wB.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' A central theme in geometric  representation theory is understanding the (many) mysterious relation-  ships between the reductive group G and its Weyl group W (see, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=',  the Kazhdan-Lusztig theory and the Springer theory).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  We are particularly interested in the conjugation action on W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Note  that W is a Coxeter group and is generated by simple reﬂections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' In  particular, any two elements in the same conjugacy class of W are con-  jugated by a sequence of simple reﬂections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' We say that two elements  are in the same cyclic shift class if they are conjugated by a sequence  of simple reﬂection, and each conjugation preserves the length.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' This  length-preserving condition is crucial in the connection to the conju-  gation problems on G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' If w and w′ are in the same cyclic shift class,  then we have an isomorphism between the quotient stacks  B ˙wB  ∆(B)  ∼= B ˙w′B  ∆(B) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  (a)  Here ∆(B) denotes the conjugation action.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Such an isomorphism plays  an important role in the interaction between the conjugacy classes of  W and unipotent conjugacy classes of G (see [10]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  2010 Mathematics Subject Classiﬁcation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' 20F55, 20G40, 14F05.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  Key words and phrases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Weyl groups, cyclic shifts, parabolic character sheaves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  1  2  XUHUA HE  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Cyclic shifts of combinatorial pieces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' In this paper, we con-  sider an analogy of (a) for parabolic subgroups.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Such an isomorphism  will play a role in the study of Lusztig’s theory of parabolic character  sheaves, which we will discuss in §0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  The object we consider is the quotient stack P ˙wP  ∆(P ), where P = LUP is  a standard parabolic subgroup of G, and w is an element in the Weyl  group which normalizes the standard Levi subgroup L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' In fact, for the  applications, the object we consider will be more technical than P ˙wP  ∆(P ),  but we ignore such complexity in the introduction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  Our ﬁrst goal is to establish isomorphisms between P ˙wP  ∆(P ) for various  pairs (w, P).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Note that the conjugation by simple reﬂections does not  send standard Levi subgroups to Levi subgroups.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  To overcome the  diﬃculty, we introduce combinatorial pieces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' A combinatorial piece is  a pair (w, K), where w is an element in the Weyl group, and K is  a subset of simple reﬂections (which represents a standard parabolic  subgroup PK of G) such that w normalizes K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  We then introduce  the cyclic shift classes of the combinatorial pieces in §3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='2 and prove in  Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='1 that if (w, K) and (w′, K′) are in the same cyclic shift  class, then we have an isomorphism between the quotient stacks  PK ˙wPK  ∆(PK)  ∼= PK′ ˙w′PK′  ∆(PK′) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  (b)  Note that we may regard the Weyl group W as a subset of the  combinatorial pieces via the map w �→ (w, ∅).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' The combinatorial pieces  (w, ∅) and (w′, ∅) are cyclic shift if and only if w and w′ are cyclic shift  in the usual sense.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' In this case, P∅ = B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Thus (b) can be regarded as  a generalization of (a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Representatives.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Our next goal is to obtain nice representatives  for certain cyclic shift classes of combinatorial pieces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  Let J be a subset of the simple reﬂections and WJ be the standard  parabolic subgroup of W generated by J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  We consider the partial  conjugacy classes on W, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=', the orbits of the conjugation by WJ on  W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' By [5], we have the decomposition  W  ∆(WJ) =  �  (w,K)  WKw  ∆(WK),  (c)  where  W  ∆(WJ) denotes the quotient stack of W by the conjugation action  of WJ, and the right hand side runs over the pairs (w, K), where w are  minimal length representatives in the right cosets WJ\\W and K is  the maximal subset of J such that (w, K) is a combinatorial piece.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  Moreover, if w is a minimal length element in its partial conjugacy  class, then w is cyclic shift (via partial conjugation, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=', a sequence of  conjugations in WJ) to an element in WKw for some (w, K) occurring  in the right side of (c).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  3  We prove an “upgraded version” of the above statement in Theorem  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Namely, if w1 is a minimal length element in its partial conjugacy  class and (w1, K1) is a combinatorial piece with K1 ⊂ J, then  (w1, K1) is cyclic shift (via partial conjugation) to (w2, K2),  (d)  where w2 is an element in WKw for some (w, K) occurring in the right  side of (c).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Applications to parabolic character sheaves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Now we dis-  cuss some applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  Lusztig introduced the parabolic character  sheaves in [8].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Roughly speaking, the parabolic character sheaves are  certain simple perverse sheaves on the quotient stack YJ =  UPJ \\G/UPJ  ∆(LJ)  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  The parabolic character sheaves rely on the following decomposition of  YJ into G-stable pieces:  YJ =  �  w  YJ,w, where YJ,w“ = ”PK ˙wPK  ∆(PK) ,  (e)  Here w runs over the minimal length representatives in the right coset  WJ\\W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' And the quotation mark means we ignore the gerbs for unipo-  tent groups.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' We refer to §2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='2 for the precise statement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  It is worth pointing out that if (w, K) is conjugate to (w′, K′), then  it is easy to construct an isomorphism  LK ˙w  ∆(LK) ∼=  LK′ ˙w′  ∆(LK′).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' However, it is  more involved to relate PK ˙wPK  ∆(PK) for diﬀerent combinatorial pieces (w, K).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  The results (b) and (d) on the cyclic shifts of combinatorial pieces allow  us to understand certain behavior of the sheaves associated with an  arbitrary combinatorial piece with respect to the decomposition (e).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  We give two applications in §4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  (1) The left-right symmetry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  Note that in the decompositions (c) and (d), we use the right cosets  WJ\\W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' One may deﬁne similar decompositions using the left cosets  W/WJ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' A priori, the decompositions obtained using the left and right  cosets might diﬀer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' However, using the cyclic shifts of combinatorial  pieces, we show that there exists a symmetry between the left cosets  and the right cosets such that the corresponding substacks in  W  ∆(WJ)  and YJ coincide.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  (2) Induction functors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  Let J ⊂ J′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  Lusztig deﬁned the functor f : Sh(YJ) → Sh(YJ′).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  Suppose that w (resp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' w′) is the minimal length representative in its  right coset WJ\\W (resp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  WJ′\\W), w and w′ are in the same WJ′-  conjugacy class and ℓ(w) = ℓ(w′).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Then we have  YJ,w“ = ”PK ˙wPK  ∆(PK) and YJ′,w′“ = ”PK′ ˙w′PK′  ∆(PK′) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  4  XUHUA HE  In Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='3, we show that the restriction of the functor f to YJ,w  and YJ′,w′ is essentially the Harish-Chandra induction functor associ-  ated to the reductive group LK′ and its Levi subgroups.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' This result is  used in the work of Li, Nadler, and Yun [11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  Acknowledgement:  XH is partially supported by funds connected  with Choh-Ming Chair at CUHK, by Hong Kong RGC grant 14300221,  and by the Xplorer prize.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' This paper is motivated by a question of  Zhiwei Yun on the parabolic character sheaves, which is used in [11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  We thank him for explaining to me the question and related materials  in [11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' We also thank George Lusztig for the helpful discussions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Cyclic shift classes  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Conjugacy graph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Let W be a Weyl group and S be the set of  simple reﬂections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Let ℓ be the length function on W and ⩽ be the  Bruhat order on W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Let δ be a group automorphism on W, which  preserves S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' We consider the δ-conjugation action on W deﬁned by  w ·δ w′ = ww′δ(w)−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  Following [3, §3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='2], we deﬁne the δ-conjugacy graph as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' It is  the direct graph with vertices in W and the edges are of the form w  s−→δ  w′, where w, w′ ∈ W, s ∈ S such that w′ = swδ(s) and ℓ(w′) ⩽ ℓ(w).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  We denote by →δ the pre-order relation induced on W by the δ-  conjugacy graph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' In other words, for w, w′ ∈ W, w →δ w′ if there exists  a sequence of elements w = w1, w2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' , wn = w and s1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' , sn−1 ∈ S  such that wi  si−→δ wi+1 for 1 ⩽ i ⩽ n − 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  We write w ≈δ w′ if w →δ w′ and w′ →δ w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  It is easy to see  that ≈δ gives an equivalence relation on W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' For w ∈ W, we write  Cycδ(w) = {w′ ∈ W;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' w ≈δ w′} and call it the δ-cyclic shift class of w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  If δ is the identity map, we may ignore the subscript δ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  Now we give an example of the conjugacy graph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  Example 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Let W = S4 be the ﬁnite Weyl group of type A3 with  the set of simple reﬂections S = {s1, s2, s3}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' We simply write sabc···  instead of sasbsc · · · .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' It is easy to see that the conjugacy class of s1s2s3  forms a connected component of the conjugacy graph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' This connected  component is listed below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  s12132  s2  �✉✉✉✉✉✉✉✉✉  s1,s3 � s23212  s2  �■  ■  ■  ■  ■  ■  ■  ■  ■  �  s123  s1  �  s3  �  s213  s3  �  s132  �  s1  � s321  �  �  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Geometric cyclic shifts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Let G be a connected reductive group  over an algebraically closed ﬁeld k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Let G = G(k) and B be a Borel  subgroup of G with maximal torus T and unipotent radical U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Let R  be the root datum of G and δ be an automorphism of R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' In particular,  5  δ(B) = B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' We still denote by δ for the corresponding automorphism  on G and on its Weyl group W = NG(T)/T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' For any w ∈ W, we  choose a representative ˙w in NG(T).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  Consider the δ-conjugation action of G deﬁned by g ·δ g′ = gg′δ(g)−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  Let  G  Adδ(G) be the quotient stack.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  We have the Bruhat decomposi-  tion G = ⊔w∈WB ˙wB.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  Each Bruhat cell B ˙wB is stable under the  δ-conjugation action by B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Let  B ˙wB  Adδ(B) be the corresponding quotient  stack and  πw :  B ˙wB  Adδ(B) −→  G  Adδ(G)  be the natural morphism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  On the other hand, we have the automorphism on T deﬁned by  t �→ ˙wδ(t) ˙w−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Let  T  Ad ˙w◦δ(T) be the quotient stack and  pw :  B ˙wB  Adδ(B) −→  T  Ad ˙w◦δ(T)  be the natural morphism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  We have the following (upgraded) geometric version of cyclic shifts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  Proposition 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Let w, w′ ∈ W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Suppose that w ≈δ w′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Then there  exist isomorphisms  B ˙wB  Adδ(B) ∼=  B ˙w′B  Adδ(B) and  T  Ad ˙w◦δ(T) ∼=  T  Ad ˙w′◦δ(T) such that  the following diagram commutes  T  Ad ˙w◦δ(T)  ∼  =  �✤  ✤  ✤  B ˙wB  Adδ(B)  pw  �  πw �  ∼  =  �✤  ✤  ✤  G  Adδ(G)  T  Ad ˙w′◦δ(T)  B ˙w′B  Adδ(B)  pw′  �  πw′ �  G  Adδ(G).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  Remark 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' (1) An isomorphism  B ˙wB  Adδ(B) →  B ˙w′B  Adδ(B) was constructed in  [6, §3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' We follow the proof in loc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='cit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  (2) The isomorphisms  B ˙wB  Adδ(B) ∼=  B ˙w′B  Adδ(B) and  T  Ad ˙w◦δ(T) ∼=  T  Ad ˙w′◦δ(T) we  construct can be regarded as the geometric lifting of the path of cyclic  shifts w = w1  s1  −→ · · ·  sn−1  −−→ wn = w′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Such isomorphisms depend on  the choice of such paths, and there seem to be no canonical choices of  isomorphisms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' It suﬃces to consider the case where w  s−→ w′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  In this case,  ℓ(w′) = ℓ(w).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' It is easy to see that if sw > w and w(s) > w, then  w′ = w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Without loss of generality, we may assume furthermore that  sw < w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Set w1 = sw.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Then w1δ(s) = w′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' We have  B ˙sB ×B B ˙w1B ∼= B ˙wB,  where B acts on B ˙sB×B ˙w1B via b·(g1, g2) = (g1b−1, bg2) and B ˙sB×B  B ˙w1B is the quotient space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Similarly, we have  B ˙w1B ×B Bδ( ˙s)B ∼= B ˙w′B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  6  XUHUA HE  We have a natural isomorphism  B ˙sB × B ˙w1B ∼= B ˙w1B × Bδ( ˙s)B,  (g1, g2) �−→ (g2, δ(g1)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  By deﬁnition, g1g2 and g2δ(g1) are in the same δ-conjugacy class of G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  This isomorphism induces the desired isomorphism  B ˙wB  Adδ(B) ∼=  B ˙w′B  Adδ(B).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  Note that Ad( ˙s) ◦ Ad( ˙w) ◦ δ = Ad( ˙w′) ◦ δ ◦ Ad( ˙s) on T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' The de-  sired isomorphism  T  Ad ˙w◦δ(T) ∼=  T  Ad ˙w′◦δ(T) is induced from the conjugation  action by ˙s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  □  Corollary 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Let w, w′ ∈ W with w ≈δ w′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  Let f :  T  Ad ˙w◦δ(T) ∼=  T  Ad ˙w′◦δ(T) be an isomorphism in Proposition 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Then we have  (πw)!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' (pw)∗ = (πw′)!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' (pw′)∗f : Sh(  T  Ad ˙w◦δ(T)) −→ Sh(  G  Adδ(G)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  Here Sh(−) denotes the derived category of complexes of sheaves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Parabolic character sheaves  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Partial conjugation on W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Let J ⊂ S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  Recall that WJ is  the subgroup of W generated by the simple reﬂections in J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Let W J  (resp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' JW) be the set of minimal coset representatives in W/WJ (resp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  WJ\\W).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' For J, K ⊂ S, we simply write JW K for JW ∩ W K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  Consider the δ-conjugation action of WJ on W deﬁned by w ·δ w′ =  ww′δ(w)−1 for w ∈ WJ and w′ ∈ W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' For w ∈ W, we write Ad(w)δ(J) =  J if for any simple reﬂection s ∈ J, there exists a simple reﬂection  s′ ∈ J such that wδ(s)w−1 = s′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' In this case, w ∈ JW if and only if  w ∈ W δ(J).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  For any J ⊂ S and w ∈ W, we set  I(J, w, δ) = max{K ⊂ J;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Ad(w)δ(K) = K}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  Now we recall B´edard’s description [1] of JW.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  Let T (J, δ) be the set of sequences (Jn, wn)n⩾0 with Jn ⊂ J and  wn ∈ W such that  (1) J0 = J;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  (2) Jn = Jn−1 ∩ Ad(wn−1)(δ(Jn−1)) for n ⩾ 1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  (3) wn ∈ JnW δ(Jn) for n ⩾ 0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  (4) wn ∈ WJnwn−1Wδ(Jn−1) for n ⩾ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  Then for any sequence (Jn, wn)n⩾0, we have that wm = wm+1 =  · · and Jm = Jm+1 = · · · for m ⩾ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' By [8, Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='5], the  assignment (Jn, wn)n⩾0 �→ wm for m ≫ 0 deﬁnes a bijection T (J, δ) →  JW.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Moreover, wn ∈ wWδ(Jn) for all n ⩾ 0 and I(J, w, δ) = Jm for  m ≫ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  We have the following description of WI(J,w,δ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Let w ∈ JW.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Then WI(J,w,δ) = �  n∈Z(Ad(w) ◦ δ)n(WJ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  7  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' By deﬁnition, Ad(w) ◦ δ(WI(J,w,δ)) = WI(J,w,δ) ⊂ WJ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  Let (Jn, wn)n⩾0 be the sequence in T (J, δ) corresponding to w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Now  we prove that ∩n∈Z(Ad(w) ◦ δ)n(WJ) ⊂ WJn for all n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  By deﬁnition ∩n∈Z(Ad(w) ◦ δ)n(WJ) ⊂ WJ = WJ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Assume that we  have proved ∩n∈Z(Ad(w) ◦ δ)n(WJ) ⊂ WJi for some i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' By deﬁnition,  w = wiδ(a) for some a ∈ WJi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Hence  ∩n∈Z (Ad(w) ◦ δ)n(WJ)  =  �  ∩n∈Z(Ad(w) ◦ δ)n(WJ)  �  ∩ Ad(w) ◦ δ  �  ∩n∈Z(Ad(w) ◦ δ)n(WJ)  �  ⊂ WJi ∩ Ad(w) ◦ δ(WJi) = WJi ∩ Ad(wi) ◦ δ(WJi)  = WJi+1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  This ﬁnishes the proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  □  We have the following classiﬁcation of the Adδ(WJ)-orbits on W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Let J ⊂ S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Then  (1) W = �  w∈JW WJ ·δ (WI(J,w,δ)w);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  (2) For any w ∈ JW, the embedding WI(J,w,δ) → W, u �→ uw induces  the bijection between the quotient stacks  WI(J,w,δ)  Adw◦δ(WI(J,w,δ))  ∼= WJ ·δ (WI(J,w,δ)w)  Adδ(WJ)  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Part (1) and the bijection of orbits in part (2) were proved in [5,  Corollary 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='6].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' It remains to show that the bijection on the orbits also  gives an isomorphism between the isotropy groups.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' In other words,  it remains to show that if (a, b) ∈ WJ × WI(J,w,δ)w with abδ(a)−1 ∈  WI(J,w,δ)w, then a ∈ WI(J,w,δ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  Let (Jn, wn)n⩾0 be the element in T (J, δ) corresponding to w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' We  argue by induction that a ∈ WJn for all n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  By deﬁnition, a ∈ WJ = WJ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Assume that a ∈ WJi for some i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  Then WI(J,w,δ)w ⊂ wiWδ(Ji) and abδ(a)−1 ∈ awiWδ(Ji).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Thus  a ∈ WJi ∩ wiWδ(Ji)w−1  i  = WJi+1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  Hence a ∈ WJn for all n ⩾ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' In particular, a ∈ WI(J,w,δ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  □  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Lusztig’s variety ZJ,δ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' For any J ⊂ S, let PJ ⊃ B be the stan-  dard parabolic subgroup of type J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Let PJ = G/PJ be the partial ﬂag  variety.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' We may identify PJ with the set of parabolic subgroups of  G that are conjugate to PJ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' For any parabolic subgroup P of G, we  denote by UP its unipotent radical.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' For g ∈ G and H ⊂ G, we simply  write gH for gHg−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Following [8], we set  ZJ,δ = {(P, P ′, gδ(UP));' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' P ∈ PJ, P ′ ∈ Pδ(J), g ∈ G, gδ(P) = P ′}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  Deﬁne the action of G × G on ZJ,δ by  (g1, g2) · (P, P ′, gδ(UP)) = (g2P, g1P ′, g1gδ(g2)−1 δ(Ug2P)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  8  XUHUA HE  Then G × G acts transitively on ZJ,δ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  Let hJ,δ = (PJ, Pδ(J), UPδ(J))  be the base point.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Then the isotropy group of hJ,δ is {(δ(l)u′, lu);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' l ∈  LJ, u ∈ UPJ, u′ ∈ UPδ(J)}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' The map G × G → G, (g, g′) �→ (g′)−1g  induces an isomorphism of stacks  ZJ,δ  ∆(G)  ∼= YJ,δ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  Here  ZJ,δ  ∆(G) is the quotient stack for the diagonal G-action on ZJ,δ and  YJ,δ =  UPJ \\G/UPδ(J)  Adδ(LJ)  is the quotient stack for the δ-conjugation action of  LJ on UPJ\\G/UPδ(J).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  Now we recall the decomposition of ZJ,δ into the G-stable pieces,  introduced by Lusztig in [8].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' For w ∈ JW, we set  ZJ,δ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='w = G∆ · (B ˙w, B)hJ,δ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  The following result is established by Lusztig in [8].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Let J ⊂ S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Then  (1) ZJ,δ = �  w∈JW ZJ,δ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='w is a decomposition into smooth, locally  closed subvarieties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  (2) For any w ∈ JW, there is a canonical map  πJ,δ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='w : ZJ,δ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='w  ∆(G) −→  LI(J,w,δ)  Ad ˙w◦δ(LI(J,w,δ))  which is an iterated gerbe for unipotent groups.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  Under the isomorphism  ZJ,δ  ∆(G) ∼= YJ,δ, we may reformulate the above  decomposition as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  For any w ∈ W, let YJ,δ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='w be the image  of B ˙wB in YJ,δ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Then for any w ∈ JW,  ZJ,δ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='w  ∆(G) ∼= YJ,δ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='w and YJ,δ =  ⊔w∈JWYJ,δ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  By [4, Proposition 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='10 (1)],  ZJ,δ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='w ∼= G ×PI(J,w,δ) (PI(J,w,δ) ˙w, PI(J,w,δ)) · hJ,δ,  where PI(J,w,δ) acts on G × (PI(J,w,δ) ˙w, PI(J,w,δ)) · hJ,δ by p · (g, z) =  (gp−1, (p, p)·z) and G×PI(J,w,δ) (PI(J,w,δ) ˙w, PI(J,w,δ))·hJ,δ is the quotient  space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' We may reformulate it as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Let w ∈ JW.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' The embedding PI(J,w,δ) ˙wPδ(I(J,w,δ) →  G induces an isomorphism  UPJ\\PI(J,w,δ) ˙wPδ(I(J,w,δ)/UPδ(J)  Adδ(LJ ∩ PI(J,w,δ))  ∼= YJ,δ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Parabolic character sheaves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' We follow [8].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' For any w ∈ W,  we consider the following diagram  T  Ad ˙w◦δ(T)  B ˙wB  Adδ(B)  pw  �  πJ,w � YJ,δ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  9  A parabolic character sheaf on YJ,δ is a simple perverse sheaf that  is a composition factor of pHi((πJ,w)!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='p∗  wL) for some w ∈ W, i ∈ Z and  L ∈ Sh(  T  Ad ˙w◦δ(T)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  On the other hand, by Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='3, for any w ∈ JW, the map  πJ,w induces an equivalence of categories  π∗  J,δ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='w : Sh(  LI(J,w,δ)  Ad ˙w◦δ(LI(J,w,δ))) ∼= Sh(ZJ,δ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='w  ∆(G)) = Sh(YJ,δ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='w).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  Note that LI(J,w,δ) is a connected reductive group.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' The character  sheaves on  LI(J,w,δ)  Ad ˙w◦δ(LI(J,w,δ)) is deﬁned by Lusztig in [7].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  It is proved by Lusztig in [8] that  Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Let J ⊂ S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Then  (1) Any parabolic character sheaf on YJ,δ is the intermediate exten-  sion of π∗  J,δ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='w(A) for a unique w ∈ JW and a character sheaf A on  LI(J,w,δ)  Ad ˙w◦δ(LI(J,w,δ)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  (2) If B is a parabolic character sheaf on YJ,δ and w ∈ JW, then any  composition factor of pHi(B |YJ,δ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='w) is of the form π∗  J,δ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='w(A) for some  character sheaf A on  LI(J,w,δ)  Ad ˙w◦δ(LI(J,w,δ)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Partial conjugation graph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Let J ⊂ S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' We consider the Adδ(WJ)-  orbits on W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' The (J, δ)-conjugacy graph, by deﬁnition, is the direct  graph with vertices in W and the edges are of the form w  s−→δ w′ for  w, w′ ∈ W, s ∈ J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  We denote by →J,δ the pre-order relation induced by  s−→δ for s ∈ J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  We write w ≈J,δ w′ if w →J,δ w′ and w′ →J,δ w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' We call the equivalece  class ≈J,δ the (J, δ)-cyclic shift classes on W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  We have the following result.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' [5, Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='4] For any w ∈ W, there exists  w′ ∈ JW and u ∈ WI(J,w′,δ) such that w →J,δ uw′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  Moreover, if w is of minimal length in WJ ·δ w, then u is of minimal  length in WI(J,w′,δ) ·δ′ u and w ≈J,δ uw′, where δ′ = Ad(w′) ◦ δ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  Remark 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' By Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='2 (1), w′ is uniquely determined by w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  However, u is not unique in general.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Partial order.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' For any w ∈ W and w′ ∈ JW, we write w′ ⩽J,δ w  if there exists u ∈ WJ such that uw′δ(u)−1 ⩽ w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' By [5, Corollary 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='6],  (a) The restriction of ⩽J,δ to JW gives a partial order on JW.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  It is easy to see that for w, w′ ∈ JW, w′ ⩽ w implies that w′ ⩽J,δ  w and w′ ⩽J,δ w implies that ℓ(w′) ⩽ ℓ(w).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' However, the converse  directions do not hold in general.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  Example 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Let W = S4 and J = {3}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' The simple reﬂections of W  are s1, s2, s3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' We simply write sabc··· instead of sasbsc · · · .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' In Figure 1,  10  XUHUA HE  we draw the Hasse diagram of JW, with respect to the usual Bruhat  order and the partial order ⩽J,id (the extra relation is in dotted line).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Hasse diagram for the partial orders on JW  s12132  s2132  s1213  s123  s121  s213  s12  s21  s23  s1  s2  1  ✴✴✴✴✴✴✴✴  ✴✴✴✴✴✴✴✴  ✎✎✎✎✎✎✎✎  ✴✴✴✴✴✴✴✴  ✎✎✎✎✎✎✎✎  ⑧⑧⑧⑧⑧⑧⑧⑧⑧⑧  ❏  ❏  ❏  ❏  ❏  ❏  ❏  ❏  ❏  ❏  ❏  ❏  ✎✎✎✎✎✎✎✎  ✎✎✎✎✎✎✎✎  ✴✴✴✴✴✴✴✴  ❏  ❏  ❏  ❏  ❏  ❏  ❏  ❏  ❏  ❏  ❏  ❏  ✴✴✴✴✴✴✴✴  ✎✎✎✎✎✎✎✎  ✴✴✴✴✴✴✴✴  ⑧  ⑧  ⑧  ⑧  ⑧  ⑧  ⑧  ⑧  ⑧  ⑧  ✎✎✎✎✎✎✎✎  t  t  t  t  t  t  t  t  t  t  t  t  By [5, Proposition 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='8], we have  (a) Let w ∈ W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Then YJ,δ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='w = �  w′∈JW ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='w′⩽J,δw YJ,δ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='w′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  Since YJ,δ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='w is irreducible, there exists a unique geometric piece YJ,δ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='w′  which is dense in YJ,δ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Therefore we have  (b) For any w ∈ W, the set {w′ ∈ W J;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' w′ ⩽J,δ w} contains a unique  maximal element with respect to ⩽J,δ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  We also would like to point out the special case of (a), which will be  used in [11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  (c) Let w ∈ W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' If WJ ·δ w ∩ JW = ∅ or w is not of minimal length  in WJ ·δ w, then YJ,δ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='w ⊂ �  w′∈JW ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='ℓ(w′)<ℓ(w) YJ,δ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='w′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Cyclic shifts of pieces  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Combinatorial pieces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' A δ-combinatorial piece is a pair (w, K),  where w ∈ W and K ⊂ S with w ∈ KW and Ad(w)δ(K) = K (and  hence w ∈ W δ(K)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' To each δ-combinatorial piece (w, K), we associate  a subset WKw of W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' In particular, if K = ∅, then we naturally identify  the δ-combinatorial piece (w, ∅) with the element w of W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' In this way,  we identify W as a subset of the set of δ-combinatorial pieces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  We say that two δ-combinatorial pieces (w, K) and (w′, K′) are δ-  conjugated by an element x ∈ W if w′ = x−1wδ(x), and Ad(x)−1(K) =  K′ (and hence x ∈ W K).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' In this case, x−1(WKw)δ(x) = WK′w′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  11  It is worth pointing out that the whole Weyl group W does not act  on the set of δ-combinatorial pieces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' The element x acts on (w, K) only  if Ad(x)−1(K) ⊂ S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Cyclic shifts of pieces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' The deﬁnition of cyclic shifts on W in  §1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='1 does not generalize to the set of δ-combinatorial pieces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  However, there is an equivalent deﬁnition of cyclic shifts on W, due  to Brou´e and Michel in [2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' The deﬁnition is as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Let w, w′ ∈ W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  Then w ≈δ w′ if there exists a sequence of elements w = w1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' , wn =  w′ and elements xi, yi ∈ W such that wi = xiyi, wi+1 = yiδ(xi) and  ℓ(wi) = ℓ(xi) + ℓ(yi) = ℓ(wi+1) for all 1 ⩽ i ⩽ n − 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' See [3, Exercise  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='7].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  Now we deﬁne cyclic shifts of the combinatorial pieces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  Let (w, K) and (w′, K′) be δ-combinatorial pieces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' We write (w, K)  x≈δ  (w′, K′) if (w, K) and (w′, K′) are δ-conjugated by x, and ℓ(w) =  ℓ(x) + ℓ(x−1w) = ℓ(w′).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Let ≈δ be the equivalence relation on the  set of δ-combinatorial pieces generated by  x≈δ for x ∈ W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' We call it the  cyclic shift relation of the δ-combinatorial pieces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' When restricting to  W, this deﬁnition coincides with the deﬁnition of Brou´e and Michel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  Similarly, for any J ⊂ S, let ≈J,δ be the equivalence relation on the  set of δ-combinatorial pieces generated by  x≈δ for x ∈ WJ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' In geometric  applications, we usually consider the ≈J,δ on the set of δ-combinatorial  pieces (w, K) with the additional assumption that K ⊂ J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Let (w, K) and (w′, K′) be δ-combinatorial pieces  with K, K′ ⊂ J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Suppose that (w, K) ≈J,δ (w′, K′).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Then there exists  isomorphisms  UPJ \\PK ˙wPδ(K)/UPδ(J)  Ad ˙w◦δ(LJ∩PK)  ∼=  UPJ \\PK′ ˙w′Pδ(K′)/UPδ(J)  Ad ˙w′◦δ(LJ∩PK′)  and  LK  Ad ˙w◦δ(LK) ∼=  LK′  Ad ˙w′◦δ(LK′) such that the following diagram commutes  LK  Ad ˙w◦δ(LK)  ∼  =  �✤  ✤  ✤  UPJ \\PK ˙wPδ(K)/UPδ(J)  Ad ˙w◦δ(LJ∩PK)  �  �  ∼  =  �✤  ✤  ✤  YJ,δ  LK′  Ad ˙w′◦δ(LK′)  UPJ \\PK′ ˙w′Pδ(K′)/UPδ(J)  Ad ˙w′◦δ(LJ∩PK′)  �  � YJ,δ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' It suﬃces to consider the case where (w, K)  x≈δ (w′, K′) for some  x ∈ WJ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Set y = x−1w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Then w′ = yδ(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' We have  PK ˙wPδ(K) = UPK ˙wPδ(K) ∼= (UPK ∩ ˙wU− ˙w−1) × Pδ(K).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  Moreover, UPK ∩ ˙wU− ˙w−1 = U ∩ ˙wU− ˙w−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Note that Ad(y)δ(K) =  Ad(x−1w)δ(K) = Ad(x)−1(K) = K′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Similarly, we have  PK ˙xPK′ ∼= (U ∩ ˙xU− ˙x−1) × PK′;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  PK′ ˙yPδ(K) ∼= (U ∩ ˙yU− ˙y−1) × Pδ(K).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  12  XUHUA HE  Since ℓ(w) = ℓ(x) + ℓ(y), we have U ∩ ˙wU− ˙w−1 ∼= (U ∩ ˙xU− ˙x−1) ×  (U ∩ ˙yU− ˙y−1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Hence  PK ˙wPδ(K) ∼= U ∩ ˙wU− ˙w−1 × Pδ(K)  ∼= (U ∩ ˙xU− ˙x−1) × (U ∩ ˙yU− ˙y−1) × Pδ(K)  ∼= (U ∩ ˙xU− ˙x−1) × PK′ ˙yPδ(K)  ∼=  �  (U ∩ ˙xU− ˙x−1) × PK′�  ×PK′ PK′ ˙yPδ(K)  ∼= PK ˙xPK′ ×PK′ PK′ ˙yPδ(K).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  The map (g1, g2) �→ (g2, δ(g1)) gives a natural isomorphism  f : PK ˙xPK′ ×PK′ PK′ ˙yPδ(K)  Adδ(PK)  ∼= PK′ ˙yPδ(K) ×Pδ(K) Pδ(K)δ( ˙x)Pδ(K′)  Adδ(PK′)  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  Since K, K′ ⊂ J and x ∈ WJ, we have PK ˙xPK′ ⊂ PK and hence  the conjugation action of PK ˙xPK′ normalizes UPJ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Thus f induces the  desired isomorphism  UPJ \\PK ˙wPδ(K)/UPδ(J)  Adδ(LJ∩PK)  ∼=  UPJ \\PK′ ˙w′Pδ(K′)/UPδ(J)  Adδ(LJ ∩PK′)  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  Note that the representative of w′ in NG(T) is unique up to right  multiplication by T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' As we consider the morphisms on the quotient  stacks, we may assume furthermore that ˙w′ is chosen so that ˙w′ =  ˙x−1 ˙wδ( ˙x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Then Ad( ˙x)−1 ◦ Ad( ˙w) ◦ δ = Ad( ˙w′) ◦ δ ◦ Ad( ˙x)−1 on LK.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  The desired isomorphism  LK  Ad ˙w◦δ(LK) ∼=  LK′  Ad ˙w′◦δ(LK′) is induced from the  conjugation action by ˙x−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  □  Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Let J ⊂ S and (w, K) be a δ-combinatorial piece.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Sup-  pose that K ⊂ J and w is of minimal length in WJ ·δ w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Then there  exists unique w′ ∈ JW, x ∈ WJ ∩ W I(J,w′,δ), u ∈ WI(J,w′,δ) such that  x−1wδ(x) = uw′, Ad(x)−1(K) ⊂ J and (w, K) ≈J,δ (uw′, Ad(x)−1(K)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' By Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='2 (1), there exists a unique w′ ∈ JW such that  w ∈ WJ ·δ WI(J,w′,δ)w′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' By Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='2 (2), there exists a unique  x ∈ WJ ∩W I(J,w′,δ) such that x−1wδ(x) ∈ WI(J,w′,δ)w′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Let u ∈ WI(J,w′,δ)  with x−1wδ(x) = uw′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  By Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='1,  WI(J,w′,δ) = ∩n∈Z(Ad(w′) ◦ δ)n(WJ) = ∩n∈Z(Ad(uw′) ◦ δ)n(WJ)  = ∩n∈Z(Ad(x)−1Ad(w) ◦ δ ◦ Ad(x))n(WJ)  = ∩n∈ZAd(x)−1(Ad(w) ◦ δ)nAd(x)(WJ)  = Ad(x)−1�  ∩n∈Z(Ad(w) ◦ δ)n(WJ)  �  ⊃ Ad(x)−1(WK).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  The second equality uses the fact that (Ad(uw′) ◦ δ)n = (Ad(w′) ◦  δ)nAd(u′) for some u′ ∈ WI(J,w′,δ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  Therefore x−1 sends any simple root in K to a root spanned by  I(J, w′, δ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Since x ∈ W I(J,w′,δ), we have Ad(x)−1(K) ⊂ I(J, w′, δ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Let  13  K′ = Ad(x)−1(K).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Then  Ad(uw′)δ(K′) = Ad(x)−1Ad(w)δAd(x)(K′) = Ad(x)−1Ad(w)δ(K)  = Ad(x)−1(K) = K′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  Thus (uw′, K′) is a δ-combinatorial piece.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' It remains to prove that  (w, K) ≈J,δ (uw′, K′).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  We associate a quadruple (Jn, wn, xn, yn)n⩾0 to w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  Here Jn ⊂ J,  wn ∈ JnW δ(Jn), xn ∈ WJn ∩ W Jn+1 and yn ∈ WJn+1 for all n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' The  quadruple is constructed as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  Set J0 = J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  Suppose that n ⩾ 0 and (Jm, xm) are deﬁned for  0 ⩽ m < n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  We set w′  n = (x0 · · · xn−1)−1wδ(x0 · · · xn−1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  We may  write w′  n as w′  n = znw′′  n, where w′′  n ∈ JnW and zn ∈ WJn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Set wn =  min(w′′  nWδ(Jn)) and Jn+1 = Jn ∩ Ad(wn)δ(Jn).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' We write zn as zn =  xnyn, where xn ∈ WJn ∩ W Jn+1 and yn ∈ WJn+1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  The quadruple  (Jn, wn, xn, yn)n⩾0 is deﬁned inductively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  By deﬁnition, (Jn, wn)n⩾0 ∈ T (J, δ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Then there exists m such that  Jm = Jm+1 = · · · , wm = wm+1 = · · · .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' We then have xm = xm+1 =  · · = 1 and ym = ym+1 = · · · .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  Moreover, Jm = I(J, wm, δ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  Set  x′ = x0x1 · · · xm ∈ WJ ∩ W I(J,wm,δ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  Then (x′)−1wx′ ∈ WJmwm =  WI(J,wm,δ)wm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' By Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='2, we have wm = w′ and x′ = x.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  Moreover, we have ℓ(w′  n) = ℓ(w′′  n) + ℓ(zn) = ℓ(w′′  n) + ℓ(xn) + ℓ(yn) =  ℓ(ynw′′  n) + ℓ(xn).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Thus  ℓ(w′  n+1) = ℓ(x−1  n w′  nδ(xn)) ⩽ ℓ(x−1  n w′  n) + ℓ(xn) = ℓ(ynw′′  n) + ℓ(xn)  = ℓ(w′  n).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  In particular, we have ℓ(w) = ℓ(w′  0) ⩾ ℓ(w′  1) ⩾ · · · ⩾ ℓ(w′  m) =  ℓ(x−1wδ(x)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' By our assumption, w is of minimal length in WJ ·δ w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  Hence ℓ(w) = ℓ(w′  1) = · · · = ℓ(w′  m) = ℓ(x−1wδ(x)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Moreover, we have  w = w′  0 ≈J,δ w′  1 ≈J,δ · · · ≈J,δ w′  m = x−1wδ(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  Note that Ad(x0)−1(WK) = Ad(x1 · · ·xm)WK′ ⊂ WJ1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Since x0 ∈  W J1, we have Ad(x0)−1(K) ⊂ J1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' By the same argument, we may  show that Ad(x0 · · · xi)−1(K) ⊂ Ji+1 for all i ⩾ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  Hence we have (w, K)  x0≈δ (w′  1, Ad(x0)−1(K))  x1≈δ · · ·  xm  ≈ δ (uw′, K′).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  □  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Applications  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Left-right symmetry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Recall that  W =  �  w∈JW  WJ ·δ (WI(J,w,δ)w).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  By [5, §2], we have the following decomposition of W indexed by W δ(J)  instead of JW:  W =  �  w∈W δ(J)  WJ ·δ (WI(J,w,δ)w).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  14  XUHUA HE  Now we show that there exists a natural bijection between JW and  W δ(J) so that the corresponding subsets of W coincide.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  Proposition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Let J ⊂ S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Then there exists a unique bijection  ι : W δ(J) → JW such that  �  w, I(J, w, δ)  �  ≈J,δ  �  ι(w), I(J, ι(w), δ)  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  In particular, WJ ·δ (WI(J,w,δ)w) = WJ ·δ (WI(J,ι(w),δ)ι(w)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Let w ∈ W δ(J) and K = I(J, w, δ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' By deﬁnition, (w, K) is a  δ-combinatorial piece.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' For any u ∈ WJ, we have  ℓ(uwδ(u)−1) ⩾ ℓ(wδ(u)−1) − ℓ(u) = ℓ(w) + ℓ(δ(u)) − ℓ(u) = ℓ(w).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  Therefore w is of minimal length in WJ ·δ w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' By Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='2, there  exists unique w′ ∈ JW, x ∈ WJ ∩ W I(J,w′,δ), u ∈ WI(J,w′,δ) such that  x−1wδ(x) = uw′, Ad(x)−1(K) ⊂ J and (w, K) ≈J,δ (uw′, Ad(x)−1(K)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  Set K′ = Ad(x)−1(K).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' By Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='1, WK = ∩n∈Z(Ad(w)◦δ)n(WJ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  Hence  WK′ = Ad(x)−1(WK) = ∩n∈ZAd(x)−1(Ad(w) ◦ δ)n(WJ)  = ∩n∈Z(Ad(uw′) ◦ δ)nAd(x)−1(WJ)  = ∩n∈Z(Ad(uw′) ◦ δ)n(WJ)  = ∩n∈Z(Ad(w′) ◦ δ)n(WJ)  = WI(J,w′,δ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  The second to last equality uses the fact that (Ad(uw′)◦δ)n = (Ad(w′)◦  δ)nAd(u′) for some u′ ∈ WI(J,w′,δ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  Therefore K′ = I(J, w′, δ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Hence xuw′ = wδ(x) ∈ W δ(I(J,w′,δ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' This  implies that u = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  So (w, K) ≈J,δ (w′, K′).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  By the deﬁnition of  cyclic shifts of combinatorial pieces, we also have WJ ·δ (WKw) = WJ ·δ  (WK′w′).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  □  Let w ∈ W δ(J) and w′ = ι(w) ∈ JW.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Since w ≈J,δ w′, we have  YJ,δ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='w = YJ,δ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='w′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Moreover, by Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='1, we have the following  commutative diagram  Sh(  LI(J,w,δ)  Ad ˙w◦δ(LI(J,w,δ)))  Ad( ˙x)−1  �  ∼  =  � Sh(YJ,δ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='w)  Sh(  LI(J,w′,δ)  Ad ˙w′◦δ(LI(J,w′,δ)))  ∼  = � Sh(YJ,δ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='w′),  where x is the unique element in WJ ∩ W I(J,w′,δ) such that w′ =  x−1wδ(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  Now we provide a nontrivial example of the map ι.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  Example 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Let W = S5, J = {1, 3} and δ is the identity map.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  Then one may check that ι(s121324) = s213243.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' In particular, the map ι is  15  diﬀerent from taking inverse, and diﬀerent from the one-step operation  xy �→ yx for x ∈ WJ and y ∈ JW.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' The functors f J  J′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' We follow [8, §6].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  Let J ⊂ J′ ⊂ S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  Let  π : PJ → PJ′ be the projection map.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Set  ZJ,J′,δ = {(P, P ′, gδ(Uπ(P )));' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' P ∈ PJ, P ′ ∈ Pδ(J), gδ(P) = P ′}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  Deﬁne the action of G × G on ZJ,J′,δ by (g1, g2) · (P, P ′, gUπ(P )) =  (g2P, g1P ′, g1gδ(g2)−1δ(Uπ(g2P ))).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Then G×G acts transitively on ZJ,J′,δ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  Let hJ,J′,δ = (PJ, Pδ(J), UPδ(J′)) be the base point.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Then we may identify  ZJ,J′,δ with (G × G)/(UPJ′ × UPδ(J′))Adδ(LJ′ ∩ PJ), where LJ′ ∩ PJ is a  standard parabolic subgroup of LJ′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  We consider the following diagram  ZJ,δ  ZJ,J′,δ  c  �  d  � ZJ′,δ,  where  c(P, P ′, gδ(Uπ(P ))) = (P, P ′, gδ(UP)),  d(P, P ′, gδ(Uπ(P ))) = (π(P), π(P ′), gδ(Uπ(P ))).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  It is easy to see that c is a locally trivial ﬁbration with ﬁbers iso-  morphic to an aﬃne space UPJ/UPJ′ and d is a locally trivial ﬁbration  with ﬁbers isomorphic to the ﬂag variety LJ′/(LJ′ ∩ PJ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Set  f J  J′ = d!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='c∗ : Sh(ZJ,δ  ∆G) −→ Sh(ZJ′,δ  ∆G ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  We may reformulate the functors as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Consider the following  diagram of stacks  YJ,δ  YJ,J′,δ  q  �  p  � YJ′,δ  where YJ,J′,δ =  UPJ′ \\G/UPδ(J′)  Adδ(LJ′∩PJ)  and q and p are natural projection maps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  Under the isomorphism  ZJ,δ  ∆(G) ∼= YJ,δ and  ZJ′,δ  ∆(G) ∼= YJ′,δ, we may rewrite  the functor f J  J′ as  f J  J′ = p!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='q∗ : Sh(YJ,δ) −→ Sh(YJ′,δ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  Let w ∈ JW and w′ ∈ J′W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Let iJ,δ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='w : YJ,δ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='w → YJ,δ and iJ′,δ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='w′ :  YJ′,δ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='w′ → YJ′,δ be the embeddings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' We deﬁne  f J,w  J′,w′ = i∗  J′,δ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='w′ p!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='q∗(iJ,δ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='w)!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' : Sh(YJ,δ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='w) −→ Sh(YJ′,δ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='w′).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  By deﬁnition, for any w ∈ JW, p(q−1(YJ,δ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='w)) = YJ′,δ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Hence by  §2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='5 (c), we have  (a) Let w ∈ JW and A be a parabolic character sheaf on YJ,δ with  support in YJ,δ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Assume that WJ′ ·δ w ∩ J′W = ∅ or w is not of  minimal length in WJ′ ·δ w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Then the support of f J  J′(A) is contained in  ⊔w′∈J′W ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='ℓ(w′)<ℓ(w)YJ′,δ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='w′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  16  XUHUA HE  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Induction functor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Let (w, K) be a δ-combinatorial piece.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Con-  sider the following diagram  LK  Ad ˙w◦δ(LK) ∼=  LK ˙w  Adδ(LK)  PK ˙wPδ(K)  Adδ(PK)  a  �  b  �  G  Adδ(G),  where a is induced from the projection map PK ˙wPδ(K) → LK ˙w and b  is induced from the embedding PK ˙wPδ(K) → G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  Following [12, §4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='1], we deﬁne  Ind(G,δ)  (LK, ˙w) = b!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='a∗ : Sh(  LK  Ad ˙w◦δ(LK)) −→ Sh(  G  Adδ(G)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  If w = 1, then K = δ(K) and PK is a δ-stable standard parabolic  subgroup of G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' In this case, Ind is the Harish-Chandra induction func-  tor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' If K = ∅, then PK = B and Ind is the Deligne-Lusztig induction  functor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  Now we prove that  Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Let J ⊂ J′ ⊂ S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Let w ∈ JW such that w is of minimal  length in WJ ·δw.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Let w′ ∈ J′W, u ∈ WI(J′,w′,δ) and x ∈ WJ′∩W I(J′,w′,δ)  such that x−1wδ(x) = uw′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Set K = I(J, w, δ), K1 = Ad(x)−1(K),  K′ = I(J′, w′, δ) and δ′ = Ad( ˙w′) ◦ δ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Then we have the following  commutative diagram  Sh(  LK  Ad ˙w◦δ(LK))  Ind  (LK′ ,δ′)  (LK1 , ˙u) ◦Ad( ˙x)−1  �  π∗  J,δ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='w  ∼  =  � Sh(YJ,δ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='w)  fJ,w  J′,w′  �  Sh(  LK′  Ad ˙w′◦δ(LK′))  π∗  J′,δ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='w′  ∼  =  � Sh(YJ′,δ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='w′).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' We have the following commutative diagram  LK  Ad ˙w◦δ(LK)  Ad( ˙x)−1  ∼  =  �  YJ,δ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='w  πJ,δ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='w  �  iJ,δ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='w  �  □  YJ,δ  q−1(YJ,δ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='w)  q  �  f  ∼  =  �  i  � YJ,J′,δ  p  �  q  �  LK1  Ad ˙u◦δ′(LK1)  X  π1  �  (LK′∩PK1) ˙uδ′(LK′∩PK1)  Adδ′(LK′∩PK1)  a  �  b  �  □  X  π2  �  b′  �  LK′  Adδ′(LK′)  YJ′,δ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='w′  πJ′,δ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='w′  �  iJ′,δ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='w′ � YJ′,δ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  17  Here X =  UPJ′ \\PK1 ˙u ˙w′Pδ(K1)/UPδ(J′)  Ad ˙u ˙w′◦δ(LJ′∩PK1)  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  By Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='4, YJ,δ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='w ∼=  UPJ \\PK ˙wPδ(K)/UPδ(J)  Ad ˙w◦δ(LJ∩PK)  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  Thus by deﬁni-  tion q−1(YJ,δ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='w) ∼=  UPJ′ \\PK ˙wPδ(K)/UPδ(J′)  Ad ˙w◦δ(LJ′∩PK)  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' By Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='2, (w, K) ≈J,δ  (uw′, K1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' The isomorphism f : q−1(YJ,δ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='w) → X1 is given in Proposi-  tion 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' The map π1 : X →  LK1  Ad ˙u◦δ′(LK1) is induced from the projection  map PK1 ˙u ˙w′Pδ(K1) → LK1 ˙u ˙w′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' The map π2 : X →  (LK′∩PK1) ˙uδ′(LK′∩PK1)  Adδ′(LK′∩PK1)  is induced from the projection  PK1 ˙u ˙w′Pδ(K1) −→ PK1 ˙u ˙w′Pδ(K1) ∩ LK′ ˙w′ = (LK′ ∩ PK1) ˙uδ′(LK′ ∩ PK1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  By Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='4, YJ′,δ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='w′ ∼=  UPJ′ \\PK′ ˙w′Pδ(K′)/UPδ(J′)  Ad ˙w′◦δ(LJ′∩PK′)  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' The map b′ : X →  YJ′,δ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='w′ is induced from the embedding PK1 ˙u ˙w′Pδ(K1) ⊂ PK′ ˙w′Pδ(K′).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  Thus  f J,w  J′,w′π∗  J,δ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='w = i∗  J′,δ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='w′p!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='q∗(iJ,δ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='w)!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='π∗  J,w,δ = i∗  J′,δ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='w′p!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='i!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='q∗π∗  J,w,δ  = (b′)!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='f!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='q∗π∗  J,w,δ = (b′)!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='π∗  1Ad( ˙x)−1  = (b′)!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='π∗  2a∗Ad( ˙x)−1 = π∗  J′,δ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='w′b!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='a∗Ad( ˙x)−1  = π∗  J′,δ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='w′Ind  (LK′,δ′)  (LK1, ˙u) ◦ Ad( ˙x)−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  The proof is ﬁnished.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  □  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' A special case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Now we discuss a special case of Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  Let J ⊂ J′ ⊂ S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Let w ∈ JW and w′ ∈ J′W such that w ∈ WJ′ ·δ w′  and ℓ(w) = ℓ(w′).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Set K = I(J, w, δ) and K′ = I(J′, w′, δ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' By Theo-  rem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='2, there exists a unique x ∈ WJ′ ∩W K′ such that x−1wδ(x) = w′  and (w, K) ≈J,δ (w′, K1), where K1 = Ad(x)−1(K) ⊂ K′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  Since  Ad(w)δ(K) = K, we have Ad(w′)δ(K1) = K1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Set δ′ = Ad( ˙w′) ◦ δ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  Then LK1 is a δ′-stable Levi subgroup and LK′ ∩PK1 is a δ′-stable par-  abolic subgroup of LK′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' The functor Ind  (LK′,δ′)  (LK1, ˙u) in Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='3 in this  case is the Harish-Chandra induction functor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  In this case, the functors f J,w  J′,w′ is just the Harish-Chandra induction  functor, composed with the conjugation by ˙x−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Generalization to loop groups.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='2 holds not only  for Weyl groups but also for arbitrary Coxeter groups.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' The same proof  works in such generality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' In particular, Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='2 holds for any aﬃne  Weyl group together with a length-preserving automorphism on it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  Let k be an algebraically closed ﬁeld and F = k((ǫ)) be the ﬁeld  of the formal Laurent series.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Let G be a connected reductive group  over F and G = G(F).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Let I be an Iwahori subgroup of G and ˜W  be the Iwahori-Weyl group of G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Let P ⊃ I be a parahoric subgroup.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  It is a pro-algebraic group.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Let UP be the pro-unipotent radical of P  and L ∼= P/UP be its reductive quotient.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' In [9], Lusztig introduced  18  XUHUA HE  the aﬃne analogy of the parabolic character sheaves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' They are certain  simple perverse sheaves on the ind-stack UP \\G/UP  ∆(L)  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  Note that the Iwahori-Weyl group ˜W is not a Coxeter group in gen-  eral, but a quasi-Coxeter group.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Namely, let G0 be the subgroup of  G generated by all the parahoric subgroups.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' The Iwahori-Weyl group  of G0 is an aﬃne Weyl group Wa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' And ˜W = Wa ⋊ Ω, where Ω is the  subgroup of length-zero elements of ˜W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' The conjugation action of any  element in Ω on Wa is a length-preserving automorphism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' We have  UP\\G/UP  ∆(L)  =  �  τ∈Ω  UP\\G0 ˙τ/UP  ∆(L)  ∼=  �  τ∈Ω  UP\\G0/Uδ ˙τ (P )  Adδ ˙τ(L)  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  Here δ ˙τ is the automorphism on G0 given by the conjugation action of  ˙τ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Now Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='3 may be applied to  UP \\G0/Uδ ˙τ (P )  Adδ ˙τ (L)  using Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='2  for the pair (Wa, Ad(τ)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  References  [1] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' B´edard, On the Brauer liftings for modular representations, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Algebra 93  (2) (1985) 332–353.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  [2] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Brou´e and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Michel, Sur certains ´el´ements r´eguliers des groupes de Weyl  et les vari´et´es de Deligne-Lusztig associ´ees, Finite reductive groups (Luminy,  1994), Progr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' 141, 73–139, Birkh¨auser Boston, Boston, MA, 1997.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  [3] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Geck and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Pfeiﬀer, Characters of ﬁnite Coxeter groups and Iwahori-Hecke  algebras, London Mathematical Society Monographs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' New Series, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' 21, The  Clarendon Press Oxford University Press, New York, 2000.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  [4] X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' He, The G-stable pieces of the wonderful compactiﬁcation, Trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Amer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' 359 (2007), no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' 7, 3005–3024.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  [5] X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' He, Minimal length elements in some double cosets of Coxeter groups, Adv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' 215 (2007), 469–503.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  [6] X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' He and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Lusztig, A generalization of Steinberg’s cross-section, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Amer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' 25 (2012), 739-757.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  [7] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Lusztig, Character sheaves on disconnected groups, I, Represent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Theory 7  (2003), 374–403.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  [8] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Lusztig, Parabolic character sheaves, I, Mosc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' 4 (2004), no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' 1,  153–179.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  [9] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Lusztig, Parabolic character sheaves, III, Mosc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' 10 (2010), no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' 3,  603–609.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  [10] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Lusztig, From conjugacy classes in the Weyl group to unipotent classes,  Represent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Theory 15 (2011), 494–530.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  [11] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Li, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Nadler and Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Yun, Functions on the commuting stack via Langlands  duality, arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='02618.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  [12] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' Shoji, Character sheaves and almost characters of reductive groups, I, Adv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' 111 (1995), no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=' 2, 244–313.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  The Institute of Mathematical Sciences and Department of Math-  ematics, The Chinese University of Hong Kong, Shatin, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content=', Hong  Kong SAR, China.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='  Email address: xuhuahe@math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='cuhk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='edu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
+page_content='hk' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/tNE1T4oBgHgl3EQfjgS9/content/2301.03264v1.pdf'}
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+Strange and charm contributions to the HVP from C★
+boundary conditions
+Anian Altherr,𝑎 Lucius Bushnaq,𝑏 Isabel Campos,𝑐 Marco Catillo,𝑎 Alessandro
+Cotellucci,𝑑 Madeleine Dale,𝑑,𝑒, 𝑓 ,𝑔 Patrick Fritzsch,𝑏 Roman Gruber,𝑎 Javad
+Komijani,𝑎 Jens Lücke,𝑑,ℎ Marina Krstić Marinković,𝑎 Soﬁe Martins,𝑖 Agostino
+Patella,𝑑,ℎ Nazario Tantalo𝑒, 𝑓 and Paola Tavella𝑎,∗
+𝑎Institut für Theoretische Physik, ETH Zürich, Wolfgang-Pauli-Str. 27, 8093 Zürich, Switzerland
+𝑏School of Mathematics, Trinity College Dublin, Dublin 2, Ireland
+𝑐Instituto de Física de Cantabria and IFCA-CSIC, Avda. de Los Castros s/n, 39005 Santander, Spain
+𝑑Humboldt Universität zu Berlin, Institut für Physik and IRIS Adlershof, Zum Großen Windkanal 6, 12489
+Berlin, German
+𝑒Università di Roma Tor Vergata, Dip. di Fisica, Via della Ricerca Scientiﬁca 1, 00133 Rome, Italy
+𝑓 INFN, Sezione di Tor Vergata, Via della Ricerca Scientiﬁca 1, 00133 Rome, Italy
+𝑔University of Cyprus, Department of Physics, 1 Panepistimiou Street, 2109 Aglantzia, Nicosia, Cyprus
+ℎDESY, Platanenallee 6, D-15738 Zeuthen, German
+𝑖CP3-Origins & IMADA, University of Southern Denmark, Campusvej 55, 5230 Odense M, Denmark
+E-mail: ptavella@phys.ethz.ch
+∗
+RC
+C
+R
+∗
+collaboration
+We present preliminary results for the determination of the leading strange and charm quark-
+connected contributions to the hadronic vacuum polarization contribution to the muon’s 𝑔 − 2.
+Measurements are performed on the RC★ collaboration’s QCD ensembles, with 3 + 1 ﬂavors of
+𝑂(𝑎) improved Wilson fermions and C★ boundary conditions. The HVP is computed on a single
+value of the lattice spacing and two lattice volumes at unphysical pion mass. In addition, we
+compare the signal-to-noise ratio for diﬀerent lattice discretizations of the vector current.
+The 39th International Symposium on Lattice Field Theory (Lattice2022),
+8-13th August, 2022
+Bonn, Germany
+∗Speaker
+© Copyright owned by the author(s) under the terms of the Creative Commons
+Attribution-NonCommercial-NoDerivatives 4.0 International License (CC BY-NC-ND 4.0).
+https://pos.sissa.it/
+arXiv:2301.04385v1  [hep-lat]  11 Jan 2023
+
+Strange and charm contributions to the HVP from C★ boundary conditions
+Paola Tavella
+1.
+Introduction
+The anomalous magnetic moment of the muon is one of the quantities which is getting a deal
+of attention in relation to new physics searches. The combined result of the BNL’s E821 experiment
+[1] and the ﬁrst run of the E989 experiment at Fermilab [2] shows a precision of 0.35 ppm and a
+tension with the Standard Model’s prediction [3] of 4.2 𝜎, if one does not include recent lattice
+determinations, most notably the result by the BMW collaboration [4]. The next runs of the E989
+experiment and the upcoming experiments at J-PARC [5] and CERN [6] aim to further reduce the
+experimental uncertainty.
+Theoretically, the dominant source of uncertainty is the leading hadronic vacuum polarization.
+The most precise result for 𝑎LO,HVP
+𝜇
+is obtained using the dispersive relations and the experimental
+data for the cross section of 𝑒+𝑒− to hadrons. Currently, the precision of the dispersive approach
+is about 0.6% [3]. Independent results can be obtained using the lattice framework, which does
+not require experimental inputs and has started to produce competitive results for the muon’s 𝑔 − 2.
+The most precise result from lattice simulations is the one from the BMW collaboration, which
+shows a precision of about 0.8% [4]. The target precision on the HVP for the next few years is of
+few per mille. To achieve this precision, it is necessary to include the strong and electromagnetic
+isospin-breaking corrections, which contribute at the percent level.
+In this work, we present preliminary results for the leading connected contributions to HVP
+from strange and charm quarks. This is the ﬁrst and necessary step for a long-term research project
+aiming to evaluate the full HVP diagram, by including the isospin-breaking eﬀects as well as the
+disconnected terms. The novelty of our approach is the use of C★ boundary conditions, which allows
+for deﬁning QED on the lattice with a local and gauge-invariant formulation. The conﬁgurations
+used for this work have been generated by the RC★ collaboration using the openQ*D-1.1 code
+[7]. The lattice setup and the methods for the observable are described in sections 2 and 3. Our
+preliminary results are presented in section 4.
+2.
+Lattice setup
+We perform measurements on two QCD ensembles generated by the RC★ collaboration. The
+conﬁgurations are produced at the SU(3) symmetric point, i.e 𝑚𝑢 = 𝑚𝑑 = 𝑚𝑠 ≃ (𝑚 𝑝ℎ𝑦𝑠
+𝑢
++
+𝑚 𝑝ℎ𝑦𝑠
+𝑑
++ 𝑚 𝑝ℎ𝑦𝑠
+𝑠
+)/3, by using the Lüscher-Weisz action for the SU(3) ﬁeld and 𝑂(𝑎) improved
+Wilson fermions. The ensembles are generated with periodic boundary conditions in time and C★
+boundary conditions in the spatial directions, i.e. all the ﬁelds are periodic up to charge conjugation
+𝑈𝜇(𝑥 + 𝐿𝑘 ˆ𝑘) = 𝑈∗
+𝜇(𝑥),
+𝜓 𝑓 (𝑥 + 𝐿𝑘 ˆ𝑘) = 𝐶−1𝜓
+𝑇
+𝑓 (𝑥),
+𝜓 𝑓 (𝑥 + 𝐿𝑘 ˆ𝑘) = −𝜓𝑇
+𝑓 (𝑥)𝐶.
+(1)
+The action parameters, lattice sizes, and pion masses are shown in Table 1. More details about
+the tuning of the parameters in the simulations, the scale setting, and the calculations of the meson
+masses are given in Ref. [8]. In particular, the values of the lattice spacing in Table 1 are determined
+from the auxiliary scale 𝑡0 with the reference value of the CLS determination (8𝑡0)1/2 = 0.415 fm
+[9]. The two ensembles are generated with the same bare parameters but diﬀerent lattice volumes.
+This gives us the possibility to get an idea about the ﬁnite-volume eﬀects. To obtain the results
+shown in section 4 we use respectively 200 and 108 independent conﬁgurations for the ensembles
+A400a00b324 and B400a00b324.
+2
+
+Strange and charm contributions to the HVP from C★ boundary conditions
+Paola Tavella
+Ensemble
+V
+𝛽
+𝜅𝑢,𝑑,𝑠
+𝜅𝑐
+𝑐sw,SU(3)
+𝑎 [fm]
+𝑚 𝜋± [MeV]
+A400a00b324
+64 × 323
+3.24
+0.1344073
+0.12784
+2.18859
+0.05393(24)
+398.5(4.7)
+B400a00b324
+80 × 483
+3.24
+0.1344073
+0.12784
+2.18859
+0.05400(14)
+401.9(1.4)
+Table 1: Parameters of the ensembles used in this work. The lattice spacings and pion masses have been
+computed in Ref. [8].
+3.
+Methods for the hadronic vacuum polarization
+In the time-momentum representation (TMR) [10], the leading HVP contribution to 𝑎𝜇 =
+(𝑔𝜇 − 2)/2 is given by the convolution
+𝑎HVP
+𝜇
+=
+�𝛼
+𝜋
+�2 ∞
+∑︁
+𝑡=0
+𝐺(𝑡) ˜𝐾(𝑡; 𝑚𝜇),
+(2)
+where 𝐺(𝑡) is the spatially summed correlator of two electromagnetic currents
+𝐺(𝑡) = −1
+3
+∑︁
+𝑘=1,2,3
+∑︁
+�𝑥
+⟨𝑉𝑘(𝑥)𝑉𝑘(0)⟩ ,
+(3)
+and ˜𝐾(𝑡; 𝑚𝜇) is the QED kernel, for which we use the expression in Appendix B in [11]. There are
+two commonly used discretizations of the vector current in lattice QCD: the local vector current
+𝑉𝑙
+𝜇, 𝑓 (𝑥) = ¯𝜓 𝑓 (𝑥)𝛾𝜇𝜓 𝑓 (𝑥),
+(4)
+and the point-split or conserved one deﬁned by
+𝑉𝑐
+𝜇, 𝑓 (𝑥) = 1
+2
+�
+¯𝜓 𝑓 (𝑥 + ˆ𝜇) �1 + 𝛾𝜇
+� 𝑈†
+𝜇(𝑥)𝜓 𝑓 (𝑥) − ¯𝜓 𝑓 (𝑥) �1 − 𝛾𝜇
+� 𝑈𝜇(𝑥)𝜓 𝑓 (𝑥 + ˆ𝜇)
+�
+,
+(5)
+where we use the label 𝑓 to denote the vector current operator of a single ﬂavor. By inserting the
+expression of the current in the expectation value in equation (3) and considering all the possible
+Wick contractions between the ﬁelds, one obtains two diﬀerent types of contributions: the connected
+terms that are ﬂavor diagonal, and the disconnected diagonal and oﬀ-diagonal ( 𝑓 ′ ≠ 𝑓 ) terms,
+⟨𝑉𝑘(𝑥)𝑉𝑘(0)⟩ =
+∑︁
+𝑓
+𝑞2
+𝑓 ×
+𝑓
+𝑓
++
+∑︁
+𝑓 , 𝑓 ′
+𝑞 𝑓 𝑞 𝑓 ′ ×
+𝑓
+𝑓
+𝑓
+𝑓
+𝑓 ′
+𝑓 ′
+.
+(6)
+In the following, we will focus only on the connected terms.
+The local vector current in equation (4) is neither conserved nor improved on the lattice. If we
+consider only the connected contractions, it renormalizes independently for each ﬂavor 𝑓 [12, 13]
+𝑉 𝑅
+𝜇, 𝑓 = 𝑍
+𝑚 𝑓
+𝑉 (𝑉𝑙
+𝜇, 𝑓 + 𝑎𝑐𝑉 𝜕𝜈𝑇𝜇𝜈, 𝑓 ),
+(7)
+where 𝑇𝜇𝜈, 𝑓 = − ¯𝜓 𝑓 1
+2 [𝛾𝜇, 𝛾𝜈]𝜓 𝑓 is the tensor current, 𝑐𝑉 is a constant, and 𝑚 𝑓 is the mass of
+the valence quark with ﬂavor 𝑓 . The current in equation (5) is instead conserved on the lattice
+but still requires 𝑂(𝑎) improvements. In this work, we do not consider any improvements at the
+3
+
+Strange and charm contributions to the HVP from C★ boundary conditions
+Paola Tavella
+0
+5
+10
+15
+20
+25
+30
+t [lattice units]
+10−7
+10−6
+10−5
+10−4
+10−3
+10−2
+10−1
+100
+G(t) [lattice units]
+cc
+cl
+ll
+0
+5
+10
+15
+20
+25
+30
+t [lattice units]
+0.8
+1.0
+1.2
+1.4
+1.6
+1.8
+2.0
+(σi(t)/Gi(t))/(σl(t)/Gl(t))
+cc/ll
+cl/ll
+ll/ll
+Figure 1: Example of comparison of the correlators 𝐺𝑘𝑘 (𝑡), with 𝑘 = 𝑐, 𝑙 (left), and the relative errors
+(right) for the light quark. 𝑐 and 𝑙 denote the conserved and the local discretization of the vector current.
+observable level, thus we neglect the term proportional to the tensor current. In this case, we see
+from equation (7) that the local vector current for a ﬂavor 𝑓 renormalizes multiplicatively through
+the mass-dependent renormalization factor 𝑍
+𝑚 𝑓
+𝑉 . We describe our method to determine 𝑍
+𝑚 𝑓
+𝑉
+in
+section 4.2. The choice of the local or conserved currents at the source and sink points of the quark
+propagator leads to diﬀerent discretizations of the correlator 𝐺(𝑡) in TMR, but share the same
+continuum limit once renormalization constants are taken into account.
+3.1 Signal-to-noise ratio
+Before performing the measurements, we study the eﬀect of the discretization of the current
+on the signal-to-noise ratio of the correlator.
+By using the two expressions of the current in
+equations (4) and (5), it is indeed possible to deﬁne three types of correlator: the local-local (𝑙𝑙),
+the conserved-conserved (𝑐𝑐), and the mixed one (𝑐𝑙). For instance, for the local-local correlator,
+the expression to be evaluated is the following
+𝐺𝑙𝑙
+𝑓 (𝑡)𝑐𝑜𝑛𝑛 =1
+3
+∑︁
+𝑘=1,2,3
+∑︁
+�𝑥
+𝑞2
+𝑓 tr
+�
+𝛾𝑘𝐷−1
+𝑓 (𝑥|0)𝛾𝑘𝐷−1
+𝑓 (0|𝑥)
+�
+,
+(8)
+with 𝐷−1(𝑥|0) being the quark propagator from 0 to 𝑥.
+For these measurements, we use 60
+conﬁgurations and 10 point sources per conﬁguration. The aim is to understand which choice is
+the most convenient in terms of signal-to-noise ratio and computational cost. With the conserved-
+conserved correlator, we do not need to determine the renormalization factor. However, we expect
+to have a noisier result when using the conserved current due to the ﬂuctuations of the gauge ﬁeld.
+Moreover, employing the conserved current both at the sink and source points requires 3 additional
+inversions of the Dirac operator per point source, one for each spatial direction ˆ𝑘 = 1, 2, 3.
+Figure 1 shows the three diﬀerent correlators of the light quark measured on the A400a00b324
+ensemble. The left panel shows the correlators plotted against time, and the right panel illustrates
+the relative statistical noise of 𝐺𝑐𝑙(𝑡) and 𝐺𝑐𝑐(𝑡) compared to the local-local correlator.
+As
+shown, the conserved-local correlator is only slightly (5% to 10%) noisier than the local-local
+one; the conserved-conserved correlator is instead much noisier. By taking into account that the
+4
+
+Strange and charm contributions to the HVP from C★ boundary conditions
+Paola Tavella
+computational cost is even four times larger, the conserved-conserved correlator is not a good choice
+to achieve the overall target precision. The other two correlators are equivalent choices unless the
+uncertainty in 𝑍𝑉 gets signiﬁcant, then the conserved-local correlator has the advantage to be less
+sensitive to the precision of the renormalization factor since it appears only once in this correlator.
+In section 4 we will show results for both local-local and local-conserved correlators, pointing
+out the signiﬁcant diﬀerence in the charm contribution, due to large discretization eﬀects.
+4.
+Strange and charm quark-connected contribution
+4.1 Tuning procedure
+To evaluate the leading order strange and charm quark-connected contribution to HVP, it is
+necessary to perform the continuum limit and the extrapolation to the physical pion mass and take
+into account all the systematics. In this work, we consider only one value for the lattice spacing and
+pion mass and two diﬀerent volumes. Before evaluating the correlator in equation (8), we tune the
+hopping parameters 𝜅 𝑓 of the valence quarks. We choose the value of 𝜅𝑠 and 𝜅𝑐 by matching the
+physical value of the masses of the mesons 𝜙 and 𝐽/𝜓 [14]
+𝑚 𝑝ℎ𝑦𝑠
+𝜙
+= 1019.461(20) MeV,
+𝑚 𝑝ℎ𝑦𝑠
+𝐽/𝜓 = 3096.900(6) MeV
+(9)
+with our lattice results, obtained respectively from the two-point functions of the interpolators
+O𝑠 = ¯𝑠𝛾𝜇𝑠,
+O𝑐 = ¯𝑐𝛾𝜇𝑐.
+(10)
+In this matching procedure we are neglecting the disconnected terms and the QED corrections,
+which enter into the physical masses and are instead missing in our calculations.
+In Tables 2 and 3 we show the diﬀerent choices of 𝜅𝑠/𝑐 and the results for the eﬀective masses
+of the vector mesons 𝑠¯𝑠 and 𝑐 ¯𝑐 for both ensembles.
+𝜅𝑠
+𝑎𝑚𝑉 (𝑠¯𝑠)
+𝑚𝑉 (𝑠¯𝑠) [MeV]
+𝜅𝑐
+𝑎𝑚𝑉 (𝑐 ¯𝑐)
+𝑚𝑉 (𝑐 ¯𝑐) [MeV]
+0.134407
+0.2644(50)
+967(19)
+0.12784
+0.8540(5)
+3125(14)
+0.1343
+0.2731(24)
+999(10)
+0.12794
+0.8463(5)
+3097(14)
+0.13422
+0.2808(22)
+1027(9)
+0.12800
+0.8418(5)
+3080(14)
+Table 2: Ensemble A400a00b324: mass of the vector mesons for several choices of the hopping parameters
+in the valence sector. Values in MeV are obtained by using the reference value (8𝑡0)1/2 = 0.415 fm [8].
+𝜅𝑠
+𝑎𝑚𝑉 (𝑠¯𝑠)
+𝑚𝑉 (𝑠¯𝑠) [MeV]
+𝜅𝑐
+𝑎𝑚𝑉 (𝑐 ¯𝑐)
+𝑚𝑉 (𝑐 ¯𝑐) [MeV]
+0.134407
+0.2522(33)
+923(13)
+0.12784
+0.8536(7)
+3123(14)
+0.134220
+0.2715(22)
+993(9)
+0.12794
+0.8458(9)
+3095(14)
+0.134152
+0.2794(19)
+1022(8)
+Table 3: Ensemble B400a00b324: mass of the vector mesons for several choices of the hopping parameters
+in the valence sector. Values in MeV are obtained by using the reference value (8𝑡0)1/2 = 0.415 fm [8].
+5
+
+Strange and charm contributions to the HVP from C★ boundary conditions
+Paola Tavella
+7.46269
+7.45156
+7.44048
+1
+s
+0.24
+0.26
+0.28
+0.30
+0.32
+amV(ss)
+amphys
+amphys error band
+Lin. interp.
+data 80x483
+data 64x323
+7.82228
+7.81616
+1
+c
+0.840
+0.845
+0.850
+0.855
+0.860
+amV(cc)
+amphys
+J/
+amphys
+J/
+ error band
+Lin. interp.
+data 80x483
+data 64x323
+Figure 2: Masses of the vector mesons 𝑠¯𝑠 (left) and 𝑐 ¯𝑐 (right) as functions of the inverse of the hopping
+parameter. The purple bands and their central value represent the physical mass of the mesons 𝜙 (left) and
+𝐽/𝜓 (right) converted to lattice units.
+We plot the masses of the vector mesons as a function of the inverse of the corresponding
+hopping parameters 𝜅−1
+𝑠/𝑐, which are linear in the bare masses of the valence quarks 𝑠 and 𝑐. In Fig.
+2 we show this dependence for both strange (left) and charm (right) quarks. The purple bands in
+the plots correspond to the physical masses in equation (9) converted to lattice units.
+4.2 Renormalization constants
+Evaluating 𝑎𝐻𝑉 𝑃,𝑠/𝑐
+𝜇
+from the local-local or conserved-local correlators requires determining
+the renormalization factor 𝑍
+𝑚 𝑓
+𝑉
+and the improvement coeﬃcient introduced in (7). In this work, we
+do not consider any improvement terms and evaluate the mass-dependent renormalization factor
+𝑍
+𝑚 𝑓
+𝑉
+of the local current from the ratio [15]
+𝑅(𝑡) =
+�
+�𝑥,𝑘
+�
+𝑉𝑐
+𝑘, 𝑓 (𝑥)𝑉𝑙
+𝑘, 𝑓 (0)
+�
+�
+�𝑥,𝑘
+�
+𝑉𝑙
+𝑘, 𝑓 (𝑥)𝑉𝑙
+𝑘, 𝑓 (0)
+� .
+(11)
+When 𝑡 is small, the quantity is aﬀected by the diﬀerent discretization eﬀects of the two currents.
+At large time, 𝑅(𝑡) saturates and we can determine 𝑍
+𝑚 𝑓
+𝑉
+by ﬁtting the plateau region to a constant.
+An example of such a ﬁt is shown in Fig. 3. We applied the same method for both ensembles and
+for both 𝑍𝑚𝑠
+𝑉
+and 𝑍𝑚𝑐
+𝑉 .
+In Table 4 we show the ﬁt ranges and the values obtained for 𝑍
+𝑚𝑠/𝑐
+𝑉
+for the tuned hopping
+parameters 𝜅𝑡𝑢𝑛
+𝑠/𝑐 . The errors are determined with the bootstrap procedure.
+Ensemble
+ﬁt range
+𝑍𝑚𝑠
+𝑉
+ﬁt range
+𝑍𝑚𝑐
+𝑉
+A400a00b324
+[15,24]
+0.6712(7)
+[24,30]
+0.6066(2)
+B400a00b324
+[15,24]
+0.6707(5)
+[23,31]
+0.6066(4)
+Table 4: Mass-dependent renormalization factor obtained from the ratio method deﬁned in Eq. (11).
+6
+
+Strange and charm contributions to the HVP from C★ boundary conditions
+Paola Tavella
+5
+10
+15
+20
+25
+30
+t [lattice units]
+0.64
+0.65
+0.66
+0.67
+0.68
+0.69
+0.70
+0.71
+Glc(t)/Gll(t)
+ﬁt range
+ZV = 0.6712 ± 0.0007
+data
+Figure 3: Determination of the renormalization constant 𝑍𝑚𝑠
+𝑉 for the local vector current with 𝜅𝑡𝑢𝑛
+𝑠
+= 0.13422
+on the A400a00b324 ensemble.
+4.3 Results
+The evaluation of the leading HVP contribution to 𝑎𝜇 requires an integration over the euclidean
+time
+𝑎HVP, 𝑓
+𝜇
+=
+�𝛼
+𝜋
+�2 ∞
+∑︁
+𝑡=0
+𝐺 𝑓 (𝑡) ˜𝐾(𝑡; 𝑚𝜇).
+(12)
+One of the problems related to this task is that the signal deteriorates with the lattice time 𝑡, due to
+the exponentially increasing errors of the correlator. Another related issue comes from the ﬁnite
+size of the box: the integration domain is indeed restricted to [0,𝑇/2], then we have to extrapolate
+the correlator to inﬁnite time. In addition, the correlator is aﬀected by ﬁnite-volume eﬀects (FVE)
+due to the ﬁnite temporal (𝑇) and spatial (𝐿) extents.
+Concerning the ﬁnite-volume eﬀects, it has been found [16] that for given 𝐿 the leading ﬁnite-𝐿
+corrections are the exponentials 𝑒−𝑚𝜋 𝐿, 𝑒−𝑚𝜋
+√
+2𝐿 and 𝑒−𝑚𝜋
+√
+3𝐿. Similarly, the leading contribution
+arising from ﬁnite 𝑇 is 𝑒−𝑚𝜋𝑇 . As a consequence, the ﬁnite-𝑇 eﬀects are higher order corrections
+since usually in the simulations 𝑇 = 2𝐿. These results have been derived for a periodic torus in four
+dimensions and are aﬀected by the choice of the boundary conditions. In our setup, the boundary
+condition in the time direction is periodic, then the results for ﬁnite-𝑇 corrections found in Ref. [16]
+still apply. However, we use C★ boundary conditions in all three spatial directions, which means
+that the ﬁnite-𝐿 corrections are in general diﬀerent. Some studies have shown that in pure QCD C★
+boundary conditions lead to small improvements for the FVE, with a leading correction 𝑒−𝑚𝜋
+√
+2𝐿
+[17]. A detailed numerical study of the ﬁnite-volume eﬀects for ensembles with C★ boundary
+conditions will be carried out in future work. In this work, we make a direct comparison of the
+results for the integrand 𝐺(𝑡) ˜𝐾(𝑡, 𝑚𝜇) and 𝑎LO,HVP
+𝜇
+on the two available QCD ensembles.
+To control the large-time behavior of the correlator, we use the following quantity
+𝐺constructed(𝑡) =
+�
+𝐺(𝑡)
+(𝑡 ≤ 𝑡0,cut)
+𝐺1-exp(𝑡)
+(𝑡0 > 𝑡0,cut)
+(13)
+7
+
+Strange and charm contributions to the HVP from C★ boundary conditions
+Paola Tavella
+0
+10
+20
+30
+40
+t [lattice units]
+0.0
+0.5
+1.0
+1.5
+2.0
+2.5
+( / )2 × G(t)K(t; m )
+1e
+10
+Strange quark
+cubic-spline
+1
+exp
+1
+exp
+data B400
+data A400
+0
+5
+10
+15
+20
+25
+30
+t [lattice units]
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+1.2
+1.4
+( / )2 × G(t)K(t; m )
+1e
+10
+Charm quark
+cubic-spline
+data B400
+data A400
+Figure 4: Comparison of the integrands for the strange (left) and charm (right) contributions between the two
+ensembles. The tail of the integrands for the strange contribution is approximated by a single exponential.
+where 𝑡0,cut is a properly chosen cut-oﬀ and 𝐺1-exp(𝑡) denotes the exponential extrapolation of the
+correlator at large time
+𝐴 exp(−𝑡 · 𝑚eﬀ).
+(14)
+The two parameters 𝑚eﬀ and 𝐴 are the eﬀective mass and the amplitude obtained through a ﬁt
+procedure to the correlator. For the masses, we use the results reported in Tables 2 and 3 for the
+tuned hopping parameters. The parametrization with a single-exponential is a crude approximation
+that introduces some systematics since we are neglecting the excited states contributing to the
+correlator. We plan to use a more accurate model for the tail of the correlator in future works.
+The plots in Fig. 4 show the integrands both for the charm and strange quarks contributions
+and the two ensembles. The lattice data for the charm contribution are suﬃciently precise and do
+not require any extrapolation or improvement. In the case of the strange contributions, the tail of the
+integrand is approximated as described above. The results of the integration are listed in Table 5.
+We estimate 𝑎LO,HVP
+𝜇
+using the two diﬀerent discretizations of the correlator: conserved-local and
+local-local. The strange contribution is not aﬀected by the choice of the correlator, the results are
+indeed compatible with the current uncertainties for both ensembles. By contrast, the contribution
+from the charm quark is particularly sensitive to the choice of discretization. The ﬁnite-size eﬀects
+are negligible for the charm quark contribution and lead instead to a diﬀerence of about 2𝜎 for the
+strange quark.
+Ensemble
+Type
+𝑎𝑠
+𝜇 × 10−10
+𝑎𝑐
+𝜇 × 10−10
+A400a00b324
+𝑙𝑙
+46.7(7)
+7.83(8)
+𝑐𝑙
+46.2(7)
+6.18(7)
+B400a00b324
+𝑙𝑙
+48.5(7)
+7.81(9)
+𝑐𝑙
+48.0(7)
+6.16(7)
+Table 5: Results for 𝑎𝑠,𝑐
+𝜇
+in units of 10−10 determined using the TMR and two diﬀerent discretizations of the
+observable: local-local and conserved-local.
+8
+
+Strange and charm contributions to the HVP from C★ boundary conditions
+Paola Tavella
+4.4 Partial errors budget
+The errors in Table 5 are the quadratic sum of the statistical and part of the systematic errors
+as follows. The uncertainties taken into account are the statistical errors from the correlators, the
+lattice spacing and 𝑍𝑉 , and the systematics from the choices of the cut-oﬀ (for the strange quark)
+and the ﬁt range used to determine 𝐴 and 𝑚eﬀ. The statistical error is determined by using the
+bootstrap method. Since 𝑍𝑉 appears as a multiplicative factor in front of the whole expression,
+we employ the standard error propagation for it. The lattice spacing’s values are determined by
+using the reference scale (8𝑡0)1/2 = 0.415 fm as an absolute value, without taking into account
+the systematics coming from the uncertainty on this scale. Thus, our current error on 𝑎 is only a
+statistical partial uncertainty. The dependence on the lattice spacing is in the QED kernel ˜𝐾(𝑡, 𝑚𝜇):
+we numerically propagate the partial error 𝛿𝑎 by repeating the evaluation of 𝑎𝜇 for 𝑁 values of
+the lattice spacing drawn from a normal distribution N (𝑎, 𝛿𝑎). We use at least 𝑁 = 100 for each
+result. Finally, we repeat the calculation for several values of the ﬁt range and the cut-oﬀ and apply
+a weighted averaging procedure to get the total systematics.
+We remark that there are still several unaccounted uncertainties. We are currently missing the
+systematics introduced by the single-exponential extrapolation of the correlator and by the use of
+the reference scale 𝑡0 without an error for the determination of the lattice spacing. In this work we
+did not perform a quantitative numerical study of the ﬁnite-size eﬀects and we measured at one
+value of the lattice spacing and pion mass, thus we have not performed yet an extrapolation of the
+results to the continuum and physical point.
+5.
+Conclusions and outlooks
+We have measured the connected contribution to the leading hadronic vacuum polarization from
+strange and charm quarks, in a setup with C★ boundary conditions in the three spatial directions.
+We performed the analysis on two ensembles with diﬀerent volumes, indicating that the ﬁnite-size
+eﬀects are under control. As expected, we ﬁnd that the charm contribution is considerably aﬀected
+by the choice of the correlator, due to the sensitivity to the discretization eﬀects. In addition, we
+have shown that a more precise determination of the lattice spacing is needed to reach the target
+precision. Our plans for future works include the evaluation of the isospin-breaking eﬀects as well
+as the disconnected terms, and a quantitative study of the ﬁnite-size eﬀects.
+Acknowledgments
+We acknowledge access to Piz Daint at the Swiss National Supercomputing Centre, Switzerland
+under the ETHZ’s share with the project IDs s1101, eth8 and go22. Financial support by the SNSF
+(Project No. 200021_200866) is gratefully acknowledged. L.B., S.M., and M.K.M received funding
+from the European Union’s Horizon 2020 research and innovation programme under the Marie
+Skłodowska-Curie grant agreement No. 813942. M.D.received funding from the European Union’s
+Horizon 2020 research and innovation programme under grant agreement No. 765048. A.C.’s and
+J.L.’s research is funded by the Deutsche Forschungsgemeinschaft Project No. 417533893/ GRK-
+2575 “Rethinking Quantum Field Theory”.
+9
+
+Strange and charm contributions to the HVP from C★ boundary conditions
+Paola Tavella
+References
+[1] Muon g-2 Collaboration collaboration, Final report of the E821 muon anomalous
+magnetic moment measurement at BNL, Physical Review D 73 (2006) 072003.
+[2] Muon 𝑔 − 2 Collaboration collaboration, Measurement of the positive muon anomalous
+magnetic moment to 0.46 ppm, Physycal Review Letters 126 (2021) 141801.
+[3] T. Aoyama et al., The anomalous magnetic moment of the muon in the Standard Model,
+Physics Reports 887 (2020) 1.
+[4] Sz. Borsanyi et al, Leading hadronic contribution to the muon magnetic moment from lattice
+QCD, Nature 593 (2021) 51.
+[5] M. Abe et al., A new approach for measuring the muon anomalous magnetic moment and
+electric dipole moment, Progress of Theoretical and Experimental Physics 2019 (2019) .
+[6] G. Abbiendi et al., Measuring the leading hadronic contribution to the muon g-2 via 𝜇𝑒
+scattering, The European Physical Journal C 77 (2017) .
+[7] RC* collaboration, openQ*D code: a versatile tool for QCD+QED simulations, The
+European Physical Journal C 80 (2020) 195.
+[8] L. Bushnaq et al., First results on QCD+QED with C* boundary conditions, 2209.13183.
+[9] M. Bruno, T. Korzec and S. Schaefer, Setting the scale for the CLS 2 + 1 ﬂavor ensembles,
+Physical Review D 95 (2017) 074504.
+[10] D. Bernecker and H. B. Meyer, Vector correlators in lattice QCD: Methods and applications,
+The European Physical Journal A 47 (2011) .
+[11] M. Della Morte et al., The hadronic vacuum polarization contribution to the muon g - 2 from
+lattice QCD, Journal of High Energy Physics 2017 (2017) .
+[12] T. Bhattacharya et al., Improved bilinears in lattice QCD with non degenerate quarks,
+Physical Review D 73 (2006) .
+[13] A. Gérardin et al, Leading hadronic contribution to (𝑔 − 2)𝜇 from lattice QCD with
+𝑁 𝑓 = 3 + 1 of 𝑂(𝑎) improved wilson quarks, Physical Review D 100 (2019) .
+[14] Particle Data Group collaboration, Review of Particle Physics, Progress of Theoretical
+and Experimental Physics 2022 (2022) 083C01.
+[15] P. Boyle et al., Isospin breaking corrections to meson masses and the hadronic vacuum
+polarization: a comparative study, Journal of High Energy Physics 2017 (2017) .
+[16] M. T. Hansen and A. Patella, Finite-volume and thermal eﬀects in the leading-HVP
+contribution to muonic (g - 2), Journal of High Energy Physics 2020 (2020) .
+[17] S. Martins, Finite-size eﬀects of the Hadronic Vacuum Polarization contribution to the muon
+(g - 2) with C* boundary conditions, Talk at Lattice 2022.
+10
+
diff --git a/udE3T4oBgHgl3EQfNgn9/content/tmp_files/load_file.txt b/udE3T4oBgHgl3EQfNgn9/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..6ef5b321d2063c9935231e372441c1a5e91dd239
--- /dev/null
+++ b/udE3T4oBgHgl3EQfNgn9/content/tmp_files/load_file.txt
@@ -0,0 +1,343 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf,len=342
+page_content='Strange and charm contributions to the HVP from C★  boundary conditions  Anian Altherr,𝑎 Lucius Bushnaq,𝑏 Isabel Campos,𝑐 Marco Catillo,𝑎 Alessandro  Cotellucci,𝑑 Madeleine Dale,𝑑,𝑒, 𝑓 ,𝑔 Patrick Fritzsch,𝑏 Roman Gruber,𝑎 Javad  Komijani,𝑎 Jens Lücke,𝑑,ℎ Marina Krstić Marinković,𝑎 Soﬁe Martins,𝑖 Agostino  Patella,𝑑,ℎ Nazario Tantalo𝑒, 𝑓 and Paola Tavella𝑎,∗  𝑎Institut für Theoretische Physik, ETH Zürich, Wolfgang-Pauli-Str.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content=' 27, 8093 Zürich, Switzerland  𝑏School of Mathematics, Trinity College Dublin, Dublin 2, Ireland  𝑐Instituto de Física de Cantabria and IFCA-CSIC, Avda.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content=' de Los Castros s/n, 39005 Santander, Spain  𝑑Humboldt Universität zu Berlin, Institut für Physik and IRIS Adlershof, Zum Großen Windkanal 6, 12489  Berlin, German  𝑒Università di Roma Tor Vergata, Dip.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content=' di Fisica, Via della Ricerca Scientiﬁca 1, 00133 Rome, Italy  𝑓 INFN, Sezione di Tor Vergata, Via della Ricerca Scientiﬁca 1, 00133 Rome, Italy  𝑔University of Cyprus, Department of Physics, 1 Panepistimiou Street, 2109 Aglantzia, Nicosia, Cyprus  ℎDESY, Platanenallee 6, D-15738 Zeuthen, German  𝑖CP3-Origins & IMADA, University of Southern Denmark, Campusvej 55, 5230 Odense M, Denmark  E-mail: ptavella@phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='ethz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='ch  ∗  RC  C  R  ∗  collaboration  We present preliminary results for the determination of the leading strange and charm quark-  connected contributions to the hadronic vacuum polarization contribution to the muon’s 𝑔 − 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='  Measurements are performed on the RC★ collaboration’s QCD ensembles, with 3 + 1 ﬂavors of  𝑂(𝑎) improved Wilson fermions and C★ boundary conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content=' The HVP is computed on a single  value of the lattice spacing and two lattice volumes at unphysical pion mass.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content=' In addition, we  compare the signal-to-noise ratio for diﬀerent lattice discretizations of the vector current.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='  The 39th International Symposium on Lattice Field Theory (Lattice2022),  8-13th August, 2022  Bonn, Germany  ∗Speaker  © Copyright owned by the author(s) under the terms of the Creative Commons  Attribution-NonCommercial-NoDerivatives 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='0 International License (CC BY-NC-ND 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='  https://pos.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='sissa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='it/  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='04385v1  [hep-lat]  11 Jan 2023  Strange and charm contributions to the HVP from C★ boundary conditions  Paola Tavella  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='  Introduction  The anomalous magnetic moment of the muon is one of the quantities which is getting a deal  of attention in relation to new physics searches.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content=' The combined result of the BNL’s E821 experiment  [1] and the ﬁrst run of the E989 experiment at Fermilab [2] shows a precision of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='35 ppm and a  tension with the Standard Model’s prediction [3] of 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='2 𝜎, if one does not include recent lattice  determinations, most notably the result by the BMW collaboration [4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content=' The next runs of the E989  experiment and the upcoming experiments at J-PARC [5] and CERN [6] aim to further reduce the  experimental uncertainty.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='  Theoretically, the dominant source of uncertainty is the leading hadronic vacuum polarization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='  The most precise result for 𝑎LO,HVP  𝜇  is obtained using the dispersive relations and the experimental  data for the cross section of 𝑒+𝑒− to hadrons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content=' Currently, the precision of the dispersive approach  is about 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='6% [3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content=' Independent results can be obtained using the lattice framework, which does  not require experimental inputs and has started to produce competitive results for the muon’s 𝑔 − 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='  The most precise result from lattice simulations is the one from the BMW collaboration, which  shows a precision of about 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='8% [4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content=' The target precision on the HVP for the next few years is of  few per mille.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content=' To achieve this precision, it is necessary to include the strong and electromagnetic  isospin-breaking corrections, which contribute at the percent level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='  In this work, we present preliminary results for the leading connected contributions to HVP  from strange and charm quarks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content=' This is the ﬁrst and necessary step for a long-term research project  aiming to evaluate the full HVP diagram, by including the isospin-breaking eﬀects as well as the  disconnected terms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content=' The novelty of our approach is the use of C★ boundary conditions, which allows  for deﬁning QED on the lattice with a local and gauge-invariant formulation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content=' The conﬁgurations  used for this work have been generated by the RC★ collaboration using the openQ*D-1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='1 code  [7].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content=' The lattice setup and the methods for the observable are described in sections 2 and 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content=' Our  preliminary results are presented in section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='  Lattice setup  We perform measurements on two QCD ensembles generated by the RC★ collaboration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content=' The  conﬁgurations are produced at the SU(3) symmetric point, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='e 𝑚𝑢 = 𝑚𝑑 = 𝑚𝑠 ≃ (𝑚 𝑝ℎ𝑦𝑠  𝑢  +  𝑚 𝑝ℎ𝑦𝑠  𝑑  + 𝑚 𝑝ℎ𝑦𝑠  𝑠  )/3, by using the Lüscher-Weisz action for the SU(3) ﬁeld and 𝑂(𝑎) improved  Wilson fermions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content=' The ensembles are generated with periodic boundary conditions in time and C★  boundary conditions in the spatial directions, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content=' all the ﬁelds are periodic up to charge conjugation  𝑈𝜇(𝑥 + 𝐿𝑘 ˆ𝑘) = 𝑈∗  𝜇(𝑥),  𝜓 𝑓 (𝑥 + 𝐿𝑘 ˆ𝑘) = 𝐶−1𝜓  𝑇  𝑓 (𝑥),  𝜓 𝑓 (𝑥 + 𝐿𝑘 ˆ𝑘) = −𝜓𝑇  𝑓 (𝑥)𝐶.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='  (1)  The action parameters, lattice sizes, and pion masses are shown in Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content=' More details about  the tuning of the parameters in the simulations, the scale setting, and the calculations of the meson  masses are given in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content=' [8].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content=' In particular, the values of the lattice spacing in Table 1 are determined  from the auxiliary scale 𝑡0 with the reference value of the CLS determination (8𝑡0)1/2 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='415 fm  [9].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content=' The two ensembles are generated with the same bare parameters but diﬀerent lattice volumes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='  This gives us the possibility to get an idea about the ﬁnite-volume eﬀects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content=' To obtain the results  shown in section 4 we use respectively 200 and 108 independent conﬁgurations for the ensembles  A400a00b324 and B400a00b324.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='  2  Strange and charm contributions to the HVP from C★ boundary conditions  Paola Tavella  Ensemble  V  𝛽  𝜅𝑢,𝑑,𝑠  𝜅𝑐  𝑐sw,SU(3)  𝑎 [fm]  𝑚 𝜋± [MeV]  A400a00b324  64 × 323  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='24  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='1344073  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='12784  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='18859  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='05393(24)  398.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='5(4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='7)  B400a00b324  80 × 483  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='24  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='1344073  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='12784  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='18859  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='05400(14)  401.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='9(1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='4)  Table 1: Parameters of the ensembles used in this work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content=' The lattice spacings and pion masses have been  computed in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content=' [8].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='  Methods for the hadronic vacuum polarization  In the time-momentum representation (TMR) [10], the leading HVP contribution to 𝑎𝜇 =  (𝑔𝜇 − 2)/2 is given by the convolution  𝑎HVP  𝜇  =  �𝛼  𝜋  �2 ∞  ∑︁  𝑡=0  𝐺(𝑡) ˜𝐾(𝑡;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content=' 𝑚𝜇),  (2)  where 𝐺(𝑡) is the spatially summed correlator of two electromagnetic currents  𝐺(𝑡) = −1  3  ∑︁  𝑘=1,2,3  ∑︁  �𝑥  ⟨𝑉𝑘(𝑥)𝑉𝑘(0)⟩ ,  (3)  and ˜𝐾(𝑡;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content=' 𝑚𝜇) is the QED kernel, for which we use the expression in Appendix B in [11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content=' There are  two commonly used discretizations of the vector current in lattice QCD: the local vector current  𝑉𝑙  𝜇, 𝑓 (𝑥) = ¯𝜓 𝑓 (𝑥)𝛾𝜇𝜓 𝑓 (𝑥),  (4)  and the point-split or conserved one deﬁned by  𝑉𝑐  𝜇, 𝑓 (𝑥) = 1  2  �  ¯𝜓 𝑓 (𝑥 + ˆ𝜇) �1 + 𝛾𝜇  � 𝑈†  𝜇(𝑥)𝜓 𝑓 (𝑥) − ¯𝜓 𝑓 (𝑥) �1 − 𝛾𝜇  � 𝑈𝜇(𝑥)𝜓 𝑓 (𝑥 + ˆ𝜇)  �  ,  (5)  where we use the label 𝑓 to denote the vector current operator of a single ﬂavor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content=' By inserting the  expression of the current in the expectation value in equation (3) and considering all the possible  Wick contractions between the ﬁelds, one obtains two diﬀerent types of contributions: the connected  terms that are ﬂavor diagonal, and the disconnected diagonal and oﬀ-diagonal ( 𝑓 ′ ≠ 𝑓 ) terms,  ⟨𝑉𝑘(𝑥)𝑉𝑘(0)⟩ =  ∑︁  𝑓  𝑞2  𝑓 ×  𝑓  𝑓  +  ∑︁  𝑓 , 𝑓 ′  𝑞 𝑓 𝑞 𝑓 ′ ×  𝑓  𝑓  𝑓  𝑓  𝑓 ′  𝑓 ′  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='  (6)  In the following, we will focus only on the connected terms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='  The local vector current in equation (4) is neither conserved nor improved on the lattice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content=' If we  consider only the connected contractions, it renormalizes independently for each ﬂavor 𝑓 [12, 13]  𝑉 𝑅  𝜇, 𝑓 = 𝑍  𝑚 𝑓  𝑉 (𝑉𝑙  𝜇, 𝑓 + 𝑎𝑐𝑉 𝜕𝜈𝑇𝜇𝜈, 𝑓 ),  (7)  where 𝑇𝜇𝜈, 𝑓 = − ¯𝜓 𝑓 1  2 [𝛾𝜇, 𝛾𝜈]𝜓 𝑓 is the tensor current, 𝑐𝑉 is a constant, and 𝑚 𝑓 is the mass of  the valence quark with ﬂavor 𝑓 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content=' The current in equation (5) is instead conserved on the lattice  but still requires 𝑂(𝑎) improvements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content=' In this work, we do not consider any improvements at the  3  Strange and charm contributions to the HVP from C★ boundary conditions  Paola Tavella  0  5  10  15  20  25  30  t [lattice units]  10−7  10−6  10−5  10−4  10−3  10−2  10−1  100  G(t) [lattice units]  cc  cl  ll  0  5  10  15  20  25  30  t [lattice units]  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='2  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='4  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='6  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='8  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='0  (σi(t)/Gi(t))/(σl(t)/Gl(t))  cc/ll  cl/ll  ll/ll  Figure 1: Example of comparison of the correlators 𝐺𝑘𝑘 (𝑡), with 𝑘 = 𝑐, 𝑙 (left), and the relative errors  (right) for the light quark.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content=' 𝑐 and 𝑙 denote the conserved and the local discretization of the vector current.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='  observable level, thus we neglect the term proportional to the tensor current.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content=' In this case, we see  from equation (7) that the local vector current for a ﬂavor 𝑓 renormalizes multiplicatively through  the mass-dependent renormalization factor 𝑍  𝑚 𝑓  𝑉 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content=' We describe our method to determine 𝑍  𝑚 𝑓  𝑉  in  section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content=' The choice of the local or conserved currents at the source and sink points of the quark  propagator leads to diﬀerent discretizations of the correlator 𝐺(𝑡) in TMR, but share the same  continuum limit once renormalization constants are taken into account.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='1 Signal-to-noise ratio  Before performing the measurements, we study the eﬀect of the discretization of the current  on the signal-to-noise ratio of the correlator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='  By using the two expressions of the current in  equations (4) and (5), it is indeed possible to deﬁne three types of correlator: the local-local (𝑙𝑙),  the conserved-conserved (𝑐𝑐), and the mixed one (𝑐𝑙).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content=' For instance, for the local-local correlator,  the expression to be evaluated is the following  𝐺𝑙𝑙  𝑓 (𝑡)𝑐𝑜𝑛𝑛 =1  3  ∑︁  𝑘=1,2,3  ∑︁  �𝑥  𝑞2  𝑓 tr  �  𝛾𝑘𝐷−1  𝑓 (𝑥|0)𝛾𝑘𝐷−1  𝑓 (0|𝑥)  �  ,  (8)  with 𝐷−1(𝑥|0) being the quark propagator from 0 to 𝑥.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='  For these measurements, we use 60  conﬁgurations and 10 point sources per conﬁguration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content=' The aim is to understand which choice is  the most convenient in terms of signal-to-noise ratio and computational cost.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content=' With the conserved-  conserved correlator, we do not need to determine the renormalization factor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content=' However, we expect  to have a noisier result when using the conserved current due to the ﬂuctuations of the gauge ﬁeld.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='  Moreover, employing the conserved current both at the sink and source points requires 3 additional  inversions of the Dirac operator per point source, one for each spatial direction ˆ𝑘 = 1, 2, 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='  Figure 1 shows the three diﬀerent correlators of the light quark measured on the A400a00b324  ensemble.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content=' The left panel shows the correlators plotted against time, and the right panel illustrates  the relative statistical noise of 𝐺𝑐𝑙(𝑡) and 𝐺𝑐𝑐(𝑡) compared to the local-local correlator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='  As  shown, the conserved-local correlator is only slightly (5% to 10%) noisier than the local-local  one;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content=' the conserved-conserved correlator is instead much noisier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content=' By taking into account that the  4  Strange and charm contributions to the HVP from C★ boundary conditions  Paola Tavella  computational cost is even four times larger, the conserved-conserved correlator is not a good choice  to achieve the overall target precision.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content=' The other two correlators are equivalent choices unless the  uncertainty in 𝑍𝑉 gets signiﬁcant, then the conserved-local correlator has the advantage to be less  sensitive to the precision of the renormalization factor since it appears only once in this correlator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='  In section 4 we will show results for both local-local and local-conserved correlators, pointing  out the signiﬁcant diﬀerence in the charm contribution, due to large discretization eﬀects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='  Strange and charm quark-connected contribution  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='1 Tuning procedure  To evaluate the leading order strange and charm quark-connected contribution to HVP, it is  necessary to perform the continuum limit and the extrapolation to the physical pion mass and take  into account all the systematics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content=' In this work, we consider only one value for the lattice spacing and  pion mass and two diﬀerent volumes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content=' Before evaluating the correlator in equation (8), we tune the  hopping parameters 𝜅 𝑓 of the valence quarks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content=' We choose the value of 𝜅𝑠 and 𝜅𝑐 by matching the  physical value of the masses of the mesons 𝜙 and 𝐽/𝜓 [14]  𝑚 𝑝ℎ𝑦𝑠  𝜙  = 1019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='461(20) MeV,  𝑚 𝑝ℎ𝑦𝑠  𝐽/𝜓 = 3096.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='900(6) MeV  (9)  with our lattice results, obtained respectively from the two-point functions of the interpolators  O𝑠 = ¯𝑠𝛾𝜇𝑠,  O𝑐 = ¯𝑐𝛾𝜇𝑐.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='  (10)  In this matching procedure we are neglecting the disconnected terms and the QED corrections,  which enter into the physical masses and are instead missing in our calculations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='  In Tables 2 and 3 we show the diﬀerent choices of 𝜅𝑠/𝑐 and the results for the eﬀective masses  of the vector mesons 𝑠¯𝑠 and 𝑐 ¯𝑐 for both ensembles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='  𝜅𝑠  𝑎𝑚𝑉 (𝑠¯𝑠)  𝑚𝑉 (𝑠¯𝑠) [MeV]  𝜅𝑐  𝑎𝑚𝑉 (𝑐 ¯𝑐)  𝑚𝑉 (𝑐 ¯𝑐) [MeV]  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='134407  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='2644(50)  967(19)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
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+page_content='2731(24)  999(10)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
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+page_content='8463(5)  3097(14)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
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+page_content='2808(22)  1027(9)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='12800  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='8418(5)  3080(14)  Table 2: Ensemble A400a00b324: mass of the vector mesons for several choices of the hopping parameters  in the valence sector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content=' Values in MeV are obtained by using the reference value (8𝑡0)1/2 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='415 fm [8].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='  𝜅𝑠  𝑎𝑚𝑉 (𝑠¯𝑠)  𝑚𝑉 (𝑠¯𝑠) [MeV]  𝜅𝑐  𝑎𝑚𝑉 (𝑐 ¯𝑐)  𝑚𝑉 (𝑐 ¯𝑐) [MeV]  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
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+page_content='2715(22)  993(9)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
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+page_content='8458(9)  3095(14)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
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+page_content='2794(19)  1022(8)  Table 3: Ensemble B400a00b324: mass of the vector mesons for several choices of the hopping parameters  in the valence sector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content=' Values in MeV are obtained by using the reference value (8𝑡0)1/2 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='415 fm [8].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='  5  Strange and charm contributions to the HVP from C★ boundary conditions  Paola Tavella  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='46269  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='45156  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='44048  1  s  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
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+page_content='32  amV(ss)  amphys  amphys error band  Lin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content=' interp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='  data 80x483  data 64x323  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='82228  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='81616  1  c  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
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+page_content='860  amV(cc)  amphys  J/  amphys  J/  error band  Lin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content=' interp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='  data 80x483  data 64x323  Figure 2: Masses of the vector mesons 𝑠¯𝑠 (left) and 𝑐 ¯𝑐 (right) as functions of the inverse of the hopping  parameter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content=' The purple bands and their central value represent the physical mass of the mesons 𝜙 (left) and  𝐽/𝜓 (right) converted to lattice units.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='  We plot the masses of the vector mesons as a function of the inverse of the corresponding  hopping parameters 𝜅−1  𝑠/𝑐, which are linear in the bare masses of the valence quarks 𝑠 and 𝑐.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content=' In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='  2 we show this dependence for both strange (left) and charm (right) quarks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content=' The purple bands in  the plots correspond to the physical masses in equation (9) converted to lattice units.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='2 Renormalization constants  Evaluating 𝑎𝐻𝑉 𝑃,𝑠/𝑐  𝜇  from the local-local or conserved-local correlators requires determining  the renormalization factor 𝑍  𝑚 𝑓  𝑉  and the improvement coeﬃcient introduced in (7).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content=' In this work, we  do not consider any improvement terms and evaluate the mass-dependent renormalization factor  𝑍  𝑚 𝑓  𝑉  of the local current from the ratio [15]  𝑅(𝑡) =  �  �𝑥,𝑘  �  𝑉𝑐  𝑘, 𝑓 (𝑥)𝑉𝑙  𝑘, 𝑓 (0)  �  �  �𝑥,𝑘  �  𝑉𝑙  𝑘, 𝑓 (𝑥)𝑉𝑙  𝑘, 𝑓 (0)  � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='  (11)  When 𝑡 is small, the quantity is aﬀected by the diﬀerent discretization eﬀects of the two currents.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='  At large time, 𝑅(𝑡) saturates and we can determine 𝑍  𝑚 𝑓  𝑉  by ﬁtting the plateau region to a constant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='  An example of such a ﬁt is shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content=' We applied the same method for both ensembles and  for both 𝑍𝑚𝑠  𝑉  and 𝑍𝑚𝑐  𝑉 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='  In Table 4 we show the ﬁt ranges and the values obtained for 𝑍  𝑚𝑠/𝑐  𝑉  for the tuned hopping  parameters 𝜅𝑡𝑢𝑛  𝑠/𝑐 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content=' The errors are determined with the bootstrap procedure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='  Ensemble  ﬁt range  𝑍𝑚𝑠  𝑉  ﬁt range  𝑍𝑚𝑐  𝑉  A400a00b324  [15,24]  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='6712(7)  [24,30]  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='6066(2)  B400a00b324  [15,24]  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='6707(5)  [23,31]  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='6066(4)  Table 4: Mass-dependent renormalization factor obtained from the ratio method deﬁned in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content=' (11).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='  6  Strange and charm contributions to the HVP from C★ boundary conditions  Paola Tavella  5  10  15  20  25  30  t [lattice units]  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='64  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='65  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='66  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='67  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='68  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='69  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='70  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='71  Glc(t)/Gll(t)  ﬁt range  ZV = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='6712 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='0007  data  Figure 3: Determination of the renormalization constant 𝑍𝑚𝑠  𝑉 for the local vector current with 𝜅𝑡𝑢𝑛  𝑠  = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='13422  on the A400a00b324 ensemble.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='3 Results  The evaluation of the leading HVP contribution to 𝑎𝜇 requires an integration over the euclidean  time  𝑎HVP, 𝑓  𝜇  =  �𝛼  𝜋  �2 ∞  ∑︁  𝑡=0  𝐺 𝑓 (𝑡) ˜𝐾(𝑡;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content=' 𝑚𝜇).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='  (12)  One of the problems related to this task is that the signal deteriorates with the lattice time 𝑡, due to  the exponentially increasing errors of the correlator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content=' Another related issue comes from the ﬁnite  size of the box: the integration domain is indeed restricted to [0,𝑇/2], then we have to extrapolate  the correlator to inﬁnite time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content=' In addition, the correlator is aﬀected by ﬁnite-volume eﬀects (FVE)  due to the ﬁnite temporal (𝑇) and spatial (𝐿) extents.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='  Concerning the ﬁnite-volume eﬀects, it has been found [16] that for given 𝐿 the leading ﬁnite-𝐿  corrections are the exponentials 𝑒−𝑚𝜋 𝐿, 𝑒−𝑚𝜋  √  2𝐿 and 𝑒−𝑚𝜋  √  3𝐿.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content=' Similarly, the leading contribution  arising from ﬁnite 𝑇 is 𝑒−𝑚𝜋𝑇 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content=' As a consequence, the ﬁnite-𝑇 eﬀects are higher order corrections  since usually in the simulations 𝑇 = 2𝐿.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content=' These results have been derived for a periodic torus in four  dimensions and are aﬀected by the choice of the boundary conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content=' In our setup, the boundary  condition in the time direction is periodic, then the results for ﬁnite-𝑇 corrections found in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content=' [16]  still apply.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content=' However, we use C★ boundary conditions in all three spatial directions, which means  that the ﬁnite-𝐿 corrections are in general diﬀerent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content=' Some studies have shown that in pure QCD C★  boundary conditions lead to small improvements for the FVE, with a leading correction 𝑒−𝑚𝜋  √  2𝐿  [17].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content=' A detailed numerical study of the ﬁnite-volume eﬀects for ensembles with C★ boundary  conditions will be carried out in future work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content=' In this work, we make a direct comparison of the  results for the integrand 𝐺(𝑡) ˜𝐾(𝑡, 𝑚𝜇) and 𝑎LO,HVP  𝜇  on the two available QCD ensembles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='  To control the large-time behavior of the correlator, we use the following quantity  𝐺constructed(𝑡) =  �  𝐺(𝑡)  (𝑡 ≤ 𝑡0,cut)  𝐺1-exp(𝑡)  (𝑡0 > 𝑡0,cut)  (13)  7  Strange and charm contributions to the HVP from C★ boundary conditions  Paola Tavella  0  10  20  30  40  t [lattice units]  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='5  ( / )2 × G(t)K(t;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content=' m )  1e  10  Strange quark  cubic-spline  1  exp  1  exp  data B400  data A400  0  5  10  15  20  25  30  t [lattice units]  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='2  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='4  ( / )2 × G(t)K(t;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content=' m )  1e  10  Charm quark  cubic-spline  data B400  data A400  Figure 4: Comparison of the integrands for the strange (left) and charm (right) contributions between the two  ensembles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content=' The tail of the integrands for the strange contribution is approximated by a single exponential.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='  where 𝑡0,cut is a properly chosen cut-oﬀ and 𝐺1-exp(𝑡) denotes the exponential extrapolation of the  correlator at large time  𝐴 exp(−𝑡 · 𝑚eﬀ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='  (14)  The two parameters 𝑚eﬀ and 𝐴 are the eﬀective mass and the amplitude obtained through a ﬁt  procedure to the correlator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content=' For the masses, we use the results reported in Tables 2 and 3 for the  tuned hopping parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content=' The parametrization with a single-exponential is a crude approximation  that introduces some systematics since we are neglecting the excited states contributing to the  correlator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content=' We plan to use a more accurate model for the tail of the correlator in future works.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='  The plots in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content=' 4 show the integrands both for the charm and strange quarks contributions  and the two ensembles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content=' The lattice data for the charm contribution are suﬃciently precise and do  not require any extrapolation or improvement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content=' In the case of the strange contributions, the tail of the  integrand is approximated as described above.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content=' The results of the integration are listed in Table 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='  We estimate 𝑎LO,HVP  𝜇  using the two diﬀerent discretizations of the correlator: conserved-local and  local-local.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content=' The strange contribution is not aﬀected by the choice of the correlator, the results are  indeed compatible with the current uncertainties for both ensembles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content=' By contrast, the contribution  from the charm quark is particularly sensitive to the choice of discretization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content=' The ﬁnite-size eﬀects  are negligible for the charm quark contribution and lead instead to a diﬀerence of about 2𝜎 for the  strange quark.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='  Ensemble  Type  𝑎𝑠  𝜇 × 10−10  𝑎𝑐  𝜇 × 10−10  A400a00b324  𝑙𝑙  46.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='7(7)  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='83(8)  𝑐𝑙  46.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='2(7)  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='18(7)  B400a00b324  𝑙𝑙  48.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='5(7)  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='81(9)  𝑐𝑙  48.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='0(7)  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='16(7)  Table 5: Results for 𝑎𝑠,𝑐  𝜇  in units of 10−10 determined using the TMR and two diﬀerent discretizations of the  observable: local-local and conserved-local.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='  8  Strange and charm contributions to the HVP from C★ boundary conditions  Paola Tavella  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='4 Partial errors budget  The errors in Table 5 are the quadratic sum of the statistical and part of the systematic errors  as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content=' The uncertainties taken into account are the statistical errors from the correlators, the  lattice spacing and 𝑍𝑉 , and the systematics from the choices of the cut-oﬀ (for the strange quark)  and the ﬁt range used to determine 𝐴 and 𝑚eﬀ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content=' The statistical error is determined by using the  bootstrap method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content=' Since 𝑍𝑉 appears as a multiplicative factor in front of the whole expression,  we employ the standard error propagation for it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content=' The lattice spacing’s values are determined by  using the reference scale (8𝑡0)1/2 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='415 fm as an absolute value, without taking into account  the systematics coming from the uncertainty on this scale.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content=' Thus, our current error on 𝑎 is only a  statistical partial uncertainty.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content=' The dependence on the lattice spacing is in the QED kernel ˜𝐾(𝑡, 𝑚𝜇):  we numerically propagate the partial error 𝛿𝑎 by repeating the evaluation of 𝑎𝜇 for 𝑁 values of  the lattice spacing drawn from a normal distribution N (𝑎, 𝛿𝑎).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content=' We use at least 𝑁 = 100 for each  result.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content=' Finally, we repeat the calculation for several values of the ﬁt range and the cut-oﬀ and apply  a weighted averaging procedure to get the total systematics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='  We remark that there are still several unaccounted uncertainties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content=' We are currently missing the  systematics introduced by the single-exponential extrapolation of the correlator and by the use of  the reference scale 𝑡0 without an error for the determination of the lattice spacing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content=' In this work we  did not perform a quantitative numerical study of the ﬁnite-size eﬀects and we measured at one  value of the lattice spacing and pion mass, thus we have not performed yet an extrapolation of the  results to the continuum and physical point.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='  Conclusions and outlooks  We have measured the connected contribution to the leading hadronic vacuum polarization from  strange and charm quarks, in a setup with C★ boundary conditions in the three spatial directions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='  We performed the analysis on two ensembles with diﬀerent volumes, indicating that the ﬁnite-size  eﬀects are under control.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content=' As expected, we ﬁnd that the charm contribution is considerably aﬀected  by the choice of the correlator, due to the sensitivity to the discretization eﬀects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content=' In addition, we  have shown that a more precise determination of the lattice spacing is needed to reach the target  precision.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content=' Our plans for future works include the evaluation of the isospin-breaking eﬀects as well  as the disconnected terms, and a quantitative study of the ﬁnite-size eﬀects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='  Acknowledgments  We acknowledge access to Piz Daint at the Swiss National Supercomputing Centre, Switzerland  under the ETHZ’s share with the project IDs s1101, eth8 and go22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content=' Financial support by the SNSF  (Project No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content=' 200021_200866) is gratefully acknowledged.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content=', S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content=', and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='M received funding  from the European Union’s Horizon 2020 research and innovation programme under the Marie  Skłodowska-Curie grant agreement No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content=' 813942.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='received funding from the European Union’s  Horizon 2020 research and innovation programme under grant agreement No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content=' 765048.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='C.’s and  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='L.’s research is funded by the Deutsche Forschungsgemeinschaft Project No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content=' 417533893/ GRK-  2575 “Rethinking Quantum Field Theory”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='  9  Strange and charm contributions to the HVP from C★ boundary conditions  Paola Tavella  References  [1] Muon g-2 Collaboration collaboration, Final report of the E821 muon anomalous  magnetic moment measurement at BNL, Physical Review D 73 (2006) 072003.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='  [2] Muon 𝑔 − 2 Collaboration collaboration, Measurement of the positive muon anomalous  magnetic moment to 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='46 ppm, Physycal Review Letters 126 (2021) 141801.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='  [3] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content=' Aoyama et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content=', The anomalous magnetic moment of the muon in the Standard Model,  Physics Reports 887 (2020) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='  [4] Sz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content=' Borsanyi et al, Leading hadronic contribution to the muon magnetic moment from lattice  QCD, Nature 593 (2021) 51.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='  [5] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content=' Abe et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content=', A new approach for measuring the muon anomalous magnetic moment and  electric dipole moment, Progress of Theoretical and Experimental Physics 2019 (2019) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='  [6] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content=' Abbiendi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content=', Measuring the leading hadronic contribution to the muon g-2 via 𝜇𝑒  scattering, The European Physical Journal C 77 (2017) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='  [7] RC* collaboration, openQ*D code: a versatile tool for QCD+QED simulations, The  European Physical Journal C 80 (2020) 195.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='  [8] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content=' Bushnaq et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content=', First results on QCD+QED with C* boundary conditions, 2209.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='13183.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='  [9] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content=' Bruno, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content=' Korzec and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content=' Schaefer, Setting the scale for the CLS 2 + 1 ﬂavor ensembles,  Physical Review D 95 (2017) 074504.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='  [10] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content=' Bernecker and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content=' Meyer, Vector correlators in lattice QCD: Methods and applications,  The European Physical Journal A 47 (2011) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='  [11] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content=' Della Morte et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content=', The hadronic vacuum polarization contribution to the muon g - 2 from  lattice QCD, Journal of High Energy Physics 2017 (2017) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='  [12] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content=' Bhattacharya et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content=', Improved bilinears in lattice QCD with non degenerate quarks,  Physical Review D 73 (2006) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='  [13] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content=' Gérardin et al, Leading hadronic contribution to (𝑔 − 2)𝜇 from lattice QCD with  𝑁 𝑓 = 3 + 1 of 𝑂(𝑎) improved wilson quarks, Physical Review D 100 (2019) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='  [14] Particle Data Group collaboration, Review of Particle Physics, Progress of Theoretical  and Experimental Physics 2022 (2022) 083C01.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='  [15] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content=' Boyle et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content=', Isospin breaking corrections to meson masses and the hadronic vacuum  polarization: a comparative study, Journal of High Energy Physics 2017 (2017) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='  [16] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content=' Hansen and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content=' Patella, Finite-volume and thermal eﬀects in the leading-HVP  contribution to muonic (g - 2), Journal of High Energy Physics 2020 (2020) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='  [17] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content=' Martins, Finite-size eﬀects of the Hadronic Vacuum Polarization contribution to the muon  (g - 2) with C* boundary conditions, Talk at Lattice 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
+page_content='  10' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/udE3T4oBgHgl3EQfNgn9/content/2301.04385v1.pdf'}
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+Time-reversal invariant ﬁnite-size topology
+R. Flores-Calderon,1, 2 Roderich Moessner,1 and Ashley M. Cook1, 2
+1Max Planck Institute for the Physics of Complex Systems, N¨othnitzer Strasse 38, 01187 Dresden, Germany
+2Max Planck Institute for Chemical Physics of Solids, N¨othnitzer Strasse 40, 01187 Dresden, Germany
+We report ﬁnite-size topology in the quintessential time-reversal (TR) invariant systems, the quantum spin
+Hall insulator (QSHI) and the three-dimensional, strong topological insulator (STI): previously-identiﬁed heli-
+cal or Dirac cone boundary states of these phases hybridize in wire or slab geometries with one open boundary
+condition for ﬁnite system size, and additional, topologically-protected, lower-dimensional boundary modes
+appear for open boundary conditions in two or more directions. For the quasi-one-dimensional (q(2-1)D) QSHI,
+we ﬁnd topologically-protected, quasi-zero-dimensional (q(2-2)D) boundary states within the hybridization gap
+of the helical edge states, determined from q(2-1)D bulk topology characterized by topologically non-trivial
+Wilson loop spectra. We show this ﬁnite-size topology furthermore occurs in 1T’-WTe2 in ribbon geometries
+with sawtooth edges, based on analysis of a tight-binding model derived from density-functional theory calcula-
+tions, motivating experimental investigation of our results. In addition, we ﬁnd quasi-two-dimensional (q(3-1)D)
+ﬁnite-size topological phases occur for the STI, yielding helical boundary modes distinguished from those of the
+QSHI by a non-trivial magneto-electric polarizability linked to the original 3D bulk STI. Finite-size topological
+phases therefore exhibit signatures associated with the non-trivial topological invariant of a higher-dimensional
+bulk, clearly distinguishing them from previously-known topological phases. Finally, we ﬁnd the q(3-2)D STI
+also exhibits ﬁnite-size topological phases, ﬁnding the ﬁrst signs of topologically-protected boundary modes
+of codimension greater than 1 due to ﬁnite-size topology. Finite-size topology of four or higher-dimensional
+systems is therefore possible in experimental settings without recourse to thermodynamically large synthetic
+dimensions.
+I
+Introduction
+The discovery of the ﬁrst topological insulator (TI), the
+quantum spin Hall insulator (QSHI) in HgTe quantum
+wells [1, 2] heralded a paradigm shift in condensed matter
+physics towards broad study of topological phases of matter.
+Understanding and characterization of topology is now
+central to the ﬁeld, with major applications ranging from
+fault-tolerant quantum computing [3, 4] to unconventional
+superconductivity [5].
+Consequently, searching for novel,
+experimentally-accessible topological systems is a major
+theme of the last few decades [2, 6–13].
+These efforts
+usually target experimental conﬁrmation of a hallmark of
+topological phases known as bulk-boundary correspondence:
+a non-trivial topological invariant of the system bulk is
+associated with topologically-robust, gapless boundary states.
+While it has long been understood that a D-dimensional
+bulk topology yields (D − 1)-dimensional gapless boundary
+states for most topological phases [14], the recent discovery
+of additional bulk-boundary correspondence even in the
+canonical phases, known as ﬁnite-size topology, shows
+this foundational aspect of topological physics is richer
+than previously-thought.
+If a system is characterized by
+a topological invariant computed in the D-dimensional
+inﬁnite bulk, but is ﬁnite in size and thin in one direction
+as illustrated in Fig. 1 (for the QSHI D = 2 while for the
+3D TI D = 3 ), such that topologically-protected boundary
+states interfere with one another, this quasi-(D − 1)- or
+q(D − 1)-dimensional bulk is characterized by an additional
+topological invariant.
+When this additional invariant takes
+non-trivial values, open boundary conditions in a second di-
+rection yield an additional set of quasi-(D − 2)-dimensional,
+topologically-protected boundary states localized on this
+boundary of the quasi-(D − 1)-dimensional system.
+As
+these quasi-(D − 2)-dimensional states are localized on the
+boundary in correspondence with a non-trivial value for a
+topological invariant of the quasi-(D − 1)-dimensional bulk,
+and robust against local perturbations respecting the symme-
+tries protecting the topological phase in the D-dimensional
+inﬁnite bulk, they constitute previously-unidentiﬁed topologi-
+cal phases of matter.
+Following the previous thinning process we end up with a
+q(D−1)-dimensional bulk with topological edge states in one
+less dimension, the situation is then just like at the start of the
+program, but with D replaced by D − 1. Thus one may think
+of applying the thinning process once again, now thinning the
+xD−1 dimension and hybridizing the previous q(D − 2) edge
+states. We then arrive at a q(D − 2) dimensional bulk with
+q(D − 2 − 1) dimensional edge states which again can be
+subjected to the same procedure. The general process is illus-
+trated in Fig. 2, while Fig. 1 c) shows the speciﬁc case of the
+3D TI q(3−2) bulk. We note that this procedure could in prin-
+ciple be applied until there are no more number of dimensions
+to thin down.
+Although theoretical discovery of the Chern insulator [15]
+preceded theoretical prediction of the TR-invariant QSHI
+derived from it [16, 17], experimental conﬁrmation of the
+QSHI [2] occurred within one year of the prediction, while
+more than two decades passed for the Chern insulator [18].
+This reﬂects a broader trend in the ﬁeld, of TR-invariant
+topological insulators being conﬁrmed experimentally more
+quickly and easily than TR-symmetry-broken topological
+insulators reliant on engineering particular magnetic or-
+ders [2, 19, 20]. Following this idea in order to more rapidly
+observe ﬁnite-size topology in experiment, we study the
+time-reversal invariant ﬁnite-size topology of the QSHI
+and the strong TI (STI), by considering these systems in
+geometries as shown in Fig. 1.
+We also note that, due to
+arXiv:2301.02134v1  [cond-mat.mes-hall]  5 Jan 2023
+
+2
+QSHI
+3D TI
+E
+E
+E
+E
+FIG. 1. Schematic of the ﬁnite-size TRI systems studied. From left to right, a) QSHI wire, b) slab of 3D TI and c) 3D TI wire. Blue and red
+cones are schematic of the gap openings of the 3D TI due to the hybridization of the the Dirac cones. Similarly blue and red helical edge states
+get hybridized (yellow/purple) in the QSHI wire and the ﬁnite-size quasi-1D edge states (blue and red) get hybridized (yellow/purple) for the
+3D TI wire. Topological edge states (pink) are present as quasi-0D modes or quasi-1D modes polarized in spin, for wire or slab conﬁgurations
+respectively.
+x x
+3
+1, ,
+1
+x
+x
+FS
+FS
+x
+2
+D
+xD
+D-
+1
+xD-
+FIG. 2. Schematic of the ﬁnite-size process for topological insulators. From left to right a D dimensional phase gets shrunk in one direction
+xD to give rise to a quasi D − 1 dimensional phase. This phase can be further shrunk in a remaining xD−1 direction so that x1, x2, . . . xD−2
+are still periodic directions and now a quasi D − 2 dimensional phase is realized.
+the vast experimental studies in TI ultra-thin ﬁlms [21–23],
+Van der Waals heterostructures [24–27], and transition-metal
+dichalcogenides in particular given their large spin-orbit
+coupling [28, 29], there may already be signs of ﬁnite-size
+topology in previous experiments. Past work, for instance,
+indicates few-layer 1T’-MoTe2 is semi-metallic [30], while
+the monolayer is predicted to be a quantum spin Hall insula-
+tor [31], suggesting the few-layer topology derives from the
+Weyl semimetal phase of the three-dimensional bulk, while
+the monolayer topological phase has a distinct origin due to a
+strictly two-dimensional bulk.
+Since ﬁnite-size topological phases occur for the Kitaev
+chain and Chern insulator, non-trivial ﬁnite-size topology is
+expected for TR-invariant systems of the QSHI and STI given
+concrete relationships between Hamiltonians for these topo-
+logical phases: the Kitaev chain Hamiltonian may be used
+to construct the Chern insulator Hamiltonian, if many chains
+are coupled forming a 2D system [32], and a Chern insula-
+tor Hamiltonian and its time-reversed partner are the basis of
+Hamiltonians for the QSHI[16, 17]. We ﬁnd that FST ex-
+tends to these TRI topological phases. As Hamiltonians for
+TR-invariant topological phases are used to construct Hamil-
+tonians for other topological phases, these results also re-
+veal that a larger set of topological phases harbor FST: a
+Weyl semimetal phase[33] Hamiltonian may be constructed
+from magnetically-doped STI and trivial insulator thin ﬁlms
+stacked alternatingly, while a stack of QSHIs corresponds di-
+
+3
+rectly to the weak 3D TI [34, 35]. Topological crystalline
+phases may furthermore be constructed, for instance, as Chern
+insulators within mirror subsectors or with the Chern insu-
+lator bulk conﬁned to a mirror-invariant plane of a three-
+dimensional Brillouin zone [36]. More generally, topological
+crystalline phases are characterized by considering symmetry-
+protection by crystalline point group symmetries in addition
+to the internal symmetries of the ten-fold way. On a technical
+level this is accomplished by expressing the Hamiltonian in
+a block diagonal form using the additional symmetry, in each
+sub-sector internal symmetries are still present and thus can be
+analyzed by classiﬁcation schemes obtained from the ten-fold
+way [37, 38].
+In this manuscript, we ﬁrst, section II, characterize ﬁnite-
+size topology in a QSHI wire.
+We start by considering a
+thin QSHI system with one open thin dimension and one in-
+ﬁnite periodic dimension. The energy and Wilson loop spec-
+tra of this q(2-1)D system reveal that the non-trivial zones in
+phase space are a subset of the original 2D bulk topological
+regions. Furthermore opening boundary conditions again in
+the remaining periodic direction shows the presence of edge
+states localized on the q(2-2)D boundaries. We end this sec-
+tion by studying the response to on-site disorder and perturba-
+tions, where the robustness of the edge states indicates a link
+to the original 2D bulk gap. Afterwards in section III, we con-
+sider a more realistic and experimentally accessible system
+1T ′ WTe2 in the QSHI phase. We ﬁnd similarly that this mate-
+rial realizes a ﬁnite-size topological phase with topologically-
+robust q(2-2)D edge states for a sawtooth ribbon geometry,
+the presence of this edge states is again veriﬁed to be pre-
+dicted by a non-trivial Wilson loop spectrum. Extending our
+analysis to the 3D case we consider in section IV the STI in
+a q(3-1)D slab geometry. In this case, interference between
+the STI Dirac cone surface states yields q(3-2)D edge states.
+We show the Wilson loop spectrum of the q(3-1)D bulk dis-
+plays topologically non-trivial signatures in correspondence
+with these boundary states, indicating Wilson loop spectra are
+a robust bulk diagnostic of ﬁnite-size topology. Additionally
+we compute the magneto-electric polarizability, which should
+be trivially zero if the system is just a 2D QSHI, instead we
+encounter the response expected for the inﬁnite 3D TI bulk.
+This central result allows us to contemplate the idea of detect-
+ing topological signatures of higher dimensional phases, say
+the 4D TI, in quasi lower dimensional systems. Finally, we
+study the case of a STI in a q(3-2)D wire geometry, where we
+once again use the Wilson loop indicator to ﬁnd a novel bulk-
+boundary correspondence restricted to a subset of the original
+3D topological phase diagram. In this ﬁnal case the number
+of edge states is seen to follow the number of ±π phases such
+that only even numbers of distinct edge states appear. In sec-
+tion VI we summarize our results and present some conclud-
+ing remarks.
+II
+QSHI wire
+As a starting point of our analysis we consider a QSHI ﬁrst
+considering the canonical Bernevig-Hughes-Zhang Hamilto-
+nian for HgTe quantum wells [1] where we also add a Rashba-
+type spin orbit coupling. Thus the Hamiltonian in momentum
+space has the form [39]:
+h(kx, ky) =(u + 2t(cos kx + cos ky))σz + sin ky σy
+(1)
++ sin kx szσx + c sxσy,
+where si, σi are Pauli matrices in spin and orbital space
+respectively. For simplicity we omit the identity in spin space
+and denote the tensor product by placing two matrices next
+to each other. The real number u corresponds to a staggered
+potential, t to a hopping parameter and c is the spin orbit
+coupling that breaks sz spin symmetry. The phase diagram
+for this Hamiltonian includes both a region in which the
+QSHI phase is realized and a region in which the Dirac
+semimetal (DSM) phase is realized, as discussed in reference
+[39] and plotted in Fig. 3 a) and b) . In the following analysis,
+we ﬁrst consider the QSHI regime, and then that of the DSM.
+Next we consider what happens if we open boundary con-
+ditions (OBC) in the x direction for a small number of lattice
+sites N. Since the helical edge modes of the QSHI are not
+completely localized at the boundary, but instead decay expo-
+nentially into the bulk [40], these boundary states interfere in
+systems of ﬁnite-width. The lattice second quantized Hamil-
+tonian with open boundary conditions in the ˆx-direction and
+periodic boundary conditions in the ˆy direction is:
+ˆH =
+�
+k,n
+Ψ†
+k,n ((u + 2t cos k)σz + sin k σy + c sxσy) Ψk,n
++ Ψ†
+ky,n+1
+�
+t σz + i
+2szσx
+�
+Ψk,n + h.c. ,
+(2)
+−2
+−1
+0
+1
+2
+u
+0.0
+0.5
+1.0
+1.5
+c
+0.0
+0.5
+1.0
+1.5
+∆
+(a)
+(b)
+−π
+−π/2
+0
+π/2
+π
+ky
+−1.0
+−0.5
+0.0
+0.5
+1.0
+E(ky)
+OBC
+PBC
+(c)
+−2
+−1
+0
+1
+2
+u
+−0.50
+−0.25
+0.00
+0.25
+0.50
+E(u)
+(d)
+FIG. 3.
+a) Direct gap heat plot of the 2D bulk hamiltonian eq. (1)
+as a function of potential u and spin-orbit coupling constant c, b)
+Topological phase diagram of the 2D bulk , showing the QSHI phase
+(yellow) and DSM gapless phase (blue) of the 2D bulk. c) Quasi-1D
+dispersion for PBC in y and OBC (PBC) in x with N = 6 sites. The
+parameters for the gap closing with OBC in x are u = 0.76, c =
+0.8, t = 1/2 d) Spectrum for PBC in y as a function of the staggered
+potential u and c = 0.8, t = 1/2.
+
+1.5
+DSM
+1.0
+C
+0
+Z2
+0.5
+0.0
+2
+-1
+0
+1
+2
+u4
+where k ≡ ky and n runs over the N sites of the open
+x direction. Here, Ψk,n are four component spinor fermion
+operators acting on the spin and orbit degrees of freedom.
+We ﬁrst examine the spectrum of Eq. 2 for small N on
+the order of a few lattice constants.
+We ﬁrst consider the
+spectrum for a particular point in phase space as shown in
+Fig. 3 c) for a small system with N = 6 with non-trivial
+2D bulk invariant, as shown in Fig. 3 b).
+Comparing the
+dispersion for the system with periodic boundary conditions
+in each direction (black lines) to that of the system with open
+boundary conditions only in the ˆx-direction (red lines), we
+see the periodic system is gapped, while the system with open
+boundary conditions is instead gapless. While gapless bound-
+ary states are expected due to the non-trivial bulk topology,
+the gaplessness in this case is not topologically-robust: the
+gapless boundary modes interfere in ﬁnite-size systems to
+open a hybridization gap in general. Under certain conditions,
+however, the boundary modes interfere destructively, corre-
+sponding to a ﬁne-tuned gapless state when hybridization
+matrix elements pass through zero. Examining the spectrum
+for the q(2-1)D bulk as a function of u as shown in Fig.
+3
+d) , we see this more general pattern of ﬁnite interference
+gaps, with a discrete set of u corresponding to gap-closings
+and destructive interference between the helical boundary
+modes.
+We will show these gap-closings can correspond
+to topological phase transitions, and some of these gapped
+regions host ﬁnite-size topological phases.
+A
+Periodic system
+To characterize the ﬁnite-size topological phases of this time-
+reversal invariant system, we now re-interpret the original
+model with OBC in the ˆx-direction as a q(2-1)D bulk, and
+characterize topology of this q(2-1)D bulk system similarly to
+characterization of a d-dimensional bulk. We therefore ﬁrst
+compute a phase diagram for the minimum direct gap over
+the Brillouin zone of the q(2-1)D bulk as a function of u, c for
+ﬁxed hopping t = 1/2, shown in Fig.4 a),b) for N = 6 and
+N = 7 layers in the ˆx-direction, respectively. A dome forms
+in the phase diagram, consisting of a set of curved, stripe-like
+regions of ﬁnite minimum direct gap separated by lines along
+which the q(2-1)D minimum direct bulk gap is zero, with
+these lines intersecting to form a checkerboard-like pattern at
+larger values of c. As the number of lattice sites in the ˆx-
+direction increases, the number of gap-closing lines increases
+while the regions of ﬁnite minimum direct gap decrease in
+size. This pattern is consistent with a picture of gap-closings
+due to interference between the helical boundary modes of the
+QSHI: the boundary modes in this q(2-1)D system possess a
+standing wave character, and the gap-closing lines correspond
+to hybridisation matrix elements passing through zero with
+tuning of system parameters. With increasing system size,
+this interference pattern becomes denser as the difference in
+wavelength between the oscillatory components of the helical
+boundary modes generically decreases.
+It is particularly interesting to compare these phase
+diagrams for the q(2-1)D bulk with the counterpart phase
+diagram of the 2D bulk shown in Fig. 3 a),b) , which reveals
+−2
+−1
+0
+1
+2
+u
+0.0
+0.5
+1.0
+1.5
+c
+0.0
+0.1
+0.2
+0.3
+0.4
+∆
+(a)
+−2
+−1
+0
+1
+2
+u
+0.0
+0.5
+1.0
+1.5
+c
+0.0
+0.1
+0.2
+0.3
+0.4
+∆
+(b)
+−2
+−1
+0
+1
+2
+u
+0.0
+0.5
+1.0
+1.5
+c
+0
+2
+4
+N±π
+(c)
+−2
+−1
+0
+1
+2
+u
+0.0
+0.5
+1.0
+1.5
+c
+0
+2
+4
+N±π
+(d)
+FIG. 4. Quasi-(2-1)D minimum direct bulk gap for a) N = 6, b)
+N = 7 and t = 1/2. Plot of the number of ±π phases N±π (red is
+2, black 0) in the Wilson loop eigenvalues for c) N = 6, d) N = 7
+that different kinds of topological phases of the 2D bulk (and
+corresponding different gapless boundary states) yield differ-
+ent interference patterns as a function of u and c. Notably,
+the checkerboard region of the phase diagram corresponds to
+the DSM phase region of the corresponding phase diagram
+for the 2D bulk, revealing that the DSM phase is generally
+gapped out in the q(2-1)D regime, and exhibits more complex
+interference pattern than does the QSHI.
+As the 2D minimum direct bulk gap remains ﬁnite over the
+region of the phase diagram where we observe this interfer-
+ence pattern between helical boundary modes of the QSHI,
+and the 2D minimum direct bulk gap remains closed due to
+topologically-protected band-touchings of the DSM, topolog-
+ical invariants of the 2D bulk do not change within these re-
+gions. However, as subsets of each of these regions possess a
+ﬁnite minimum direct gap in the q(2-1)D spectrum, it is possi-
+ble to further characterize the topology of the q(2-1)D system
+if suitable topological invariant(s) are identiﬁed. To further
+characterize ﬁnite-size topology of this quasi-1D TRI system
+with Wilson loop spectra, we compute the Wilson loop eigen-
+values [41], which distinguish between topologically-distinct
+phases of matter as they characterize holonomy in a system
+due to parallel transport through non-contractible loops in the
+BZ [42–44].
+The Wilson loop spectra for the q(2-1)D system are com-
+puted by integrating the Berry connection over the remaining
+k ≡ ky momentum coordinate, using the following expres-
+sion: [41]
+W = Pe−
+� π
+−π dkA(k),
+(3)
+where A(k) is the non-Abelian Berry connection over the
+occupied bands and P is the path ordering operator. Since
+
+5
+we compute the Wilson matrix for a tight binding system we
+discretize Eq. (3). The set of Wilson loop eigenvalue phases
+is the Wannier charge center spectrum characterizing polar-
+ization. In a topologically non-trivial phase, Wannier charge
+center(s) are ﬁxed to value(s) of ±π, so we compute the num-
+ber of these non-trivial phases as N±π. The phase diagrams
+characterizing N±π vs. u and c are shown in Fig. 4 c), d)
+for systems with N = 6 or N = 7 layers in the ˆx-direction,
+respectively.
+These N±π vs. c and u phase diagrams shown in Fig. 4 c)
+and d) reveal alternating regions of N±π = 0 and N±π = 2,
+indicating the system undergoes a variety of topological phase
+transitions.
+We even observe stripe-like regions at smaller
+c, which intersect to form checkerboard patterns at larger c.
+These lines across which N±π changes in value are in direct
+correspondence with lines shown in Fig. 4 a) and b), respec-
+tively, along which the q(2-1)D minimum direct gap goes to
+zero. Taken together, these phase diagrams in Fig. 4 reveal
+a topological phase transition occurs every time the q(2-1)D
+minimum direct bulk gap goes to zero.
+The phase diagrams for N = 6 layers differ dramatically
+from those for N = 7 layers, reﬂecting the dependence of
+this topology on ﬁnite-size effects. From the plots, one can
+see that, as the number of layers in the ˆx-direction increases,
+the number of topologically-distinct regions also increases in
+agreement with the number of lines along which the q(2-1)D
+minimum direct bulk gap is zero.
+The topological phase
+diagram of the 2D bulk Hamiltonian (1) studied in Ref. [39]
+is therefore being further divided into topologically-distinct
+regions in the q(2-1)D regime in a strongly N-dependent
+manner, revealing that topological phase transitions due to
+ﬁnite-size topology may occur without the minimum direct
+gap of the 2D bulk going to zero.
+B
+Bulk-boundary correspondence and disorder
+Having characterized ﬁnite-size topology of the q(2-1)D
+bulk of Hamiltonian Eq. (1) with open boundary conditions
+in the ˆx-direction and periodic in ˆy, we now explore the
+additional
+bulk-boundary
+correspondence
+of
+ﬁnite-size
+topological phases. We ﬁrst study the spectral signatures of
+this bulk-boundary correspondence that appear for non-trivial
+Wilson loop spectra in accordance with the modern theory
+of polarization of Ref. [45].
+N±π ̸= 0 for the q1D bulk
+corresponds to topologically-protected, q0D bound states for
+open boundary conditions in the ˆy-direction in addition to
+open boundary conditions in the ˆx-direction. With system
+size in the ˆy-direction of Ly, such a bulk-boundary corre-
+spondence characterized in the q1D bulk by N±π is clear for
+Ly ≫ Lx as shown in Fig. 5 a) b). In this case, one ﬁnds
+in-gap states close to zero energy within the q(2-1)D bulk gap
+of the energy spectrum. The separation in energy between
+these states decreases exponentially to zero as a function of
+Ly, realizing a four-fold degenerate manifold of zero-energy
+states.
+Such states are not present for periodic boundary
+conditions in the ˆy-direction, further indicating they appear
+as a consequence of bulk-boundary correspondence for the
+ﬁnite-size topological phase.
+−2
+−1
+0
+1
+2
+u
+−0.5
+−0.2
+0.0
+0.2
+0.5
+E(u)
+(a)
+−1.5
+−0.2
+1.1
+2.4
+u
+-0.15
+0
+0.2
+0.4
+E(u)
+(b)
+0
+0.5
+1.0
+1.4
+c
+−0.2
+−0.1
+0.0
+0.1
+0.2
+E(c)
+(c)
+0
+0.5
+1.0
+1.4
+c
+−0.2
+−0.1
+0.0
+0.1
+0.2
+E(c)
+(d)
+0.0
+0.3
+0.7
+1.0
+1.4
+c
+0.0
+0.5
+1.0
+1.5
+2.0
+∆
+(e)
+x
+0 2 4 6
+y
+285
+290
+295
+300
+density
+0.00
+0.02
+(f)
+FIG. 5.
+a) Spectrum for OBC (red)in both directions, PBC in y
+(black) as a function of the staggered potential u and c = 0.6, t =
+1/2, N = 6. b) Spectrum for OBC (red) in both directions, PBC in
+y (black) as a function of the staggered potential u and c = 0.8, t =
+1/2, N = 6 with a particle-hole symmetry and sublattice symmetry
+breaking on-site potential 0.1 cos(2πn/N)σx. c) Disorder-averaged
+spectrum for N = 6 sites and u = 1, t = 1/2 as a function of c for
+200 uniformly distributed random particle hole symmetric potentials
+of strength κ = 0.5u. d) Disorder-averaged spectrum with the same
+parameters but for 200 particle-hole symmetry-breaking disorder po-
+tentials of strength κ = 0.2u. e) 2D minimum direct bulk gap as a
+function of c for u = 1. f)Density proﬁle of q(2-2)D state for the
+same number of sites, c = 0.8, u = 1.0 and Ly = 300.
+To further explore the extent to which these in-gap states are
+due to an additional bulk-boundary correspondence of ﬁnite-
+size topological phases, we compute the probability density
+for these in-gap states. We ﬁnd these states are localized at
+the boundaries of the q1D system as shown in Fig. 5 f). Prob-
+ability density peaks at the corners of the system as seen in
+Fig. 5 f) and decays over ﬁfteen to twenty unit cells to zero
+for x approaching the q(2-1)D bulk. As the system is time-
+reversal invariant, we also compute the spin polarization for
+these q(2-2)D boundary modes. We ﬁnd the q(2-2)D bound-
+ary modes are spin-polarized in the ±ˆz direction, with a spin
+up/down pair localized at each end of the q(2-1)D system.
+We also study the robustness of the in-gap q(2-2)D bound-
+ary states against symmetry-breaking due to disorder.
+We
+introduce disorder in the q(2-1)D system for OBC as a uni-
+
+6
+form random potential, with strength κ. The disorder average
+spectrum for 200 disorder realizations of the form κns0σz is
+shown in Fig. 5 c) as a function of spin-orbit coupling c for
+κn ∈ (−0.2u, 0.2u). The q(2-2)D states are present over a
+wide range in c. Surprisingly, they survive even for disorder
+strengths κn greater than the q(2-1)D minimum direct bulk
+gap for the QSHI phase. The edge states may move away
+from zero energy, if the perturbation breaks particle-hole
+symmetry, such effect is shown in Fig. 5 b) as a function of u,
+where an onsite perturbation 0.1 cos(2πn/N)s0σx is present.
+For disorder effects we considered a term of the form Vis0σ0,
+the spectrum is thus shown in Fig. 5 d) where the edge modes
+deviate from zero energy, as in the case of an SSH chain with
+next nearest neighbours studied in reference [46]. However,
+the q(2-2)D boundary modes persist and remain strongly
+localized, with their pair degeneracy preserved.
+Interestingly, the topological invariant remains ﬁxed at
+non-trivial values even when a particle-hole breaking term is
+present in the Hamiltonian. This reﬂects the dependence of
+this non-trivial topology on the presence of the topologically-
+protected boundary states of the higher-dimensional phase,
+which require only time-reversal symmetry to remain robust
+up to the minimum direct 2D bulk gap going to zero. We
+further ﬁnd N±π still predicts the existence of edge states
+in the nontrivial region.
+The validity of the invariant and
+bulk-boundary correspondence in the absence of particle
+hole symmetry will be further veriﬁed for the case of the
+1T ′-WTe2 wire. The phase is therefore protected by time-
+reversal symmetry alone while particle-hole symmetry is
+required only to anchor the in-gap states to zero energy. This
+analysis parallels the one on ref. [46] where analogously the
+invariant and phase are protected by only inversion symmetry
+while both inversion and particle-hole symmetry secure the
+zero-energy value.
+For particle-hole-symmetric disorder
+Fig.5 c) the perturbation strength is protected not by the
+q(2-1)D gap but rather the 2D bulk gap of the system, which,
+for c = 0.8, u = 1.0, is ∆ ≈ 0.5 as seen in Fig. 5 e). If
+the perturbation breaks time reversal symmetry, however, the
+Kramers degeneracy of the q(2-2)D bound states is broken as
+expected.
+We conclude from this analysis that the q(2-1)D wire with
+spinful time-reversal symmetry, realized for a system with a
+2D bulk and open boundary conditions in one direction, ex-
+hibits ﬁnite-size topological phases for subsets of the topo-
+logically non-trivial regions of the 2D bulk topological phase
+diagram. In these subsets, bounded by lines along which the
+minimum direct q(2-1)D bulk goes to zero rather than the
+minimum direct 2D bulk gap, in general, the wire harbors
+topologically-protected q(2-2)D boundary modes for open
+boundary conditions in two directions appearing in Kramers
+pairs. In the quasi-1D bulk, these subsets correspond to Wil-
+son loop spectra with some Wilson loop eigenvalue phases
+ﬁxed to ±π, protected by spinful time-reversal symmetry.
+These signatures of non-trivial topology are therefore asso-
+ciated with time-reversal invariant, q(2-1)D ﬁnite-size topo-
+logical phases due to interference between topologically-
+protected gapless boundary modes resulting from 2D bulk
+topology, either of the quantum spin Hall insulator or the
+2D Dirac semimetal. In contrast, the ten-fold way classiﬁ-
+cation scheme of topological phases of matter determines a
+1D system in class AII [47] has trivial topological classiﬁ-
+cation. These results are therefore evidence of topologically
+non-trivial phases of matter outside of the ten-fold way clas-
+siﬁcation scheme.
+III
+1T ′-WTe2 wire
+Although the previous model is based on the celebrated
+HgTe quantum wells, which allowed for the discovery of the
+ﬁrst QSHI, it may not be most suitable for the experimental
+discovery of ﬁnite-size topology. The need for a small sample
+size in one direction may be easier to achieve for monolayers
+such as the 1T ′-TWe2 QSHI [48]. We thus consider the model
+studied in reference [49] which combines density-functional
+theory calculations, symmetry considerations and ﬁtting to
+experimental data. Since the ﬁnite-size topology comes from
+the hybridization of the edge states, we consider only the
+lattice termination which results in a Dirac crossing near the
+Fermi energy. That is we study the sawtooth y ribbon with
+open boundary conditions in the x direction. The 1T ′-WTe2
+Hamiltonian is presented in the Supplementary Material.
+Under such circumstances we expect the Dirac crossing
+to gap out in general on larger and larger energy scales as
+the system size in the x direction Nx decreases. Such a gap
+opening does occur for the original material parameters for
+even Nx values ranging from 4 to 20.
+It is worth noting
+that the gap still exists even for larger Nx but its magnitude
+becomes very small compared to other material energy
+scales.
+Such a gapped system may then host topological
+q(2-2)D edge states if the Wilson loop spectrum is nontrivial.
+Speciﬁcally, we ﬁnd that for Nx = 8, 10, 12 the gap has a ±π
+phase in the Wilson loop spectrum. Even in the case where
+the spectrum is trivial, for example at Nx = 6, we may still
+tune the system so that a gap closing occurs and a nontrivial
+Wilson loop phase appears.
+To do so, we may apply an
+electric ﬁeld perpendicular to the monolayer corresponding to
+addition of a symmetry-allowed Rashba spin-orbit coupling
+term to the Hamiltonian. Since the original model already
+includes such couplings, we further include a change of the
+in-plane SOC parameters by a quantity ∆λSOC.
+For the case of Nx = 6, we obtain a phase diagram for the
+number of Wilson loop eigenvalues with phase ±π, N±π, vs.
+spin-orbit coupling anisotropy, ∆λSOC, showing a change in
+N±π from 0 to 1 with increasing ∆λSOC as shown in Fig. 6
+a). Based on our previous results for a canonical toy model
+of the QSHI, we expect q(2-2)D edge states to appear if we
+open boundary conditions in the ˆy-direction as well. Such
+edge states due to an additional bulk-boundary correspon-
+dence characterized by N±π of the q(2-1)D bulk do exist, as
+shown in Fig. 6 b)corresponding to a line of four-fold degen-
+erate, in-gap states as a function of ∆λSOC. The four-fold de-
+generacy corresponds to a two-fold Kramers degeneracy due
+to spinful time-reversal symmetry, and two-fold degeneracy
+
+7
+0.0
+0.2
+0.4
+∆λSOC
+0.10
+0.15
+0.20
+0.25
+E
+(a)
+−0.2
+−0.1
+0.0
+0.1
+0.2
+∆λSOC
+−0.05
+0.00
+0.05
+0.10
+E
+(b)
+0.0
+0.2
+0.4
+∆λSOC
+0.0
+0.5
+1.0
+N±π
+(c)
+x
+0
+2
+4
+6
+y
+0
+5
+10
+density
+0.00
+0.05
+(d)
+FIG. 6.
+a) Energy spectrum (eV) as a function of the change in
+Rashba spin orbit coupling ∆λSOC for a Nx = 6 saw-tooth termi-
+nated 1T ′-TWe2 wire. b) Energy spectrum (eV) for the system with
+Nx = 12 as a function of ∆λSOC showing edge states at zero ﬁeld.
+c) Number of Wilson loop spectrum ±π phases for Nx = 6 as a
+function of ∆λSOC d) Wave function probability density for one edge
+state at ∆λSOC = 0.35eV and Nx = 6, Ny = 200 for the same
+saw-tooth terminated 1T ′-TWe2 wire.
+corresponding to boundary modes localized at the left and
+right edge as in the previous simple model of eqref. (1). For a
+ﬁxed Rashba spin orbit coupling change of ∆λSOC = 0.35eV ,
+we ﬁnd that the edge states localize on each end of the wire as
+shown in Fig. 6 c).
+IV
+3D TI slab
+We now study the ﬁnite size topology of the quintessen-
+tial 3D TI in symmetry class AII [38, 47]. The classiﬁca-
+tion in this case is dictated by four Z2 topological invariants
+(ν0; ν1, ν2, ν3) [34, 35] , where the last three invariants are
+related to the translational invariance of the system classify-
+ing the weak TI phase (WTI) while the ν0 parameter classiﬁes
+the strong TI phase (STI). In the following, we study the STI
+phase with trivial lower-dimensional invariants corresponding
+to (1; 000), which is realized in the model Bloch Hamiltonian
+[50]:
+H(k) = −2λ
+�
+µ
+sin kµσzsµ + σxs0(M − t
+�
+µ
+cos kµ),
+(4)
+where the Pauli matrices {σi},{sj} act on orbital and spin
+degrees of freedom respectively, λ is a spin orbit coupling
+parameter that breaks spin conservation, M is an onsite
+staggered potential, and t is a nearest-neighbor hopping
+integral. In the following, we take all energies to be in units
+of t by setting t = 1, and consider the regime in which
+1 < M < 3 and λ positive, for which the model realizes the
+desired strong TI phase. First, we specialize to the case of
+a thin slab in the ˆx-direction of N layers. In that case, we
+expect in analogy to the QSHI that the Dirac cones from the
+upper and lower surfaces interfere due to the thin bulk and
+hybridize to open a gap even for open boundary conditions.
+The hybridization gap, just as in the previous 2D case, is
+expected to sometimes protect a non-trivial ﬁnite size topolog-
+ical phase. To study this, we once again characterize topology
+using the Wilson loop spectrum, now as a function of ky or
+kz with OBC in x to characterize topology ﬁrst of a q(3-1)D
+bulk, in regions of the phase diagram where the 3D bulk cor-
+responds to the strong TI. As the isotropy of the Hamiltonian
+Eq. (4) suggests, there is no difference between the Wilson
+loop eigenvalues of W(ky) and W(kz), thus we consider only
+W(kz), where each Wilson loop matrix is now deﬁned as:
+W(ky) = Pe−
+� π
+−π dkzAz(ky, kz),
+(5)
+W(kz) = Pe−
+� π
+−π dkyAy(ky, kz).
+(6)
+A typical Wannier charge center spectrum vs. the remain-
+ing momentum component, kz, is plotted in Fig. 7, which
+shows the spectral ﬂow a) characteristic of a TR invariant
+topological insulator for some values and a trivial spectrum
+b) for others within the (1; 000) 3D bulk phase classiﬁcation.
+The non-trivial spectral ﬂow only appears for certain
+parameter regimes: these regions can be distinguished in a
+systematic way by counting the number of ﬁxed ±π phases
+in the Wilson loop spectrum, as in the previous case. This
+regions of parameter space which have an energy gap are
+again the ”bubbles” observed in the QSHI case. We plot the
+phase diagram as a function of the model parameters in Fig. 8
+a),b) for N = 5, 6 layers, respectively. The phase diagram
+changes dramatically for each value of N, the number of
+layers, indicative of the ﬁnite-size topology. The pattern of
+trivial and nontrivial regions is entirely contained with the
+non-trivial region of the 3D bulk topological phase diagram
+for Hamiltonian (4), indicating the 3D minimum direct bulk
+gap remains ﬁnite during these topological phase transitions
+of the q(3-1)D bulk. We remark that the sudden changes in
+color near λ = 0 seem to be just an artifact of the numerical
+precision when approaching the STI gap-closing in the 3D
+bulk.
+One of the consequences of the system being in a topolog-
+ically non-trivial regime, according to the Wilson loop spec-
+tra of the q(3-1)D bulk, is an additional bulk-boundary corre-
+spondence: opening boundary conditions in a second direc-
+tion in these regions of phase space, we ﬁnd topologically-
+protected q(3-2)D states that now are localized at the edges
+of the slab, as shown in Fig. 8 c). These q(3-2)D states ap-
+pear within the q(3-1)D bulk gap similarly to the case of q(2-
+2)D boundary states appearing in the q(2-1)D bulk gap of the
+QSHI. A topological phase diagram for the q(3-1)D system
+with open-boundary conditions in the ˆy-direction as a func-
+tion of M is also shown in Fig. 8 d), demonstrating the di-
+rect correspondence of the topologically-protected boundary
+
+8
+modes with the topologically non-trivial regions of the q(3-
+1)D bulk in Fig. 8 a). This indicates that N±π, the number of
+±π phases in the Wilson loop eigenvalue spectrum, character-
+izes ﬁnite-size topological phases resulting from interference
+of the topologically-protected Dirac cones of the 3D TI, in
+addition to characterizing ﬁnite-size topological phases due to
+interference between the helical boundary modes of the QSHI.
+−3π −2π −π
+0
+π
+2π
+3π
+φkz
+−2π
+−π
+0
+π
+2π
+kz
+(a)
+−3π −2π −π
+0
+π
+2π
+3π
+φkz
+−2π
+−π
+0
+π
+2π
+kz
+(b)
+FIG. 7. a) Wilson loop nontrivial eigenvalue spectrum as a function
+of kz for OBC in x and PBC in y, z. The parameters are M =
+2.0, λ = 0.2 and N = 6 layers. b) Wilson loop trivial eigenvalue
+spectrum as a function of kz for OBC in x and PBC in y, z. The
+parameters are M = 1.6, λ = 0.1 and N = 6 layers.
+While the ﬁnite-size topological phase in the q(3-1)D
+system exhibits helical boundary modes analogous to those of
+the QSHI, this topological phase is not just a QSHI. Notably,
+the 3D minimum direct gap remains ﬁnite in this region of the
+phase diagram where non-trivial ﬁnite-size topological phases
+occur, so the 3D bulk is still in the topological phase (1; 000).
+The ﬁnite-size topological phase therefore exhibits signatures
+associated with a non-trivial intrinsically 3D topological
+invariant.
+This is indicated by adding perturbations to the
+system to probe the magneto-electric polarizability of the
+system, which depends on the intrinsically 3D topological
+invariant, a connection identiﬁed in previous work by Essin et
+al. [51].
+We then compare the result to a q(3-1)D stack of 2D QSHI
+in the x direction with the same perturbation to demonstrate
+the ﬁnite-size topological phase of the q(3-1)D system is
+distinct from a QSHI. The type of perturbations we consider
+to determine the magnetoelectric polarizability in these two
+cases are TRS-breaking terms in the form of weak Zeeman
+ﬁeld in only the uppermost and lowest layers i.e. V = κ · s
+with | κ |≈ 0.1. This could correspond to ferromagnetically-
+ordered magnetic dopants in just these layers. This situation
+is illustrated schematically in Fig. 9 a). We ﬁrst consider
+a Zeeman ﬁeld oriented in the yz-plane and labeled κ∥ as
+shown in Fig. 9 a) for both the (1; 000) system (q(3-1)D STI)
+and the (0; 001) system (q2D WTI, or stack of QSHIs). In
+this case, these systems react similarly, their spectra gapping
+out as shown in Fig.9 b). This is expected, as the perturbation
+breaks TR symmetry.
+However, the responses of the two systems are strikingly
+distinct if we instead consider an applied Zeeman ﬁeld
+oriented along the ˆx-axis, or ﬁeld κ⊥ as shown in Fig. 9 a).
+In the case of the (1; 000) system (q(3-1)D STI), two of the
+q1D boundary states gap out, leaving two gapless boundary
+1
+1.5
+2
+2.5
+3
+M
+0.0
+0.2
+0.4
+0.6
+λ
+0
+2
+4
+6
+8
+N±π
+(a)
+1
+1.5
+2
+2.5
+3
+M
+0.0
+0.2
+0.4
+0.6
+λ
+0
+2
+4
+6
+8
+N±π
+(b)
+−π
+−π/2
+0
+π/2
+π
+kz
+−0.3
+−0.2
+−0.1
+0.0
+0.1
+0.2
+0.3
+E(kz)
+(c)
+1.0
+1.5
+2.0
+2.5
+3.0
+M
+−0.2
+−0.1
+0.0
+0.1
+0.2
+E(M)
+(d)
+FIG. 8.
+Phase diagram from wilson loop spectrum for a slab with
+a) N = 5, b) N = 6, black-0, yellow-2 ±π phases. c)Quasi-1D
+dispersion for OBC in x N = 6, PBC in z and OBC (PBC) in y as a
+function of kz. The parameters are M = 1.8, λ = 0.1. d) Spectrum
+for OBC in x, y as a function of M, for discretized values of kz with
+N = 5 and 100 sites in the remaining directions, λ = 0.1.
+modes remaining. They constitute chiral boundary modes of
+a QHE on each surface as shown in Fig. 9 c), corresponding
+to a layer-dependent Hall conductivity σxy as shown in
+Fig. 9 d). This is a known manifestation of the quantized
+magnetoelectric polarizability of the STI, resulting from the
+non-trivial value of the strong invariant, these results can be
+directly compared with past work for systems with a 3D bulk
+rather than q(3-1)D bulk [51]. Notably, the layer-dependent
+Hall conductivity exhibits this non-trivial response only for
+topologically non-trivial ﬁnite-size topological phases as
+characterized by N±π. This agrees with the response theory
+of previously-studied ﬁnite-size topological phases, and
+reﬂects the fact that only occupied states of the non-trivial
+bubbles carry Berry phase contributions to the underlying 3D
+topological invariant.
+In constrast, there is no topological magnetoelectric effect
+and no QHE in the surface layers of the QSHI stack. Instead,
+the states maintain their degeneracy and helicity, for small
+ﬁelds, which is consistent when we view the ﬁeld as paral-
+lel to the edge surfaces hosting the helical boundary states of
+the QSHI layers. Therefore, although the spectrum of q(3-1)D
+STI slab appears to be similar to the spectrum of a QSHI stack,
+its response to TRS-breaking perturbations reveals that it is a
+ﬁnite-size topological phase arising from (1; 000) topology of
+the 3D bulk.
+V
+3D TI wire
+We ﬁnally consider a q(3-2)D wire geometry for the STI,
+demonstrating that ﬁnite-size topology arises from inter-
+ference between topologically-protected boundary states of
+ﬁnite-size topological phases, as well as interference be-
+
+9
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+(a)
+−π
+−π/2
+0
+π/2
+π
+kz
+−0.2
+−0.1
+0.0
+0.1
+0.2
+E(kz)
+(b)
+−π
+−π/2
+0
+π/2
+π
+kz
+−0.2
+−0.1
+0.0
+0.1
+0.2
+E(kz)
+(c)
+1
+2
+3
+4
+5
+6
+i
+0.0
+0.1
+0.2
+0.3
+0.4
+0.5
+σxy/σ0
+(d)
+FIG. 9. a) Diagram of perturbations and edge states (pink) on a q(3-
+1)D STI slab, parallel ﬁeld (purple) and perpendicular ﬁeld (black),
+we consider the perturbations for OBC in x, y and PBC in z. b)
+Spectrum of STI slab with OBC in x and y, Nx = 5, Ny = 100. A
+constant Zeeman ﬁeld ordering κ = 0.1 parallel to the slab top and
+bottom layers is present. The parameters are M = 1.8, λ = 0.1.
+c) Same parameters as in c) but now with a perpendicular ﬁeld the
+system exhibits a QHE.d) Layer conductivity (Chern number) for
+Nx = 6, M = 2.0,λ = 0.2 .
+tween the topologically-protected boundary states of topologi-
+cal phases in the ten-fold way. We therefore consider the same
+Hamiltonian Eq. (4) as considered in the previous section, but
+now with open boundary conditions in ˆx- and ˆy-directions and
+periodic boundary conditions in the ˆz-direction, with the num-
+ber of lattice sites in the ˆx- and ˆy-directions, Nx and Ny, re-
+spectively, each much less than Nz, the number of lattice sites
+in the ˆz-direction (so Nx, Ny ≪ Nz).
+According to the ten-fold way classiﬁcation scheme for
+topological phases of matter, this is an effectively 1D sys-
+tem in class AII, which is topologically-trivial [37, 38, 47].
+Here, we show ﬁnite-size topological phases are nonetheless
+possible in this system, ﬁrst characterizing ﬁnite-size topol-
+ogy of the q1D bulk through analysis of Wilson loop spectra,
+and then by demonstrating an additional bulk-boundary corre-
+spondence yielding q(3-3)D topologically-protected boundary
+modes in the q1D wire, ultimately resulting from interference
+between the topologically-protected Dirac cone surface states
+of the STI.
+For the q(3-2)D bulk of the STI with periodic boundary
+conditions only in the ˆz-direction, we compute Wilson loop
+spectra by integrating over this one good momentum com-
+ponent, similarly to the Wilson loop spectra calculations for
+the q(3-2)D bulk of the QSHI in Section II. The topological
+phase diagrams of the STI q(3-2)D bulk are then determined
+by computing the number of eigenvalues in the Wilson
+loop spectrum with ±π phases, or N±π.
+Although in the
+previous cases the spectrum only had two ±π phases or none
+corresponding to nontrivial and trivial regions, we ﬁnd for
+the 3D TI wire that some regions of the phase diagram have
+1
+1.5
+2
+2.5
+3
+M
+0.0
+0.1
+0.2
+0.3
+λ
+0
+2
+4
+6
+8
+N±π
+(a)
+1
+1.5
+2.0
+2.5
+3
+M
+0
+0.1
+0.2
+0.3
+λ
+0.0
+0.1
+0.2
+∆
+(b)
+1
+1.5
+2
+2.5
+3
+M
+0.0
+0.1
+0.2
+0.3
+λ
+0
+2
+4
+6
+8
+N±π
+(c)
+1
+1.5
+2.0
+2.5
+3
+M
+0
+0.1
+0.2
+0.3
+λ
+0.0
+0.1
+0.2
+∆
+(d)
+1
+1.5
+2
+2.5
+3
+M
+0.0
+0.1
+0.2
+0.3
+λ
+0
+2
+4
+6
+8
+N±π
+(e)
+1
+1.5
+2.0
+2.5
+3
+M
+0
+0.1
+0.2
+0.3
+λ
+0.0
+0.1
+0.2
+∆
+(f)
+FIG. 10.
+a) Phase diagram for the same ﬁnite size parameters but
+PBC in z, red reﬂects 4 ±π phases, yellow 2, blue 0. with Nx =
+Ny = 4 b) Heat plot of direct gap for the same system parameters.
+c),d) and e),f) same as before, but for Nx = 4, Ny = 5 and Nx =
+Ny = 6 respectfully.
+four ±π phase eigenvalues as shown in red in Fig. 10 a) for
+Nx = Ny = 4. In the case of Nx = Ny = 6, the phase
+diagram changes again and now there are not only two and
+four ±π phases but also six ±π phases as shown in blue in
+Fig. 10 e). The change of invariant is consistent with a gap
+closing of the q(3-2)D bulk as shown in Fig.10 b),f) where
+the gap closings coincide with the change of number of ±π
+phases in the Wilson loop spectrum.
+1.0
+1.5
+2.0
+2.5
+3.0
+M
+−0.2
+−0.1
+0.0
+0.1
+0.2
+E(M)
+(a)
+1.0
+1.5
+2.0
+2.5
+3.0
+M
+−0.2
+−0.1
+0.0
+0.1
+0.2
+E(M)
+(b)
+FIG. 11.
+a) Spectrum for OBC in x,y,z as a function of M, with
+Nx, Ny = 4 and Nz = 50 sites in the remaining directions with
+λ = 0.1. b) Same plot but for Nx = 4, Ny = 5 and Nz = 100.
+
+10
+As in previous cases, we ﬁnd the topological phase dia-
+grams for the q(3-2)D bulk of the STI depend strongly on
+system size. In the case of Nx = 4, Ny = 5, we ﬁnd that
+the region with four ±π phases occurs for smaller parameter
+regions and is furthermore shifted in M and skewed relative
+to the corresponding regions in the Nx = Ny = 4, reﬂecting
+the difference between x and y directions in phase space. The
+skewness is also more prominent as we increase the number
+of sites as seen for Nx = Ny = 6 in Fig. 10 e). In this case,
+even though the topologically non-trivial regions diminish
+in size, they are more strongly skewed. The deformation is
+such that, starting in a trivial region according to N±π near
+M = 1.75, with almost zero λ, we can drive the system
+into a topologically non-trivial regime as determined by
+N±π by increasing the spin-orbit coupling to λ ≈ 0.1. A
+comparison of the phase diagrams in Fig. 10, indicates that,
+as the number of sites increases, the regions present originally
+in Nx = Ny = 4 remain for Nx = Ny = 6 although now
+shifted to greater M and reduced in size over phase space.
+We notice also that the new regions appear from the left.
+The topological phase diagram and corresponding q(3-2)D
+minimum direct bulk gap phase diagram for Nx = Ny = 6
+are shown in Fig. 10 e), f), respectively.
+While there are
+similarities between results for this system size and the
+smaller ones, there is a topological region for which six
+Wilson loop eigenvalues have phases ﬁxed to ±π.
+The
+regions of greater N±π appear to be subsets of regions with
+lesser N±π: the blue region is contained within a red region,
+and red regions are contained within yellow regions.
+The
+states again localize at the boundaries of the wire and states
+occur in Kramers pairs. These results indicate the number of
+±π phases in the Wilson loop spectrum, N±π, corresponds
+to half the number of zero energy edge states N(E = 0) in
+the q(3-2)D STI system with OBC in all directions. We can
+verify this relation appears to hold for the q(2-1)D QSHI wire
+and the q(3-1)D STI slab as well. As N±π > 2 occurs for the
+q1D STI wire, this comes to suggest an integer classiﬁcation
+2Z for the q(3-2)D STI ﬁnite-size topological phases, to be
+explored in greater detail in future work.
+Based on the topological phase diagrams for the q(3-
+2)D bulk, we now check for a ﬁnite-size topological bulk-
+boundary correspondence in this geometry by opening bound-
+ary conditions in the ˆz-direction, searching for topologically-
+protected boundary modes localized at the ends of the q(3-2)D
+wire. In analogy to the q(2-1)D QSHI wire, we study the non-
+trivial number of ±π eigenvalues in the Wilson loop spectrum,
+Fig. 11 a),b). The system with N±π = 4 phases has now eight
+edge states within the q(3-2)D bulk gap. These states occur in
+Kramers pairs, with each state in a given Kramers pair local-
+ized at the same edge There are, however, differences between
+these states observable in the probability density distributions.
+We show the probability densities as a function of layer index
+in each of the ˆz- and ˆy-directions, respectively,for four of the
+in-gap states, in Figs. 12 a) and b), respectively. The cor-
+responding probability densities as a function of layer in the
+ˆz-direction and ˆy-direction for the other four in-gap states are
+shown in Figs. 12 c) and d), respectively. We see that the sec-
+ond set of four are distinguished from the ﬁrst four by their
+localization: the second set of four are pushed inwards from
+the edge in both the ˆz- and ˆy-direction relative to the ﬁrst four
+in-gap states. We ﬁnd similar physics for Nx = Ny = 6 in the
+N±π = 6 phase: there are 12 q(3-3)D edge states at zero en-
+ergy within the q(3-2)D bulk gap. This change in localization
+suggests that there is a distinction between edge states which
+may give way to distinct phases not distinguished by just the
+parity of the number of edge states.
+0
+20
+40
+60
+80
+z
+0.0
+0.5
+1.0
+|ψ|2
+×10−2
+(a)
+1
+2
+3
+4
+y
+0.5
+0.7
+1.0
+|ψ|2
+×10−2
+(b)
+0
+20
+40
+60
+80
+z
+0.0
+0.2
+0.4
+|ψ|2
+×10−2
+(c)
+1
+2
+3
+4
+y
+0.3
+0.4
+0.5
+0.6
+|ψ|2
+×10−2
+(d)
+FIG. 12.
+a) Probability density plot for one q(3-3)D edge mode as
+a function of wire length z with M = 1.25, λ = 0.1,Nx = Ny =
+4, Nz = 80 b) same edge state as a function of site index y , c)
+Probability density for another quasi-0D edge mode within the same
+model parameters as a function of wire length d) now as a function
+of site index y.
+VI
+Concluding remarks
+In this work, we have studied ﬁnite-size topology in time-
+reversal invariant systems, emerging from the hybridization
+of helical boundary modes in QSHIs and of Dirac cones in the
+strong TI. In the case of the QSHI, we ﬁnd the helical bound-
+ary modes generically interfere to realize regions in phase
+space where the q(2-1)D bulk spectrum (periodic boundary
+conditions in one direction and open boundary conditions in
+the other) is gapped. These regions are separated from one
+another by critical points at which the q(2-1)D minimum
+direct bulk gap is zero. We characterize the topology of these
+gapped regions by computing Wilson loop spectra, ﬁnding
+topologically non-trivial gapped phases of the q(2-1)D
+bulk corresponding to a non-trivial number of Wilson loop
+eigenvalues with phase ﬁxed to ±π.
+For open boundary conditions in each direction and a q(2-
+1)D wire geometry, these Wilson loop eigenvalues with phase
+±π correspond to topologically-protected q(2-2)D boundary
+modes localized at the ends of the wire. These q(2-2)D bound-
+ary modes occur in Kramers pairs and are robust against dis-
+
+11
+x
+quasi-3D slab with additional OBCs in z
+boundary mode interference
+quasi-2D FST boundary mode
+3D boundary mode
+3D boundary mode
+quasi-3D slab from 4D bulk
+y
+y
+x
+z
+z
+FIG. 13. a) Schematic diagram of a 4D topological phase consisting of some x, y, z real space directions and an Lz orbital degree of freedom
+which gets thinned in the orbital direction. In this case the quasi-3D slab spectrum from the 4D bulk results from the hybridization of
+the original 3D boundary modes. b) The previous q(4-1)D slab possess an additional bulk-boundary correspondence when additional open
+boundary conditions in the z direction are considered. This results in q(4-2)D boundary modes.
+order respecting spinful time-reversal symmetry, maintaining
+a fourfold degeneracy for particle-hole symmetric disorder,
+and splitting into doubly-degenerate Kramers pairs for disor-
+der breaking particle-hole symmetry. In these cases, the in-
+gap, q(2-2)D modes are still topologically-robust in that they
+must correspond to time-reversal invariant charge transfer in
+an aperiodic Thouless pump from valence bands to conduc-
+tion bands, and this connectivity between q(2-1)D bulk va-
+lence and conduction bands is observed in topological phase
+diagrams.
+We ﬁrst observe this ﬁnite-size topology of the QSHI for
+a canonical Hamiltonian describing HgTe quantum wells,
+but also ﬁnd the ﬁnite-size topological phase occurs in a
+tight-binding model for 1T’-WTe2 ribbons with sawtooth
+edges derived from density functional theory calculations,
+thus potentially relevant to experiment.
+In the case of the
+strong topological insulator protected by time-reversal sym-
+metry, we ﬁnd ﬁnite-size topological phases both for q(3-1)D
+slab geometries and q(3-2)D wire geometries. Wilson loop
+spectra are used to characterize the topology of the q(3-1)D
+and q(3-2)D bulk: the winding of the Wilson loop eigenvalue
+phases characterizes the q(3-1)D topology, similarly to
+characterization of 2D topological phases in the bulk, while
+the q(3-2)D wire topology in this case is also characterized
+by the number of ±π Wilson loop eigenvalue phases as in
+the case of the q(2-1)D QSHI. For open boundary conditions
+in two directions, the q(3-1)D STI slab exhibits helical
+boundary modes in the ﬁnite-size topological phase, but
+also exhibits signatures of the magneto-electric polarizability
+of the STI, distinguishing this ﬁnite-size topological phase
+from the QSHI. In the case of the q(3-2)D wire, q(3-3)D
+boundary modes occur for open boundary conditions in all
+three directions, similarly to those of the q(2-1)D QSHI.
+However, results indicate that topological classiﬁcation for
+the q(3-2)D STI is integer rather than Z2, with unusual
+localization of the quasi-0D topological boundary modes.
+Importantly, these results show that ﬁnite-size topology yields
+topologically-protected boundary modes of codimension
+greater than 1.
+We close by pointing out an intriguing possible extension
+of the work to a system with dimension D > 3. For example,
+a four-dimensional topological phase is expected in a q(4-1)D
+setting, as pictured schematically in Fig. 13 for a small sys-
+tem size in some fourth dimension. These extra non-spatial
+dimensions could come from physical degrees of freedom,
+typically considered for three-dimensional systems, such as
+a p orbital degree of freedom as considered in Fig. 13 a). One
+could now imagine an inﬁnite 4D bulk deﬁned by the ˆx-, ˆy-
+, ˆz-, and ˆLz (angular momentum)-axes. For non-trivial 4D
+bulk topological invariant, open boundary conditions in the
+ˆLz-direction and a large system size in the ˆLz-direction, three-
+dimensional topologically-protected boundary modes are re-
+alized. For the physical scenario of small system sizes in the
+
+12
+ˆLz-direction as shown in Fig. 13 a), these three-dimensional
+boundary modes could interfere to realize a topologically non-
+trivial FST phase, such that additional topologically-protected
+boundary modes are realized when boundary conditions are
+additionally opened in a second real-space direction, such as
+the ˆz-direction as shown in Fig. 13 b). This raises the possibil-
+ity of topologically-protected boundary states for systems in
+one to three-dimensions reﬂecting higher-dimensional, D > 3
+bulk topology.
+[1] B. Andrei Bernevig, Taylor L. Hughes,
+and Shou-Cheng
+Zhang, “Quantum spin hall effect and topological phase transi-
+tion in HgTe quantum wells,” Science 314, 1757–1761 (2006),
+https://www.science.org/doi/pdf/10.1126/science.1133734.
+[2] Markus K¨onig, Steffen Wiedmann, Christoph Br¨une, Andreas
+Roth, Hartmut Buhmann, Laurens W. Molenkamp, Xiao-Liang
+Qi,
+and Shou-Cheng Zhang, “Quantum spin hall insulator
+state in HgTe quantum wells,” Science 318, 766–770 (2007),
+https://www.science.org/doi/pdf/10.1126/science.1148047.
+[3] Chetan Nayak, Steven H. Simon, Ady Stern, Michael Freed-
+man, and Sankar Das Sarma, “Non-abelian anyons and topo-
+logical quantum computation,” Rev. Mod. Phys. 80, 1083–1159
+(2008).
+[4] A.Yu. Kitaev, “Fault-tolerant quantum computation by anyons,”
+Annals of Physics 303, 2–30 (2003).
+[5] Dominic V. Else, Ryan Thorngren, and T. Senthil, “Non-fermi
+liquids as ersatz fermi liquids: General constraints on com-
+pressible metals,” Phys. Rev. X 11, 021005 (2021).
+[6] K. v. Klitzing, G. Dorda,
+and M. Pepper, “New method
+for high-accuracy determination of the ﬁne-structure constant
+based on quantized hall resistance,” Phys. Rev. Lett. 45, 494–
+497 (1980).
+[7] D. C. Tsui, H. L. Stormer,
+and A. C. Gossard, “Two-
+dimensional magnetotransport in the extreme quantum limit,”
+Phys. Rev. Lett. 48, 1559–1562 (1982).
+[8] R. B. Laughlin, “Anomalous quantum hall effect: An incom-
+pressible quantum ﬂuid with fractionally charged excitations,”
+Phys. Rev. Lett. 50, 1395–1398 (1983).
+[9] D. Hsieh,
+Y. Xia,
+L. Wray,
+D. Qian,
+A. Pal,
+J. H.
+Dil,
+J.
+Osterwalder,
+F.
+Meier,
+G.
+Bihlmayer,
+C.
+L.
+Kane, Y. S. Hor, R. J. Cava,
+and M. Z. Hasan, “Ob-
+servation
+of
+unconventional
+quantum
+spin
+textures
+in
+topological
+insulators,”
+Science
+323,
+919–922
+(2009),
+https://www.science.org/doi/pdf/10.1126/science.1167733.
+[10] Jiho Noh, Wladimir A Benalcazar, Sheng Huang, Matthew J
+Collins, Kevin P Chen, Taylor L Hughes,
+and Mikael C
+Rechtsman, “Topological protection of photonic mid-gap de-
+fect modes,” Nature Photonics 12, 408–415 (2018).
+[11] Christopher W Peterson,
+Wladimir A Benalcazar,
+Tay-
+lor L Hughes,
+and Gaurav Bahl, “A quantized microwave
+quadrupole insulator with topologically protected corner
+states,” Nature 555, 346–350 (2018).
+[12] Stefan Imhof, Christian Berger, Florian Bayer, Johannes
+Brehm, Laurens W Molenkamp, Tobias Kiessling, Frank
+Schindler, Ching Hua Lee, Martin Greiter, Titus Neupert, et al.,
+“Topolectrical-circuit realization of topological corner modes,”
+Nature Physics 14, 925–929 (2018).
+[13] Marc Serra-Garcia, Valerio Peri, Roman S¨usstrunk, Osama R
+Bilal, Tom Larsen, Luis Guillermo Villanueva, and Sebastian D
+Huber, “Observation of a phononic quadrupole topological in-
+sulator,” Nature 555, 342–345 (2018).
+[14] Frank Schindler,
+Ashley M. Cook,
+Maia G. Vergniory,
+Zhijun Wang, Stuart S. P. Parkin, B. Andrei Bernevig,
+and
+Titus
+Neupert,
+“Higher-order
+topological
+in-
+sulators,”
+Science
+Advances
+4,
+eaat0346
+(2018),
+https://www.science.org/doi/pdf/10.1126/sciadv.aat0346.
+[15] F. D. M. Haldane, “Model for a quantum hall effect with-
+out landau levels: Condensed-matter realization of the ”parity
+anomaly”,” Phys. Rev. Lett. 61, 2015–2018 (1988).
+[16] Charles L Kane and Eugene J Mele, “Quantum spin hall effect
+in graphene,” Physical review letters 95, 226801 (2005).
+[17] C. L. Kane and E. J. Mele, “Z2 topological order and the quan-
+tum spin hall effect,” Phys. Rev. Lett. 95, 146802 (2005).
+[18] Cui-Zu Chang, Jinsong Zhang, Xiao Feng, Jie Shen, Zuocheng
+Zhang, Minghua Guo, Kang Li, Yunbo Ou, Pang Wei, Li-Li
+Wang, Zhong-Qing Ji, Yang Feng, Shuaihua Ji, Xi Chen, Jin-
+feng Jia, Xi Dai, Zhong Fang, Shou-Cheng Zhang, Ke He,
+Yayu Wang, Li Lu, Xu-Cun Ma, and Qi-Kun Xue, “Experi-
+mental observation of the quantum anomalous hall effect in a
+magnetic topological insulator,” Science 340, 167–170 (2013),
+https://www.science.org/doi/pdf/10.1126/science.1234414.
+[19] Yugui Yao, Fei Ye, Xiao-Liang Qi, Shou-Cheng Zhang, and
+Zhong Fang, “Spin-orbit gap of graphene: First-principles cal-
+culations,” Phys. Rev. B 75, 041401 (2007).
+[20] Hongki Min, J. E. Hill, Nikolai A. Sinitsyn, B. R. Sahu,
+Leonard Kleinman, and Allan H. MacDonald, “Intrinsic and
+rashba spin-orbit interactions in graphene sheets,” Physical Re-
+view B 74, 165310 (2006).
+[21] Arthur
+Leis,
+Michael
+Schleenvoigt,
+Vasily
+Cherepanov,
+Felix L¨upke, Peter Sch¨uffelgen, Gregor Mussler, Detlev
+Gr¨utzmacher, Bert Voigtl¨ander, and F. Stefan Tautz, “Lifting
+the spin-momentum locking in ultra-thin topological insulator
+ﬁlms,” Advanced Quantum Technologies 4, 2100083 (2021),
+https://onlinelibrary.wiley.com/doi/pdf/10.1002/qute.202100083.
+[22] Yi Zhang, Ke He, Cui-Zu Chang, Can-Li Song, Li-Li Wang,
+Xi Chen, Jin-Feng Jia, Zhong Fang, Xi Dai, Wen-Yu Shan,
+Shun-Qing Shen, Qian Niu, Xiao-Liang Qi, Shou-Cheng
+Zhang, Xu-Cun Ma,
+and Qi-Kun Xue, “Crossover of the
+three-dimensional topological insulator Bi2Se3 to the two-
+dimensional limit,” Nature Physics 6, 584–588 (2010).
+[23] Yusuke Sakamoto, Toru Hirahara, Hidetoshi Miyazaki, Shin-
+ichi Kimura,
+and Shuji Hasegawa, “Spectroscopic evidence
+of a topological quantum phase transition in ultrathin Bi2Se3
+ﬁlms,” Phys. Rev. B 81, 165432 (2010).
+[24] A. K. Geim and I. V. Grigorieva, “Van der waals heterostruc-
+tures,” Nature 499, 419–425 (2013).
+[25] Chaowei Hu, Kyle N. Gordon, Pengfei Liu, Jinyu Liu, Xiaoqing
+Zhou, Peipei Hao, Dushyant Narayan, Eve Emmanouilidou,
+Hongyi Sun, Yuntian Liu, Harlan Brawer, Arthur P. Ramirez,
+Lei Ding, Huibo Cao, Qihang Liu, Dan Dessau, and Ni Ni,
+“A van der waals antiferromagnetic topological insulator with
+weak interlayer magnetic coupling,” Nature Communications
+11, 97 (2020).
+[26] Su Kong Chong, Kyu Bum Han, Akira Nagaoka, Ryuichi
+Tsuchikawa,
+Renlong
+Liu,
+Haoliang
+Liu,
+Zeev
+Valy
+Vardeny,
+Dmytro
+A.
+Pesin,
+Changgu
+Lee,
+Taylor
+D.
+Sparks,
+and
+Vikram
+V.
+Deshpande,
+“Topological
+insulator-based van der waals heterostructures for effec-
+
+13
+tive
+control
+of
+massless
+and
+massive
+dirac
+fermions,”
+Nano Letters 18, 8047–8053 (2018), pMID: 30406664,
+https://doi.org/10.1021/acs.nanolett.8b04291.
+[27] Liangzhi Kou,
+Shu-Chun Wu,
+Claudia Felser,
+Thomas
+Frauenheim,
+Changfeng Chen,
+and Binghai Yan, “Ro-
+bust 2d topological insulators in van der waals heterostruc-
+tures,” ACS Nano 8, 10448–10454 (2014), pMID: 25226453,
+https://doi.org/10.1021/nn503789v.
+[28] Sajid Husain, Rahul Gupta, Ankit Kumar, Prabhat Kumar, Nil-
+amani Behera, Rimantas Brucas, Sujeet Chaudhary, and Peter
+Svedlindh, “Emergence of spin–orbit torques in 2d transition
+metal dichalcogenides: A status update,” Applied Physics Re-
+views 7, 041312 (2020), https://doi.org/10.1063/5.0025318.
+[29] Daniele Varsano, Maurizia Palummo, Elisa Molinari, and Mas-
+simo Rontani, “A monolayer transition-metal dichalcogenide as
+a topological excitonic insulator,” Nature Nanotechnology 15,
+367–372 (2020).
+[30] Peng Song, Chuanghan Hsu, Meng Zhao, Xiaoxu Zhao, Tay-
+Rong Chang, Jinghua Teng, Hsin Lin,
+and Kian Ping Loh,
+“Few-layer 1t’ MoTe2 as gapless semimetal with thickness de-
+pendent carrier transport,” 2D Materials 5, 031010 (2018).
+[31] Xiaofeng
+Qian,
+Junwei
+Liu,
+Liang
+Fu,
+and
+Ju
+Li,
+“Quantum spin hall effect in two-dimensional transition
+metal dichalcogenides,” Science 346, 1344–1347 (2014),
+https://www.science.org/doi/pdf/10.1126/science.1256815.
+[32] A Yu Kitaev, “Unpaired majorana fermions in quantum wires,”
+Physics-Uspekhi 44, 131–136 (2001).
+[33] A. A. Burkov and Leon Balents, “Weyl semimetal in a topolog-
+ical insulator multilayer,” Phys. Rev. Lett. 107, 127205 (2011).
+[34] J. E. Moore and L. Balents, “Topological invariants of time-
+reversal-invariant band structures,” Phys. Rev. B 75, 121306
+(2007).
+[35] Liang Fu, C. L. Kane, and E. J. Mele, “Topological insulators
+in three dimensions,” Phys. Rev. Lett. 98, 106803 (2007).
+[36] Yoichi Ando and Liang Fu, “Topological crystalline insu-
+lators and topological superconductors:
+From concepts to
+materials,” Annual Review of Condensed Matter Physics 6,
+361–381 (2015), https://doi.org/10.1146/annurev-conmatphys-
+031214-014501.
+[37] Ching-Kai Chiu, Jeffrey C. Y. Teo, Andreas P. Schnyder, and
+Shinsei Ryu, “Classiﬁcation of topological quantum matter
+with symmetries,” Rev. Mod. Phys. 88, 035005 (2016).
+[38] Alexei Kitaev, “Periodic table for topological insulators and
+superconductors,” AIP Conference Proceedings 1134, 22–30
+(2009), https://aip.scitation.org/doi/pdf/10.1063/1.3149495.
+[39] Lara Ulcakar, Jernej Mravlje, Anton Ramsak, and Toma z Re-
+jec, “Slow quenches in two-dimensional time-reversal symmet-
+ric Z2 topological insulators,” Phys. Rev. B 97, 195127 (2018).
+[40] Bin Zhou, Hai-Zhou Lu, Rui-Lin Chu, Shun-Qing Shen, and
+Qian Niu, “Finite size effects on helical edge states in a quan-
+tum spin-hall system,” Phys. Rev. Lett. 101, 246807 (2008).
+[41] A. Alexandradinata, Xi Dai, and B. Andrei Bernevig, “Wilson-
+loop characterization of inversion-symmetric topological insu-
+lators,” Phys. Rev. B 89, 155114 (2014).
+[42] Rapha¨el Leone, “The geometry of (non)-abelian adiabatic
+pumping,” Journal of Physics A: Mathematical and Theoretical
+44, 295301 (2011).
+[43] Artur
+Ekert,
+Marie
+Ericsson,
+Patrick
+Hayden,
+Hi-
+toshi
+Inamori,
+Jonathan
+A.
+Jones,
+Daniel
+K.
+L.
+Oi,
+and
+Vlatko
+Vedral,
+“Geometric
+quantum
+computa-
+tion,” Journal of Modern Optics 47, 2501–2513 (2000),
+https://www.tandfonline.com/doi/pdf/10.1080/09500340008232177.
+[44] A. Recati, T. Calarco, P. Zanardi, J. I. Cirac,
+and P. Zoller,
+“Holonomic quantum computation with neutral atoms,” Phys.
+Rev. A 66, 032309 (2002).
+[45] R. D. King-Smith and David Vanderbilt, “Theory of polariza-
+tion of crystalline solids,” Phys. Rev. B 47, 1651–1654 (1993).
+[46] Linhu Li, Zhihao Xu,
+and Shu Chen, “Topological phases
+of generalized su-schrieffer-heeger models,” Phys. Rev. B 89,
+085111 (2014).
+[47] Jeffrey C. Y. Teo and C. L. Kane, “Topological defects and gap-
+less modes in insulators and superconductors,” Phys. Rev. B 82,
+115120 (2010).
+[48] Shujie Tang, Chaofan Zhang, Dillon Wong, Zahra Pedram-
+razi, Hsin-Zon Tsai, Chunjing Jia, Brian Moritz, Martin
+Claassen, Hyejin Ryu, Salman Kahn, Juan Jiang, Hao Yan,
+Makoto Hashimoto, Donghui Lu, Robert G. Moore, Chan-
+Cuk Hwang, Choongyu Hwang, Zahid Hussain, Yulin Chen,
+Miguel M. Ugeda, Zhi Liu, Xiaoming Xie, Thomas P. Dev-
+ereaux, Michael F. Crommie, Sung-Kwan Mo, and Zhi-Xun
+Shen, “Quantum spin hall state in monolayer 1T′-WTe2,” Na-
+ture Physics 13, 683–687 (2017).
+[49] Alexander Lau, Rajyavardhan Ray, D´aniel Varjas,
+and An-
+ton R. Akhmerov, “Inﬂuence of lattice termination on the edge
+states of the quantum spin hall insulator monolayer 1T′-WTe2,”
+Phys. Rev. Materials 3, 054206 (2019).
+[50] G. Rosenberg and M. Franz, “Witten effect in a crystalline topo-
+logical insulator,” Phys. Rev. B 82, 035105 (2010).
+[51] Andrew M. Essin, Joel E. Moore, and David Vanderbilt, “Mag-
+netoelectric polarizability and axion electrodynamics in crys-
+talline insulators,” Phys. Rev. Lett. 102, 146805 (2009).
+
+14
+Supplemental material for “Time-reversal invariant ﬁnite-size topology”
+R. Flores-Calderon,1 Roderich Moessner,1 and Ashley M. Cook1,2,∗
+1Max Planck Institute for Chemical Physics of Solids, N¨othnitzer Strasse 40, 01187 Dresden, Germany
+2Max Planck Institute for the Physics of Complex Systems, N¨othnitzer Strasse 38, 01187 Dresden, Germany
+∗Electronic address: cooka@pks.mpg.de
+(Dated: January 6, 2023)
+S1
+Tight-binding model for 1T ′-WTe2
+In the main text we discussed a realistic model for realizing ﬁnite-size topology in a 1T ′ − WTe2 monolayer. We adapted the
+ﬁnite-size calculation from the model explored and derived in reference [49]. The model predicts that the four bands closest to
+the Fermi level are composed mainly of contributions from two 3dx2−y2 type orbitals centered at W and two 5px type orbitals
+centered at a subset of Te. With this information at hand and some experimental ﬁtting the authors construct a minimal tight
+binding model that includes also a spin orbit interaction given by:
+HWTe2(k) =s0
+��µp
+2 + tpx cos (akx) + tpy cos (bky)
+�
+Γ−
+1 +
+�µd
+2 + tdx cos (akx)
+�
+Γ+
+1 + tdABe−ibky �
+1 + eiakx�
+eik·∆1Γ+
+2
++ tpAB
+�
+1 + eiakx�
+eik·∆2Γ−
+2 + t0AB
+�
+1 − eiakx�
+eik·∆3Γ3 − 2it0x sin (akx)
+�
+eik·∆4Γ+
+4 + e−ik·∆4Γ−
+4
+�
++ t0ABx
+�
+e−iakx − e2iakx�
+eik·∆3Γ3 + H.c.
+�
++ [(λz
+dxsz + λy
+dxsy) sin (akx)] Γ+
+5 +
+��
+λz
+pxsz + λy
+pxsy
+�
+sin (akx)
+�
+Γ−
+5
+− iλy
+0ABsy
+�
+1 + eiakx�
+eik·∆3Γ6 − i (λz
+0sz + λy
+0sy)
+�
+eik·∆4Γ+
+4 − e−ik·∆4Γ−
+4
+�
+− i (λz
+0sz + λy
+0sy)
+×
+�
+e−ibkyeik·∆4Γ+
+4 − eibkye−ik·∆4Γ−
+4
+�
++ H.c.,
+(S1)
+,where si are Pauli matrices representing the spin degree of freedom and they deﬁned the gamma matrices as:
+Γ0 = τ0σ0
+(S2)
+Γ±
+1 = τ0
+2 (σ0 ± σ3)
+(S3)
+Γ±
+2 = 1
+4 (τ1 + iτ2) (σ0 ± σ3)
+(S4)
+Γ3 = 1
+2 (τ1 + iτ2) iσ2
+(S5)
+Γ±
+4 = 1
+4 (τ0 ± τ3) (σ1 + iσ2)
+(S6)
+Γ±
+5 = τ3
+2 (σ0 ± σ3)
+(S7)
+Γ6 = 1
+2 (τ1 + iτ2) σ1
+(S8)
+,where τi, σi are Pauli matrices acting in sublattice and orbital degrees of freedom respectively. Finally the constants from the
+previous Hamiltonian that reproduce the experimental results are:
+µp
+−1.75eV
+λy
+0AB
+0.011eV
+µd
+0.74eV
+λy
+0
+0.051eV
+tpx
+1.13eV
+λz
+0
+0.012eV
+tdx
+−0.41eV
+λ′y
+0
+0.050eV
+tpAB
+0.40eV
+λ′z
+0
+0.012eV
+tdAB
+0.51eV
+λy
+px
+−0.040eV
+t0AB
+0.39eV
+λz
+px
+−0.010eV
+t0ABx
+0.29eV
+λy
+dx
+−0.031eV
+t0x
+0.14eV
+λz
+dx
+−0.008eV
+tpy
+0.13eV
+a
+3.477 ˚A
+b
+6.249 ˚A
+rAd
+(−0.25a, 0.32b)
+rBp
+(0.25a, 0.07b)
+rAp
+(−0.25a, −0.07b)
+rBd
+(0.25a, −0.32b)
+(S9)
+
+15
+Finally we extended the model with an inclusion of a perpendicular electric ﬁeld in the weak limit where the effect manifests
+itself as a change of Rashba spin orbit interaction, in the previous Hamiltonian this is modelled as a replacement λi → λi + ∆λ,
+with i = x, y.
+
diff --git a/xNA0T4oBgHgl3EQfMf_C/content/tmp_files/load_file.txt b/xNA0T4oBgHgl3EQfMf_C/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..504bde5a53a9bc886c3827111f0b38a933b74953
--- /dev/null
+++ b/xNA0T4oBgHgl3EQfMf_C/content/tmp_files/load_file.txt
@@ -0,0 +1,1039 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf,len=1038
+page_content='Time-reversal invariant ﬁnite-size topology  R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' Flores-Calderon,1, 2 Roderich Moessner,1 and Ashley M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' Cook1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' 2  1Max Planck Institute for the Physics of Complex Systems,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' N¨othnitzer Strasse 38,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' 01187 Dresden,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' Germany  2Max Planck Institute for Chemical Physics of Solids,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' N¨othnitzer Strasse 40,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' 01187 Dresden,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' Germany  We report ﬁnite-size topology in the quintessential time-reversal (TR) invariant systems,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' the quantum spin  Hall insulator (QSHI) and the three-dimensional,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' strong topological insulator (STI): previously-identiﬁed heli-  cal or Dirac cone boundary states of these phases hybridize in wire or slab geometries with one open boundary  condition for ﬁnite system size,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' and additional,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' topologically-protected,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' lower-dimensional boundary modes  appear for open boundary conditions in two or more directions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' For the quasi-one-dimensional (q(2-1)D) QSHI,  we ﬁnd topologically-protected, quasi-zero-dimensional (q(2-2)D) boundary states within the hybridization gap  of the helical edge states, determined from q(2-1)D bulk topology characterized by topologically non-trivial  Wilson loop spectra.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' We show this ﬁnite-size topology furthermore occurs in 1T’-WTe2 in ribbon geometries  with sawtooth edges, based on analysis of a tight-binding model derived from density-functional theory calcula-  tions, motivating experimental investigation of our results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' In addition, we ﬁnd quasi-two-dimensional (q(3-1)D)  ﬁnite-size topological phases occur for the STI, yielding helical boundary modes distinguished from those of the  QSHI by a non-trivial magneto-electric polarizability linked to the original 3D bulk STI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' Finite-size topological  phases therefore exhibit signatures associated with the non-trivial topological invariant of a higher-dimensional  bulk, clearly distinguishing them from previously-known topological phases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' Finally, we ﬁnd the q(3-2)D STI  also exhibits ﬁnite-size topological phases, ﬁnding the ﬁrst signs of topologically-protected boundary modes  of codimension greater than 1 due to ﬁnite-size topology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' Finite-size topology of four or higher-dimensional  systems is therefore possible in experimental settings without recourse to thermodynamically large synthetic  dimensions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  I  Introduction  The discovery of the ﬁrst topological insulator (TI), the  quantum spin Hall insulator (QSHI) in HgTe quantum  wells [1, 2] heralded a paradigm shift in condensed matter  physics towards broad study of topological phases of matter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  Understanding and characterization of topology is now  central to the ﬁeld, with major applications ranging from  fault-tolerant quantum computing [3, 4] to unconventional  superconductivity [5].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  Consequently, searching for novel,  experimentally-accessible topological systems is a major  theme of the last few decades [2, 6–13].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  These efforts  usually target experimental conﬁrmation of a hallmark of  topological phases known as bulk-boundary correspondence:  a non-trivial topological invariant of the system bulk is  associated with topologically-robust, gapless boundary states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  While it has long been understood that a D-dimensional  bulk topology yields (D − 1)-dimensional gapless boundary  states for most topological phases [14], the recent discovery  of additional bulk-boundary correspondence even in the  canonical phases, known as ﬁnite-size topology, shows  this foundational aspect of topological physics is richer  than previously-thought.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  If a system is characterized by  a topological invariant computed in the D-dimensional  inﬁnite bulk, but is ﬁnite in size and thin in one direction  as illustrated in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' 1 (for the QSHI D = 2 while for the  3D TI D = 3 ), such that topologically-protected boundary  states interfere with one another, this quasi-(D − 1)- or  q(D − 1)-dimensional bulk is characterized by an additional  topological invariant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  When this additional invariant takes  non-trivial values, open boundary conditions in a second di-  rection yield an additional set of quasi-(D − 2)-dimensional,  topologically-protected boundary states localized on this  boundary of the quasi-(D − 1)-dimensional system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  As  these quasi-(D − 2)-dimensional states are localized on the  boundary in correspondence with a non-trivial value for a  topological invariant of the quasi-(D − 1)-dimensional bulk,  and robust against local perturbations respecting the symme-  tries protecting the topological phase in the D-dimensional  inﬁnite bulk, they constitute previously-unidentiﬁed topologi-  cal phases of matter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  Following the previous thinning process we end up with a  q(D−1)-dimensional bulk with topological edge states in one  less dimension, the situation is then just like at the start of the  program, but with D replaced by D − 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' Thus one may think  of applying the thinning process once again, now thinning the  xD−1 dimension and hybridizing the previous q(D − 2) edge  states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' We then arrive at a q(D − 2) dimensional bulk with  q(D − 2 − 1) dimensional edge states which again can be  subjected to the same procedure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' The general process is illus-  trated in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' 2, while Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' 1 c) shows the speciﬁc case of the  3D TI q(3−2) bulk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' We note that this procedure could in prin-  ciple be applied until there are no more number of dimensions  to thin down.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  Although theoretical discovery of the Chern insulator [15]  preceded theoretical prediction of the TR-invariant QSHI  derived from it [16, 17], experimental conﬁrmation of the  QSHI [2] occurred within one year of the prediction, while  more than two decades passed for the Chern insulator [18].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  This reﬂects a broader trend in the ﬁeld, of TR-invariant  topological insulators being conﬁrmed experimentally more  quickly and easily than TR-symmetry-broken topological  insulators reliant on engineering particular magnetic or-  ders [2, 19, 20].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' Following this idea in order to more rapidly  observe ﬁnite-size topology in experiment, we study the  time-reversal invariant ﬁnite-size topology of the QSHI  and the strong TI (STI), by considering these systems in  geometries as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  We also note that, due to  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='02134v1  [cond-mat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='mes-hall]  5 Jan 2023  2  QSHI  3D TI  E  E  E  E  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' Schematic of the ﬁnite-size TRI systems studied.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' From left to right, a) QSHI wire, b) slab of 3D TI and c) 3D TI wire.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' Blue and red  cones are schematic of the gap openings of the 3D TI due to the hybridization of the the Dirac cones.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' Similarly blue and red helical edge states  get hybridized (yellow/purple) in the QSHI wire and the ﬁnite-size quasi-1D edge states (blue and red) get hybridized (yellow/purple) for the  3D TI wire.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' Topological edge states (pink) are present as quasi-0D modes or quasi-1D modes polarized in spin, for wire or slab conﬁgurations  respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  x x  3  1, ,  1  x  x  FS  FS  x  2  D  xD  D-  1  xD-  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' Schematic of the ﬁnite-size process for topological insulators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' From left to right a D dimensional phase gets shrunk in one direction  xD to give rise to a quasi D − 1 dimensional phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' This phase can be further shrunk in a remaining xD−1 direction so that x1, x2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' xD−2  are still periodic directions and now a quasi D − 2 dimensional phase is realized.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  the vast experimental studies in TI ultra-thin ﬁlms [21–23],  Van der Waals heterostructures [24–27], and transition-metal  dichalcogenides in particular given their large spin-orbit  coupling [28, 29], there may already be signs of ﬁnite-size  topology in previous experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' Past work, for instance,  indicates few-layer 1T’-MoTe2 is semi-metallic [30], while  the monolayer is predicted to be a quantum spin Hall insula-  tor [31], suggesting the few-layer topology derives from the  Weyl semimetal phase of the three-dimensional bulk, while  the monolayer topological phase has a distinct origin due to a  strictly two-dimensional bulk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  Since ﬁnite-size topological phases occur for the Kitaev  chain and Chern insulator,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' non-trivial ﬁnite-size topology is  expected for TR-invariant systems of the QSHI and STI given  concrete relationships between Hamiltonians for these topo-  logical phases: the Kitaev chain Hamiltonian may be used  to construct the Chern insulator Hamiltonian,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' if many chains  are coupled forming a 2D system [32],' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' and a Chern insula-  tor Hamiltonian and its time-reversed partner are the basis of  Hamiltonians for the QSHI[16,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' 17].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' We ﬁnd that FST ex-  tends to these TRI topological phases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' As Hamiltonians for  TR-invariant topological phases are used to construct Hamil-  tonians for other topological phases, these results also re-  veal that a larger set of topological phases harbor FST: a  Weyl semimetal phase[33] Hamiltonian may be constructed  from magnetically-doped STI and trivial insulator thin ﬁlms  stacked alternatingly, while a stack of QSHIs corresponds di-  3  rectly to the weak 3D TI [34, 35].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' Topological crystalline  phases may furthermore be constructed, for instance, as Chern  insulators within mirror subsectors or with the Chern insu-  lator bulk conﬁned to a mirror-invariant plane of a three-  dimensional Brillouin zone [36].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' More generally, topological  crystalline phases are characterized by considering symmetry-  protection by crystalline point group symmetries in addition  to the internal symmetries of the ten-fold way.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' On a technical  level this is accomplished by expressing the Hamiltonian in  a block diagonal form using the additional symmetry, in each  sub-sector internal symmetries are still present and thus can be  analyzed by classiﬁcation schemes obtained from the ten-fold  way [37, 38].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  In this manuscript, we ﬁrst, section II, characterize ﬁnite-  size topology in a QSHI wire.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  We start by considering a  thin QSHI system with one open thin dimension and one in-  ﬁnite periodic dimension.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' The energy and Wilson loop spec-  tra of this q(2-1)D system reveal that the non-trivial zones in  phase space are a subset of the original 2D bulk topological  regions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' Furthermore opening boundary conditions again in  the remaining periodic direction shows the presence of edge  states localized on the q(2-2)D boundaries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' We end this sec-  tion by studying the response to on-site disorder and perturba-  tions, where the robustness of the edge states indicates a link  to the original 2D bulk gap.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' Afterwards in section III, we con-  sider a more realistic and experimentally accessible system  1T ′ WTe2 in the QSHI phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' We ﬁnd similarly that this mate-  rial realizes a ﬁnite-size topological phase with topologically-  robust q(2-2)D edge states for a sawtooth ribbon geometry,  the presence of this edge states is again veriﬁed to be pre-  dicted by a non-trivial Wilson loop spectrum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' Extending our  analysis to the 3D case we consider in section IV the STI in  a q(3-1)D slab geometry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' In this case, interference between  the STI Dirac cone surface states yields q(3-2)D edge states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  We show the Wilson loop spectrum of the q(3-1)D bulk dis-  plays topologically non-trivial signatures in correspondence  with these boundary states, indicating Wilson loop spectra are  a robust bulk diagnostic of ﬁnite-size topology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' Additionally  we compute the magneto-electric polarizability, which should  be trivially zero if the system is just a 2D QSHI, instead we  encounter the response expected for the inﬁnite 3D TI bulk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  This central result allows us to contemplate the idea of detect-  ing topological signatures of higher dimensional phases, say  the 4D TI, in quasi lower dimensional systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' Finally, we  study the case of a STI in a q(3-2)D wire geometry, where we  once again use the Wilson loop indicator to ﬁnd a novel bulk-  boundary correspondence restricted to a subset of the original  3D topological phase diagram.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' In this ﬁnal case the number  of edge states is seen to follow the number of ±π phases such  that only even numbers of distinct edge states appear.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' In sec-  tion VI we summarize our results and present some conclud-  ing remarks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  II  QSHI wire  As a starting point of our analysis we consider a QSHI ﬁrst  considering the canonical Bernevig-Hughes-Zhang Hamilto-  nian for HgTe quantum wells [1] where we also add a Rashba-  type spin orbit coupling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' Thus the Hamiltonian in momentum  space has the form [39]:  h(kx, ky) =(u + 2t(cos kx + cos ky))σz + sin ky σy  (1)  + sin kx szσx + c sxσy,  where si, σi are Pauli matrices in spin and orbital space  respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' For simplicity we omit the identity in spin space  and denote the tensor product by placing two matrices next  to each other.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' The real number u corresponds to a staggered  potential, t to a hopping parameter and c is the spin orbit  coupling that breaks sz spin symmetry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' The phase diagram  for this Hamiltonian includes both a region in which the  QSHI phase is realized and a region in which the Dirac  semimetal (DSM) phase is realized, as discussed in reference  [39] and plotted in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' 3 a) and b) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' In the following analysis,  we ﬁrst consider the QSHI regime, and then that of the DSM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  Next we consider what happens if we open boundary con-  ditions (OBC) in the x direction for a small number of lattice  sites N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' Since the helical edge modes of the QSHI are not  completely localized at the boundary, but instead decay expo-  nentially into the bulk [40], these boundary states interfere in  systems of ﬁnite-width.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' The lattice second quantized Hamil-  tonian with open boundary conditions in the ˆx-direction and  periodic boundary conditions in the ˆy direction is:  ˆH =  �  k,n  Ψ†  k,n ((u + 2t cos k)σz + sin k σy + c sxσy) Ψk,n  + Ψ†  ky,n+1  �  t σz + i  2szσx  �  Ψk,n + h.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' ,  (2)  −2  −1  0  1  2  u  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='5  c  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='5  ∆  (a)  (b)  −π  −π/2  0  π/2  π  ky  −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='0  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='0  E(ky)  OBC  PBC  (c)  −2  −1  0  1  2  u  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='50  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='25  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='25  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='50  E(u)  (d)  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  a) Direct gap heat plot of the 2D bulk hamiltonian eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' (1)  as a function of potential u and spin-orbit coupling constant c, b)  Topological phase diagram of the 2D bulk , showing the QSHI phase  (yellow) and DSM gapless phase (blue) of the 2D bulk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' c) Quasi-1D  dispersion for PBC in y and OBC (PBC) in x with N = 6 sites.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' The  parameters for the gap closing with OBC in x are u = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='76, c =  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='8, t = 1/2 d) Spectrum for PBC in y as a function of the staggered  potential u and c = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='8, t = 1/2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='5  DSM  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='0  C  0  Z2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='0  2  1  0  1  2  u4  where k ≡ ky and n runs over the N sites of the open  x direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' Here, Ψk,n are four component spinor fermion  operators acting on the spin and orbit degrees of freedom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  We ﬁrst examine the spectrum of Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' 2 for small N on  the order of a few lattice constants.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  We ﬁrst consider the  spectrum for a particular point in phase space as shown in  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' 3 c) for a small system with N = 6 with non-trivial  2D bulk invariant, as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' 3 b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  Comparing the  dispersion for the system with periodic boundary conditions  in each direction (black lines) to that of the system with open  boundary conditions only in the ˆx-direction (red lines), we  see the periodic system is gapped, while the system with open  boundary conditions is instead gapless.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' While gapless bound-  ary states are expected due to the non-trivial bulk topology,  the gaplessness in this case is not topologically-robust: the  gapless boundary modes interfere in ﬁnite-size systems to  open a hybridization gap in general.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' Under certain conditions,  however, the boundary modes interfere destructively, corre-  sponding to a ﬁne-tuned gapless state when hybridization  matrix elements pass through zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' Examining the spectrum  for the q(2-1)D bulk as a function of u as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  3  d) , we see this more general pattern of ﬁnite interference  gaps, with a discrete set of u corresponding to gap-closings  and destructive interference between the helical boundary  modes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  We will show these gap-closings can correspond  to topological phase transitions, and some of these gapped  regions host ﬁnite-size topological phases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  A  Periodic system  To characterize the ﬁnite-size topological phases of this time-  reversal invariant system, we now re-interpret the original  model with OBC in the ˆx-direction as a q(2-1)D bulk, and  characterize topology of this q(2-1)D bulk system similarly to  characterization of a d-dimensional bulk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' We therefore ﬁrst  compute a phase diagram for the minimum direct gap over  the Brillouin zone of the q(2-1)D bulk as a function of u, c for  ﬁxed hopping t = 1/2, shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='4 a),b) for N = 6 and  N = 7 layers in the ˆx-direction, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' A dome forms  in the phase diagram, consisting of a set of curved, stripe-like  regions of ﬁnite minimum direct gap separated by lines along  which the q(2-1)D minimum direct bulk gap is zero, with  these lines intersecting to form a checkerboard-like pattern at  larger values of c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' As the number of lattice sites in the ˆx-  direction increases, the number of gap-closing lines increases  while the regions of ﬁnite minimum direct gap decrease in  size.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' This pattern is consistent with a picture of gap-closings  due to interference between the helical boundary modes of the  QSHI: the boundary modes in this q(2-1)D system possess a  standing wave character, and the gap-closing lines correspond  to hybridisation matrix elements passing through zero with  tuning of system parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' With increasing system size,  this interference pattern becomes denser as the difference in  wavelength between the oscillatory components of the helical  boundary modes generically decreases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  It is particularly interesting to compare these phase  diagrams for the q(2-1)D bulk with the counterpart phase  diagram of the 2D bulk shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' 3 a),b) , which reveals  −2  −1  0  1  2  u  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='5  c  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='4  ∆  (a)  −2  −1  0  1  2  u  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='5  c  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='4  ∆  (b)  −2  −1  0  1  2  u  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='5  c  0  2  4  N±π  (c)  −2  −1  0  1  2  u  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='5  c  0  2  4  N±π  (d)  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' Quasi-(2-1)D minimum direct bulk gap for a) N = 6, b)  N = 7 and t = 1/2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' Plot of the number of ±π phases N±π (red is  2, black 0) in the Wilson loop eigenvalues for c) N = 6, d) N = 7  that different kinds of topological phases of the 2D bulk (and  corresponding different gapless boundary states) yield differ-  ent interference patterns as a function of u and c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' Notably,  the checkerboard region of the phase diagram corresponds to  the DSM phase region of the corresponding phase diagram  for the 2D bulk, revealing that the DSM phase is generally  gapped out in the q(2-1)D regime, and exhibits more complex  interference pattern than does the QSHI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  As the 2D minimum direct bulk gap remains ﬁnite over the  region of the phase diagram where we observe this interfer-  ence pattern between helical boundary modes of the QSHI,  and the 2D minimum direct bulk gap remains closed due to  topologically-protected band-touchings of the DSM, topolog-  ical invariants of the 2D bulk do not change within these re-  gions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' However, as subsets of each of these regions possess a  ﬁnite minimum direct gap in the q(2-1)D spectrum, it is possi-  ble to further characterize the topology of the q(2-1)D system  if suitable topological invariant(s) are identiﬁed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' To further  characterize ﬁnite-size topology of this quasi-1D TRI system  with Wilson loop spectra, we compute the Wilson loop eigen-  values [41], which distinguish between topologically-distinct  phases of matter as they characterize holonomy in a system  due to parallel transport through non-contractible loops in the  BZ [42–44].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  The Wilson loop spectra for the q(2-1)D system are com-  puted by integrating the Berry connection over the remaining  k ≡ ky momentum coordinate, using the following expres-  sion: [41]  W = Pe−  � π  −π dkA(k),  (3)  where A(k) is the non-Abelian Berry connection over the  occupied bands and P is the path ordering operator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' Since  5  we compute the Wilson matrix for a tight binding system we  discretize Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' (3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' The set of Wilson loop eigenvalue phases  is the Wannier charge center spectrum characterizing polar-  ization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' In a topologically non-trivial phase, Wannier charge  center(s) are ﬁxed to value(s) of ±π, so we compute the num-  ber of these non-trivial phases as N±π.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' The phase diagrams  characterizing N±π vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' u and c are shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' 4 c), d)  for systems with N = 6 or N = 7 layers in the ˆx-direction,  respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  These N±π vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' c and u phase diagrams shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' 4 c)  and d) reveal alternating regions of N±π = 0 and N±π = 2,  indicating the system undergoes a variety of topological phase  transitions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  We even observe stripe-like regions at smaller  c, which intersect to form checkerboard patterns at larger c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  These lines across which N±π changes in value are in direct  correspondence with lines shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' 4 a) and b), respec-  tively, along which the q(2-1)D minimum direct gap goes to  zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' Taken together, these phase diagrams in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' 4 reveal  a topological phase transition occurs every time the q(2-1)D  minimum direct bulk gap goes to zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  The phase diagrams for N = 6 layers differ dramatically  from those for N = 7 layers, reﬂecting the dependence of  this topology on ﬁnite-size effects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' From the plots, one can  see that, as the number of layers in the ˆx-direction increases,  the number of topologically-distinct regions also increases in  agreement with the number of lines along which the q(2-1)D  minimum direct bulk gap is zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  The topological phase  diagram of the 2D bulk Hamiltonian (1) studied in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' [39]  is therefore being further divided into topologically-distinct  regions in the q(2-1)D regime in a strongly N-dependent  manner, revealing that topological phase transitions due to  ﬁnite-size topology may occur without the minimum direct  gap of the 2D bulk going to zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  B  Bulk-boundary correspondence and disorder  Having characterized ﬁnite-size topology of the q(2-1)D  bulk of Hamiltonian Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' (1) with open boundary conditions  in the ˆx-direction and periodic in ˆy, we now explore the  additional  bulk-boundary  correspondence  of  ﬁnite-size  topological phases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' We ﬁrst study the spectral signatures of  this bulk-boundary correspondence that appear for non-trivial  Wilson loop spectra in accordance with the modern theory  of polarization of Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' [45].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  N±π ̸= 0 for the q1D bulk  corresponds to topologically-protected, q0D bound states for  open boundary conditions in the ˆy-direction in addition to  open boundary conditions in the ˆx-direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' With system  size in the ˆy-direction of Ly, such a bulk-boundary corre-  spondence characterized in the q1D bulk by N±π is clear for  Ly ≫ Lx as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' 5 a) b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' In this case, one ﬁnds  in-gap states close to zero energy within the q(2-1)D bulk gap  of the energy spectrum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' The separation in energy between  these states decreases exponentially to zero as a function of  Ly, realizing a four-fold degenerate manifold of zero-energy  states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  Such states are not present for periodic boundary  conditions in the ˆy-direction, further indicating they appear  as a consequence of bulk-boundary correspondence for the  ﬁnite-size topological phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  −2  −1  0  1  2  u  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='5  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='5  E(u)  (a)  −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='5  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='2  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='1  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='4  u  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='15  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='4  E(u)  (b)  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='4  c  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='2  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='2  E(c)  (c)  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='4  c  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='2  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='2  E(c)  (d)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='7  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='4  c  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='0  ∆  (e)  x  0 2 4 6  y  285  290  295  300  density  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='02  (f)  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  a) Spectrum for OBC (red)in both directions, PBC in y  (black) as a function of the staggered potential u and c = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='6, t =  1/2, N = 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' b) Spectrum for OBC (red) in both directions, PBC in  y (black) as a function of the staggered potential u and c = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='8, t =  1/2, N = 6 with a particle-hole symmetry and sublattice symmetry  breaking on-site potential 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='1 cos(2πn/N)σx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' c) Disorder-averaged  spectrum for N = 6 sites and u = 1, t = 1/2 as a function of c for  200 uniformly distributed random particle hole symmetric potentials  of strength κ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='5u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' d) Disorder-averaged spectrum with the same  parameters but for 200 particle-hole symmetry-breaking disorder po-  tentials of strength κ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='2u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' e) 2D minimum direct bulk gap as a  function of c for u = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' f)Density proﬁle of q(2-2)D state for the  same number of sites, c = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='8, u = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='0 and Ly = 300.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  To further explore the extent to which these in-gap states are  due to an additional bulk-boundary correspondence of ﬁnite-  size topological phases, we compute the probability density  for these in-gap states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' We ﬁnd these states are localized at  the boundaries of the q1D system as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' 5 f).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' Prob-  ability density peaks at the corners of the system as seen in  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' 5 f) and decays over ﬁfteen to twenty unit cells to zero  for x approaching the q(2-1)D bulk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' As the system is time-  reversal invariant, we also compute the spin polarization for  these q(2-2)D boundary modes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' We ﬁnd the q(2-2)D bound-  ary modes are spin-polarized in the ±ˆz direction, with a spin  up/down pair localized at each end of the q(2-1)D system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  We also study the robustness of the in-gap q(2-2)D bound-  ary states against symmetry-breaking due to disorder.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  We  introduce disorder in the q(2-1)D system for OBC as a uni-  6  form random potential, with strength κ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' The disorder average  spectrum for 200 disorder realizations of the form κns0σz is  shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' 5 c) as a function of spin-orbit coupling c for  κn ∈ (−0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='2u, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='2u).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' The q(2-2)D states are present over a  wide range in c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' Surprisingly, they survive even for disorder  strengths κn greater than the q(2-1)D minimum direct bulk  gap for the QSHI phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' The edge states may move away  from zero energy, if the perturbation breaks particle-hole  symmetry, such effect is shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' 5 b) as a function of u,  where an onsite perturbation 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='1 cos(2πn/N)s0σx is present.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  For disorder effects we considered a term of the form Vis0σ0,  the spectrum is thus shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' 5 d) where the edge modes  deviate from zero energy, as in the case of an SSH chain with  next nearest neighbours studied in reference [46].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' However,  the q(2-2)D boundary modes persist and remain strongly  localized, with their pair degeneracy preserved.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  Interestingly, the topological invariant remains ﬁxed at  non-trivial values even when a particle-hole breaking term is  present in the Hamiltonian.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' This reﬂects the dependence of  this non-trivial topology on the presence of the topologically-  protected boundary states of the higher-dimensional phase,  which require only time-reversal symmetry to remain robust  up to the minimum direct 2D bulk gap going to zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' We  further ﬁnd N±π still predicts the existence of edge states  in the nontrivial region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  The validity of the invariant and  bulk-boundary correspondence in the absence of particle  hole symmetry will be further veriﬁed for the case of the  1T ′-WTe2 wire.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' The phase is therefore protected by time-  reversal symmetry alone while particle-hole symmetry is  required only to anchor the in-gap states to zero energy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' This  analysis parallels the one on ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' [46] where analogously the  invariant and phase are protected by only inversion symmetry  while both inversion and particle-hole symmetry secure the  zero-energy value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  For particle-hole-symmetric disorder  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='5 c) the perturbation strength is protected not by the  q(2-1)D gap but rather the 2D bulk gap of the system, which,  for c = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='8, u = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='0, is ∆ ≈ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='5 as seen in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' 5 e).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' If  the perturbation breaks time reversal symmetry, however, the  Kramers degeneracy of the q(2-2)D bound states is broken as  expected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  We conclude from this analysis that the q(2-1)D wire with  spinful time-reversal symmetry, realized for a system with a  2D bulk and open boundary conditions in one direction, ex-  hibits ﬁnite-size topological phases for subsets of the topo-  logically non-trivial regions of the 2D bulk topological phase  diagram.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' In these subsets, bounded by lines along which the  minimum direct q(2-1)D bulk goes to zero rather than the  minimum direct 2D bulk gap, in general, the wire harbors  topologically-protected q(2-2)D boundary modes for open  boundary conditions in two directions appearing in Kramers  pairs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' In the quasi-1D bulk, these subsets correspond to Wil-  son loop spectra with some Wilson loop eigenvalue phases  ﬁxed to ±π, protected by spinful time-reversal symmetry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  These signatures of non-trivial topology are therefore asso-  ciated with time-reversal invariant, q(2-1)D ﬁnite-size topo-  logical phases due to interference between topologically-  protected gapless boundary modes resulting from 2D bulk  topology, either of the quantum spin Hall insulator or the  2D Dirac semimetal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' In contrast, the ten-fold way classiﬁ-  cation scheme of topological phases of matter determines a  1D system in class AII [47] has trivial topological classiﬁ-  cation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' These results are therefore evidence of topologically  non-trivial phases of matter outside of the ten-fold way clas-  siﬁcation scheme.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  III  1T ′-WTe2 wire  Although the previous model is based on the celebrated  HgTe quantum wells, which allowed for the discovery of the  ﬁrst QSHI, it may not be most suitable for the experimental  discovery of ﬁnite-size topology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' The need for a small sample  size in one direction may be easier to achieve for monolayers  such as the 1T ′-TWe2 QSHI [48].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' We thus consider the model  studied in reference [49] which combines density-functional  theory calculations, symmetry considerations and ﬁtting to  experimental data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' Since the ﬁnite-size topology comes from  the hybridization of the edge states, we consider only the  lattice termination which results in a Dirac crossing near the  Fermi energy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' That is we study the sawtooth y ribbon with  open boundary conditions in the x direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' The 1T ′-WTe2  Hamiltonian is presented in the Supplementary Material.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  Under such circumstances we expect the Dirac crossing  to gap out in general on larger and larger energy scales as  the system size in the x direction Nx decreases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' Such a gap  opening does occur for the original material parameters for  even Nx values ranging from 4 to 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  It is worth noting  that the gap still exists even for larger Nx but its magnitude  becomes very small compared to other material energy  scales.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  Such a gapped system may then host topological  q(2-2)D edge states if the Wilson loop spectrum is nontrivial.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  Speciﬁcally, we ﬁnd that for Nx = 8, 10, 12 the gap has a ±π  phase in the Wilson loop spectrum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' Even in the case where  the spectrum is trivial, for example at Nx = 6, we may still  tune the system so that a gap closing occurs and a nontrivial  Wilson loop phase appears.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  To do so, we may apply an  electric ﬁeld perpendicular to the monolayer corresponding to  addition of a symmetry-allowed Rashba spin-orbit coupling  term to the Hamiltonian.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' Since the original model already  includes such couplings, we further include a change of the  in-plane SOC parameters by a quantity ∆λSOC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  For the case of Nx = 6, we obtain a phase diagram for the  number of Wilson loop eigenvalues with phase ±π, N±π, vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  spin-orbit coupling anisotropy, ∆λSOC, showing a change in  N±π from 0 to 1 with increasing ∆λSOC as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' 6  a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' Based on our previous results for a canonical toy model  of the QSHI, we expect q(2-2)D edge states to appear if we  open boundary conditions in the ˆy-direction as well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' Such  edge states due to an additional bulk-boundary correspon-  dence characterized by N±π of the q(2-1)D bulk do exist, as  shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' 6 b)corresponding to a line of four-fold degen-  erate, in-gap states as a function of ∆λSOC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' The four-fold de-  generacy corresponds to a two-fold Kramers degeneracy due  to spinful time-reversal symmetry, and two-fold degeneracy  7  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='4  ∆λSOC  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='15  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='20  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='25  E  (a)  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='2  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='2  ∆λSOC  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='10  E  (b)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='4  ∆λSOC  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='0  N±π  (c)  x  0  2  4  6  y  0  5  10  density  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='05  (d)  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  a) Energy spectrum (eV) as a function of the change in  Rashba spin orbit coupling ∆λSOC for a Nx = 6 saw-tooth termi-  nated 1T ′-TWe2 wire.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' b) Energy spectrum (eV) for the system with  Nx = 12 as a function of ∆λSOC showing edge states at zero ﬁeld.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  c) Number of Wilson loop spectrum ±π phases for Nx = 6 as a  function of ∆λSOC d) Wave function probability density for one edge  state at ∆λSOC = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='35eV and Nx = 6, Ny = 200 for the same  saw-tooth terminated 1T ′-TWe2 wire.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  corresponding to boundary modes localized at the left and  right edge as in the previous simple model of eqref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' (1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' For a  ﬁxed Rashba spin orbit coupling change of ∆λSOC = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='35eV ,  we ﬁnd that the edge states localize on each end of the wire as  shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' 6 c).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  IV  3D TI slab  We now study the ﬁnite size topology of the quintessen-  tial 3D TI in symmetry class AII [38, 47].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' The classiﬁca-  tion in this case is dictated by four Z2 topological invariants  (ν0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' ν1, ν2, ν3) [34, 35] , where the last three invariants are  related to the translational invariance of the system classify-  ing the weak TI phase (WTI) while the ν0 parameter classiﬁes  the strong TI phase (STI).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' In the following, we study the STI  phase with trivial lower-dimensional invariants corresponding  to (1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' 000), which is realized in the model Bloch Hamiltonian  [50]:  H(k) = −2λ  �  µ  sin kµσzsµ + σxs0(M − t  �  µ  cos kµ),  (4)  where the Pauli matrices {σi},{sj} act on orbital and spin  degrees of freedom respectively, λ is a spin orbit coupling  parameter that breaks spin conservation, M is an onsite  staggered potential, and t is a nearest-neighbor hopping  integral.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' In the following, we take all energies to be in units  of t by setting t = 1, and consider the regime in which  1 < M < 3 and λ positive, for which the model realizes the  desired strong TI phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' First, we specialize to the case of  a thin slab in the ˆx-direction of N layers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' In that case, we  expect in analogy to the QSHI that the Dirac cones from the  upper and lower surfaces interfere due to the thin bulk and  hybridize to open a gap even for open boundary conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  The hybridization gap, just as in the previous 2D case, is  expected to sometimes protect a non-trivial ﬁnite size topolog-  ical phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' To study this, we once again characterize topology  using the Wilson loop spectrum, now as a function of ky or  kz with OBC in x to characterize topology ﬁrst of a q(3-1)D  bulk, in regions of the phase diagram where the 3D bulk cor-  responds to the strong TI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' As the isotropy of the Hamiltonian  Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' (4) suggests, there is no difference between the Wilson  loop eigenvalues of W(ky) and W(kz), thus we consider only  W(kz), where each Wilson loop matrix is now deﬁned as:  W(ky) = Pe−  � π  −π dkzAz(ky, kz),  (5)  W(kz) = Pe−  � π  −π dkyAy(ky, kz).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  (6)  A typical Wannier charge center spectrum vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' the remain-  ing momentum component, kz, is plotted in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' 7, which  shows the spectral ﬂow a) characteristic of a TR invariant  topological insulator for some values and a trivial spectrum  b) for others within the (1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' 000) 3D bulk phase classiﬁcation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  The non-trivial spectral ﬂow only appears for certain  parameter regimes: these regions can be distinguished in a  systematic way by counting the number of ﬁxed ±π phases  in the Wilson loop spectrum, as in the previous case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' This  regions of parameter space which have an energy gap are  again the ”bubbles” observed in the QSHI case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' We plot the  phase diagram as a function of the model parameters in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' 8  a),b) for N = 5, 6 layers, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' The phase diagram  changes dramatically for each value of N, the number of  layers, indicative of the ﬁnite-size topology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' The pattern of  trivial and nontrivial regions is entirely contained with the  non-trivial region of the 3D bulk topological phase diagram  for Hamiltonian (4), indicating the 3D minimum direct bulk  gap remains ﬁnite during these topological phase transitions  of the q(3-1)D bulk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' We remark that the sudden changes in  color near λ = 0 seem to be just an artifact of the numerical  precision when approaching the STI gap-closing in the 3D  bulk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  One of the consequences of the system being in a topolog-  ically non-trivial regime, according to the Wilson loop spec-  tra of the q(3-1)D bulk, is an additional bulk-boundary corre-  spondence: opening boundary conditions in a second direc-  tion in these regions of phase space, we ﬁnd topologically-  protected q(3-2)D states that now are localized at the edges  of the slab, as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' 8 c).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' These q(3-2)D states ap-  pear within the q(3-1)D bulk gap similarly to the case of q(2-  2)D boundary states appearing in the q(2-1)D bulk gap of the  QSHI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' A topological phase diagram for the q(3-1)D system  with open-boundary conditions in the ˆy-direction as a func-  tion of M is also shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' 8 d), demonstrating the di-  rect correspondence of the topologically-protected boundary  8  modes with the topologically non-trivial regions of the q(3-  1)D bulk in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' 8 a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' This indicates that N±π, the number of  ±π phases in the Wilson loop eigenvalue spectrum, character-  izes ﬁnite-size topological phases resulting from interference  of the topologically-protected Dirac cones of the 3D TI, in  addition to characterizing ﬁnite-size topological phases due to  interference between the helical boundary modes of the QSHI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  −3π −2π −π  0  π  2π  3π  φkz  −2π  −π  0  π  2π  kz  (a)  −3π −2π −π  0  π  2π  3π  φkz  −2π  −π  0  π  2π  kz  (b)  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' a) Wilson loop nontrivial eigenvalue spectrum as a function  of kz for OBC in x and PBC in y, z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' The parameters are M =  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='0, λ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='2 and N = 6 layers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' b) Wilson loop trivial eigenvalue  spectrum as a function of kz for OBC in x and PBC in y, z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' The  parameters are M = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='6, λ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='1 and N = 6 layers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  While the ﬁnite-size topological phase in the q(3-1)D  system exhibits helical boundary modes analogous to those of  the QSHI, this topological phase is not just a QSHI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' Notably,  the 3D minimum direct gap remains ﬁnite in this region of the  phase diagram where non-trivial ﬁnite-size topological phases  occur, so the 3D bulk is still in the topological phase (1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' 000).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  The ﬁnite-size topological phase therefore exhibits signatures  associated with a non-trivial intrinsically 3D topological  invariant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  This is indicated by adding perturbations to the  system to probe the magneto-electric polarizability of the  system, which depends on the intrinsically 3D topological  invariant, a connection identiﬁed in previous work by Essin et  al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' [51].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  We then compare the result to a q(3-1)D stack of 2D QSHI  in the x direction with the same perturbation to demonstrate  the ﬁnite-size topological phase of the q(3-1)D system is  distinct from a QSHI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' The type of perturbations we consider  to determine the magnetoelectric polarizability in these two  cases are TRS-breaking terms in the form of weak Zeeman  ﬁeld in only the uppermost and lowest layers i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' V = κ · s  with | κ |≈ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' This could correspond to ferromagnetically-  ordered magnetic dopants in just these layers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' This situation  is illustrated schematically in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' 9 a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' We ﬁrst consider  a Zeeman ﬁeld oriented in the yz-plane and labeled κ∥ as  shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' 9 a) for both the (1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' 000) system (q(3-1)D STI)  and the (0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' 001) system (q2D WTI, or stack of QSHIs).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' In  this case, these systems react similarly, their spectra gapping  out as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='9 b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' This is expected, as the perturbation  breaks TR symmetry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  However, the responses of the two systems are strikingly  distinct if we instead consider an applied Zeeman ﬁeld  oriented along the ˆx-axis, or ﬁeld κ⊥ as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' 9 a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  In the case of the (1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' 000) system (q(3-1)D STI), two of the  q1D boundary states gap out, leaving two gapless boundary  1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='5  2  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='5  3  M  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
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+page_content='6  λ  0  2  4  6  8  N±π  (a)  1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
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+page_content='6  λ  0  2  4  6  8  N±π  (b)  −π  −π/2  0  π/2  π  kz  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='3  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
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+page_content='3  E(kz)  (c)  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
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+page_content='0  M  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
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+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
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+page_content='2  E(M)  (d)  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  Phase diagram from wilson loop spectrum for a slab with  a) N = 5, b) N = 6, black-0, yellow-2 ±π phases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' c)Quasi-1D  dispersion for OBC in x N = 6, PBC in z and OBC (PBC) in y as a  function of kz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' The parameters are M = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='8, λ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' d) Spectrum  for OBC in x, y as a function of M, for discretized values of kz with  N = 5 and 100 sites in the remaining directions, λ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  modes remaining.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' They constitute chiral boundary modes of  a QHE on each surface as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' 9 c), corresponding  to a layer-dependent Hall conductivity σxy as shown in  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' 9 d).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' This is a known manifestation of the quantized  magnetoelectric polarizability of the STI, resulting from the  non-trivial value of the strong invariant, these results can be  directly compared with past work for systems with a 3D bulk  rather than q(3-1)D bulk [51].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' Notably, the layer-dependent  Hall conductivity exhibits this non-trivial response only for  topologically non-trivial ﬁnite-size topological phases as  characterized by N±π.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' This agrees with the response theory  of previously-studied ﬁnite-size topological phases, and  reﬂects the fact that only occupied states of the non-trivial  bubbles carry Berry phase contributions to the underlying 3D  topological invariant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  In constrast, there is no topological magnetoelectric effect  and no QHE in the surface layers of the QSHI stack.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' Instead,  the states maintain their degeneracy and helicity, for small  ﬁelds, which is consistent when we view the ﬁeld as paral-  lel to the edge surfaces hosting the helical boundary states of  the QSHI layers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' Therefore, although the spectrum of q(3-1)D  STI slab appears to be similar to the spectrum of a QSHI stack,  its response to TRS-breaking perturbations reveals that it is a  ﬁnite-size topological phase arising from (1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' 000) topology of  the 3D bulk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  V  3D TI wire  We ﬁnally consider a q(3-2)D wire geometry for the STI,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
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+page_content='it>x  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='(a)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='−π  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='−π/2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='π/2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='π  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='kz  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='−0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='2  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='2  E(kz)  (b)  −π  −π/2  0  π/2  π  kz  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='2  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='2  E(kz)  (c)  1  2  3  4  5  6  i  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='5  σxy/σ0  (d)  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' a) Diagram of perturbations and edge states (pink) on a q(3-  1)D STI slab, parallel ﬁeld (purple) and perpendicular ﬁeld (black),  we consider the perturbations for OBC in x, y and PBC in z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' b)  Spectrum of STI slab with OBC in x and y, Nx = 5, Ny = 100.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' A  constant Zeeman ﬁeld ordering κ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='1 parallel to the slab top and  bottom layers is present.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' The parameters are M = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='8, λ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  c) Same parameters as in c) but now with a perpendicular ﬁeld the  system exhibits a QHE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='d) Layer conductivity (Chern number) for  Nx = 6, M = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='0,λ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  tween the topologically-protected boundary states of topologi-  cal phases in the ten-fold way.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' We therefore consider the same  Hamiltonian Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' (4) as considered in the previous section, but  now with open boundary conditions in ˆx- and ˆy-directions and  periodic boundary conditions in the ˆz-direction, with the num-  ber of lattice sites in the ˆx- and ˆy-directions, Nx and Ny, re-  spectively, each much less than Nz, the number of lattice sites  in the ˆz-direction (so Nx, Ny ≪ Nz).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  According to the ten-fold way classiﬁcation scheme for  topological phases of matter, this is an effectively 1D sys-  tem in class AII, which is topologically-trivial [37, 38, 47].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  Here, we show ﬁnite-size topological phases are nonetheless  possible in this system, ﬁrst characterizing ﬁnite-size topol-  ogy of the q1D bulk through analysis of Wilson loop spectra,  and then by demonstrating an additional bulk-boundary corre-  spondence yielding q(3-3)D topologically-protected boundary  modes in the q1D wire, ultimately resulting from interference  between the topologically-protected Dirac cone surface states  of the STI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  For the q(3-2)D bulk of the STI with periodic boundary  conditions only in the ˆz-direction, we compute Wilson loop  spectra by integrating over this one good momentum com-  ponent, similarly to the Wilson loop spectra calculations for  the q(3-2)D bulk of the QSHI in Section II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' The topological  phase diagrams of the STI q(3-2)D bulk are then determined  by computing the number of eigenvalues in the Wilson  loop spectrum with ±π phases, or N±π.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  Although in the  previous cases the spectrum only had two ±π phases or none  corresponding to nontrivial and trivial regions, we ﬁnd for  the 3D TI wire that some regions of the phase diagram have  1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='5  2  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='5  3  M  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='3  λ  0  2  4  6  8  N±π  (a)  1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='5  3  M  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='3  λ  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='2  ∆  (b)  1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='5  2  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='5  3  M  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='3  λ  0  2  4  6  8  N±π  (c)  1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='5  3  M  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='3  λ  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='2  ∆  (d)  1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='5  2  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='5  3  M  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='3  λ  0  2  4  6  8  N±π  (e)  1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='5  3  M  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='3  λ  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='2  ∆  (f)  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  a) Phase diagram for the same ﬁnite size parameters but  PBC in z, red reﬂects 4 ±π phases, yellow 2, blue 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' with Nx =  Ny = 4 b) Heat plot of direct gap for the same system parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  c),d) and e),f) same as before, but for Nx = 4, Ny = 5 and Nx =  Ny = 6 respectfully.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  four ±π phase eigenvalues as shown in red in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' 10 a) for  Nx = Ny = 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' In the case of Nx = Ny = 6, the phase  diagram changes again and now there are not only two and  four ±π phases but also six ±π phases as shown in blue in  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' 10 e).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' The change of invariant is consistent with a gap  closing of the q(3-2)D bulk as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='10 b),f) where  the gap closings coincide with the change of number of ±π  phases in the Wilson loop spectrum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='5  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='0  M  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='2  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='2  E(M)  (a)  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='5  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='0  M  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='2  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='2  E(M)  (b)  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  a) Spectrum for OBC in x,y,z as a function of M, with  Nx, Ny = 4 and Nz = 50 sites in the remaining directions with  λ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' b) Same plot but for Nx = 4, Ny = 5 and Nz = 100.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  10  As in previous cases, we ﬁnd the topological phase dia-  grams for the q(3-2)D bulk of the STI depend strongly on  system size.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' In the case of Nx = 4, Ny = 5, we ﬁnd that  the region with four ±π phases occurs for smaller parameter  regions and is furthermore shifted in M and skewed relative  to the corresponding regions in the Nx = Ny = 4, reﬂecting  the difference between x and y directions in phase space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' The  skewness is also more prominent as we increase the number  of sites as seen for Nx = Ny = 6 in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' 10 e).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' In this case,  even though the topologically non-trivial regions diminish  in size, they are more strongly skewed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' The deformation is  such that, starting in a trivial region according to N±π near  M = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='75, with almost zero λ, we can drive the system  into a topologically non-trivial regime as determined by  N±π by increasing the spin-orbit coupling to λ ≈ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' A  comparison of the phase diagrams in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' 10, indicates that,  as the number of sites increases, the regions present originally  in Nx = Ny = 4 remain for Nx = Ny = 6 although now  shifted to greater M and reduced in size over phase space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  We notice also that the new regions appear from the left.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  The topological phase diagram and corresponding q(3-2)D  minimum direct bulk gap phase diagram for Nx = Ny = 6  are shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' 10 e), f), respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  While there are  similarities between results for this system size and the  smaller ones, there is a topological region for which six  Wilson loop eigenvalues have phases ﬁxed to ±π.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  The  regions of greater N±π appear to be subsets of regions with  lesser N±π: the blue region is contained within a red region,  and red regions are contained within yellow regions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  The  states again localize at the boundaries of the wire and states  occur in Kramers pairs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' These results indicate the number of  ±π phases in the Wilson loop spectrum, N±π, corresponds  to half the number of zero energy edge states N(E = 0) in  the q(3-2)D STI system with OBC in all directions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' We can  verify this relation appears to hold for the q(2-1)D QSHI wire  and the q(3-1)D STI slab as well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' As N±π > 2 occurs for the  q1D STI wire, this comes to suggest an integer classiﬁcation  2Z for the q(3-2)D STI ﬁnite-size topological phases, to be  explored in greater detail in future work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  Based on the topological phase diagrams for the q(3-  2)D bulk, we now check for a ﬁnite-size topological bulk-  boundary correspondence in this geometry by opening bound-  ary conditions in the ˆz-direction, searching for topologically-  protected boundary modes localized at the ends of the q(3-2)D  wire.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' In analogy to the q(2-1)D QSHI wire, we study the non-  trivial number of ±π eigenvalues in the Wilson loop spectrum,  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' 11 a),b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' The system with N±π = 4 phases has now eight  edge states within the q(3-2)D bulk gap.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' These states occur in  Kramers pairs, with each state in a given Kramers pair local-  ized at the same edge There are, however, differences between  these states observable in the probability density distributions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  We show the probability densities as a function of layer index  in each of the ˆz- and ˆy-directions, respectively,for four of the  in-gap states, in Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' 12 a) and b), respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' The cor-  responding probability densities as a function of layer in the  ˆz-direction and ˆy-direction for the other four in-gap states are  shown in Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' 12 c) and d), respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' We see that the sec-  ond set of four are distinguished from the ﬁrst four by their  localization: the second set of four are pushed inwards from  the edge in both the ˆz- and ˆy-direction relative to the ﬁrst four  in-gap states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' We ﬁnd similar physics for Nx = Ny = 6 in the  N±π = 6 phase: there are 12 q(3-3)D edge states at zero en-  ergy within the q(3-2)D bulk gap.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' This change in localization  suggests that there is a distinction between edge states which  may give way to distinct phases not distinguished by just the  parity of the number of edge states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  0  20  40  60  80  z  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='0  |ψ|2  ×10−2  (a)  1  2  3  4  y  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='7  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='0  |ψ|2  ×10−2  (b)  0  20  40  60  80  z  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='4  |ψ|2  ×10−2  (c)  1  2  3  4  y  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='6  |ψ|2  ×10−2  (d)  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  a) Probability density plot for one q(3-3)D edge mode as  a function of wire length z with M = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='25, λ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='1,Nx = Ny =  4, Nz = 80 b) same edge state as a function of site index y , c)  Probability density for another quasi-0D edge mode within the same  model parameters as a function of wire length d) now as a function  of site index y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  VI  Concluding remarks  In this work, we have studied ﬁnite-size topology in time-  reversal invariant systems, emerging from the hybridization  of helical boundary modes in QSHIs and of Dirac cones in the  strong TI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' In the case of the QSHI, we ﬁnd the helical bound-  ary modes generically interfere to realize regions in phase  space where the q(2-1)D bulk spectrum (periodic boundary  conditions in one direction and open boundary conditions in  the other) is gapped.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' These regions are separated from one  another by critical points at which the q(2-1)D minimum  direct bulk gap is zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' We characterize the topology of these  gapped regions by computing Wilson loop spectra, ﬁnding  topologically non-trivial gapped phases of the q(2-1)D  bulk corresponding to a non-trivial number of Wilson loop  eigenvalues with phase ﬁxed to ±π.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  For open boundary conditions in each direction and a q(2-  1)D wire geometry, these Wilson loop eigenvalues with phase  ±π correspond to topologically-protected q(2-2)D boundary  modes localized at the ends of the wire.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' These q(2-2)D bound-  ary modes occur in Kramers pairs and are robust against dis-  11  x  quasi-3D slab with additional OBCs in z  boundary mode interference  quasi-2D FST boundary mode  3D boundary mode  3D boundary mode  quasi-3D slab from 4D bulk  y  y  x  z  z  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' a) Schematic diagram of a 4D topological phase consisting of some x, y, z real space directions and an Lz orbital degree of freedom  which gets thinned in the orbital direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' In this case the quasi-3D slab spectrum from the 4D bulk results from the hybridization of  the original 3D boundary modes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' b) The previous q(4-1)D slab possess an additional bulk-boundary correspondence when additional open  boundary conditions in the z direction are considered.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' This results in q(4-2)D boundary modes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  order respecting spinful time-reversal symmetry, maintaining  a fourfold degeneracy for particle-hole symmetric disorder,  and splitting into doubly-degenerate Kramers pairs for disor-  der breaking particle-hole symmetry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' In these cases, the in-  gap, q(2-2)D modes are still topologically-robust in that they  must correspond to time-reversal invariant charge transfer in  an aperiodic Thouless pump from valence bands to conduc-  tion bands, and this connectivity between q(2-1)D bulk va-  lence and conduction bands is observed in topological phase  diagrams.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  We ﬁrst observe this ﬁnite-size topology of the QSHI for  a canonical Hamiltonian describing HgTe quantum wells,  but also ﬁnd the ﬁnite-size topological phase occurs in a  tight-binding model for 1T’-WTe2 ribbons with sawtooth  edges derived from density functional theory calculations,  thus potentially relevant to experiment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  In the case of the  strong topological insulator protected by time-reversal sym-  metry, we ﬁnd ﬁnite-size topological phases both for q(3-1)D  slab geometries and q(3-2)D wire geometries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' Wilson loop  spectra are used to characterize the topology of the q(3-1)D  and q(3-2)D bulk: the winding of the Wilson loop eigenvalue  phases characterizes the q(3-1)D topology, similarly to  characterization of 2D topological phases in the bulk, while  the q(3-2)D wire topology in this case is also characterized  by the number of ±π Wilson loop eigenvalue phases as in  the case of the q(2-1)D QSHI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' For open boundary conditions  in two directions, the q(3-1)D STI slab exhibits helical  boundary modes in the ﬁnite-size topological phase, but  also exhibits signatures of the magneto-electric polarizability  of the STI, distinguishing this ﬁnite-size topological phase  from the QSHI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' In the case of the q(3-2)D wire, q(3-3)D  boundary modes occur for open boundary conditions in all  three directions, similarly to those of the q(2-1)D QSHI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  However, results indicate that topological classiﬁcation for  the q(3-2)D STI is integer rather than Z2, with unusual  localization of the quasi-0D topological boundary modes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  Importantly, these results show that ﬁnite-size topology yields  topologically-protected boundary modes of codimension  greater than 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  We close by pointing out an intriguing possible extension  of the work to a system with dimension D > 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' For example,  a four-dimensional topological phase is expected in a q(4-1)D  setting, as pictured schematically in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' 13 for a small sys-  tem size in some fourth dimension.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' These extra non-spatial  dimensions could come from physical degrees of freedom,  typically considered for three-dimensional systems, such as  a p orbital degree of freedom as considered in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' 13 a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' One  could now imagine an inﬁnite 4D bulk deﬁned by the ˆx-, ˆy-  , ˆz-, and ˆLz (angular momentum)-axes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' For non-trivial 4D  bulk topological invariant, open boundary conditions in the  ˆLz-direction and a large system size in the ˆLz-direction, three-  dimensional topologically-protected boundary modes are re-  alized.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' For the physical scenario of small system sizes in the  12  ˆLz-direction as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' 13 a), these three-dimensional  boundary modes could interfere to realize a topologically non-  trivial FST phase, such that additional topologically-protected  boundary modes are realized when boundary conditions are  additionally opened in a second real-space direction, such as  the ˆz-direction as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' 13 b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' This raises the possibil-  ity of topologically-protected boundary states for systems in  one to three-dimensions reﬂecting higher-dimensional, D > 3  bulk topology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  [1] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' Andrei Bernevig, Taylor L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' Hughes,  and Shou-Cheng  Zhang, “Quantum spin hall effect and topological phase transi-  tion in HgTe quantum wells,” Science 314, 1757–1761 (2006),  https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='science.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='org/doi/pdf/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='1126/science.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='1133734.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  [2] Markus K¨onig, Steffen Wiedmann, Christoph Br¨une, Andreas  Roth, Hartmut Buhmann, Laurens W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' Molenkamp, Xiao-Liang  Qi,  and Shou-Cheng Zhang, “Quantum spin hall insulator  state in HgTe quantum wells,” Science 318, 766–770 (2007),  https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='science.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='org/doi/pdf/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='1126/science.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='1148047.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  [3] Chetan Nayak, Steven H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' Simon, Ady Stern, Michael Freed-  man, and Sankar Das Sarma, “Non-abelian anyons and topo-  logical quantum computation,” Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' Mod.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' 80, 1083–1159  (2008).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  [4] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='Yu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' Kitaev, “Fault-tolerant quantum computation by anyons,”  Annals of Physics 303, 2–30 (2003).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  [5] Dominic V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' Else, Ryan Thorngren, and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' Senthil, “Non-fermi  liquids as ersatz fermi liquids: General constraints on com-  pressible metals,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' X 11, 021005 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  [6] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' Klitzing, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' Dorda,  and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' Pepper, “New method  for high-accuracy determination of the ﬁne-structure constant  based on quantized hall resistance,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' 45, 494–  497 (1980).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  [7] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' Tsui, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' Stormer,  and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' Gossard, “Two-  dimensional magnetotransport in the extreme quantum limit,”  Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' 48, 1559–1562 (1982).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  [8] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' Laughlin, “Anomalous quantum hall effect: An incom-  pressible quantum ﬂuid with fractionally charged excitations,”  Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' 50, 1395–1398 (1983).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  [9] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' Hsieh,  Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' Xia,  L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' Wray,  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' Qian,  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' Pal,  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  Dil,  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  Osterwalder,  F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  Meier,  G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  Bihlmayer,  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  Kane, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' Hor, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' Cava,  and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' Hasan, “Ob-  servation  of  unconventional  quantum  spin  textures  in  topological  insulators,”  Science  323,  919–922  (2009),  https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='science.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='org/doi/pdf/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='1126/science.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='1167733.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  [10] Jiho Noh, Wladimir A Benalcazar, Sheng Huang, Matthew J  Collins, Kevin P Chen, Taylor L Hughes,  and Mikael C  Rechtsman, “Topological protection of photonic mid-gap de-  fect modes,” Nature Photonics 12, 408–415 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  [11] Christopher W Peterson,  Wladimir A Benalcazar,  Tay-  lor L Hughes,  and Gaurav Bahl, “A quantized microwave  quadrupole insulator with topologically protected corner  states,” Nature 555, 346–350 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  [12] Stefan Imhof, Christian Berger, Florian Bayer, Johannes  Brehm, Laurens W Molenkamp, Tobias Kiessling, Frank  Schindler, Ching Hua Lee, Martin Greiter, Titus Neupert, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=',  “Topolectrical-circuit realization of topological corner modes,”  Nature Physics 14, 925–929 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  [13] Marc Serra-Garcia, Valerio Peri, Roman S¨usstrunk, Osama R  Bilal, Tom Larsen, Luis Guillermo Villanueva, and Sebastian D  Huber, “Observation of a phononic quadrupole topological in-  sulator,” Nature 555, 342–345 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  [14] Frank Schindler,  Ashley M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' Cook,  Maia G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' Vergniory,  Zhijun Wang, Stuart S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' Parkin, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' Andrei Bernevig,  and  Titus  Neupert,  “Higher-order  topological  in-  sulators,”  Science  Advances  4,  eaat0346  (2018),  https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='science.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='org/doi/pdf/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='1126/sciadv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='aat0346.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  [15] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' Haldane, “Model for a quantum hall effect with-  out landau levels: Condensed-matter realization of the ”parity  anomaly”,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' 61, 2015–2018 (1988).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  [16] Charles L Kane and Eugene J Mele, “Quantum spin hall effect  in graphene,” Physical review letters 95, 226801 (2005).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  [17] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' Kane and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' Mele, “Z2 topological order and the quan-  tum spin hall effect,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' 95, 146802 (2005).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  [18] Cui-Zu Chang, Jinsong Zhang, Xiao Feng, Jie Shen, Zuocheng  Zhang, Minghua Guo, Kang Li, Yunbo Ou, Pang Wei, Li-Li  Wang, Zhong-Qing Ji, Yang Feng, Shuaihua Ji, Xi Chen, Jin-  feng Jia, Xi Dai, Zhong Fang, Shou-Cheng Zhang, Ke He,  Yayu Wang, Li Lu, Xu-Cun Ma, and Qi-Kun Xue, “Experi-  mental observation of the quantum anomalous hall effect in a  magnetic topological insulator,” Science 340, 167–170 (2013),  https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='science.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='org/doi/pdf/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='1126/science.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='1234414.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  [19] Yugui Yao, Fei Ye, Xiao-Liang Qi, Shou-Cheng Zhang, and  Zhong Fang, “Spin-orbit gap of graphene: First-principles cal-  culations,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' B 75, 041401 (2007).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  [20] Hongki Min, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' Hill, Nikolai A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' Sinitsyn, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' Sahu,  Leonard Kleinman, and Allan H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' MacDonald, “Intrinsic and  rashba spin-orbit interactions in graphene sheets,” Physical Re-  view B 74, 165310 (2006).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  [21] Arthur  Leis,  Michael  Schleenvoigt,  Vasily  Cherepanov,  Felix L¨upke, Peter Sch¨uffelgen, Gregor Mussler, Detlev  Gr¨utzmacher, Bert Voigtl¨ander, and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' Stefan Tautz, “Lifting  the spin-momentum locking in ultra-thin topological insulator  ﬁlms,” Advanced Quantum Technologies 4, 2100083 (2021),  https://onlinelibrary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='wiley.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='com/doi/pdf/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='1002/qute.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='202100083.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  [22] Yi Zhang, Ke He, Cui-Zu Chang, Can-Li Song, Li-Li Wang,  Xi Chen, Jin-Feng Jia, Zhong Fang, Xi Dai, Wen-Yu Shan,  Shun-Qing Shen, Qian Niu, Xiao-Liang Qi, Shou-Cheng  Zhang, Xu-Cun Ma,  and Qi-Kun Xue, “Crossover of the  three-dimensional topological insulator Bi2Se3 to the two-  dimensional limit,” Nature Physics 6, 584–588 (2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  [23] Yusuke Sakamoto, Toru Hirahara, Hidetoshi Miyazaki, Shin-  ichi Kimura,  and Shuji Hasegawa, “Spectroscopic evidence  of a topological quantum phase transition in ultrathin Bi2Se3  ﬁlms,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' B 81, 165432 (2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  [24] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' Geim and I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' Grigorieva, “Van der waals heterostruc-  tures,” Nature 499, 419–425 (2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  [25] Chaowei Hu, Kyle N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' Gordon, Pengfei Liu, Jinyu Liu, Xiaoqing  Zhou, Peipei Hao, Dushyant Narayan, Eve Emmanouilidou,  Hongyi Sun, Yuntian Liu, Harlan Brawer, Arthur P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' Ramirez,  Lei Ding, Huibo Cao, Qihang Liu, Dan Dessau, and Ni Ni,  “A van der waals antiferromagnetic topological insulator with  weak interlayer magnetic coupling,” Nature Communications  11, 97 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  [26] Su Kong Chong, Kyu Bum Han, Akira Nagaoka, Ryuichi  Tsuchikawa,  Renlong  Liu,  Haoliang  Liu,  Zeev  Valy  Vardeny,  Dmytro  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  Pesin,  Changgu  Lee,  Taylor  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  Sparks,  and  Vikram  V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  Deshpande,  “Topological  insulator-based van der waals heterostructures for effec-  13  tive  control  of  massless  and  massive  dirac  fermions,”  Nano Letters 18, 8047–8053 (2018), pMID: 30406664,  https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='1021/acs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='nanolett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='8b04291.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  [27] Liangzhi Kou,  Shu-Chun Wu,  Claudia Felser,  Thomas  Frauenheim,  Changfeng Chen,  and Binghai Yan, “Ro-  bust 2d topological insulators in van der waals heterostruc-  tures,” ACS Nano 8, 10448–10454 (2014), pMID: 25226453,  https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='1021/nn503789v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  [28] Sajid Husain, Rahul Gupta, Ankit Kumar, Prabhat Kumar, Nil-  amani Behera, Rimantas Brucas, Sujeet Chaudhary, and Peter  Svedlindh, “Emergence of spin–orbit torques in 2d transition  metal dichalcogenides: A status update,” Applied Physics Re-  views 7, 041312 (2020), https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='1063/5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='0025318.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  [29] Daniele Varsano, Maurizia Palummo, Elisa Molinari, and Mas-  simo Rontani, “A monolayer transition-metal dichalcogenide as  a topological excitonic insulator,” Nature Nanotechnology 15,  367–372 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  [30] Peng Song, Chuanghan Hsu, Meng Zhao, Xiaoxu Zhao, Tay-  Rong Chang, Jinghua Teng, Hsin Lin,  and Kian Ping Loh,  “Few-layer 1t’ MoTe2 as gapless semimetal with thickness de-  pendent carrier transport,” 2D Materials 5, 031010 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  [31] Xiaofeng  Qian,  Junwei  Liu,  Liang  Fu,  and  Ju  Li,  “Quantum spin hall effect in two-dimensional transition  metal dichalcogenides,” Science 346, 1344–1347 (2014),  https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='science.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='org/doi/pdf/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='1126/science.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='1256815.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  [32] A Yu Kitaev, “Unpaired majorana fermions in quantum wires,”  Physics-Uspekhi 44, 131–136 (2001).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  [33] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' Burkov and Leon Balents, “Weyl semimetal in a topolog-  ical insulator multilayer,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' 107, 127205 (2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  [34] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' Moore and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' Balents, “Topological invariants of time-  reversal-invariant band structures,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' B 75, 121306  (2007).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  [35] Liang Fu, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' Kane, and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' Mele, “Topological insulators  in three dimensions,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' 98, 106803 (2007).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  [36] Yoichi Ando and Liang Fu, “Topological crystalline insu-  lators and topological superconductors:  From concepts to  materials,” Annual Review of Condensed Matter Physics 6,  361–381 (2015), https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='1146/annurev-conmatphys-  031214-014501.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  [37] Ching-Kai Chiu, Jeffrey C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' Teo, Andreas P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' Schnyder, and  Shinsei Ryu, “Classiﬁcation of topological quantum matter  with symmetries,” Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' Mod.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' 88, 035005 (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  [38] Alexei Kitaev, “Periodic table for topological insulators and  superconductors,” AIP Conference Proceedings 1134, 22–30  (2009), https://aip.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='scitation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='org/doi/pdf/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='1063/1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='3149495.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  [39] Lara Ulcakar, Jernej Mravlje, Anton Ramsak, and Toma z Re-  jec, “Slow quenches in two-dimensional time-reversal symmet-  ric Z2 topological insulators,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' B 97, 195127 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  [40] Bin Zhou, Hai-Zhou Lu, Rui-Lin Chu, Shun-Qing Shen, and  Qian Niu, “Finite size effects on helical edge states in a quan-  tum spin-hall system,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' 101, 246807 (2008).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  [41] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' Alexandradinata, Xi Dai, and B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' Andrei Bernevig, “Wilson-  loop characterization of inversion-symmetric topological insu-  lators,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' B 89, 155114 (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  [42] Rapha¨el Leone, “The geometry of (non)-abelian adiabatic  pumping,” Journal of Physics A: Mathematical and Theoretical  44, 295301 (2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  [43] Artur  Ekert,  Marie  Ericsson,  Patrick  Hayden,  Hi-  toshi  Inamori,  Jonathan  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  Jones,  Daniel  K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  Oi,  and  Vlatko  Vedral,  “Geometric  quantum  computa-  tion,” Journal of Modern Optics 47, 2501–2513 (2000),  https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='tandfonline.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='com/doi/pdf/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='1080/09500340008232177.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  [44] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' Recati, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' Calarco, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' Zanardi, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' Cirac,  and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' Zoller,  “Holonomic quantum computation with neutral atoms,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' A 66, 032309 (2002).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  [45] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' King-Smith and David Vanderbilt, “Theory of polariza-  tion of crystalline solids,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' B 47, 1651–1654 (1993).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  [46] Linhu Li, Zhihao Xu,  and Shu Chen, “Topological phases  of generalized su-schrieffer-heeger models,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' B 89,  085111 (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  [47] Jeffrey C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' Teo and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' Kane, “Topological defects and gap-  less modes in insulators and superconductors,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' B 82,  115120 (2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  [48] Shujie Tang, Chaofan Zhang, Dillon Wong, Zahra Pedram-  razi, Hsin-Zon Tsai, Chunjing Jia, Brian Moritz, Martin  Claassen, Hyejin Ryu, Salman Kahn, Juan Jiang, Hao Yan,  Makoto Hashimoto, Donghui Lu, Robert G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' Moore, Chan-  Cuk Hwang, Choongyu Hwang, Zahid Hussain, Yulin Chen,  Miguel M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' Ugeda, Zhi Liu, Xiaoming Xie, Thomas P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' Dev-  ereaux, Michael F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' Crommie, Sung-Kwan Mo, and Zhi-Xun  Shen, “Quantum spin hall state in monolayer 1T′-WTe2,” Na-  ture Physics 13, 683–687 (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  [49] Alexander Lau, Rajyavardhan Ray, D´aniel Varjas,  and An-  ton R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' Akhmerov, “Inﬂuence of lattice termination on the edge  states of the quantum spin hall insulator monolayer 1T′-WTe2,”  Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' Materials 3, 054206 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  [50] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' Rosenberg and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' Franz, “Witten effect in a crystalline topo-  logical insulator,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' B 82, 035105 (2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  [51] Andrew M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' Essin, Joel E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' Moore, and David Vanderbilt, “Mag-  netoelectric polarizability and axion electrodynamics in crys-  talline insulators,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' 102, 146805 (2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  14  Supplemental material for “Time-reversal invariant ﬁnite-size topology”  R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' Flores-Calderon,1 Roderich Moessner,1 and Ashley M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' Cook1,2,∗  1Max Planck Institute for Chemical Physics of Solids, N¨othnitzer Strasse 40, 01187 Dresden, Germany  2Max Planck Institute for the Physics of Complex Systems, N¨othnitzer Strasse 38, 01187 Dresden, Germany  ∗Electronic address: cooka@pks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='mpg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='de  (Dated: January 6, 2023)  S1  Tight-binding model for 1T ′-WTe2  In the main text we discussed a realistic model for realizing ﬁnite-size topology in a 1T ′ − WTe2 monolayer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' We adapted the  ﬁnite-size calculation from the model explored and derived in reference [49].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' The model predicts that the four bands closest to  the Fermi level are composed mainly of contributions from two 3dx2−y2 type orbitals centered at W and two 5px type orbitals  centered at a subset of Te.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' With this information at hand and some experimental ﬁtting the authors construct a minimal tight  binding model that includes also a spin orbit interaction given by:  HWTe2(k) =s0  ��µp  2 + tpx cos (akx) + tpy cos (bky)  �  Γ−  1 +  �µd  2 + tdx cos (akx)  �  Γ+  1 + tdABe−ibky �  1 + eiakx�  eik·∆1Γ+  2  + tpAB  �  1 + eiakx�  eik·∆2Γ−  2 + t0AB  �  1 − eiakx�  eik·∆3Γ3 − 2it0x sin (akx)  �  eik·∆4Γ+  4 + e−ik·∆4Γ−  4  �  + t0ABx  �  e−iakx − e2iakx�  eik·∆3Γ3 + H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='  �  + [(λz  dxsz + λy  dxsy) sin (akx)] Γ+  5 +  ��  λz  pxsz + λy  pxsy  �  sin (akx)  �  Γ−  5  − iλy  0ABsy  �  1 + eiakx�  eik·∆3Γ6 − i (λz  0sz + λy  0sy)  �  eik·∆4Γ+  4 − e−ik·∆4Γ−  4  �  − i (λz  0sz + λy  0sy)  ×  �  e−ibkyeik·∆4Γ+  4 − eibkye−ik·∆4Γ−  4  �  + H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=',  (S1)  ,where si are Pauli matrices representing the spin degree of freedom and they deﬁned the gamma matrices as:  Γ0 = τ0σ0  (S2)  Γ±  1 = τ0  2 (σ0 ± σ3)  (S3)  Γ±  2 = 1  4 (τ1 + iτ2) (σ0 ± σ3)  (S4)  Γ3 = 1  2 (τ1 + iτ2) iσ2  (S5)  Γ±  4 = 1  4 (τ0 ± τ3) (σ1 + iσ2)  (S6)  Γ±  5 = τ3  2 (σ0 ± σ3)  (S7)  Γ6 = 1  2 (τ1 + iτ2) σ1  (S8)  ,where τi, σi are Pauli matrices acting in sublattice and orbital degrees of freedom respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content=' Finally the constants from the  previous Hamiltonian that reproduce the experimental results are:  µp  −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='75eV  λy  0AB  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='011eV  µd  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='74eV  λy  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='051eV  tpx  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
+page_content='13eV  λz  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xNA0T4oBgHgl3EQfMf_C/content/2301.02134v1.pdf'}
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+A Modular Multi-stage Lightweight Graph
+Transformer Network for Human Pose and Shape
+Estimation from 2D Human Pose
+Ayman Ali, Ekkasit Pinyoanuntapong, Pu Wang, Mohsen Dorodchi
+College of Computing and Informatics
+University of North Carolina at Charlotte
+Charlotte, United States
+aali26, epinyoan, pwang13, mdorodch@uncc.edu
+Abstract—In this research, we address the challenge faced by
+existing deep learning-based human mesh reconstruction meth-
+ods in balancing accuracy and computational efﬁciency. These
+methods typically prioritize accuracy, resulting in large network
+sizes and excessive computational complexity, which may hinder
+their practical application in real-world scenarios, such as virtual
+reality systems. To address this issue, we introduce a modular
+multi-stage lightweight graph-based transformer network for
+human pose and shape estimation from 2D human pose, a
+pose-based human mesh reconstruction approach that priori-
+tizes computational efﬁciency without sacriﬁcing reconstruction
+accuracy. Our method consists of a 2D-to-3D lifter module that
+utilizes graph transformers to analyze structured and implicit
+joint correlations in 2D human poses, and a mesh regression
+module that combines the extracted pose features with a mesh
+template to produce the ﬁnal human mesh parameters.
+I. INTRODUCTION
+The ﬁeld of computer vision has witnessed signiﬁcant ad-
+vancements with the advent of deep learning models in human
+pose estimation from monocular images. Speciﬁcally, 2D pose
+estimation involves determining the locations of human joint
+coordinates within a single image. In recent years, the research
+community has shown great interest in reconstructing 3D
+human mesh representations due to their practical applications
+in human-computer interaction, gaming, and virtual systems.
+Despite the progress in both 2D and 3D pose estimation and
+human mesh reconstruction, reconstructing human mesh from
+a single image remains challenging due to factors such as
+depth ambiguity, complex backgrounds, challenging postures,
+and a lack of annotated in-the-wild datasets.
+The fundamental process of reconstructing a 3D human
+mesh involves estimating the pose and shape parameters based
+on statistical body models, such as SMPL [1] and [2]. The
+pose parameters θ deﬁne the global root orientation and the
+relative rotations of human body joints represented in an axis-
+angle sequence. Moreover, the shape parameters β represent
+the learned linear gender-based body shape derived from the
+CAESAR dataset [3] using principal component analysis.
+The literature on human mesh reconstruction primarily
+consists of two paradigms: optimization-based and regression-
+based approaches. Optimization-based methods minimize the
+difference between the re-projected 2D pose regressed from
+the human mesh and the estimated 2D pose. In contrast,
+regression-based methods directly predict the pose and shape
+parameters.
+While deep learning models have progressed in human mesh
+reconstruction, the choice of input data has a signiﬁcant impact
+on the system’s pipeline. Recent advances have adopted an
+end-to-end pipeline where the input is the scene image, and
+the output is the predicted mesh. However, this approach can
+be computationally intensive and does not meet the efﬁciency
+requirements of various real-world applications, such as gam-
+ing and real-time mesh recovery.
+To address the computational overhead, some researchers
+have proposed using skeleton data as the input, as it is sparse
+[4]. However, solely relying on skeleton data is insufﬁcient to
+address the computational intensity. Zheng et al. [5] proposed
+a lightweight graph-based transformer architecture to focus on
+efﬁciency.
+Nevertheless, reconstructing mesh parameters remains com-
+plex, as it is inﬂuenced by a variety of factors, including 1)
+Dataset Characteristics where the performance of a model is
+not signiﬁcantly impacted by the indoor/outdoor setting or
+the number of data points, but rather by human pose and
+shape, camera characteristics, and backbone features [6]. Fur-
+thermore, a diverse range of these attributes can improve the
+performance, while occlusion and SMPL ﬁttings can enhance
+recovery accuracy. 2) Dataset Mix is another factor that affects
+the complexity of the task. The choice of datasets is critical for
+the generalizability and accuracy of the model [6]. It is imper-
+ative to use the same combination of datasets when evaluating
+and comparing the impact of other factors, such as training
+algorithms. Comparing two network architectures on different
+dataset combinations is considered unfair. To establish a robust
+baseline model, it is recommended to use more challenging
+datasets and increase their contribution during training. Finally,
+Noisy annotations, which in case of having high proportions of
+noisy data samples, can negatively impact model performance,
+particularly when both SMPL annotations and keypoints are
+affected. However, slightly noisy SMPL data can still have a
+positive effect on training.
+arXiv:2301.13403v1  [cs.CV]  31 Jan 2023
+
+Our objective in this research is to design a modular and
+end-to-end capable graph-based transformer network that is
+capable of estimating the human shape and pose, demonstrat-
+ing comparable performance with state-of-the-art methods.
+Speciﬁcally, we propose the following strategies to achieve
+this goal:
+• Construct a modular, multi-stage pipeline that is capable
+of end-to-end estimation of human parameters.
+• separate the learning of human pose, shape, and camera
+parameters to improve accuracy and robustness of the
+model.
+II. SYSTEM DESCRIPTION
+A. Preliminary
+The task of Human Mesh Recovery (HMR) from images
+without the utilization of auxiliary devices, such as depth
+sensors, poses a challenge due to various factors such as
+depth ambiguity, complex backgrounds, and diverse human
+poses. Typically, deep learning networks are trained to estimate
+the human pose parameters using a skinned vertex-based
+parametric human model such as SMPL [1].
+Kanazawa et al. proposed a method that minimizes the 2D
+reprojection loss of joints without relying on paired 2D-to-3D
+supervision to estimate the pose and shape parameters from an
+image [7]. Kolotouros et al. proposed a method that iteratively
+optimizes the estimated parameters to produce a pixel-level
+alignment with the original image [8]. Further, Kocabas et
+al. introduced adversarial training to enhance the quality of
+the estimated mesh by utilizing the large-scale motion capture
+dataset AMASS [9].
+Recent advancements in 2D pose estimation have prompted
+researchers to explore the potential of using off-the-shelf 2D
+pose estimation networks, such as HRNet [10], to estimate
+human mesh parameters. The 2D skeleton estimated from an
+image is fed to the human mesh parameters estimation network
+for further processing and analysis.
+Graph Convolution Networks (GCN) have received con-
+siderable attention in recent years due to their ability to intu-
+itively model data, such as articulated models. In particular,
+many studies have adopted GCN to model 3D human pose
+estimation [11], [12]. In the context of human skeletons, joints
+and bones are mapped to vertices and edges, respectively,
+thus forming a graph represented mathematically as G = v, ϵ.
+Inspired by [5], we use GCN to model the 2D pose features,
+where the output of the GCN layer is expressed as:
+X′ = σ(A × W)
+(1)
+Where σ(.) represents the Gaussian Error Linear Unit (GELU),
+A represents the adjacency matrix, and W represents the
+learnable weight matrix.
+Transformer Transformer [13] has remodeled many deep
+learning models in computer vision. The ability to capture
+the global context understanding in the features space led
+to signiﬁcant advancements. Self-attention can be described
+as a function to compute the attention matrix given a query
+matrix Q ∈ RN×d, key matrix K ∈ RN×d and value matrix
+V ∈ RN×d where N represents the number of vectors in
+the sequence, and d is the dimension. A scaling factor ( 1
+√
+d)
+is utilized to alleviate the growth of the softmax function’s
+magnitude. The scaled-dot product attention can be expressed
+as:
+Attention(Q, K, V ) = Softmax(QKT
+√dk
+)V
+(2)
+Multi-headed self-attention utilized parallel scaled-dot atten-
+tions to project the queries, keys, and values h times with
+different linear projections to dk, dk, and DV dimensions. A
+concatenation of the h head attention output can be expressed
+as:
+MSA(Q, K, V ) = Concat(H1, H2, ...., Hh)Wout
+where Hi = Attention(Qi, Ki, Vi), i ∈ [1, 2, ..., h]
+(3)
+B. System Architecture
+At ﬁrst, a projection layer encodes the 2D pose estimation
+to create latent space embedding to be consumed by the 3D
+lifter. Supervised training is adopted to train a 3D lifter module
+where we minimize the distance between the predicted 3D and
+the ground truth. In addition to using L1 regularization, we use
+the weak perspective camera model to reproject 3D to the 2D
+pose to ensure better accuracy and alignment. Furthermore, the
+shape parameters are applied to the mean template mesh. We
+experimented with using the mean mesh, which is represented
+by M ∈ R6890, and the rest pose regressed from the mean
+template mesh. We found that using mean mesh provided more
+gain than using the rest pose. The pose angles are predicated
+by the iterative regressor that consumes the features generated
+by the pose and shape estimator. Finally, forward kinematics
+are employed to calculate the human mesh.
+1) 3D-lifter Module: The 3D-lifter module leverages the
+graph transformer as described in [5] to extract both global and
+local features from human pose data. First, a projection layer
+encodes the pose into a latent space. The resulting features are
+then fed into multiple parallel graph transformer blocks, which
+have small embedding dimensions for improved efﬁciency.
+The outputs from these parallel branches are fused to generate
+features that are used to predict 3D pose estimation, human
+shape, and camera parameters.
+Given a 2D skeleton denoted as S ∈ Rj×2, where j repre-
+sents the number of joints and 2 denotes the joint coordinates
+in the X, Y plane, the 2D-to-3D lifting task is performed by
+the Pose Analysis Module (PAM). PAM returns: 1) features
+embedding F ∈ RJ×D, where J and D denote the number
+of joints and the dimensions of the features latent space,
+respectively; 2) 3D joints P ∈ RJ×3, where J denotes the
+number of joints and 3 denotes the coordinates of the joints in
+[X, Y, Z]; 3) human shape β ∈ R10, where 10 represents the
+ﬁrst 10 coefﬁcients of the PCA shape space; and 4) camera
+parameters C ∈ R3, where 3 denotes the global rotation,
+translation, and scale.
+
+Image
+Image 
+Preprocessing
+2D Pose 
+Estimation
+Human 
+Detector
+2D Pose 
+Estimation
+Feature 
+Embedding
+Graph 
+Transformers
+Fusion
+3d Joints
+Head
+Shape Head
+Pose and Shape Estimator
+Transformer
+Template 
+Transformer
+Pose 
+Transformer
+Feature 
+Embedding
+Iterative 
+Regression
+Mesh 
+Vertices
+Pose 
++ 
+Shape
+(17, 2)
+(17, 128)
+(17, 3)
+(10,)
+(6890, 3)
+(17, 3)
+(17, 128) 
+or
+(15, 128)
+(34, 128) 
+or
+(32, 128)
+Joints 
+Regressor
+(6890, 3)
+(17, 3)
+3D-to-3D lifter
+Output either from previous module or from raw data
+Fig. 1. Modular Multi-stage Lightweight Graph Transformer Network for Human Pose and Shape Estimation from 2D Human Pose
+2) Pose and Shape Estimator: The Pose and Shape Es-
+timator module aims to estimate human mesh parameters,
+speciﬁcally joint angles. System modularity is a crucial goal in
+this work, and to that end, the module is designed to consume
+either the 3D-lifter features in an end-to-end training setup
+or the 3D pose in individual module training. However, due
+to its lightweight design, the module may not have enough
+capacity to accurately estimate the pose angle with its small
+embedding size. To address this, the module is augmented
+with a mean mesh template as introduced in [5] to enrich
+the feature representation through an additional branch. The
+features produced by the pose feature and mesh template
+branches are then fused to generate the ﬁnal features space,
+which is subsequently consumed by the iterative 3D regression
+as described in [14] to infer the ﬁnal 3D pose angle.
+Given the pose features on the ﬁrst branch, expressed as
+Fpose ∈ RJ×D where J denotes the number of joints and
+D denotes the dimensions, and the mesh template features
+on the second branch, expressed as Ftemplate ∈ RT ×D. Both
+branches are processed by the same transformer architecture to
+model the features. The resulting features from both branches
+are combined into a single ﬁnal embedding, represented as
+FP SE
+∈ R(J+T )×D. Finally, the iterative 3D regression
+consumes the fused features to generate the pose angles,
+expressed as θ ∈ R72.
+III. EXPERIMENTAL EVALUATION
+A. Datasets
+The Human3.6M dataset [15] is a widely adopted, video-
+based, and large-scale indoor dataset that was captured us-
+ing an accurate marker-based motion-capturing system. The
+dataset comprises 11 professional actors performing 17 pre-
+deﬁned actions. In accordance with previous studies, such as
+[4] and [14], we selected 5 subjects for training and utilized
+2 subjects’ samples for evaluation.
+The 3DPW dataset [16] is an outdoor dataset consisting
+of 60 video sequences that total 51,000 frames captured in
+an uncontrolled environment. The dataset features ground-
+truth 3D pose and mesh annotations. In accordance with the
+evaluation protocol established in previous studies, such as [4]
+and [14], we adopted the test dataset only.
+The MuCo-3DHP dataset [17] is a large-scale dataset for
+3D human pose estimation and mesh reconstruction in natural
+environments. The dataset includes over 13 million frames
+of video data recorded by 5 actors performing 7 actions
+in various outdoor settings. The dataset comprises ground-
+truth 3D pose and mesh annotations and has been utilized
+in numerous research studies to evaluate the performance of
+different algorithms for 3D human pose estimation and mesh
+reconstruction. Similar to [4] and [14], we utilized this dataset
+for mixed training.
+The MSCOCO keypoints dataset [18] is a subset of the
+larger MSCOCO dataset that was created for the purpose of
+
+0.4
+0.2
+1.
+0.0
+avie
+0.2
+-0.4 >
+-0.6
+0.8
+-1.0
+0.80.60.40.20.00.20.40.6 0.8
+XaxisMethods
+Humans.6M
+MPJPE
+PA-MPJPE
+Image
+Based
+HMR
+CVPR 2018
+88.0
+56.8
+GraphCMR
+CVPR 2019
+-
+50.1
+SPIN
+ICCV 2019
+-
+41.1
+METRO
+CVPR 2021
+54.0
+36.7
+MeshGraphormer
+ICCV 2021
+51.2
+34.5
+PyMAF
+ICCV 2021
+57.7
+40.5
+Video
+Based
+VIBE
+CVPR 2020
+65.6
+41.4
+TCMR
+CVPR 2021
+62.3
+41.1
+Pose
+Based
+Pose2Mesh
+ECCV 2020
+64.9
+47.0
+Baseline
+-
+68.3
+50.0
+GTRS
+-
+64.3
+45.4
+Our
+-
+65.9
+47.13
+TABLE I
+OUR EXTENSIVE EXPERIMENTS SHOWED OUR PIPELINE SCORE COMPARABLE RESULTS TO VARIOUS CONTRIBUTIONS
+human pose estimation in images. The dataset includes over
+200,000 images with ground-truth keypoint annotations for 17
+different body joints. The dataset has been widely used in
+research to evaluate the performance of different algorithms
+for human pose estimation and has served as a benchmark
+for comparing the performance of various approaches. In
+accordance with previous studies, such as [4] and [14], we
+adopted the MSCOCO dataset for mixed training.
+B. Metrics for Evaluation
+The mean per-joint position error (MPJPE) is a commonly
+used metric in the ﬁeld of 3D human pose estimation to
+assess the performance of algorithms. It quantiﬁes the average
+Euclidean distance between the predicted and ground-truth 3D
+joint positions in a dataset, after aligning them through a rigid
+transformation that minimizes the distance between the two
+sets of points. The MPJPE is expressed in millimeters, with
+lower values indicating higher accuracy in pose estimation.
+The Procrustes aligned mean per-joint position error (PA-
+MPJPE) is a variant of the MPJPE metric that also evaluates
+the accuracy of 3D human pose estimation algorithms. Similar
+to MPJPE, it measures the average Euclidean distance between
+the predicted and ground-truth joint positions. However, PA-
+MPJPE incorporates an additional alignment step using the
+Procrustes analysis method, which aligns the predicted and
+ground-truth positions by applying a non-rigid transformation
+that minimizes the overall distance between the two sets of
+points. The PA-MPJPE is also reported in millimeters, with
+lower values indicating more accurate pose estimation.
+The mean per-vertex error (MPVE) is a metric for evaluating
+the performance of algorithms for 3D human mesh reconstruc-
+tion. It quantiﬁes the average Euclidean distance between the
+predicted and ground-truth 3D mesh vertices in a dataset, after
+aligning them through a rigid transformation that minimizes
+the distance between the two sets of points. The MPVE is
+expressed in millimeters, with lower values indicating higher
+accuracy in mesh reconstruction.
+IV. CONCLUSION
+In this work, we present a pose-based framework for recon-
+structing human mesh parameters from 2D poses. This frame-
+work utilizes a 3D-lifter that leverages structured and implicit
+joint correlations through the employment of paralleled graph
+transformer blocks. As a result, the model is able to efﬁciently
+integrate the extracted pose features with the mesh template
+to produce human mesh parameters. Although the proposed
+framework demonstrates competitive performance, it may not
+be capable of reconstructing all human body shapes solely
+from 2D pose inputs. While image-based methods may achieve
+more precise reconstructions, pose-based approaches maintain
+their signiﬁcance owing to their versatility and lightweight
+design. Additionally, the modular design of the proposed
+framework allows for training to be conducted in individual
+or end-to-end modules.
+REFERENCES
+[1] Matthew Loper, Naureen Mahmood, Javier Romero, Gerard Pons-Moll,
+and Michael J Black. Smpl: A skinned multi-person linear model. ACM
+transactions on graphics (TOG), 34(6):1–16, 2015.
+[2] Javier Romero, Dimitrios Tzionas, and Michael J Black.
+Embodied
+hands: Modeling and capturing hands and bodies together. arXiv preprint
+arXiv:2201.02610, 2022.
+[3] Kathleen M Robinette, Sherri Blackwell, Hein Daanen, Mark Boehmer,
+and Scott Fleming. Civilian american and european surface anthropome-
+try resource (caesar), ﬁnal report. volume 1. summary. Technical report,
+Sytronics Inc Dayton Oh, 2002.
+[4] Hongsuk Choi, Gyeongsik Moon, and Kyoung Mu Lee. Pose2mesh:
+Graph convolutional network for 3d human pose and mesh recovery
+from a 2d human pose. In European Conference on Computer Vision,
+pages 769–787. Springer, 2020.
+[5] Ce Zheng, Matias Mendieta, Pu Wang, Aidong Lu, and Chen Chen. A
+lightweight graph transformer network for human mesh reconstruction
+from 2d human pose. In Proceedings of the 30th ACM International
+Conference on Multimedia, pages 5496–5507, 2022.
+[6] Hui En Pang, Zhongang Cai, Lei Yang, Tianwei Zhang, and Ziwei
+Liu. Benchmarking and analyzing 3d human pose and shape estimation
+beyond algorithms. In Thirty-sixth Conference on Neural Information
+Processing Systems Datasets and Benchmarks Track, 2022.
+[7] Angjoo Kanazawa, Michael J Black, David W Jacobs, and Jitendra
+Malik. End-to-end recovery of human shape and pose. In Proceedings of
+the IEEE conference on computer vision and pattern recognition, pages
+7122–7131, 2018.
+[8] Muhammed Kocabas, Nikos Athanasiou, and Michael J Black. Vibe:
+Video inference for human body pose and shape estimation. In Pro-
+ceedings of the IEEE/CVF conference on computer vision and pattern
+recognition, pages 5253–5263, 2020.
+[9] Naureen Mahmood, Nima Ghorbani, Nikolaus F Troje, Gerard Pons-
+Moll, and Michael J Black. Amass: Archive of motion capture as surface
+shapes. In Proceedings of the IEEE/CVF international conference on
+computer vision, pages 5442–5451, 2019.
+
+[10] Ke Sun, Bin Xiao, Dong Liu, and Jingdong Wang. Deep high-resolution
+representation learning for human pose estimation. In Proceedings of
+the IEEE/CVF conference on computer vision and pattern recognition,
+pages 5693–5703, 2019.
+[11] Zhiming Zou and Wei Tang. Modulated graph convolutional network
+for 3d human pose estimation.
+In Proceedings of the IEEE/CVF
+International Conference on Computer Vision, pages 11477–11487,
+2021.
+[12] Long Zhao, Xi Peng, Yu Tian, Mubbasir Kapadia, and Dimitris N
+Metaxas. Semantic graph convolutional networks for 3d human pose
+regression. In Proceedings of the IEEE/CVF conference on computer
+vision and pattern recognition, pages 3425–3435, 2019.
+[13] Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion
+Jones, Aidan N Gomez, Lukasz Kaiser, and Illia Polosukhin. Attention
+is all you need. In Advances in neural information processing systems,
+pages 5998–6008, 2017.
+[14] Nikos Kolotouros, Georgios Pavlakos, Michael J Black, and Kostas
+Daniilidis. Learning to reconstruct 3d human pose and shape via model-
+ﬁtting in the loop.
+In Proceedings of the IEEE/CVF International
+Conference on Computer Vision, pages 2252–2261, 2019.
+[15] Catalin Ionescu, Dragos Papava, Vlad Olaru, and Cristian Sminchisescu.
+Human3. 6m: Large scale datasets and predictive methods for 3d human
+sensing in natural environments. IEEE transactions on pattern analysis
+and machine intelligence, 36(7):1325–1339, 2013.
+[16] Timo Von Marcard, Roberto Henschel, Michael J Black, Bodo Rosen-
+hahn, and Gerard Pons-Moll. Recovering accurate 3d human pose in the
+wild using imus and a moving camera. In Proceedings of the European
+Conference on Computer Vision (ECCV), pages 601–617, 2018.
+[17] Dushyant Mehta, Helge Rhodin, Dan Casas, Pascal Fua, Oleksandr
+Sotnychenko, Weipeng Xu, and Christian Theobalt.
+Monocular 3d
+human pose estimation in the wild using improved cnn supervision.
+In 2017 international conference on 3D vision (3DV), pages 506–516.
+IEEE, 2017.
+[18] Tsung-Yi Lin, Michael Maire, Serge Belongie, James Hays, Pietro
+Perona, Deva Ramanan, Piotr Doll´ar, and C Lawrence Zitnick. Microsoft
+coco: Common objects in context. In European conference on computer
+vision, pages 740–755. Springer, 2014.
+
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+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf,len=241
+page_content='A Modular Multi-stage Lightweight Graph  Transformer Network for Human Pose and Shape  Estimation from 2D Human Pose  Ayman Ali, Ekkasit Pinyoanuntapong, Pu Wang, Mohsen Dorodchi  College of Computing and Informatics  University of North Carolina at Charlotte  Charlotte, United States  aali26, epinyoan, pwang13, mdorodch@uncc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content='edu  Abstract—In this research, we address the challenge faced by  existing deep learning-based human mesh reconstruction meth-  ods in balancing accuracy and computational efﬁciency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content=' These  methods typically prioritize accuracy, resulting in large network  sizes and excessive computational complexity, which may hinder  their practical application in real-world scenarios, such as virtual  reality systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content=' To address this issue, we introduce a modular  multi-stage lightweight graph-based transformer network for  human pose and shape estimation from 2D human pose, a  pose-based human mesh reconstruction approach that priori-  tizes computational efﬁciency without sacriﬁcing reconstruction  accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content=' Our method consists of a 2D-to-3D lifter module that  utilizes graph transformers to analyze structured and implicit  joint correlations in 2D human poses, and a mesh regression  module that combines the extracted pose features with a mesh  template to produce the ﬁnal human mesh parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content='  I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content=' INTRODUCTION  The ﬁeld of computer vision has witnessed signiﬁcant ad-  vancements with the advent of deep learning models in human  pose estimation from monocular images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content=' Speciﬁcally, 2D pose  estimation involves determining the locations of human joint  coordinates within a single image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content=' In recent years, the research  community has shown great interest in reconstructing 3D  human mesh representations due to their practical applications  in human-computer interaction, gaming, and virtual systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content='  Despite the progress in both 2D and 3D pose estimation and  human mesh reconstruction, reconstructing human mesh from  a single image remains challenging due to factors such as  depth ambiguity, complex backgrounds, challenging postures,  and a lack of annotated in-the-wild datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content='  The fundamental process of reconstructing a 3D human  mesh involves estimating the pose and shape parameters based  on statistical body models, such as SMPL [1] and [2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content=' The  pose parameters θ deﬁne the global root orientation and the  relative rotations of human body joints represented in an axis-  angle sequence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content=' Moreover, the shape parameters β represent  the learned linear gender-based body shape derived from the  CAESAR dataset [3] using principal component analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content='  The literature on human mesh reconstruction primarily  consists of two paradigms: optimization-based and regression-  based approaches.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content=' Optimization-based methods minimize the  difference between the re-projected 2D pose regressed from  the human mesh and the estimated 2D pose.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content=' In contrast,  regression-based methods directly predict the pose and shape  parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content='  While deep learning models have progressed in human mesh  reconstruction, the choice of input data has a signiﬁcant impact  on the system’s pipeline.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content=' Recent advances have adopted an  end-to-end pipeline where the input is the scene image, and  the output is the predicted mesh.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content=' However, this approach can  be computationally intensive and does not meet the efﬁciency  requirements of various real-world applications, such as gam-  ing and real-time mesh recovery.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content='  To address the computational overhead, some researchers  have proposed using skeleton data as the input, as it is sparse  [4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content=' However, solely relying on skeleton data is insufﬁcient to  address the computational intensity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content=' Zheng et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content=' [5] proposed  a lightweight graph-based transformer architecture to focus on  efﬁciency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content='  Nevertheless, reconstructing mesh parameters remains com-  plex, as it is inﬂuenced by a variety of factors, including 1)  Dataset Characteristics where the performance of a model is  not signiﬁcantly impacted by the indoor/outdoor setting or  the number of data points, but rather by human pose and  shape, camera characteristics, and backbone features [6].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content=' Fur-  thermore, a diverse range of these attributes can improve the  performance, while occlusion and SMPL ﬁttings can enhance  recovery accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content=' 2) Dataset Mix is another factor that affects  the complexity of the task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content=' The choice of datasets is critical for  the generalizability and accuracy of the model [6].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content=' It is imper-  ative to use the same combination of datasets when evaluating  and comparing the impact of other factors, such as training  algorithms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content=' Comparing two network architectures on different  dataset combinations is considered unfair.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content=' To establish a robust  baseline model, it is recommended to use more challenging  datasets and increase their contribution during training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content=' Finally,  Noisy annotations, which in case of having high proportions of  noisy data samples, can negatively impact model performance,  particularly when both SMPL annotations and keypoints are  affected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content=' However, slightly noisy SMPL data can still have a  positive effect on training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content='  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content='13403v1  [cs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content='CV]  31 Jan 2023  Our objective in this research is to design a modular and  end-to-end capable graph-based transformer network that is  capable of estimating the human shape and pose, demonstrat-  ing comparable performance with state-of-the-art methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content='  Speciﬁcally, we propose the following strategies to achieve  this goal:  Construct a modular, multi-stage pipeline that is capable  of end-to-end estimation of human parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content='  separate the learning of human pose, shape, and camera  parameters to improve accuracy and robustness of the  model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content='  II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content=' SYSTEM DESCRIPTION  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content=' Preliminary  The task of Human Mesh Recovery (HMR) from images  without the utilization of auxiliary devices, such as depth  sensors, poses a challenge due to various factors such as  depth ambiguity, complex backgrounds, and diverse human  poses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content=' Typically, deep learning networks are trained to estimate  the human pose parameters using a skinned vertex-based  parametric human model such as SMPL [1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content='  Kanazawa et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content=' proposed a method that minimizes the 2D  reprojection loss of joints without relying on paired 2D-to-3D  supervision to estimate the pose and shape parameters from an  image [7].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content=' Kolotouros et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content=' proposed a method that iteratively  optimizes the estimated parameters to produce a pixel-level  alignment with the original image [8].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content=' Further, Kocabas et  al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content=' introduced adversarial training to enhance the quality of  the estimated mesh by utilizing the large-scale motion capture  dataset AMASS [9].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content='  Recent advancements in 2D pose estimation have prompted  researchers to explore the potential of using off-the-shelf 2D  pose estimation networks, such as HRNet [10], to estimate  human mesh parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content=' The 2D skeleton estimated from an  image is fed to the human mesh parameters estimation network  for further processing and analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content='  Graph Convolution Networks (GCN) have received con-  siderable attention in recent years due to their ability to intu-  itively model data, such as articulated models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content=' In particular,  many studies have adopted GCN to model 3D human pose  estimation [11], [12].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content=' In the context of human skeletons, joints  and bones are mapped to vertices and edges, respectively,  thus forming a graph represented mathematically as G = v, ϵ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content='  Inspired by [5], we use GCN to model the 2D pose features,  where the output of the GCN layer is expressed as:  X′ = σ(A × W)  (1)  Where σ(.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content=') represents the Gaussian Error Linear Unit (GELU),  A represents the adjacency matrix, and W represents the  learnable weight matrix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content='  Transformer Transformer [13] has remodeled many deep  learning models in computer vision.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content=' The ability to capture  the global context understanding in the features space led  to signiﬁcant advancements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content=' Self-attention can be described  as a function to compute the attention matrix given a query  matrix Q ∈ RN×d, key matrix K ∈ RN×d and value matrix  V ∈ RN×d where N represents the number of vectors in  the sequence, and d is the dimension.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content=' A scaling factor ( 1  √  d)  is utilized to alleviate the growth of the softmax function’s  magnitude.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content=' The scaled-dot product attention can be expressed  as:  Attention(Q, K, V ) = Softmax(QKT  √dk  )V  (2)  Multi-headed self-attention utilized parallel scaled-dot atten-  tions to project the queries, keys, and values h times with  different linear projections to dk, dk, and DV dimensions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content=' A  concatenation of the h head attention output can be expressed  as:  MSA(Q, K, V ) = Concat(H1, H2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content='., Hh)Wout  where Hi = Attention(Qi, Ki, Vi), i ∈ [1, 2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content=', h]  (3)  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content=' System Architecture  At ﬁrst, a projection layer encodes the 2D pose estimation  to create latent space embedding to be consumed by the 3D  lifter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content=' Supervised training is adopted to train a 3D lifter module  where we minimize the distance between the predicted 3D and  the ground truth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content=' In addition to using L1 regularization, we use  the weak perspective camera model to reproject 3D to the 2D  pose to ensure better accuracy and alignment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content=' Furthermore, the  shape parameters are applied to the mean template mesh.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content=' We  experimented with using the mean mesh, which is represented  by M ∈ R6890, and the rest pose regressed from the mean  template mesh.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content=' We found that using mean mesh provided more  gain than using the rest pose.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content=' The pose angles are predicated  by the iterative regressor that consumes the features generated  by the pose and shape estimator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content=' Finally, forward kinematics  are employed to calculate the human mesh.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content='  1) 3D-lifter Module: The 3D-lifter module leverages the  graph transformer as described in [5] to extract both global and  local features from human pose data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content=' First, a projection layer  encodes the pose into a latent space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content=' The resulting features are  then fed into multiple parallel graph transformer blocks, which  have small embedding dimensions for improved efﬁciency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content='  The outputs from these parallel branches are fused to generate  features that are used to predict 3D pose estimation, human  shape, and camera parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content='  Given a 2D skeleton denoted as S ∈ Rj×2, where j repre-  sents the number of joints and 2 denotes the joint coordinates  in the X, Y plane, the 2D-to-3D lifting task is performed by  the Pose Analysis Module (PAM).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content=' PAM returns: 1) features  embedding F ∈ RJ×D, where J and D denote the number  of joints and the dimensions of the features latent space,  respectively;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content=' 2) 3D joints P ∈ RJ×3, where J denotes the  number of joints and 3 denotes the coordinates of the joints in  [X, Y, Z];' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content=' 3) human shape β ∈ R10, where 10 represents the  ﬁrst 10 coefﬁcients of the PCA shape space;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content=' and 4) camera  parameters C ∈ R3, where 3 denotes the global rotation,  translation, and scale.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content='  Image  Image  Preprocessing  2D Pose  Estimation  Human  Detector  2D Pose  Estimation  Feature  Embedding  Graph  Transformers  Fusion  3d Joints  Head  Shape Head  Pose and Shape Estimator  Transformer  Template  Transformer  Pose  Transformer  Feature  Embedding  Iterative  Regression  Mesh  Vertices  Pose  +  Shape  (17,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content=' 2)  (17,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content=' 128)  (17,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content=' 3)  (10,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content=')  (6890,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content=' 3)  (17,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content=' 3)  (17,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content=' 128)  or  (15,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content=' 128)  (34,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content=' 128)  or  (32,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content=' 128)  Joints  Regressor  (6890,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content=' 3)  (17,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content=' 3)  3D-to-3D lifter  Output either from previous module or from raw data  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content=' Modular Multi-stage Lightweight Graph Transformer Network for Human Pose and Shape Estimation from 2D Human Pose  2) Pose and Shape Estimator: The Pose and Shape Es-  timator module aims to estimate human mesh parameters,  speciﬁcally joint angles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content=' System modularity is a crucial goal in  this work, and to that end, the module is designed to consume  either the 3D-lifter features in an end-to-end training setup  or the 3D pose in individual module training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content=' However, due  to its lightweight design, the module may not have enough  capacity to accurately estimate the pose angle with its small  embedding size.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content=' To address this, the module is augmented  with a mean mesh template as introduced in [5] to enrich  the feature representation through an additional branch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content=' The  features produced by the pose feature and mesh template  branches are then fused to generate the ﬁnal features space,  which is subsequently consumed by the iterative 3D regression  as described in [14] to infer the ﬁnal 3D pose angle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content='  Given the pose features on the ﬁrst branch, expressed as  Fpose ∈ RJ×D where J denotes the number of joints and  D denotes the dimensions, and the mesh template features  on the second branch, expressed as Ftemplate ∈ RT ×D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content=' Both  branches are processed by the same transformer architecture to  model the features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content=' The resulting features from both branches  are combined into a single ﬁnal embedding, represented as  FP SE  ∈ R(J+T )×D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content=' Finally, the iterative 3D regression  consumes the fused features to generate the pose angles,  expressed as θ ∈ R72.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content='  III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content=' EXPERIMENTAL EVALUATION  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content=' Datasets  The Human3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content='6M dataset [15] is a widely adopted, video-  based, and large-scale indoor dataset that was captured us-  ing an accurate marker-based motion-capturing system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content=' The  dataset comprises 11 professional actors performing 17 pre-  deﬁned actions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content=' In accordance with previous studies, such as  [4] and [14], we selected 5 subjects for training and utilized  2 subjects’ samples for evaluation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content='  The 3DPW dataset [16] is an outdoor dataset consisting  of 60 video sequences that total 51,000 frames captured in  an uncontrolled environment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content=' The dataset features ground-  truth 3D pose and mesh annotations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content=' In accordance with the  evaluation protocol established in previous studies, such as [4]  and [14], we adopted the test dataset only.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content='  The MuCo-3DHP dataset [17] is a large-scale dataset for  3D human pose estimation and mesh reconstruction in natural  environments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content=' The dataset includes over 13 million frames  of video data recorded by 5 actors performing 7 actions  in various outdoor settings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content=' The dataset comprises ground-  truth 3D pose and mesh annotations and has been utilized  in numerous research studies to evaluate the performance of  different algorithms for 3D human pose estimation and mesh  reconstruction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content=' Similar to [4] and [14], we utilized this dataset  for mixed training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content='  The MSCOCO keypoints dataset [18] is a subset of the  larger MSCOCO dataset that was created for the purpose of  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content='2  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content='  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content='0  avie  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content='4 >  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content='80.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content='60.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content='40.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content='20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content='00.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content='20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content='40.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content='8  XaxisMethods  Humans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content='6M  MPJPE  PA-MPJPE  Image  Based  HMR  CVPR 2018  88.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content='0  56.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content='8  GraphCMR  CVPR 2019 50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content='1  SPIN  ICCV 2019 41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content='1  METRO  CVPR 2021  54.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content='0  36.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content='7  MeshGraphormer  ICCV 2021  51.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content='2  34.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content='5  PyMAF  ICCV 2021  57.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content='7  40.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content='5  Video  Based  VIBE  CVPR 2020  65.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content='6  41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content='4  TCMR  CVPR 2021  62.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content='3  41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content='1  Pose  Based  Pose2Mesh  ECCV 2020  64.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content='9  47.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content='0  Baseline 68.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content='3  50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content='0  GTRS 64.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content='3  45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content='4  Our 65.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content='9  47.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content='13  TABLE I  OUR EXTENSIVE EXPERIMENTS SHOWED OUR PIPELINE SCORE COMPARABLE RESULTS TO VARIOUS CONTRIBUTIONS  human pose estimation in images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content=' The dataset includes over  200,000 images with ground-truth keypoint annotations for 17  different body joints.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content=' The dataset has been widely used in  research to evaluate the performance of different algorithms  for human pose estimation and has served as a benchmark  for comparing the performance of various approaches.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content=' In  accordance with previous studies, such as [4] and [14], we  adopted the MSCOCO dataset for mixed training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content='  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content=' Metrics for Evaluation  The mean per-joint position error (MPJPE) is a commonly  used metric in the ﬁeld of 3D human pose estimation to  assess the performance of algorithms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content=' It quantiﬁes the average  Euclidean distance between the predicted and ground-truth 3D  joint positions in a dataset, after aligning them through a rigid  transformation that minimizes the distance between the two  sets of points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content=' The MPJPE is expressed in millimeters, with  lower values indicating higher accuracy in pose estimation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content='  The Procrustes aligned mean per-joint position error (PA-  MPJPE) is a variant of the MPJPE metric that also evaluates  the accuracy of 3D human pose estimation algorithms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content=' Similar  to MPJPE, it measures the average Euclidean distance between  the predicted and ground-truth joint positions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content=' However, PA-  MPJPE incorporates an additional alignment step using the  Procrustes analysis method, which aligns the predicted and  ground-truth positions by applying a non-rigid transformation  that minimizes the overall distance between the two sets of  points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content=' The PA-MPJPE is also reported in millimeters, with  lower values indicating more accurate pose estimation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content='  The mean per-vertex error (MPVE) is a metric for evaluating  the performance of algorithms for 3D human mesh reconstruc-  tion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content=' It quantiﬁes the average Euclidean distance between the  predicted and ground-truth 3D mesh vertices in a dataset, after  aligning them through a rigid transformation that minimizes  the distance between the two sets of points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content=' The MPVE is  expressed in millimeters, with lower values indicating higher  accuracy in mesh reconstruction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content='  IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content=' CONCLUSION  In this work, we present a pose-based framework for recon-  structing human mesh parameters from 2D poses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content=' This frame-  work utilizes a 3D-lifter that leverages structured and implicit  joint correlations through the employment of paralleled graph  transformer blocks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content=' As a result, the model is able to efﬁciently  integrate the extracted pose features with the mesh template  to produce human mesh parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content=' Although the proposed  framework demonstrates competitive performance, it may not  be capable of reconstructing all human body shapes solely  from 2D pose inputs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content=' While image-based methods may achieve  more precise reconstructions, pose-based approaches maintain  their signiﬁcance owing to their versatility and lightweight  design.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content=' Additionally, the modular design of the proposed  framework allows for training to be conducted in individual  or end-to-end modules.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content='  REFERENCES  [1] Matthew Loper, Naureen Mahmood, Javier Romero, Gerard Pons-Moll,  and Michael J Black.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content=' Smpl: A skinned multi-person linear model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content=' ACM  transactions on graphics (TOG), 34(6):1–16, 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content='  [2] Javier Romero, Dimitrios Tzionas, and Michael J Black.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content='  Embodied  hands: Modeling and capturing hands and bodies together.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content=' arXiv preprint  arXiv:2201.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content='02610, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content='  [3] Kathleen M Robinette, Sherri Blackwell, Hein Daanen, Mark Boehmer,  and Scott Fleming.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content=' Civilian american and european surface anthropome-  try resource (caesar), ﬁnal report.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content=' volume 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content=' summary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content=' Technical report,  Sytronics Inc Dayton Oh, 2002.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content='  [4] Hongsuk Choi, Gyeongsik Moon, and Kyoung Mu Lee.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content=' Pose2mesh:  Graph convolutional network for 3d human pose and mesh recovery  from a 2d human pose.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content=' In European Conference on Computer Vision,  pages 769–787.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content=' Springer, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content='  [5] Ce Zheng, Matias Mendieta, Pu Wang, Aidong Lu, and Chen Chen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content=' A  lightweight graph transformer network for human mesh reconstruction  from 2d human pose.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content=' In Proceedings of the 30th ACM International  Conference on Multimedia, pages 5496–5507, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content='  [6] Hui En Pang, Zhongang Cai, Lei Yang, Tianwei Zhang, and Ziwei  Liu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content=' Benchmarking and analyzing 3d human pose and shape estimation  beyond algorithms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content=' In Thirty-sixth Conference on Neural Information  Processing Systems Datasets and Benchmarks Track, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content='  [7] Angjoo Kanazawa, Michael J Black, David W Jacobs, and Jitendra  Malik.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content=' End-to-end recovery of human shape and pose.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content=' In Proceedings of  the IEEE conference on computer vision and pattern recognition, pages  7122–7131, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content='  [8] Muhammed Kocabas, Nikos Athanasiou, and Michael J Black.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content=' Vibe:  Video inference for human body pose and shape estimation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content=' In Pro-  ceedings of the IEEE/CVF conference on computer vision and pattern  recognition, pages 5253–5263, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content='  [9] Naureen Mahmood, Nima Ghorbani, Nikolaus F Troje, Gerard Pons-  Moll, and Michael J Black.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content=' Amass: Archive of motion capture as surface  shapes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content=' In Proceedings of the IEEE/CVF international conference on  computer vision, pages 5442–5451, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content='  [10] Ke Sun, Bin Xiao, Dong Liu, and Jingdong Wang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content=' Deep high-resolution  representation learning for human pose estimation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content=' In Proceedings of  the IEEE/CVF conference on computer vision and pattern recognition,  pages 5693–5703, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content='  [11] Zhiming Zou and Wei Tang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content=' Modulated graph convolutional network  for 3d human pose estimation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content='  In Proceedings of the IEEE/CVF  International Conference on Computer Vision, pages 11477–11487,  2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content='  [12] Long Zhao, Xi Peng, Yu Tian, Mubbasir Kapadia, and Dimitris N  Metaxas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content=' Semantic graph convolutional networks for 3d human pose  regression.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content=' In Proceedings of the IEEE/CVF conference on computer  vision and pattern recognition, pages 3425–3435, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content='  [13] Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion  Jones, Aidan N Gomez, Lukasz Kaiser, and Illia Polosukhin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content=' Attention  is all you need.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content=' In Advances in neural information processing systems,  pages 5998–6008, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content='  [14] Nikos Kolotouros, Georgios Pavlakos, Michael J Black, and Kostas  Daniilidis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content=' Learning to reconstruct 3d human pose and shape via model-  ﬁtting in the loop.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content='  In Proceedings of the IEEE/CVF International  Conference on Computer Vision, pages 2252–2261, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content='  [15] Catalin Ionescu, Dragos Papava, Vlad Olaru, and Cristian Sminchisescu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content='  Human3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content=' 6m: Large scale datasets and predictive methods for 3d human  sensing in natural environments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content=' IEEE transactions on pattern analysis  and machine intelligence, 36(7):1325–1339, 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content='  [16] Timo Von Marcard, Roberto Henschel, Michael J Black, Bodo Rosen-  hahn, and Gerard Pons-Moll.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content=' Recovering accurate 3d human pose in the  wild using imus and a moving camera.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content=' In Proceedings of the European  Conference on Computer Vision (ECCV), pages 601–617, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content='  [17] Dushyant Mehta, Helge Rhodin, Dan Casas, Pascal Fua, Oleksandr  Sotnychenko, Weipeng Xu, and Christian Theobalt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content='  Monocular 3d  human pose estimation in the wild using improved cnn supervision.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content='  In 2017 international conference on 3D vision (3DV), pages 506–516.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content='  IEEE, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content='  [18] Tsung-Yi Lin, Michael Maire, Serge Belongie, James Hays, Pietro  Perona, Deva Ramanan, Piotr Doll´ar, and C Lawrence Zitnick.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content=' Microsoft  coco: Common objects in context.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content=' In European conference on computer  vision, pages 740–755.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
+page_content=' Springer, 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xdFQT4oBgHgl3EQfwzbn/content/2301.13403v1.pdf'}
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+1
+Fine Robotic Manipulation
+without Force/Torque Sensor
+Shilin Shan1,∗ and Quang-Cuong Pham2
+Abstract—Force Sensing and Force Control are essential to
+many industrial applications. Typically, a 6-axis Force/Torque
+(F/T) sensor is mounted between the robot’s wrist and the end-
+effector in order to measure the forces and torques exerted by
+the environment onto the robot (the external wrench). Although
+a typical 6-axis F/T sensor can provide highly accurate mea-
+surements, it is expensive and vulnerable to drift and external
+impacts. Existing methods aiming at estimating the external
+wrench using only the robot’s internal signals are limited in
+scope: for example, wrench estimation accuracy was mostly
+validated in free-space motions and simple contacts as opposed
+to tasks like assembly that require high-precision force control.
+Here we present a Neural Network based method and argue that
+by devoting particular attention to the training data structure,
+it is possible to accurately estimate the external wrench in
+a wide range of scenarios based solely on internal signals.
+As an illustration, we demonstrate a pin insertion experiment
+with 100-micron clearance and a hand-guiding experiment, both
+performed without external F/T sensors or joint torque sensors.
+Our result opens the possibility of equipping the existing 2.7
+million industrial robots with Force Sensing and Force Control
+capabilities without any additional hardware.
+Index Terms—External Wrench Estimation, Machine Learn-
+ing, Mechanisms Modeling & Control, Human-robot Interaction
+I. INTRODUCTION
+Force Sensing and Force Control are essential to many
+industrial applications, from contact-based inspection to as-
+sembly, sanding, deburring, and polishing [1]–[3]. Typically,
+a 6-axis Force/Torque (F/T) sensor is mounted between the
+robot’s wrist and the end-effector in order to measure the
+forces and torques exerted by the environment onto the robot
+(the external wrench). Although a typical 6-axis F/T sensor
+can provide highly accurate measurements, it is expensive and
+vulnerable to drift and external impacts. Consequently, there
+has been a signiﬁcant research effort aimed at estimating the
+external wrench using only the robot’s internal signals, such
+as joint position, joint velocity, or motor current readings.
+To that aim, there are two main approaches in the literature:
+model-based and model-free. In the model-based approach,
+parameterized models of the robot’s dynamics are developed
+and identiﬁed using standard parameter identiﬁcation tech-
+niques [4]–[7]. The main difﬁculty here lies in the accurate
+and reliable modeling and identiﬁcation of highly nonlinear,
+1 Shilin Shan is with School of Mechanical and Aerospace Engineering,
+Nanyang Technological University, Singapore (address: 50 Nanyang Ave, Sin-
+gapore 639798; phone: +65 6790 5568; e-mail: shilin.shan153@gmail.com)
+2 Quang-Cuong Pham is with Eureka Robotics and Singapore Centre for
+3D Printing (SC3DP), School of Mechanical and Aerospace Engineering,
+Nanyang Technological University, Singapore. (e-mail: cuong@ntu.edu.sg)
+∗ Corresponding author: Shilin Shan
+Fig. 1: Snapshot of the sensorless tight pin insertion and
+hand-guiding experiment setup. Video demonstrations of the
+experiments in Section V is available in the supplementary
+materials or at: https://youtu.be/04 f3coFzaQ
+nonsmooth phenomena such as hysteresis and joint friction.
+Model-free methods, based, e.g., on Neural Networks, have
+been developed to overcome this difﬁculty [8]–[10]. However,
+such methods have been so far limited in scope: for example,
+wrench estimation accuracy was mostly validated in free-space
+motions and simple contacts as opposed to complex industrial
+tasks that require high-precision force control.
+In general, to our knowledge, no method – whether model-
+based or model-free – has been shown to accurately and
+reliably estimate the external wrench in both free-space and in-
+contact motions. This requirement is crucial for achieving non-
+trivial tasks like tight assembly and hand-guiding, alternating
+between free-space and in-contact robot motions. These tasks
+have yet to be demonstrated in existing works and are, more
+generally, necessary for large-scale industrial deployment.
+Here we present a model-free method (based on Neural Net-
+works) and argue that the above requirement can be satisﬁed
+if particular attention is devoted to the structure of the training
+dataset. In particular, we highlight the importance of collecting
+training data for both free-space and in-contact motions. Doing
+so enables us to accurately and reliably estimate external
+wrench using only internal signals such as joint position,
+velocity, acceleration, and current readings.
+More speciﬁcally,
+• We propose a pure Neural Network based method that
+takes joint currents and states as input and returns the end-
+effector wrench. The Neural Network maps the input vari-
+ables needed for a dynamic model to the output wrench
+directly, so no additional Dynamic Model identiﬁcation
+and joint torque sensing are required. In addition, the
+use of joint current allows wrench estimation without
+arXiv:2301.13413v1  [cs.RO]  31 Jan 2023
+
+DENSO
+F/T Sensor
+DisabledADENSO
+F/T Sensor
+Disabled2
+the embedded joint torque sensors, which reduces robot
+manufacturing costs.
+• We present a pipeline that collects data automatically and
+efﬁciently in wrench estimation problems by emphasizing
+the data collection procedure. The training data was
+collected with not only the free-space trajectories but
+also constrained in-contact motions so as to induce dis-
+turbances that create more variability in the data set. The
+trained model has high accuracy in typical industrial tasks
+like tight pin insertion and high-precision hand-guiding,
+which, to our knowledge, have yet to be demonstrated
+with the existing methods.
+As an illustration, we demonstrate the pin insertion experiment
+with 100-micron clearance and the hand-guiding experiment,
+both performed without F/T sensors at runtime. Note that
+a 6-axis F/T sensor would be needed for the one-time data
+collection on a single manipulator in the training phase. For
+large-scale industrial applications, a well-trained Neural Net-
+work can be applied to any manipulators of the same model,
+either manufactured or to be manufactured, to equip them with
+force/torque sensing ability without physical sensors.
+The paper is organized as follows. In Section II, we discuss
+the literature on wrench estimation and dynamics identiﬁca-
+tion. In Section III, we present the basic model structure and
+the concepts for data sets generation. In Section IV, we discuss
+in detail the data collection procedure and model enhancement
+approaches for broader work-space coverage. In Section V, we
+present four experiments in free-space and in-contact scenarios
+to demonstrate the robustness of the proposed method. Fig. 1
+shows a snapshot of the sensorless pin insertion and hand-
+guiding experiments.
+II. RELATED WORK
+Previous works on contact detection [4], [11] introduced
+using the generalized momentum to identify the Inverse Dy-
+namic Model, and a generalized-momentum-based disturbance
+observer is designed in [5]. By integrating with the Kalman
+Filter, the combined approach [6] allows accurate force estima-
+tion that can be used for basic force control tasks. The author
+also addressed that joint friction, an essential component in
+dynamic modeling, can be calculated by considering Coulomb
+friction, viscous friction, stiction, and Stribeck velocity. Earlier
+studies [12]–[14] have also shown that non-linear behaviors
+like hysteresis and back-lashes can be well identiﬁed, thus
+compensated by such a modeling method. On the other hand,
+deciding the friction model parameters may require complex
+experiments.
+Although mathematical analysis provides strong intuitions
+to the robot dynamics, identifying the Inverse Dynamic Model
+through mathematical analysis of mechanical models is still
+complicated. In order to simplify modeling complexity, recent
+studies have proposed semi-parametric approaches to train
+Neural Network models to learn joint motor friction [15]
+or compensate for all the non-modeled effects [16]. Given
+that parameter identiﬁcations are still required for rigid body
+dynamics, these methods reduce only modeling complexity,
+whereas even more experiments would be needed to learn a
+friction model separately.
+Another approach is to avoid manually selecting the whole
+model structure and make the model learn through one-time
+data collection. Non-parametric regression-based approaches
+have been studied for model identiﬁcation in early research
+[17], [18]. Multiple studies have built on these methods and
+demonstrated the ease of training of non-parametric learning-
+based approaches, including Gaussian Process Regression
+(GPR) and Locally Weighted Projection Regression (LWPR)
+[8], [9], [19]. Without choosing the model structure manually,
+regression-based approaches avoid human bias on the model
+structure, thus allowing a model to learn the optimal structure
+given simple hyper-parameters. Being trained and veriﬁed with
+hand-guiding experiments [9], GPR shows high accuracy in
+hand-guided trajectory tracking. However, trajectory tracking
+only is not representative of various industrial tasks. Further-
+more, this method may not be transferable to other tasks; as
+discussed in Section III, the hand-guiding data set could be
+biased due to the strong correlation between the end-effector
+force and motion.
+Following Section I, we propose to use Neural Networks,
+particularly Multilayer Perceptron (MLP), to avoid complex
+mathematical modeling while ensuring estimation accuracy,
+as it has been proven effective in approximating nonlinear
+mapping in many areas. Also discussed in [20], Neural Net-
+works performed well in approximating the forward/inverse
+kinematics, and Jacobian matrix [21]–[23]. Recent works have
+proposed a variety of Neural Network structures, including
+MLP [24], Recurrent Neural Network (RNN) [25], and Con-
+volutional Neural Network (CNN) [26]–[28], being applied in
+different tasks. Though demonstrating promising results, the
+works mentioned above are hard to compare as they were
+implemented in a very different context that requires image
+input or surgical robot setup. Some closely related applications
+of MLP in industrial manipulator collision checking can be
+found in [10], [29], where models are trained to predict
+external torque for threshold determination or directly detect
+contact during motions. Even though Neural Network is less
+intuitive in revealing robot dynamics, it generally outperforms
+most methods in nonlinear mapping and noise cancellation,
+thereby being robust in uncertain environments given sufﬁcient
+training data.
+III. MODEL AND TRAINING SET STRUCTURE
+A. Model Structure
+Given the broad application of Neural Networks in re-
+gression problems for robotics, multiple structures, i.e., MLP,
+RNN, CNN, have been proposed for similar tasks as discussed
+above. Considering model simplicity and ease of implemen-
+tation, we choose the model to have a fundamental MLP
+structure with only a few hidden layers. As shown in the
+experiments, since MLP already shows high accuracy in
+multiple tasks, we will not discuss the use of more complex
+structures like CNN and RNN in this paper. On the other hand,
+when a simple model covers a large joint-space or work-space,
+it will underﬁt the training data such that estimation becomes
+inaccurate. Our solution is to enlarge the hidden layers or
+increase Network depth to capture higher non-linearity and
+
+3
+diversities introduced by dissimilar Inverse Kinematics Classes
+(IK Classes for short). Therefore, a model should be retrained
+and optimized whenever new data is collected from distal IK
+Classes. A detailed discussion of the relationship between the
+model and data size is included in Section IV.
+Fig. 2 helps to visualize a sample model structure with
+two hidden layers, each having 256 neurons. The input to
+the Neural Network is a 24×1 vector that concatenates the
+6×1 joint current, 6×1 joint position, 6×1 joint velocity, and
+6×1 joint acceleration vector. The model output is a 6×1
+vector consisting of the 3×1 force vector and 3×1 torque
+vector in the XYZ direction, all represented in the F/T Sensor
+(end-effector) frame. We implemented the model and data
+loader, then trained the model with PyTorch. The loss function,
+activation function, and optimization method are MSEloss,
+ReLu, and Adam Optimizer, respectively.
+Fig. 2: Structure of the proposed MLP model
+B. Training Set Structure
+The training set consists of two data set: Free-space Data
+Set and Contact Data Set.
+The Free-space Data Set (FSDS) was collected when the
+robot end-effector followed pre-planned trajectories. FSDS
+aims to train the Neural Network for the essential force/torque
+sensing ability, so it includes random contact, measured by an
+F/T Sensor, at the end-effector throughout data collection. It
+is the training set’s fundamental component, or backbone, for
+it can provide a model with some basic information about
+the robot. With only FSDS, a model is expected to estimate
+wrench accurately within the work-space for data collection
+regardless of motion complexity. In other words, the robot can
+achieve simple tasks like contact detection after being trained
+by FSDS.
+The Contact Data Set (CDS) is useful in ﬁne-tuning and
+enhancing a model’s performance in more complex scenarios.
+The robot joints’ states, currents, and external forces/torques
+vibrate at high frequencies in force control tasks, such as
+constrained sliding on a plane and pin insertion. The resulting
+controlled trajectories that the end-effector follows are not pre-
+planned smooth trajectories but real-time evaluated trajectories
+with many uncertainties. Therefore, CDS trains the model to
+make clear estimations even though joint currents and states
+are noisy.
+We distinguish and identify FSDS and CDS as the backbone
+and ﬁne-tuning data sets for the reason that CDS may teach the
+model biased information about the robot dynamics. During
+FSDS collection, all trajectories are pre-determined, and end-
+effector forces are random, suggesting that the instantaneous
+end-effector motion, and thereby joint states, are uncorrelated
+with the wrench. In contrast, in contact tasks, the end-effector
+always moves in directions minimizing contact force error. For
+sliding motions, the friction force is always opposite to the
+motion parallel to contact planes. A worse scenario could be
+hand-guiding, where end-effector motion is always compliant
+with force and torque. Therefore, our concern is that CDS from
+a speciﬁc task may reduce accuracy for other tasks. Although
+such a phenomenon is not obvious in the experiments, where
+one ﬁne-tuned model by hand-guiding data set can still be
+used for in-contact sliding, discriminating against the biased
+information hopefully ensures the desired outcome.
+IV. TRAINING SET COLLECTION AND MODEL TRAINING
+Data collection and experiments demonstrated in the next
+section were carried out on Denso-VS060, a 6-axis industrial
+robot. We used Ubuntu and Robot Operating System (ROS) for
+hardware interface, robot motion planning, and joint current
+and state extraction. An ATI Gamma F/T Sensor SI-32-2.5 was
+used for force control and simultaneously training data collec-
+tion. The CPU model was: Intel(R) Xeon(R) CPU E5-2630 v3
+@ 2.40GHz, and the additional computational resources (four
+GPUs) involved in Neural Network training were of the type:
+GeForce GTX 1080 Ti. Data loading and training typically
+take 10 minutes with the above device speciﬁcations and the
+following training data size. There was no GPU used to assist
+in real-time wrench estimation.
+The end-effector for FSDS collection was a 3D-printed
+sphere with 50mm diameter, which allowed easy grasping
+and twisting. The end-effector for CDS collection was an alu-
+minum cylinder pin with 20mm diameter. Both end-effectors
+were mounted directly on the F/T Sensor.
+A. Training Sets Generation
+1) Free-space Data Set (FSDS): FSDS was collected when
+the robot end-effector followed randomized trajectories in a
+cuboid work-space. To begin with, multiple end-effector posi-
+tions were randomly generated in sequence inside the work-
+space. Each point was assigned a rotation matrix for the end-
+effector, with Euler angles θx, θy, and θz randomly selected
+from the speciﬁed ranges. Afterward, a trajectory planner
+explored every point in sequence and planned the shortest
+trajectory from one point to the next. Data was collected by
+randomly applying forces on the end-effector manually and
+continuously when it followed the pre-planned trajectories. A
+position-controlled robot was used for experiments, so its joint
+velocity and acceleration were calculated through the ﬁrst and
+second derivatives of joint position. Although current and ac-
+celeration signals were very noisy, the input to the model was
+not ﬁltered as we expect a short estimation delay and that the
+
+256×1
+256×1
+24×1
+6×1
+Force
+Torque4
+model may eliminate the effect of noise through learning. The
+real-time Force/Torque Sensor reading, joint current, position,
+velocity, and acceleration were simultaneously recorded as the
+training data at 100HZ.
+2) Contact Data Set (CDS): We collected the preliminary
+CDS through direct end-effector contact with planes to intro-
+duce less data bias and train a model that can accomplish
+most of the experiments designed in section V. The data
+set was collected when the end-effector made contact and
+slid on a steel plate with controlled contact force. With the
+plate location ﬁxed inside the work-space for FSDS, multiple
+contact points were generated in sequence in the speciﬁed
+rectangular region on the plate. The end-effector repeated the
+following for each contact point: (1) Making contact with
+the plate at a random angle, then pushing the plate with a
+reference force for 30 seconds. In order to induce disturbances,
+a random reference force was sampled within the range [4N,
+30N] every 0.2s. (2) Sliding towards the next contact point
+while maintaining the force. (3) Leaving off the plate after
+reaching the next point. Similarly, the real-time Force/Torque
+Sensor reading and joint states were recorded simultaneously
+at 100HZ throughout the steps above.
+As shown in Fig. 5a, contact force was controlled through
+end-effector position control in the corresponding direction.
+The F/T Sensor feedback error was passed to a P controller
+to decide the displacement perpendicular to the plate. Sliding
+motions parallel to the plate followed the pre-planned straight
+trajectories between points, so sliding friction was not con-
+trolled. Using the Inverse Kinematics Model, we can evaluate
+the commanded joint positions and send them to the robot
+with the desired X, Y, and Z coordinates.
+CDS collection should repeat for multiple contact planes
+so that CDS covers a possibly large portion of the work-
+space. However, this may require a ﬂexible experiment setup
+where the plane location and orientation are adjustable. The
+ideal data collection setup for commercialization and large-
+scale deployment would have two robots pushing against each
+other to simulate in-contact effects. Optionally, the contact
+plate could be mounted to the robot’s end-effector so that the
+plane locations and trajectories are programmable. Due to the
+setup constraint, we collect CDS on two contact planes with
+three different IK Classes.
+B. Training Set Details
+We collected three data sets, each including both FSDS and
+CDS, with three IK Classes. The exact work-space size and
+location, contact plane size and location, and total data frames
+can be found in Table I. Fig. 3 helps to visualize these regions
+and the corresponding IK Classes in OpenRave simulated envi-
+ronment. Training data distributions, particularly joint position
+and velocity distribution, are shown in Appendix Fig. A.1 in
+histograms.
+C. Model Enhancement for Large Work-space
+It is validated in the literature of deep learning [30] that
+MLP has the potential to ﬁt any non-linear equations given
+IK Class 1
+Space Size (m)
+Space Center (m)
+FSDS Frames
+0.20 × 0.50 × 0.15
+[0.35, 0.00, 0.30]
+991,500
+Plane Size (m)
+Plane Center (m)
+CDS Frames
+Horizontal 0.15 × 0.20
+[0.35, -0.14, 0.30]
+1,653,000
+IK Class 2
+Space Size (m)
+Space Center (m)
+FSDS Frames
+0.25 × 0.20 × 0.40
+[0.40, 0.15, 0.60]
+1,098,500
+Plane Size (m)
+Plane Center (m)
+CDS Frames
+Vertical 0.20 × 0.30
+[0.40, 0.20, 0.60]
+2,635,000
+IK Class 3
+Space Size (m)
+Space Center (m)
+FSDS Frames
+0.20 × 0.20 × 0.20
+[0.35, 0.15, 0.65]
+825,500
+Plane Size (m)
+Plane Center (m)
+CDS Frames
+Vertical 0.15 × 0.20
+[0.37, 0.20, 0.65]
+1,686,500
+TABLE I: The work-space speciﬁcations, plane speciﬁcations,
+and training data size for three data sets. Coordinates are
+represented in the robot base frame.
+Fig. 3: Visualization of the data region for three work-spaces
+with three different IK Classes. The transparent blue box and
+opaque red plane indicate the bounding boxes and location of
+the ﬁxed plates, respectively. The postures of Denso from left
+to right show the center of the nearest joint position clusters,
+or IK solutions, based on which the data was collected.
+appropriate model structure and sufﬁcient training data. How-
+ever, a learning-based model generally loses accuracy when
+covering data with higher non-linearity. This phenomenon is
+obvious whenever new training data is collected from different
+joint speciﬁcations and distal IK Classes. An intuitive solution
+is increasing the model size, that is, adding more hidden layers
+or neurons. On the other hand, instantaneous wrench feedbacks
+are crucial in real-time tasks, especially high-precision force-
+control tasks like assembly. A large model will lead to a
+long inference time given a general industrial application
+scenario, where additional computational resources like GPUs
+are costly. Therefore, a tradeoff between model size and
+inference time must be made according to the expected model
+performance in applications.
+In order to optimize the model structure for experiments,
+we train models of three different hidden layer sizes (LS)
+with either single or entire data sets coverage, then compare
+the RMSE of all wrench dimensions on the same test set
+(150,000 frames). All models have the same depth of two
+hidden layers. The numerical results are shown in Table II.
+Estimation accuracy generally increases for all dimensions
+as we enlarge hidden layers, but inference time increases
+from 0.05ms for LS128 to 0.20ms for LS256 and 0.80ms for
+LS512 in our implementation. It is also clear that the accuracy
+of a smaller model drops signiﬁcantly when covering three
+
+Z
+Y
+XZ
+Y
+XZ
+X5
+data sets, but it is not obvious for larger models. Estimation
+accuracy and inference time should be tested carefully when
+larger models or data sets are desired.
+It was observed that the training data down-sampled by
+ﬁve times trained the model for a similar estimation accuracy,
+but the training set with four-ﬁfths of the trajectory removed
+resulted in poor accuracy. This suggests that the coverage
+of trajectories and their complexities dominate the model
+accuracy instead of simply the training data size. Hopefully,
+estimation accuracy can be improved further if the training set
+trajectories are optimized.
+Test Set RMSE (N for F; Nm for T)
+LS
+Datasets
+Fx
+Fy
+Fz
+Tx
+Ty
+Tz
+128
+1
+4.08
+3.84
+5.23
+0.24
+0.25
+0.08
+256
+1
+3.45
+3.35
+4.50
+0.22
+0.23
+0.08
+512
+1
+2.70
+2.96
+4.04
+0.18
+0.18
+0.08
+128
+1,2,3
+5.62
+5.29
+6.90
+0.33
+0.36
+0.11
+256
+1,2,3
+3.91
+3.71
+5.23
+0.26
+0.27
+0.09
+512
+1,2,3
+3.11
+2.99
+4.43
+0.22
+0.20
+0.08
+TABLE II: RMSE on the same test set (randomly sampled
+from data set 1) produced by models with different hidden
+layer size (LS) and training data coverage. Fx, Fy, and Fz
+stands for end-effector forces in XYZ directions. Tx, Ty, and
+Tz stands for end-effector torques in XYZ directions.
+V. EXPERIMENT RESULTS
+A. Wrench Estimation in Free Motion
+Given that the model with 512 hidden neurons has a
+relatively high accuracy while the inference time is less than
+1 ms in our implementation, we use this structure for all
+experiments presented in the following sections.
+The free-motion experiment served as a online test set for
+the trained model. Test trajectories were generated randomly in
+the same manner as the FSDS collection in the work-space for
+IK Class 1. When the robot was executing, periodical forces
+and torques were applied to a spherical end-effector mounted
+on the F/T sensor. Fig. 4 shows a comparison between a part
+of the real-time estimated wrench and the real-time reading
+from the Force/Torque sensor when the end-effector followed
+pre-planned free-space trajectories. RMSEs in this and all
+the remaining experiments are calculated regarding the data
+presented in ﬁgures. The plot suggests that although the model
+missed some peak values, it can still follow the overall wrench
+variation despite random end-effector trajectories. The magni-
+tude of RMSE is also acceptable, considering the force/torque
+variation ranges.
+B. Force Control For In-contact Spiral Sliding
+The end-effector followed a pre-planned spiral trajectory
+with the ﬁxed plate location. Similarly, force control was
+achieved through position control as suggested in Fig. 5a,
+but we used the estimated result from the Neural Network
+Estimator to replace the F/T sensor for control feedback. That
+means that the contact force was controlled with real-time
+estimated force with a simple P controller. Fig. 5b shows the
+block diagram for closed-loop control of contact force.
+Fig. 4: Comparison between the estimated (red) and real
+wrench (blue dashed) for random pre-planned free-motion
+trajectories. Forces and torque are represented in the F/T
+Sensor (end-effector) frame.
+In the experiment, the end-effector ﬁrst moved towards the
+plate, then tried to apply a constant force of 15N with a contact
+angle of 10°, and ﬁnally started sliding following a spiral
+trajectory after the force was stabilized. The plate location
+is the same as that for data collection with IK Class 1. Fig.
+6 compares the estimated wrench and sensor reading during
+sliding. The effect of force control can be interpreted from the
+force along the Z-axis. It is obvious that forces and torques
+parallel to the plate undergo sinusoidal variation due to the
+periodic friction change during spiral sliding. Although spiral
+trajectories are excluded from the training set, the model can
+still perform accurate wrench estimation learning from simple
+straight motions. Again, neither the input data to nor output
+data from the model were ﬁltered. The estimated wrench is
+noisy due to the unprocessed input and simple controller, but
+the overall accuracy is promising.
+C. Force/Torque Control for Tight Assembly
+In addition to the contact force control task, a strong proof
+of the estimator’s reliability is completing a typical industrial
+task - tight assembly. In the general scenario of pin insertion,
+forces and torques in all directions are under control, so the
+
+40
+30
+Fx (N)
+0
+-10
+-20
+-30
+Range:.59.52 N
+RMSE.=.3.86.N
+40
+0
+5
+10
+15
+20
+30
+20
+10
+(N)
+0
+И
+-10
+-20
+Range:49.29N
+RMSE=
+30
+0
+5
+10
+15
+20
+10
+0
+-10
+rry
+-20
+30
+-40
+Range:45.59N
+RMSE=4.51N
+50
+5
+10
+15
+20
+1.5
+1.0
+(Nm)
+0.5
+0.0
+-0.5
+XI
+1.0
+1.5
+Range: 2.76.Nm
+-2.0
+RMSE..0.29.Nm
+0
+5
+10
+15
+20
+1.5
+1.0
+0.5
+(Nm)
+0.0
+-0.5
+1.0
+-1.5
+2.0
+Range:3:31 Nm
+RMSE=0.23Nm
+-2.5
+5
+10
+15
+20
+1.5
+1.0
+(wN)
+0.5
+0.0
+N
+0.5
+1.0
+Range: 1.35'Nm
+RMSE = 0:14 Nm
+-1.5
+0
+5
+10
+15
+20
+Time (s)6
+(a)
+(b)
+Fig. 5: (a) Block diagram for force control on contact planes.
+Xp, Yp, and Zp are the end-effector coordinate in the plate’s
+frame. Fd is the desired force on the plate. Fp is the force
+perpendicular to the plate evaluated from the F/T sensor
+measurement. (b) Block diagram for force control on planes
+with Neural Network estimation. I indicates the joint current.
+Fig. 6: Comparison between the estimated (red) and real
+wrench (blue dashed) for in-contact spiral sliding. Forces and
+torque are represented in the F/T Sensor (end-effector) frame.
+task requires high force-sensing accuracy with only a slight
+lag in time.
+In this experiment, we used one pair of aluminum pin
+and hole with 20mm diameters and 100-micron clearance.
+In the force-controlled insertion, the hole was placed in the
+work-space for IK Class 1, and the pin was mounted on the
+F/T sensor (for comparison purposes only) through coupling.
+Insertion started 3mm above the hole with 2mm horizontal
+position error and 5° orientation error. Again, the estimated
+wrench was used as the control feedback, and the control
+algorithm for pin insertion was designed as follows: (1) forces
+and torques were transformed into the pin-tip frame; (2) [0N,
+0N, 10N, 0Nm, 0Nm] reference force and torque were used
+as the controller setpoint (end-effector twist not controlled).
+The algorithm results in a three-phase insertion as shown
+in Fig. 7, where the pin moved downward before making
+contact, automatically located and aligned with the hole while
+maintaining the contact force, and ﬁnally ﬁtted into the hole
+after being aligned. Note that the relative initial orientation
+error of the pin and hole was roughly 5°, but the hole’s
+orientation was assumed unknown. Torque control was thus
+needed to align the pin and hole while locating the hole center.
+During insertion, the pin made multiple-point contact with
+the hole as a need for torque control. It was observed that
+torques being transmitted to joints are different with the same
+torque on the sensor in the multiple-point and single-point
+contact scenario, such that joint current measurements are
+different. It suggests that one joint current reading may corre-
+spond to two different end-effector torque under single-point
+and multiple-point contact, given some robot conﬁgurations.
+Such a phenomenon is always true at speciﬁc conﬁgurations
+like wrist singularity. Even with the robot being close to
+those conﬁgurations, the model trained with noisy data still
+cannot capture the slight current changes. As a result, in the
+insertion experiment, torque estimation was relatively accurate
+in the ﬁrst 5 seconds when the pin made single-point contact
+with the hole. However, the model failed to estimate torque
+accurately in the complex multiple-contact part and stuck with
+only 12mm inserted. Minimum pin-insertion training data was
+then collected to allow full insertion of 18mm.
+Fig. 8 shows the comparison between the estimated and
+true wrench for the whole insertion process. However, torque
+estimation for multiple-point contact is still inaccurate, as ex-
+plained above, even though the pin was successfully inserted.
+The accuracy may be improved by including more complex
+motions and force control tasks in the training set. Another
+approach could be manipulating and training the model with
+the residual between the measured and estimated free-space
+current instead so that the model learns for slight current
+variations more effectively.
+D. Sensorless Hand-guiding
+With hand-guiding, a typical human-robot interaction task,
+we demonstrate how the model can be ﬁne-tuned for different
+tasks by the corresponding data set. As discussed in Section
+III, the hand-guiding data set was not used for backbone
+training with concern that the end-effector and joint motions
+
+20
+15
+10
+(N)
+5
+0
+-5 
+Range: 12.24 N
+RMSE = 1.41 N
+-10
+0
+10
+20
+30
+40
+50
+60
+70
+80
+20
+15
+10
+(N) 
+5
+-10
+Range: 12:82 N
+RMSE= 1.81 N
+-15,
+0
+10
+20
+30
+40
+50
+60
+70
+80
+(N)
+Range: 23:18 N
+RMSE= 2:40 N
+30
+0
+10
+20
+30
+40
+50
+60
+70
+80
+0.5
+ (Nm)
+0.0
+XI
+-0.5
+1.0
+Range: 0.86: Nm
+RMSE·=·0.12·Nm
+0
+10
+20
+30 
+40
+50
+60
+70
+80
+0.5
+(Nm)
+0.0
+0.5
+1.0
+Range: 0.84 Nm
+RMSE = 0.11 Nm
+0
+10
+20
+30
+40
+50
+60
+70 
+80
+0.4
+0.2 
+(WN)
+0.0
+0.2
+N
+0.4
+0.6
+Range: 0.14 Nm
+RMSE='0.04 Nm
+-0.8
+0
+10
+20
+30 
+40
+50
+60
+70
+80
+Time (s)Xp
+Industrial Robot
+Inverse
+qc
+b
+dz
+Zp
+Fa
+Kr
+Kinematics
+Fp
+Force/Torque
+Environment
+SensorXp
+Industrial Robot
+qc
+Zp
+Inverse
+dz
+Fa
+Kinematics
+q
+1
+Fp
+q
+p
+Neural
+dt
+Network
+Estimator
+d?
+p
+dt2
+I7
+Fig. 7: Three-phase insertion procedure governed by [0N, 0N,
+10N, 0Nm, 0Nm] reference forces and torques. In phase one,
+the pin moved to the hole until making contact with 10N
+reference force. In phase two, it rotated to align with the hole
+and automatically located the hole center due to zero reference
+forces and torques except for the Z direction. In phase three,
+the pin was aligned, and thus inserted further.
+Fig. 8: Comparison between the estimated (red) and real
+wrench (blue dashed) in force/torque controlled pin insertion
+task. Forces and torque are represented in the F/T Sensor (end-
+effector) frame.
+are always compliant with forces. The compliant motion could
+generate biased data with which the Neural Network may
+underﬁt the actual dynamics. In other words, the forces and
+robot motions strongly correlate due to hand-guiding.
+The hand-guiding data set includes 321,000 data frames
+collected with IK Class 1 recorded at 100Hz. The end-effector,
+the same as that for FSDS collection, was guided to follow
+Fig. 9: Comparison between the estimated (red) and real
+wrench (blue dashed) in hand-guiding. Forces and torque are
+represented in the F/T Sensor (end-effector) frame.
+straight and spiral trajectories that explore the pre-deﬁned
+work-space. Again, we used a simple P controller for data
+collection, then trained the model with unprocessed data to
+ensure that it learned in a noisy environment. The ﬁne-tuned
+model was then tested in the same work-space. A part of
+the record is shown in Fig. 9. With the almost overlapped
+estimation with the ground-truth, we conclude that the Neural
+Network estimator has great potential to be used for various
+tasks through ﬁne-tuning. Even though the estimated wrench
+was noisy due to the discontinuous trajectory, the stability
+could be improved with further signal processing.
+E. Error Quantiﬁcation in the Frequency Domain
+Considering the complex environment in which a robot
+could operate, studying the model behavior under different
+contact force frequencies is crucial. More speciﬁcally, we
+studied the estimation error and phase lag as a function of
+force oscillation frequency. Data was collected in the work-
+space for IK Class 1 with the same plate location for training
+data collection. Ten contact points were evenly sampled on
+the plate, and for each point, the end-effector oscillated be-
+tween two reference positions penetrating into the plane. The
+exact penetration depths were determined through preliminary
+experiments, so the resulting force vibration had an identical
+
+20
+15
+10
+(N) XJ
+-10
+Range: 14.09'N
+RMSE=2.53N
+-15
+0
+2
+4
+6
+8
+10
+12
+14
+16
+18
+10
+5
+(N) 
+0
+-5
+-10
+-15
+Range:. 10.03..N
+RMSE.1.44.N
+0
+2
+4
+6
+8
+10
+12
+14
+16
+18
+10
+(N)
+-15
+-29
+Range:21:13N
+RMSE=:2:82:N
+30
+0
+2
+4
+6
+8
+10
+12
+14
+16
+18
+0.6
+0.4
+(Nm)
+0.2 
+0.0
+XI
+-0.2
+0.4
+0.6
+Range:.0.70.Nm
+RMSE..0.10.Nm
+0
+2
+4
+6
+8
+10
+12
+14
+16
+18
+0.5 
+(Nm)
+0.0
+-0.5
+1.0
+Range: 0.92 Nm
+RMSE= 0.19 Nm
+0
+2
+4
+6
+8
+10
+12
+14
+16
+18
+0.4
+0.2
+(Nm)
+0.0
+N
+-0.2
+0.4
+Range: 0.09 Nm
+RMSE= 0.03 Nm
+0.6
+0
+2
+4
+6
+8
+10
+12
+14
+16
+18
+Time (s)40
+20
+(N)
+0
+-20
+-40
+Range::73.67·N
+RMSE=:3:53·N
+0
+10
+20
+30
+40
+50
+60
+70
+80
+40
+20
+0
+-20
+40
+Range:76:44 N
+RMSE= 3:93 N
+0
+10
+20
+30
+40
+50
+60
+70
+80
+40
+20
+-20
+-40
+Range:.84.42.N
+RMSE = 4.91 N
+-60
+0
+10
+20
+30
+40
+50
+60
+70
+80
+2
+(Nm)
+0
+Range: 3.54
+Nm
+RMSE = 0.20 Nm
+10
+20
+30
+40
+50
+60
+70
+80
+2
+(Nm)
+Range: 3.47: Nm
+RMSE = 0.20 Nm
+3
+10
+20
+30
+40
+50 
+60
+70
+80
+2
+(Nm)
+Range: 3.39: Nm
+RMSE = 0.24 Nm
+0
+10
+20
+30
+40
+50
+60
+70
+80
+Time (s)8
+mean and range of 15N and 10N for all frequencies. Note that
+direct force control was not applied as the oscillation range
+shrank signiﬁcantly at higher frequencies even though the
+reference force is unchanged. Data were recorded at multiple
+frequencies from 0.1Hz to 10Hz for each contact point, and
+645,500 data frames were recorded in total.
+Although RMSE is intuitive and widely used for error
+analysis, our experiments show that RMSE from the same
+model can vary depending on the force variation range. It can
+be interpreted easily by comparing Fig. 8 and Fig. 9, where
+the latter plot looks more accurate intuitively but actually has
+larger errors. Normalized RMSE could be a better choice,
+but selecting the appropriate lower and upper bound for
+normalization still depends on the force range required in
+different tasks. Therefore, we quantify the estimation error
+as the ratio and offset between the estimated force and the
+true force in the same frame. More speciﬁcally, we used linear
+regression to obtain a ﬁrst-order approximation of the mapping
+from the true force to the estimated force in each frequency.
+The physical meaning for ratio and offset is the magnitude gain
+from the true to estimated force and the mean error between
+the forces, respectively.
+With the direct position-control pattern, as shown in Fig.
+10, the estimated force tends to overshoot after reaching
+the desired position, and that is caused by the overshot in
+motor current. Higher frequencies do not allow the current to
+stabilize, such that the overshot error dominates as frequency
+increases. Such an interpretation can be visualized in Fig. 11,
+where both the gain and offset have a local maximum at 1Hz
+oscillation. When frequency increases further, the overshot
+would be eliminated, so the local minimum at 3Hz suggests the
+overall accuracy in an overshot-free and marginally stable con-
+dition. Oscillation becomes irregular after 3Hz, with shrinking
+oscillation ranges and non-identical current behaviors in each
+period. Such chaotic behavior, though similar to that in most
+industrial applications, makes it hard to analyze intuitively, but
+both the ratio and offset stay in reasonable ranges. The RMSE
+plot suggests that the absolute error is roughly 2N with a
+15N and 10N force oscillation mean and range. By calculating
+the cross-correlation of the estimation and measurement data
+series, there is no apparent relationship found between time
+lead or lag and oscillation frequency.
+VI. CONCLUSION
+In this paper, we propose an approach to estimating the end-
+effector wrench with Neural Networks. The model takes the
+joint currents and states as the input and makes estimations of
+the wrench in real-time. It avoids using embedded joint torque
+sensors and can replace 6-axis end-effector F/T sensors in
+industrial applications. The implemented model also achieved
+high estimation accuracy and stability in various industrial
+tasks, being trained with the Free-space and Contact Data Sets.
+One limitation with the current implementation that we
+foresee is the long time taken for large-scale data collection.
+Although the procedure is automatic, random-generated trajec-
+tories could be inefﬁcient in covering the dynamic information
+of the robot. A systematic approach to generating trajectories
+Fig. 10: Comparison between the true and estimated force with
+0.1Hz force oscillation frequency. (a) Blue (dashed) and red
+lines indicate true and estimated force respectively, (b) the J2’s
+current recorded simultaneously in force oscillation.
+Fig. 11: The linear regression result of the mapping from true
+force to estimated force. Figures from top to bottom show (a)
+Gain (ratio) from true to estimated force, (b) mean error of
+between true and estimated force, (c) RMSE over all data at
+each frequency with force oscillation from 10N to 20N.
+may signiﬁcantly reduce the data collection time while allow-
+ing for higher accuracy.
+All the experiments were carried out under low-speed
+operations – the most common mode for contact tasks. Further
+studies could be done to address the potential issues with high-
+speed operations. Such an improvement will allow accurate
+estimation in static and high-speed operations on which the
+
+(N)
+-10
+z 
+orce.
+-15
+-20
+-25
+0
+5
+10
+15
+20
+25
+-10
+: 2 Current (%)
+-15
+-20
+-25
+-30
+loint :
+-35
+-40
+0
+5
+10
+15
+20
+25
+Time (s)1.8
+1.6
+Ratio
+1.4
+1.2
+1.0
+0.8
+10-1
+100
+101
+10
+Offset (N)
+5
+0
+10-1
+100
+101
+5
+4
+(N)
+RMSE (
+3
+1
+0
+10-1
+100
+101
+Frequency (Hz)9
+current model identiﬁcation method shows less convincing
+results.
+Since no dynamic information is required for model train-
+ing, a similar method can be easily applied to different types
+of robot arms by following a standard data collection pipeline.
+The results in complex control tasks are also promising if the
+proposed method was applied in other areas like legged and
+surgical robots when a physical sensor was not preferred in
+actual applications.
+Another promising avenue for future research is to combine
+the sensorless F/T estimation here with recent robust force
+control methods [3], which can further alleviate possible
+instabilities caused by estimation errors or delays. Such a
+combination could enable even more sensitive sensorless ma-
+nipulation. From an economic perspective, the result presented
+here opens the possibility of equipping the existing 2.7 million
+industrial robots and the 600,000 new units installed per year
+with Force Sensing and Force Control capabilities without any
+additional hardware required for the users.
+VII. ACKNOWLEDGEMENT
+This research was supported by the National Research Foun-
+dation, Prime Minister’s Ofﬁce, Singapore under its Medium
+Sized Centre funding scheme, Singapore Centre for 3D Print-
+ing, CES SDC Pte Ltd, and Chip Eng Seng Corporation Ltd.
+REFERENCES
+[1] B. Siciliano, O. Khatib, and T. Kr¨oger, Springer handbook of robotics,
+vol. 200. Springer, 2008.
+[2] F. Su´arez-Ruiz, X. Zhou, and Q.-C. Pham, “Can robots assemble an ikea
+chair?,” Science Robotics, vol. 3, no. 17, p. eaat6385, 2018.
+[3] H. Pham and Q.-C. Pham, “Convex controller synthesis for robot
+contact,” IEEE Robotics and Automation Letters, vol. 5, no. 2, pp. 3330–
+3337, 2020.
+[4] A. De Luca and R. Mattone, “Sensorless robot collision detection
+and hybrid force/motion control,” in Proceedings of the 2005 IEEE
+international conference on robotics and automation, pp. 999–1004,
+IEEE, 2005.
+[5] M. Van Damme, P. Beyl, B. Vanderborght, V. Grosu, R. Van Ham,
+I. Vanderniepen, A. Matthys, and D. Lefeber, “Estimating robot end-
+effector force from noisy actuator torque measurements,” in 2011 IEEE
+International Conference on Robotics and Automation, pp. 1108–1113,
+IEEE, 2011.
+[6] A. Wahrburg, J. B¨os, K. D. Listmann, F. Dai, B. Matthias, and H. Ding,
+“Motor-current-based estimation of cartesian contact forces and torques
+for robotic manipulators and its application to force control,” IEEE
+Transactions on Automation Science and Engineering, vol. 15, no. 2,
+pp. 879–886, 2017.
+[7] S. K. Kommuri, S. Han, and S. Lee, “External torque estimation using
+higher order sliding-mode observer for robot manipulators,” IEEE/ASME
+Transactions on Mechatronics, vol. 27, no. 1, pp. 513–523, 2022.
+[8] D. Nguyen-Tuong and J. Peters, “Local gaussian process regression for
+real-time model-based robot control,” in 2008 IEEE/RSJ International
+Conference on Intelligent Robots and Systems, pp. 380–385, IEEE, 2008.
+[9] D. Nguyen-Tuong, M. Seeger, and J. Peters, “Model learning with
+local gaussian process regression,” Advanced Robotics, vol. 23, no. 15,
+pp. 2015–2034, 2009.
+[10] A.-N. Sharkawy, P. N. Koustoumpardis, and N. Aspragathos, “Human–
+robot collisions detection for safe human–robot interaction using one
+multi-input–output neural network,” Soft Computing, vol. 24, no. 9,
+pp. 6687–6719, 2020.
+[11] A. De Luca and R. Mattone, “Actuator failure detection and isolation
+using generalized momenta,” in 2003 IEEE international conference on
+robotics and automation (cat. No. 03CH37422), vol. 1, pp. 634–639,
+IEEE, 2003.
+[12] N. M. Kircanski and A. A. Goldenberg, “An experimental study of
+nonlinear stiffness, hysteresis, and friction effects in robot joints with
+harmonic drives and torque sensors,” The International Journal of
+Robotics Research, vol. 16, no. 2, pp. 214–239, 1997.
+[13] H. Olsson, K. J. ˚Astr¨om, C. C. De Wit, M. G¨afvert, and P. Lischinsky,
+“Friction models and friction compensation,” Eur. J. Control, vol. 4,
+no. 3, pp. 176–195, 1998.
+[14] M. Ruderman, F. Hoffmann, and T. Bertram, “Modeling and iden-
+tiﬁcation of elastic robot joints with hysteresis and backlash,” IEEE
+Transactions on Industrial Electronics, vol. 56, no. 10, pp. 3840–3847,
+2009.
+[15] X. Liu, F. Zhao, S. S. Ge, Y. Wu, and X. Mei, “End-effector force
+estimation for ﬂexible-joint robots with global friction approximation
+using neural networks,” IEEE Transactions on Industrial Informatics,
+vol. 15, no. 3, pp. 1730–1741, 2018.
+[16] J. Hu and R. Xiong, “Contact force estimation for robot manipulator
+using semiparametric model and disturbance kalman ﬁlter,” IEEE Trans-
+actions on Industrial Electronics, vol. 65, no. 4, pp. 3365–3375, 2017.
+[17] S. Schaal, C. G. Atkeson, and S. Vijayakumar, “Scalable techniques
+from nonparametric statistics for real time robot learning,” Applied
+Intelligence, vol. 17, no. 1, pp. 49–60, 2002.
+[18] S. Vijayakumar and S. Schaal, “Local dimensionality reduction for
+locally weighted learning,” in Proceedings 1997 IEEE International
+Symposium on Computational Intelligence in Robotics and Automation
+CIRA’97.’Towards New Computational Principles for Robotics and
+Automation’, pp. 220–225, IEEE, 1997.
+[19] A. Gijsberts and G. Metta, “Real-time model learning using incremental
+sparse spectrum gaussian process regression,” Neural networks, vol. 41,
+pp. 59–69, 2013.
+[20] O. Sigaud, C. Sala¨un, and V. Padois, “On-line regression algorithms
+for learning mechanical models of robots: a survey,” Robotics and
+Autonomous Systems, vol. 59, no. 12, pp. 1115–1129, 2011.
+[21] S. Lee and R. M. Kil, “Robot kinematic control based on bidirectional
+mapping neural network,” in 1990 IJCNN international joint conference
+on neural networks, pp. 327–335, IEEE, 1990.
+[22] L. H. Sang and M.-C. Han, “The estimation for forward kinematic solu-
+tion of stewart platform using the neural network,” in Proceedings 1999
+IEEE/RSJ International Conference on Intelligent Robots and Systems.
+Human and Environment Friendly Robots with High Intelligence and
+Emotional Quotients (Cat. No. 99CH36289), vol. 1, pp. 501–506, IEEE,
+1999.
+[23] H. Sadjadian and H. Taghirad, “Numerical methods for computing the
+forward kinematics of a redundant parallel manipulator,” in Proceedings
+of the IEEE Conference on Mechatronics and Robotics, pp. 557–562,
+Citeseer, 2004.
+[24] N. Yilmaz, J. Y. Wu, P. Kazanzides, and U. Tumerdem, “Neural network
+based inverse dynamics identiﬁcation and external force estimation on
+the da vinci research kit,” in 2020 IEEE International Conference on
+Robotics and Automation (ICRA), pp. 1387–1393, IEEE, 2020.
+[25] M. Hanafusa and J. Ishikawa, “External force estimation for non-
+linear systems using recurrent neural network,” in 2019 IEEE/ASME
+International Conference on Advanced Intelligent Mechatronics (AIM),
+pp. 1055–1061, IEEE, 2019.
+[26] D.-H. Lee, W. Hwang, and S.-C. Lim, “Interaction force estimation using
+camera and electrical current without force/torque sensor,” IEEE Sensors
+Journal, vol. 18, no. 21, pp. 8863–8872, 2018.
+[27] J. Xia and K. Kiguchi, “Sensorless real-time force estimation in micro-
+surgery robots using a time series convolutional neural network,” IEEE
+Access, vol. 9, pp. 149447–149455, 2021.
+[28] A. Marban, V. Srinivasan, W. Samek, J. Fern´andez, and A. Casals,
+“A recurrent convolutional neural network approach for sensorless
+force estimation in robotic surgery,” Biomedical Signal Processing and
+Control, vol. 50, pp. 134–150, 2019.
+[29] D. Kim, D. Lim, and J. Park, “Transferable collision detection learning
+for collaborative manipulator using versatile modularized neural net-
+work,” IEEE Transactions on Robotics, 2021.
+[30] M. A. Nielsen, Neural networks and deep learning, vol. 25. Determi-
+nation press San Francisco, CA, USA, 2015.
+
+10
+Shilin Shan received the B.E. de-
+gree in Mechanical Engineering from
+Nanyang
+Technological
+University,
+Singapore in 2021. He is currently
+working towards the Ph.D. degree in
+Mechanical Engineering at the School
+of Mechanical and Aerospace Engi-
+neering, Nanyang Technological Uni-
+versity, Singapore.
+His research interests include robot
+manipulations and deep learning.
+Quang-Cuong Pham was born in
+Hanoi, Vietnam. He is an alumnus of
+´Ecole Normale Sup´erieure, rue d’Ulm
+(France) and holds a Ph.D. in Neu-
+roscience from Universit´e Pierre et
+Marie Curie (France). He was a visit-
+ing researcher at the University of S˜ao
+Paulo (Brazil) in 2010, and a JSPS
+Fellow at the University of Tokyo
+(Japan) in 2011-2013. He joined NTU
+(Singapore) in 2013 and is currently
+an Associate Professor in the School of Mechanical and
+Aerospace Engineering. He was a recipient of the Best Paper
+Award at the conference Robotics: Science and Systems, 2012.
+His research has featured in major international media, in-
+cluding The New York Times, The Guardian, The Economist,
+CNN, Science, Nature, etc. He is a Co-founder and Director
+of Eureka Robotics (https://eurekarobotics.com/), a deep tech
+startup devoted to solving the toughest automation challenges
+in manufacturing.
+
+11
+APPENDIX
+(a)
+(b)
+(c)
+Fig. A.1: The joint-space training data distribution of joint positions and velocities for (a) IK1; (b) IK2; (c) IK3.
+
+120000
+1200000
+60000
+600000
+11 
+160000
+600000
+80000
+300000
+J2 
+20
+700000
+60000
+35000
+13
+-100
+90000
+140000
+700000
+-100
+140000
+450000
+70000
+225000
+100
+70000
+700000
+35000
+350000
+6
+loint Position (Degree)
+Joint Velocity (degree/s)350000
+900000
+450000
+-50
+120000
+900000
+60000
+450000
+2
+50
+100
+12000
+700000
+60000
+350000
+-100
+160000
+12000
+80000
+200000
+-100
+-50
+400000
+15
+-100
+100000
+Co
+50000
+6000
+6
+loint Position (Degree)
+Joint Velocity (degree/s)250000
+700000
+125000
+350000
+140000
+-4
+900000
+70000
+450000
+J2 
+10000
+50000
+50000
+100
+18000
+60000
+90000
+300000
+4
+100
+250000
+900000
+450000
+50
+100
+9000
+900000
+Count
+45000
+450000
+91
+-50
+loint Position (Degree)
+Joint Velocity (degree/s)12
+LIST OF FIGURES
+1
+Pin insertion and hand-guiding snapshot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+1
+2
+Structure of MLP model
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+3
+3
+Data set workspace and contact plane visualization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+4
+4
+Estimation and ground-truth comparison for free-motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+5
+5
+Block diagrams for contact control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+6
+6
+Estimation and ground-truth comparison for spiral sliding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+6
+7
+Three-phase pin insertion algorithm visualization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+7
+8
+Estimation and ground-truth comparison for pin insertion
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+7
+9
+Estimation and ground-truth comparison for hand-guiding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+7
+10
+Estimation and current measurement comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+8
+11
+Estimation error plotted against external force frequency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+8
+A.1
+Training data distribution visualization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+11
+LIST OF TABLES
+I
+Work-space and contact plane speciﬁcations for data sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+4
+II
+Test set error . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+5
+
diff --git a/z9FQT4oBgHgl3EQfzjal/content/tmp_files/load_file.txt b/z9FQT4oBgHgl3EQfzjal/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..00ab40a9ccc505731ffbfee2500da0f40603c403
--- /dev/null
+++ b/z9FQT4oBgHgl3EQfzjal/content/tmp_files/load_file.txt
@@ -0,0 +1,1369 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf,len=1368
+page_content='1  Fine Robotic Manipulation  without Force/Torque Sensor  Shilin Shan1,∗ and Quang-Cuong Pham2  Abstract—Force Sensing and Force Control are essential to  many industrial applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Typically, a 6-axis Force/Torque  (F/T) sensor is mounted between the robot’s wrist and the end-  effector in order to measure the forces and torques exerted by  the environment onto the robot (the external wrench).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Although  a typical 6-axis F/T sensor can provide highly accurate mea-  surements, it is expensive and vulnerable to drift and external  impacts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Existing methods aiming at estimating the external  wrench using only the robot’s internal signals are limited in  scope: for example, wrench estimation accuracy was mostly  validated in free-space motions and simple contacts as opposed  to tasks like assembly that require high-precision force control.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='  Here we present a Neural Network based method and argue that  by devoting particular attention to the training data structure,  it is possible to accurately estimate the external wrench in  a wide range of scenarios based solely on internal signals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='  As an illustration, we demonstrate a pin insertion experiment  with 100-micron clearance and a hand-guiding experiment, both  performed without external F/T sensors or joint torque sensors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='  Our result opens the possibility of equipping the existing 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='7  million industrial robots with Force Sensing and Force Control  capabilities without any additional hardware.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='  Index Terms—External Wrench Estimation, Machine Learn-  ing, Mechanisms Modeling & Control, Human-robot Interaction  I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' INTRODUCTION  Force Sensing and Force Control are essential to many  industrial applications, from contact-based inspection to as-  sembly, sanding, deburring, and polishing [1]–[3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Typically,  a 6-axis Force/Torque (F/T) sensor is mounted between the  robot’s wrist and the end-effector in order to measure the  forces and torques exerted by the environment onto the robot  (the external wrench).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Although a typical 6-axis F/T sensor  can provide highly accurate measurements, it is expensive and  vulnerable to drift and external impacts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Consequently, there  has been a signiﬁcant research effort aimed at estimating the  external wrench using only the robot’s internal signals, such  as joint position, joint velocity, or motor current readings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='  To that aim, there are two main approaches in the literature:  model-based and model-free.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' In the model-based approach,  parameterized models of the robot’s dynamics are developed  and identiﬁed using standard parameter identiﬁcation tech-  niques [4]–[7].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' The main difﬁculty here lies in the accurate  and reliable modeling and identiﬁcation of highly nonlinear,  1 Shilin Shan is with School of Mechanical and Aerospace Engineering,  Nanyang Technological University, Singapore (address: 50 Nanyang Ave, Sin-  gapore 639798;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' phone: +65 6790 5568;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' e-mail: shilin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='shan153@gmail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='com)  2 Quang-Cuong Pham is with Eureka Robotics and Singapore Centre for  3D Printing (SC3DP), School of Mechanical and Aerospace Engineering,  Nanyang Technological University, Singapore.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' (e-mail: cuong@ntu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='edu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='sg)  ∗ Corresponding author: Shilin Shan  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' 1: Snapshot of the sensorless tight pin insertion and  hand-guiding experiment setup.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Video demonstrations of the  experiments in Section V is available in the supplementary  materials or at: https://youtu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='be/04 f3coFzaQ  nonsmooth phenomena such as hysteresis and joint friction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='  Model-free methods, based, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=', on Neural Networks, have  been developed to overcome this difﬁculty [8]–[10].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' However,  such methods have been so far limited in scope: for example,  wrench estimation accuracy was mostly validated in free-space  motions and simple contacts as opposed to complex industrial  tasks that require high-precision force control.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='  In general, to our knowledge, no method – whether model-  based or model-free – has been shown to accurately and  reliably estimate the external wrench in both free-space and in-  contact motions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' This requirement is crucial for achieving non-  trivial tasks like tight assembly and hand-guiding, alternating  between free-space and in-contact robot motions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' These tasks  have yet to be demonstrated in existing works and are, more  generally, necessary for large-scale industrial deployment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='  Here we present a model-free method (based on Neural Net-  works) and argue that the above requirement can be satisﬁed  if particular attention is devoted to the structure of the training  dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' In particular, we highlight the importance of collecting  training data for both free-space and in-contact motions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Doing  so enables us to accurately and reliably estimate external  wrench using only internal signals such as joint position,  velocity, acceleration, and current readings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='  More speciﬁcally,  We propose a pure Neural Network based method that  takes joint currents and states as input and returns the end-  effector wrench.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' The Neural Network maps the input vari-  ables needed for a dynamic model to the output wrench  directly, so no additional Dynamic Model identiﬁcation  and joint torque sensing are required.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' In addition, the  use of joint current allows wrench estimation without  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='13413v1  [cs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='RO]  31 Jan 2023  DENSO  F/T Sensor  DisabledADENSO  F/T Sensor  Disabled2  the embedded joint torque sensors, which reduces robot  manufacturing costs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='  We present a pipeline that collects data automatically and  efﬁciently in wrench estimation problems by emphasizing  the data collection procedure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' The training data was  collected with not only the free-space trajectories but  also constrained in-contact motions so as to induce dis-  turbances that create more variability in the data set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' The  trained model has high accuracy in typical industrial tasks  like tight pin insertion and high-precision hand-guiding,  which, to our knowledge, have yet to be demonstrated  with the existing methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='  As an illustration, we demonstrate the pin insertion experiment  with 100-micron clearance and the hand-guiding experiment,  both performed without F/T sensors at runtime.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Note that  a 6-axis F/T sensor would be needed for the one-time data  collection on a single manipulator in the training phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' For  large-scale industrial applications, a well-trained Neural Net-  work can be applied to any manipulators of the same model,  either manufactured or to be manufactured, to equip them with  force/torque sensing ability without physical sensors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='  The paper is organized as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' In Section II, we discuss  the literature on wrench estimation and dynamics identiﬁca-  tion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' In Section III, we present the basic model structure and  the concepts for data sets generation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' In Section IV, we discuss  in detail the data collection procedure and model enhancement  approaches for broader work-space coverage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' In Section V, we  present four experiments in free-space and in-contact scenarios  to demonstrate the robustness of the proposed method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' 1  shows a snapshot of the sensorless pin insertion and hand-  guiding experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='  II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' RELATED WORK  Previous works on contact detection [4], [11] introduced  using the generalized momentum to identify the Inverse Dy-  namic Model, and a generalized-momentum-based disturbance  observer is designed in [5].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' By integrating with the Kalman  Filter, the combined approach [6] allows accurate force estima-  tion that can be used for basic force control tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' The author  also addressed that joint friction, an essential component in  dynamic modeling, can be calculated by considering Coulomb  friction, viscous friction, stiction, and Stribeck velocity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Earlier  studies [12]–[14] have also shown that non-linear behaviors  like hysteresis and back-lashes can be well identiﬁed, thus  compensated by such a modeling method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' On the other hand,  deciding the friction model parameters may require complex  experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='  Although mathematical analysis provides strong intuitions  to the robot dynamics, identifying the Inverse Dynamic Model  through mathematical analysis of mechanical models is still  complicated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' In order to simplify modeling complexity, recent  studies have proposed semi-parametric approaches to train  Neural Network models to learn joint motor friction [15]  or compensate for all the non-modeled effects [16].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Given  that parameter identiﬁcations are still required for rigid body  dynamics, these methods reduce only modeling complexity,  whereas even more experiments would be needed to learn a  friction model separately.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='  Another approach is to avoid manually selecting the whole  model structure and make the model learn through one-time  data collection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Non-parametric regression-based approaches  have been studied for model identiﬁcation in early research  [17], [18].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Multiple studies have built on these methods and  demonstrated the ease of training of non-parametric learning-  based approaches, including Gaussian Process Regression  (GPR) and Locally Weighted Projection Regression (LWPR)  [8], [9], [19].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Without choosing the model structure manually,  regression-based approaches avoid human bias on the model  structure, thus allowing a model to learn the optimal structure  given simple hyper-parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Being trained and veriﬁed with  hand-guiding experiments [9], GPR shows high accuracy in  hand-guided trajectory tracking.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' However, trajectory tracking  only is not representative of various industrial tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Further-  more, this method may not be transferable to other tasks;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' as  discussed in Section III, the hand-guiding data set could be  biased due to the strong correlation between the end-effector  force and motion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='  Following Section I, we propose to use Neural Networks,  particularly Multilayer Perceptron (MLP), to avoid complex  mathematical modeling while ensuring estimation accuracy,  as it has been proven effective in approximating nonlinear  mapping in many areas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Also discussed in [20], Neural Net-  works performed well in approximating the forward/inverse  kinematics, and Jacobian matrix [21]–[23].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Recent works have  proposed a variety of Neural Network structures, including  MLP [24], Recurrent Neural Network (RNN) [25], and Con-  volutional Neural Network (CNN) [26]–[28], being applied in  different tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Though demonstrating promising results, the  works mentioned above are hard to compare as they were  implemented in a very different context that requires image  input or surgical robot setup.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Some closely related applications  of MLP in industrial manipulator collision checking can be  found in [10], [29], where models are trained to predict  external torque for threshold determination or directly detect  contact during motions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Even though Neural Network is less  intuitive in revealing robot dynamics, it generally outperforms  most methods in nonlinear mapping and noise cancellation,  thereby being robust in uncertain environments given sufﬁcient  training data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='  III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' MODEL AND TRAINING SET STRUCTURE  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Model Structure  Given the broad application of Neural Networks in re-  gression problems for robotics, multiple structures, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=', MLP,  RNN, CNN, have been proposed for similar tasks as discussed  above.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Considering model simplicity and ease of implemen-  tation, we choose the model to have a fundamental MLP  structure with only a few hidden layers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' As shown in the  experiments, since MLP already shows high accuracy in  multiple tasks, we will not discuss the use of more complex  structures like CNN and RNN in this paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' On the other hand,  when a simple model covers a large joint-space or work-space,  it will underﬁt the training data such that estimation becomes  inaccurate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Our solution is to enlarge the hidden layers or  increase Network depth to capture higher non-linearity and  3  diversities introduced by dissimilar Inverse Kinematics Classes  (IK Classes for short).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Therefore, a model should be retrained  and optimized whenever new data is collected from distal IK  Classes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' A detailed discussion of the relationship between the  model and data size is included in Section IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' 2 helps to visualize a sample model structure with  two hidden layers, each having 256 neurons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' The input to  the Neural Network is a 24×1 vector that concatenates the  6×1 joint current, 6×1 joint position, 6×1 joint velocity, and  6×1 joint acceleration vector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' The model output is a 6×1  vector consisting of the 3×1 force vector and 3×1 torque  vector in the XYZ direction, all represented in the F/T Sensor  (end-effector) frame.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' We implemented the model and data  loader, then trained the model with PyTorch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' The loss function,  activation function, and optimization method are MSEloss,  ReLu, and Adam Optimizer, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' 2: Structure of the proposed MLP model  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Training Set Structure  The training set consists of two data set: Free-space Data  Set and Contact Data Set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='  The Free-space Data Set (FSDS) was collected when the  robot end-effector followed pre-planned trajectories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' FSDS  aims to train the Neural Network for the essential force/torque  sensing ability, so it includes random contact, measured by an  F/T Sensor, at the end-effector throughout data collection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' It  is the training set’s fundamental component, or backbone, for  it can provide a model with some basic information about  the robot.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' With only FSDS, a model is expected to estimate  wrench accurately within the work-space for data collection  regardless of motion complexity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' In other words, the robot can  achieve simple tasks like contact detection after being trained  by FSDS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='  The Contact Data Set (CDS) is useful in ﬁne-tuning and  enhancing a model’s performance in more complex scenarios.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='  The robot joints’ states, currents, and external forces/torques  vibrate at high frequencies in force control tasks, such as  constrained sliding on a plane and pin insertion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' The resulting  controlled trajectories that the end-effector follows are not pre-  planned smooth trajectories but real-time evaluated trajectories  with many uncertainties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Therefore, CDS trains the model to  make clear estimations even though joint currents and states  are noisy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='  We distinguish and identify FSDS and CDS as the backbone  and ﬁne-tuning data sets for the reason that CDS may teach the  model biased information about the robot dynamics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' During  FSDS collection, all trajectories are pre-determined, and end-  effector forces are random, suggesting that the instantaneous  end-effector motion, and thereby joint states, are uncorrelated  with the wrench.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' In contrast, in contact tasks, the end-effector  always moves in directions minimizing contact force error.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' For  sliding motions, the friction force is always opposite to the  motion parallel to contact planes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' A worse scenario could be  hand-guiding, where end-effector motion is always compliant  with force and torque.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Therefore, our concern is that CDS from  a speciﬁc task may reduce accuracy for other tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Although  such a phenomenon is not obvious in the experiments, where  one ﬁne-tuned model by hand-guiding data set can still be  used for in-contact sliding, discriminating against the biased  information hopefully ensures the desired outcome.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='  IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' TRAINING SET COLLECTION AND MODEL TRAINING  Data collection and experiments demonstrated in the next  section were carried out on Denso-VS060, a 6-axis industrial  robot.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' We used Ubuntu and Robot Operating System (ROS) for  hardware interface, robot motion planning, and joint current  and state extraction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' An ATI Gamma F/T Sensor SI-32-2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='5 was  used for force control and simultaneously training data collec-  tion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' The CPU model was: Intel(R) Xeon(R) CPU E5-2630 v3  @ 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='40GHz, and the additional computational resources (four  GPUs) involved in Neural Network training were of the type:  GeForce GTX 1080 Ti.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Data loading and training typically  take 10 minutes with the above device speciﬁcations and the  following training data size.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' There was no GPU used to assist  in real-time wrench estimation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='  The end-effector for FSDS collection was a 3D-printed  sphere with 50mm diameter, which allowed easy grasping  and twisting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' The end-effector for CDS collection was an alu-  minum cylinder pin with 20mm diameter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Both end-effectors  were mounted directly on the F/T Sensor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Training Sets Generation  1) Free-space Data Set (FSDS): FSDS was collected when  the robot end-effector followed randomized trajectories in a  cuboid work-space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' To begin with, multiple end-effector posi-  tions were randomly generated in sequence inside the work-  space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Each point was assigned a rotation matrix for the end-  effector, with Euler angles θx, θy, and θz randomly selected  from the speciﬁed ranges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Afterward, a trajectory planner  explored every point in sequence and planned the shortest  trajectory from one point to the next.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Data was collected by  randomly applying forces on the end-effector manually and  continuously when it followed the pre-planned trajectories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' A  position-controlled robot was used for experiments, so its joint  velocity and acceleration were calculated through the ﬁrst and  second derivatives of joint position.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Although current and ac-  celeration signals were very noisy, the input to the model was  not ﬁltered as we expect a short estimation delay and that the  256×1  256×1  24×1  6×1  Force  Torque4  model may eliminate the effect of noise through learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' The  real-time Force/Torque Sensor reading, joint current, position,  velocity, and acceleration were simultaneously recorded as the  training data at 100HZ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='  2) Contact Data Set (CDS): We collected the preliminary  CDS through direct end-effector contact with planes to intro-  duce less data bias and train a model that can accomplish  most of the experiments designed in section V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' The data  set was collected when the end-effector made contact and  slid on a steel plate with controlled contact force.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' With the  plate location ﬁxed inside the work-space for FSDS, multiple  contact points were generated in sequence in the speciﬁed  rectangular region on the plate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' The end-effector repeated the  following for each contact point: (1) Making contact with  the plate at a random angle, then pushing the plate with a  reference force for 30 seconds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' In order to induce disturbances,  a random reference force was sampled within the range [4N,  30N] every 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='2s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' (2) Sliding towards the next contact point  while maintaining the force.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' (3) Leaving off the plate after  reaching the next point.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Similarly, the real-time Force/Torque  Sensor reading and joint states were recorded simultaneously  at 100HZ throughout the steps above.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='  As shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' 5a, contact force was controlled through  end-effector position control in the corresponding direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='  The F/T Sensor feedback error was passed to a P controller  to decide the displacement perpendicular to the plate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Sliding  motions parallel to the plate followed the pre-planned straight  trajectories between points, so sliding friction was not con-  trolled.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Using the Inverse Kinematics Model, we can evaluate  the commanded joint positions and send them to the robot  with the desired X, Y, and Z coordinates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='  CDS collection should repeat for multiple contact planes  so that CDS covers a possibly large portion of the work-  space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' However, this may require a ﬂexible experiment setup  where the plane location and orientation are adjustable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' The  ideal data collection setup for commercialization and large-  scale deployment would have two robots pushing against each  other to simulate in-contact effects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Optionally, the contact  plate could be mounted to the robot’s end-effector so that the  plane locations and trajectories are programmable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Due to the  setup constraint, we collect CDS on two contact planes with  three different IK Classes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Training Set Details  We collected three data sets, each including both FSDS and  CDS, with three IK Classes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' The exact work-space size and  location, contact plane size and location, and total data frames  can be found in Table I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' 3 helps to visualize these regions  and the corresponding IK Classes in OpenRave simulated envi-  ronment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Training data distributions, particularly joint position  and velocity distribution, are shown in Appendix Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='1 in  histograms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Model Enhancement for Large Work-space  It is validated in the literature of deep learning [30] that  MLP has the potential to ﬁt any non-linear equations given  IK Class 1  Space Size (m)  Space Center (m)  FSDS Frames  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='20 × 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='50 × 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='15  [0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='35, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='00, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='30]  991,500  Plane Size (m)  Plane Center (m)  CDS Frames  Horizontal 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='15 × 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='20  [0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='35, -0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='14, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='30]  1,653,000  IK Class 2  Space Size (m)  Space Center (m)  FSDS Frames  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='25 × 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='20 × 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='40  [0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='40, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='15, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='60]  1,098,500  Plane Size (m)  Plane Center (m)  CDS Frames  Vertical 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='20 × 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='30  [0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='40, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='20, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='60]  2,635,000  IK Class 3  Space Size (m)  Space Center (m)  FSDS Frames  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='20 × 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='20 × 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='20  [0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='35, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='15, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='65]  825,500  Plane Size (m)  Plane Center (m)  CDS Frames  Vertical 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='15 × 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='20  [0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='37, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='20, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='65]  1,686,500  TABLE I: The work-space speciﬁcations, plane speciﬁcations,  and training data size for three data sets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Coordinates are  represented in the robot base frame.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' 3: Visualization of the data region for three work-spaces  with three different IK Classes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' The transparent blue box and  opaque red plane indicate the bounding boxes and location of  the ﬁxed plates, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' The postures of Denso from left  to right show the center of the nearest joint position clusters,  or IK solutions, based on which the data was collected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='  appropriate model structure and sufﬁcient training data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' How-  ever, a learning-based model generally loses accuracy when  covering data with higher non-linearity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' This phenomenon is  obvious whenever new training data is collected from different  joint speciﬁcations and distal IK Classes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' An intuitive solution  is increasing the model size, that is, adding more hidden layers  or neurons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' On the other hand, instantaneous wrench feedbacks  are crucial in real-time tasks, especially high-precision force-  control tasks like assembly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' A large model will lead to a  long inference time given a general industrial application  scenario, where additional computational resources like GPUs  are costly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Therefore, a tradeoff between model size and  inference time must be made according to the expected model  performance in applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='  In order to optimize the model structure for experiments,  we train models of three different hidden layer sizes (LS)  with either single or entire data sets coverage, then compare  the RMSE of all wrench dimensions on the same test set  (150,000 frames).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' All models have the same depth of two  hidden layers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' The numerical results are shown in Table II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='  Estimation accuracy generally increases for all dimensions  as we enlarge hidden layers, but inference time increases  from 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='05ms for LS128 to 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='20ms for LS256 and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='80ms for  LS512 in our implementation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' It is also clear that the accuracy  of a smaller model drops signiﬁcantly when covering three  Z  Y  XZ  Y  XZ  X5  data sets, but it is not obvious for larger models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Estimation  accuracy and inference time should be tested carefully when  larger models or data sets are desired.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='  It was observed that the training data down-sampled by  ﬁve times trained the model for a similar estimation accuracy,  but the training set with four-ﬁfths of the trajectory removed  resulted in poor accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' This suggests that the coverage  of trajectories and their complexities dominate the model  accuracy instead of simply the training data size.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Hopefully,  estimation accuracy can be improved further if the training set  trajectories are optimized.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='  Test Set RMSE (N for F;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Nm for T)  LS  Datasets  Fx  Fy  Fz  Tx  Ty  Tz  128  1  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='08  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='84  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='23  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='24  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='25  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='08  256  1  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='45  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='35  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='50  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='22  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='23  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='08  512  1  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='70  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='96  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='04  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='18  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='18  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='08  128  1,2,3  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='62  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='29  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='90  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='33  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='36  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='11  256  1,2,3  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='91  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='71  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='23  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='26  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='27  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='09  512  1,2,3  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='11  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='99  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='43  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='22  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='20  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='08  TABLE II: RMSE on the same test set (randomly sampled  from data set 1) produced by models with different hidden  layer size (LS) and training data coverage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Fx, Fy, and Fz  stands for end-effector forces in XYZ directions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Tx, Ty, and  Tz stands for end-effector torques in XYZ directions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='  V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' EXPERIMENT RESULTS  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Wrench Estimation in Free Motion  Given that the model with 512 hidden neurons has a  relatively high accuracy while the inference time is less than  1 ms in our implementation, we use this structure for all  experiments presented in the following sections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='  The free-motion experiment served as a online test set for  the trained model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Test trajectories were generated randomly in  the same manner as the FSDS collection in the work-space for  IK Class 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' When the robot was executing, periodical forces  and torques were applied to a spherical end-effector mounted  on the F/T sensor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' 4 shows a comparison between a part  of the real-time estimated wrench and the real-time reading  from the Force/Torque sensor when the end-effector followed  pre-planned free-space trajectories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' RMSEs in this and all  the remaining experiments are calculated regarding the data  presented in ﬁgures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' The plot suggests that although the model  missed some peak values, it can still follow the overall wrench  variation despite random end-effector trajectories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' The magni-  tude of RMSE is also acceptable, considering the force/torque  variation ranges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Force Control For In-contact Spiral Sliding  The end-effector followed a pre-planned spiral trajectory  with the ﬁxed plate location.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Similarly, force control was  achieved through position control as suggested in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' 5a,  but we used the estimated result from the Neural Network  Estimator to replace the F/T sensor for control feedback.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' That  means that the contact force was controlled with real-time  estimated force with a simple P controller.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' 5b shows the  block diagram for closed-loop control of contact force.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' 4: Comparison between the estimated (red) and real  wrench (blue dashed) for random pre-planned free-motion  trajectories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Forces and torque are represented in the F/T  Sensor (end-effector) frame.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='  In the experiment, the end-effector ﬁrst moved towards the  plate, then tried to apply a constant force of 15N with a contact  angle of 10°, and ﬁnally started sliding following a spiral  trajectory after the force was stabilized.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' The plate location  is the same as that for data collection with IK Class 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='  6 compares the estimated wrench and sensor reading during  sliding.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' The effect of force control can be interpreted from the  force along the Z-axis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' It is obvious that forces and torques  parallel to the plate undergo sinusoidal variation due to the  periodic friction change during spiral sliding.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Although spiral  trajectories are excluded from the training set, the model can  still perform accurate wrench estimation learning from simple  straight motions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Again, neither the input data to nor output  data from the model were ﬁltered.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' The estimated wrench is  noisy due to the unprocessed input and simple controller, but  the overall accuracy is promising.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Force/Torque Control for Tight Assembly  In addition to the contact force control task, a strong proof  of the estimator’s reliability is completing a typical industrial  task - tight assembly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' In the general scenario of pin insertion,  forces and torques in all directions are under control, so the  40  30  Fx (N)  0  10  20  30  Range:.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='59.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='52 N  RMSE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='=.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='86.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='N  40  0  5  10  15  20  30  20  10  (N)  0  И  10  20  Range:49.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='29N  RMSE=  30  0  5  10  15  20  10  0  10  rry  20  30  40  Range:45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='59N  RMSE=4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='51N  50  5  10  15  20  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='0  (Nm)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='5  XI  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='5  Range: 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='76.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='Nm  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='0  RMSE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='.0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='Nm  0  5  10  15  20  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='5  (Nm)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='0  Range:3:31 Nm  RMSE=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='23Nm  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='5  5  10  15  20  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='0  (wN)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='0  N  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='0  Range: 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content="35'Nm  RMSE = 0:14 Nm  1." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='5  0  5  10  15  20  Time (s)6  (a)  (b)  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' 5: (a) Block diagram for force control on contact planes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='  Xp, Yp, and Zp are the end-effector coordinate in the plate’s  frame.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Fd is the desired force on the plate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Fp is the force  perpendicular to the plate evaluated from the F/T sensor  measurement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' (b) Block diagram for force control on planes  with Neural Network estimation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' I indicates the joint current.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' 6: Comparison between the estimated (red) and real  wrench (blue dashed) for in-contact spiral sliding.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Forces and  torque are represented in the F/T Sensor (end-effector) frame.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='  task requires high force-sensing accuracy with only a slight  lag in time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='  In this experiment, we used one pair of aluminum pin  and hole with 20mm diameters and 100-micron clearance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='  In the force-controlled insertion, the hole was placed in the  work-space for IK Class 1, and the pin was mounted on the  F/T sensor (for comparison purposes only) through coupling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='  Insertion started 3mm above the hole with 2mm horizontal  position error and 5° orientation error.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Again, the estimated  wrench was used as the control feedback, and the control  algorithm for pin insertion was designed as follows: (1) forces  and torques were transformed into the pin-tip frame;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' (2) [0N,  0N, 10N, 0Nm, 0Nm] reference force and torque were used  as the controller setpoint (end-effector twist not controlled).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='  The algorithm results in a three-phase insertion as shown  in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' 7, where the pin moved downward before making  contact, automatically located and aligned with the hole while  maintaining the contact force, and ﬁnally ﬁtted into the hole  after being aligned.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Note that the relative initial orientation  error of the pin and hole was roughly 5°, but the hole’s  orientation was assumed unknown.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Torque control was thus  needed to align the pin and hole while locating the hole center.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='  During insertion, the pin made multiple-point contact with  the hole as a need for torque control.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' It was observed that  torques being transmitted to joints are different with the same  torque on the sensor in the multiple-point and single-point  contact scenario, such that joint current measurements are  different.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' It suggests that one joint current reading may corre-  spond to two different end-effector torque under single-point  and multiple-point contact, given some robot conﬁgurations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='  Such a phenomenon is always true at speciﬁc conﬁgurations  like wrist singularity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Even with the robot being close to  those conﬁgurations, the model trained with noisy data still  cannot capture the slight current changes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' As a result, in the  insertion experiment, torque estimation was relatively accurate  in the ﬁrst 5 seconds when the pin made single-point contact  with the hole.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' However, the model failed to estimate torque  accurately in the complex multiple-contact part and stuck with  only 12mm inserted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Minimum pin-insertion training data was  then collected to allow full insertion of 18mm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' 8 shows the comparison between the estimated and  true wrench for the whole insertion process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' However, torque  estimation for multiple-point contact is still inaccurate, as ex-  plained above, even though the pin was successfully inserted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='  The accuracy may be improved by including more complex  motions and force control tasks in the training set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Another  approach could be manipulating and training the model with  the residual between the measured and estimated free-space  current instead so that the model learns for slight current  variations more effectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Sensorless Hand-guiding  With hand-guiding, a typical human-robot interaction task,  we demonstrate how the model can be ﬁne-tuned for different  tasks by the corresponding data set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' As discussed in Section  III, the hand-guiding data set was not used for backbone  training with concern that the end-effector and joint motions  20  15  10  (N)  5  0  5  Range: 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='24 N  RMSE = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='41 N  10  0  10  20  30  40  50  60  70  80  20  15  10  (N)  5  10  Range: 12:82 N  RMSE= 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='81 N  15,  0  10  20  30  40  50  60  70  80  (N)  Range: 23:18 N  RMSE= 2:40 N  30  0  10  20  30  40  50  60  70  80  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='5  (Nm)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='0  XI  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='0  Range: 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='86: Nm  RMSE·=·0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='12·Nm  0  10  20  30  40  50  60  70  80  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='5  (Nm)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='0  Range: 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='84 Nm  RMSE = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='11 Nm  0  10  20  30  40  50  60  70  80  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='2  (WN)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='2  N  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='6  Range: 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content="14 Nm  RMSE='0." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='04 Nm  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='8  0  10  20  30  40  50  60  70  80  Time (s)Xp  Industrial Robot  Inverse  qc  b  dz  Zp  Fa  Kr  Kinematics  Fp  Force/Torque  Environment  SensorXp  Industrial Robot  qc  Zp  Inverse  dz  Fa  Kinematics  q  1  Fp  q  p  Neural  dt  Network  Estimator  d?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='  p  dt2  I7  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' 7: Three-phase insertion procedure governed by [0N, 0N,  10N, 0Nm, 0Nm] reference forces and torques.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' In phase one,  the pin moved to the hole until making contact with 10N  reference force.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' In phase two, it rotated to align with the hole  and automatically located the hole center due to zero reference  forces and torques except for the Z direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' In phase three,  the pin was aligned, and thus inserted further.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' 8: Comparison between the estimated (red) and real  wrench (blue dashed) in force/torque controlled pin insertion  task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Forces and torque are represented in the F/T Sensor (end-  effector) frame.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='  are always compliant with forces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' The compliant motion could  generate biased data with which the Neural Network may  underﬁt the actual dynamics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' In other words, the forces and  robot motions strongly correlate due to hand-guiding.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='  The hand-guiding data set includes 321,000 data frames  collected with IK Class 1 recorded at 100Hz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' The end-effector,  the same as that for FSDS collection, was guided to follow  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' 9: Comparison between the estimated (red) and real  wrench (blue dashed) in hand-guiding.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Forces and torque are  represented in the F/T Sensor (end-effector) frame.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='  straight and spiral trajectories that explore the pre-deﬁned  work-space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Again, we used a simple P controller for data  collection, then trained the model with unprocessed data to  ensure that it learned in a noisy environment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' The ﬁne-tuned  model was then tested in the same work-space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' A part of  the record is shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' With the almost overlapped  estimation with the ground-truth, we conclude that the Neural  Network estimator has great potential to be used for various  tasks through ﬁne-tuning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Even though the estimated wrench  was noisy due to the discontinuous trajectory, the stability  could be improved with further signal processing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='  E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Error Quantiﬁcation in the Frequency Domain  Considering the complex environment in which a robot  could operate, studying the model behavior under different  contact force frequencies is crucial.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' More speciﬁcally, we  studied the estimation error and phase lag as a function of  force oscillation frequency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Data was collected in the work-  space for IK Class 1 with the same plate location for training  data collection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Ten contact points were evenly sampled on  the plate, and for each point, the end-effector oscillated be-  tween two reference positions penetrating into the plane.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' The  exact penetration depths were determined through preliminary  experiments, so the resulting force vibration had an identical  20  15  10  (N) XJ  10  Range: 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content="09'N  RMSE=2." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='53N  15  0  2  4  6  8  10  12  14  16  18  10  5  (N)  0  5  10  15  Range:.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='03.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='.N  RMSE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='N  0  2  4  6  8  10  12  14  16  18  10  (N)  15  29  Range:21:13N  RMSE=:2:82:N  30  0  2  4  6  8  10  12  14  16  18  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='4  (Nm)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='0  XI  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='6  Range:.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='70.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='Nm  RMSE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='.0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='Nm  0  2  4  6  8  10  12  14  16  18  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='5  (Nm)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='0  Range: 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='92 Nm  RMSE= 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='19 Nm  0  2  4  6  8  10  12  14  16  18  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='2  (Nm)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='0  N  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='4  Range: 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='09 Nm  RMSE= 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='03 Nm  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='6  0  2  4  6  8  10  12  14  16  18  Time (s)40  20  (N)  0  20  40  Range::73.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='67·N  RMSE=:3:53·N  0  10  20  30  40  50  60  70  80  40  20  0  20  40  Range:76:44 N  RMSE= 3:93 N  0  10  20  30  40  50  60  70  80  40  20  20  40  Range:.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='84.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='N  RMSE = 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='91 N  60  0  10  20  30  40  50  60  70  80  2  (Nm)  0  Range: 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='54  Nm  RMSE = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='20 Nm  10  20  30  40  50  60  70  80  2  (Nm)  Range: 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='47: Nm  RMSE = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='20 Nm  3  10  20  30  40  50  60  70  80  2  (Nm)  Range: 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='39: Nm  RMSE = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='24 Nm  0  10  20  30  40  50  60  70  80  Time (s)8  mean and range of 15N and 10N for all frequencies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Note that  direct force control was not applied as the oscillation range  shrank signiﬁcantly at higher frequencies even though the  reference force is unchanged.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Data were recorded at multiple  frequencies from 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='1Hz to 10Hz for each contact point, and  645,500 data frames were recorded in total.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='  Although RMSE is intuitive and widely used for error  analysis, our experiments show that RMSE from the same  model can vary depending on the force variation range.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' It can  be interpreted easily by comparing Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' 8 and Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' 9, where  the latter plot looks more accurate intuitively but actually has  larger errors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Normalized RMSE could be a better choice,  but selecting the appropriate lower and upper bound for  normalization still depends on the force range required in  different tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Therefore, we quantify the estimation error  as the ratio and offset between the estimated force and the  true force in the same frame.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' More speciﬁcally, we used linear  regression to obtain a ﬁrst-order approximation of the mapping  from the true force to the estimated force in each frequency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='  The physical meaning for ratio and offset is the magnitude gain  from the true to estimated force and the mean error between  the forces, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='  With the direct position-control pattern, as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='  10, the estimated force tends to overshoot after reaching  the desired position, and that is caused by the overshot in  motor current.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Higher frequencies do not allow the current to  stabilize, such that the overshot error dominates as frequency  increases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Such an interpretation can be visualized in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' 11,  where both the gain and offset have a local maximum at 1Hz  oscillation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' When frequency increases further, the overshot  would be eliminated, so the local minimum at 3Hz suggests the  overall accuracy in an overshot-free and marginally stable con-  dition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Oscillation becomes irregular after 3Hz, with shrinking  oscillation ranges and non-identical current behaviors in each  period.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Such chaotic behavior, though similar to that in most  industrial applications, makes it hard to analyze intuitively, but  both the ratio and offset stay in reasonable ranges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' The RMSE  plot suggests that the absolute error is roughly 2N with a  15N and 10N force oscillation mean and range.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' By calculating  the cross-correlation of the estimation and measurement data  series, there is no apparent relationship found between time  lead or lag and oscillation frequency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='  VI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' CONCLUSION  In this paper, we propose an approach to estimating the end-  effector wrench with Neural Networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' The model takes the  joint currents and states as the input and makes estimations of  the wrench in real-time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' It avoids using embedded joint torque  sensors and can replace 6-axis end-effector F/T sensors in  industrial applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' The implemented model also achieved  high estimation accuracy and stability in various industrial  tasks, being trained with the Free-space and Contact Data Sets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='  One limitation with the current implementation that we  foresee is the long time taken for large-scale data collection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='  Although the procedure is automatic, random-generated trajec-  tories could be inefﬁcient in covering the dynamic information  of the robot.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' A systematic approach to generating trajectories  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' 10: Comparison between the true and estimated force with  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='1Hz force oscillation frequency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' (a) Blue (dashed) and red  lines indicate true and estimated force respectively, (b) the J2’s  current recorded simultaneously in force oscillation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' 11: The linear regression result of the mapping from true  force to estimated force.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Figures from top to bottom show (a)  Gain (ratio) from true to estimated force, (b) mean error of  between true and estimated force, (c) RMSE over all data at  each frequency with force oscillation from 10N to 20N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='  may signiﬁcantly reduce the data collection time while allow-  ing for higher accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='  All the experiments were carried out under low-speed  operations – the most common mode for contact tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Further  studies could be done to address the potential issues with high-  speed operations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Such an improvement will allow accurate  estimation in static and high-speed operations on which the  (N)  10  z  orce.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='  15  20  25  0  5  10  15  20  25  10  : 2 Current (%)  15  20  25  30  loint :  35  40  0  5  10  15  20  25  Time (s)1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='6  Ratio  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='4  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='2  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='8  10-1  100  101  10  Offset (N)  5  0  10-1  100  101  5  4  (N)  RMSE (  3  1  0  10-1  100  101  Frequency (Hz)9  current model identiﬁcation method shows less convincing  results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='  Since no dynamic information is required for model train-  ing, a similar method can be easily applied to different types  of robot arms by following a standard data collection pipeline.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='  The results in complex control tasks are also promising if the  proposed method was applied in other areas like legged and  surgical robots when a physical sensor was not preferred in  actual applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='  Another promising avenue for future research is to combine  the sensorless F/T estimation here with recent robust force  control methods [3], which can further alleviate possible  instabilities caused by estimation errors or delays.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Such a  combination could enable even more sensitive sensorless ma-  nipulation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' From an economic perspective, the result presented  here opens the possibility of equipping the existing 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='7 million  industrial robots and the 600,000 new units installed per year  with Force Sensing and Force Control capabilities without any  additional hardware required for the users.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='  VII.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' ACKNOWLEDGEMENT  This research was supported by the National Research Foun-  dation, Prime Minister’s Ofﬁce, Singapore under its Medium  Sized Centre funding scheme, Singapore Centre for 3D Print-  ing, CES SDC Pte Ltd, and Chip Eng Seng Corporation Ltd.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='  REFERENCES  [1] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Siciliano, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Khatib, and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Kr¨oger, Springer handbook of robotics,  vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' 200.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Springer, 2008.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='  [2] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Su´arez-Ruiz, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Zhou, and Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='-C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Pham, “Can robots assemble an ikea  chair?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=',” Science Robotics, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' 3, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' 17, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' eaat6385, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='  [3] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Pham and Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='-C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Pham, “Convex controller synthesis for robot  contact,” IEEE Robotics and Automation Letters, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' 5, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' 2, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' 3330–  3337, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='  [4] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' De Luca and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Mattone, “Sensorless robot collision detection  and hybrid force/motion control,” in Proceedings of the 2005 IEEE  international conference on robotics and automation, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' 999–1004,  IEEE, 2005.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='  [5] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Van Damme, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Beyl, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Vanderborght, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Grosu, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Van Ham,  I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Vanderniepen, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Matthys, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Lefeber, “Estimating robot end-  effector force from noisy actuator torque measurements,” in 2011 IEEE  International Conference on Robotics and Automation, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' 1108–1113,  IEEE, 2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='  [6] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Wahrburg, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' B¨os, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Listmann, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Dai, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Matthias, and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Ding,  “Motor-current-based estimation of cartesian contact forces and torques  for robotic manipulators and its application to force control,” IEEE  Transactions on Automation Science and Engineering, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' 15, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' 2,  pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' 879–886, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='  [7] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Kommuri, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Han, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Lee, “External torque estimation using  higher order sliding-mode observer for robot manipulators,” IEEE/ASME  Transactions on Mechatronics, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' 27, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' 1, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' 513–523, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='  [8] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Nguyen-Tuong and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Peters, “Local gaussian process regression for  real-time model-based robot control,” in 2008 IEEE/RSJ International  Conference on Intelligent Robots and Systems, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' 380–385, IEEE, 2008.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='  [9] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Nguyen-Tuong, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Seeger, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Peters, “Model learning with  local gaussian process regression,” Advanced Robotics, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' 23, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' 15,  pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' 2015–2034, 2009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='  [10] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='-N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Sharkawy, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Koustoumpardis, and N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Aspragathos, “Human–  robot collisions detection for safe human–robot interaction using one  multi-input–output neural network,” Soft Computing, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' 24, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' 9,  pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' 6687–6719, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='  [11] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' De Luca and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Mattone, “Actuator failure detection and isolation  using generalized momenta,” in 2003 IEEE international conference on  robotics and automation (cat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' 03CH37422), vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' 1, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' 634–639,  IEEE, 2003.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='  [12] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Kircanski and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Goldenberg, “An experimental study of  nonlinear stiffness, hysteresis, and friction effects in robot joints with  harmonic drives and torque sensors,” The International Journal of  Robotics Research, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' 16, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' 2, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' 214–239, 1997.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='  [13] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Olsson, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' ˚Astr¨om, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' De Wit, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' G¨afvert, and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Lischinsky,  “Friction models and friction compensation,” Eur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Control, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' 4,  no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' 3, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' 176–195, 1998.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='  [14] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Ruderman, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Hoffmann, and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Bertram, “Modeling and iden-  tiﬁcation of elastic robot joints with hysteresis and backlash,” IEEE  Transactions on Industrial Electronics, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' 56, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' 10, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' 3840–3847,  2009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='  [15] X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Liu, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Zhao, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Ge, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Wu, and X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Mei, “End-effector force  estimation for ﬂexible-joint robots with global friction approximation  using neural networks,” IEEE Transactions on Industrial Informatics,  vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' 15, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' 3, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' 1730–1741, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='  [16] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Hu and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Xiong, “Contact force estimation for robot manipulator  using semiparametric model and disturbance kalman ﬁlter,” IEEE Trans-  actions on Industrial Electronics, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' 65, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' 4, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' 3365–3375, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='  [17] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Schaal, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Atkeson, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Vijayakumar, “Scalable techniques  from nonparametric statistics for real time robot learning,” Applied  Intelligence, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' 17, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' 1, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' 49–60, 2002.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='  [18] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Vijayakumar and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Schaal, “Local dimensionality reduction for  locally weighted learning,” in Proceedings 1997 IEEE International  Symposium on Computational Intelligence in Robotics and Automation  CIRA’97.’Towards New Computational Principles for Robotics and  Automation’, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' 220–225, IEEE, 1997.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='  [19] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Gijsberts and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Metta, “Real-time model learning using incremental  sparse spectrum gaussian process regression,” Neural networks, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' 41,  pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' 59–69, 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='  [20] O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Sigaud, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Sala¨un, and V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Padois, “On-line regression algorithms  for learning mechanical models of robots: a survey,” Robotics and  Autonomous Systems, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' 59, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' 12, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' 1115–1129, 2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='  [21] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Lee and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Kil, “Robot kinematic control based on bidirectional  mapping neural network,” in 1990 IJCNN international joint conference  on neural networks, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' 327–335, IEEE, 1990.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='  [22] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Sang and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='-C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Han, “The estimation for forward kinematic solu-  tion of stewart platform using the neural network,” in Proceedings 1999  IEEE/RSJ International Conference on Intelligent Robots and Systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='  Human and Environment Friendly Robots with High Intelligence and  Emotional Quotients (Cat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' 99CH36289), vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' 1, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' 501–506, IEEE,  1999.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='  [23] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Sadjadian and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Taghirad, “Numerical methods for computing the  forward kinematics of a redundant parallel manipulator,” in Proceedings  of the IEEE Conference on Mechatronics and Robotics, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' 557–562,  Citeseer, 2004.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='  [24] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Yilmaz, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Wu, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Kazanzides, and U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Tumerdem, “Neural network  based inverse dynamics identiﬁcation and external force estimation on  the da vinci research kit,” in 2020 IEEE International Conference on  Robotics and Automation (ICRA), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' 1387–1393, IEEE, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='  [25] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Hanafusa and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Ishikawa, “External force estimation for non-  linear systems using recurrent neural network,” in 2019 IEEE/ASME  International Conference on Advanced Intelligent Mechatronics (AIM),  pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' 1055–1061, IEEE, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='  [26] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='-H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Lee, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Hwang, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='-C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Lim, “Interaction force estimation using  camera and electrical current without force/torque sensor,” IEEE Sensors  Journal, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' 18, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' 21, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' 8863–8872, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='  [27] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Xia and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Kiguchi, “Sensorless real-time force estimation in micro-  surgery robots using a time series convolutional neural network,” IEEE  Access, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' 9, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' 149447–149455, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='  [28] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Marban, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Srinivasan, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Samek, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Fern´andez, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Casals,  “A recurrent convolutional neural network approach for sensorless  force estimation in robotic surgery,” Biomedical Signal Processing and  Control, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' 50, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' 134–150, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='  [29] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Kim, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Lim, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Park, “Transferable collision detection learning  for collaborative manipulator using versatile modularized neural net-  work,” IEEE Transactions on Robotics, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='  [30] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Nielsen, Neural networks and deep learning, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' 25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' Determi-  nation press San Francisco, CA, USA, 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='  10  Shilin Shan received the B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' de-  gree in Mechanical Engineering from  Nanyang  Technological  University,  Singapore in 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content=' He is currently  working towards the Ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
+page_content='D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/z9FQT4oBgHgl3EQfzjal/content/2301.13413v1.pdf'}
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+Multilingual Detection of Check-Worthy Claims
+using World Languages and Adapter Fusion⋆
+Ipek Baris Schlicht1,2 , Lucie Flek3 , and Paolo Rosso1
+1 PRHLT Research Center, Universitat Polit`ecnica de Val`encia, Spain
+2 DW Innovation, Germany
+3 CAISA Lab, University of Marburg, Germany
+{ibarsch@doctor,prosso@dsic}.upv.es, lucie.flek@uni-marburg.de
+Abstract. Check-worthiness detection is the task of identifying claims,
+worthy to be investigated by fact-checkers. Resource scarcity for non-
+world languages and model learning costs remain major challenges for the
+creation of models supporting multilingual check-worthiness detection.
+This paper proposes cross-training adapters on a subset of world languages,
+combined by adapter fusion, to detect claims emerging globally in multiple
+languages. (1) With a vast number of annotators available for world
+languages and the storage-eﬃcient adapter models, this approach is more
+cost eﬃcient. Models can be updated more frequently and thus stay up-
+to-date. (2) Adapter fusion provides insights and allows for interpretation
+regarding the inﬂuence of each adapter model on a particular language.
+The proposed solution often outperformed the top multilingual approaches
+in our benchmark tasks.
+Keywords: Fact-checking · Checkworthiness Detection · Mutilingual ·
+Adapters .
+1
+Introduction
+There is an increasing demand for automated tools that support fact-checkers
+and investigative journalists, especially in the event of breaking or controversial
+news [11,19]. Identifying and prioritizing claims for fact-checking, aka. check-
+worthy (CW) claim detection, is the ﬁrst task of such automated systems [9].
+This task helps guiding fact-checkers to potentially harmful claims for further
+investigation. CW claims, as shown in Table 1, are veriﬁable, of public interest
+and may invoke emotional responses [20]. Most studies in this area focus on
+monolingual approaches, predominantly using English datasets for learning the
+model. Support for multilingualism has become an essential feature for fact-
+checkers who investigate non-English resources [8].
+Although transformers achieved competitive results on several multilingual ap-
+plications [4,3] including CW detection [21,18], there are still two main challenges
+in the CW task: (1) Because of the task complexity, there are a few publicly
+⋆ This paper is accepted at ECIR 2023.
+arXiv:2301.05494v1  [cs.CL]  13 Jan 2023
+
+2
+Schlicht et al.
+Table 1: An example of a check-worthy claim from CT21.
+Those who falsely claim Vaccines are 100% safe and who laugh at anti-vaxxers will be dependent on
+those who refuse to tell the oﬃcial lies to say that wide-spread vaccination *is* critical. 23 die in
+Norway after receiving COVID-19 vaccine: [URL] via [MENTION]
+available datasets in multiple languages. Updating a multilingual model to detect
+even recently emerged claims requires data annotation and timely retraining.
+Finding fact-checking experts to annotate samples would be hard, especially in
+low-resourced languages. (2) Storing standalone copies of each ﬁne-tuned model
+for every supported language requires vast storage capacities. Because of the
+limited budgets of non-proﬁt organizations and media institutes, it would be
+infeasible to update the models frequently.
+World Languages (WLs) are languages spoken in multiple countries, while
+non-native speakers can still communicate with each other using the WL as a
+foreign language. English, Arabic and Spanish are examples of WLs 4. It would
+appear that ﬁnding expert annotators for collecting samples in a WL is easier
+than ﬁnding expert annotators for low-resourced languages.
+As a resource-eﬃcient alternative to fully ﬁne-tuning transformer models,
+adapters [14,31] have been recently proposed. Adapters are lightweight and
+modular neural networks, learning tasks with fewer parameters and transferring
+knowledge across tasks [14,31,22] as well as languages [24]. Fine-tuned adapters
+require less storage than fully ﬁne-tuned pre-trained models.
+In this paper, we propose cross-lingual training of datasets in WLs with
+adapters to mitigate resource scarcity and provide a cost-eﬃcient solution. We
+ﬁrst train Task Adapters (TAs) [23] for each WL and incorporate an interpretable
+Adapter Fusion (AF) [22] to combine WL TAs for an eﬀective knowledge transfer
+among the heterogeneous sources.
+Our contributions for this paper are summarized as follows 5:
+– We extensively analyze the WL AF models on the multilingual CW claim
+detection task and evaluate the models on zero-shot learning (i.e., the target
+languages were unseen during training). We show that the models could
+perform better than monolingual TAs and fully ﬁne-tuned models. They also
+outperformed the related best performing methods in some languages. In
+addition, zero-shot learning is possible with the WL AF models.
+– We construct an evaluation to quantify the performance of the models on
+claims about global/local topics across the languages. Our approach for
+curating the evaluation set could be reused for the assessment of other
+multilingual, social tasks.
+– We present a detailed ablation study for understanding the limitations of AF
+models and their behavior on the CW task.
+4 https://bit.ly/3eMIZ9q
+5 We share our source code at https://bit.ly/3rH6yXu.
+
+Multilingual Detection of Check-Worthy Claims using WL+AF
+3
+2
+Related Work
+2.1
+Identifying Check-Worthy Claims
+Early studies applied feature engineering to machine learning models and neural
+network models to identify CW claims in political debates and speeches. Claim-
+Buster [13,12] was one of the ﬁrst approaches using a Support Vector Machine
+(SVM) classiﬁer trained on lexical, aﬀective feature sets. Gencheva et al. [7]
+combined sentence-level and contextual information from political debates for
+training neural network architectures. Lespagnol et al. [17] employed information
+nutritional labels [6] and word embeddings as features. Vasileva et al. [35] applied
+multitask learning from diﬀerent fact-checking organizations to decide whether a
+statement is CW. Jaradat et al. [15] used MUSE word embeddings to support
+the CW detection task in English and Arabic.
+CheckThat! (CT) organized multilingual CW detection tasks since 2020 [2,21,18].
+They support more languages every year and an increasing number of multilingual
+systems have been submitted. Schlicht et al. [28] proposed a model supporting
+all languages in the dataset. They used a multilingual sentence transformer [26]
+and then ﬁne-tuned the model jointly on a language identiﬁcation task. Similarly,
+Uyangodage et al. [34] ﬁne-tuned mBERT on a dataset containing balanced
+samples for each language. Recently, Du et al. [5] ﬁne-tuned mT5 [37] on the CW
+detection task, jointly with multiple related tasks and languages by inserting
+prompts. All of the listed methods were limited to the languages they were
+trained on.
+Kartal and Kutlu [16] evaluated mBERT for zero-shot learning in English,
+Arabic and Turkish, and observed the performance drop in cross-training. A
+more eﬀective method would be required for cross-lingual training. Furthermore,
+none of the approaches tackled the resource eﬃciency issue. In this paper, we use
+adapters and train them only on WLs for resource eﬃciency and evaluate unseen
+languages, leveraging AF to understand which target language in the dataset
+beneﬁts from transferring knowledge from WLs.
+2.2
+Adapters
+Adapters have been successfully applied to pre-trained models for eﬃcient ﬁne-
+tuning to various applications. Early studies [14,22] used adapters for task
+adaptation in English. Pfeiﬀer et al. [22] propose an AF module for learning to
+combine TAs as an alternative to multi-task learning. Some researchers [33,24,25]
+exploit language-speciﬁc adapters for cross-lingual transfer. This paper builds
+upon the works of [22,25]. We exploit a cross-lingual training set to learn TAs
+and then use AF to combine them eﬀectively and provide interpretability on
+which source TAs are eﬃcient on the target language.
+
+4
+Schlicht et al.
+Table 2: Statistics of CT21 and CT22.
+CT21
+CT22
+Split Total %CW Total %CW
+ar
+Train 3444
+22.15
+2513
+38.28
+Dev
+661
+40.09
+235
+42.55
+Test
+600
+40.33
+682
+35.28
+es
+Train 2495
+8.02
+4990
+38.14
+Dev
+1247
+8.74
+2500
+12.20
+Test
+1248
+9.62
+4998
+14.09
+en
+Train 822
+35.28
+2122
+21.07
+Dev
+140
+42.86
+195
+22.56
+Test
+350
+5.43
+149
+26.17
+tr Test
+1013
+18.07
+303
+4.62
+bg Test
+357
+21.29
+130
+43.85
+nl Test
+-
+-
+666
+47.45
+Table 3: Statistics of Global and Local Top-
+ics
+CT21
+CT22
+Split
+Total %CW Total %CW
+ar Global 269
+43.12
+116
+46.55
+Local
+40
+42.5
+-
+-
+es Global 1208
+9.93
+148
+22.97
+Local
+-
+-
+917
+12.43
+nl Global -
+-
+103
+56.31
+Local
+-
+-
+15
+46.67
+en Global 349
+5.44
+14
+28.57
+tr Global 887
+8.91
+-
+-
+bg Global 356
+21.35
+25
+32
+3
+Datasets
+3.1
+Task Datasets
+We looked for multilingual datasets in WLs and other languages for the exper-
+iments. CT21 [29] and CT22 [18] are the only publicly available datasets that
+meet this requirement. CT21 includes English, Arabic, Turkish, Spanish, and
+Bulgarian samples. It deals mainly with Covid-19 events, except for the Spanish
+samples, which focus only on politics. Compared with CT21, CT22 also includes
+samples in Dutch. The English, Arabic, Bulgarian, and Dutch samples in the
+dataset build on the corpora on Covid-19 [1]. The researchers collected new
+samples in Turkish and Spanish. The Spanish samples were augmented with
+CT21.
+The statistics of the datasets are shown in Table 2. English, Spanish and
+Arabic are the WLs contained in the datasets. Both datasets are imbalanced,
+i,e. CW samples are under-represented across the languages. Although English
+is considered a high-resource language, there are considerably fewer English
+samples than samples in other languages. Since some samples of the datasets
+could overlap, we conducted our research experiments per dataset.
+3.2
+Topical Evaluation Dataset
+Some countries are culturally dissimilar or might have diﬀerent political agendas,
+thus CW topics might diﬀer among countries. For example, while vaccination
+was a globally CW topic throughout the COVID-19 pandemic, some COVID-19
+myths were believed only by a few communities [30]. An ideal multilingual system
+should perform well on global as well as local topics.
+Global topics are the topics present in all languages in all datasets, while local
+topics are present in only one language. We created dedicated datasets to evaluate
+the performance of the WL models for identifying CW claims across global and
+
+Multilingual Detection of Check-Worthy Claims using WL+AF
+5
+Adapter Fusion
+WL1 Task Adapter
+Multi-Head Attention
+WL1 Language Adapter ...
+Target Language Adapter
+Add & Norm
+Add & Norm
+WLn Task Adapter
+Add & Norm
+Feed Forward
+WLn Language Adapter
+Fig. 1: The architecture of the WL+AF models within a transformer. WL+AF+LA
+is the setup when the LAs (blocks with the dashed lines) are stacked into the task
+adapters.
+local topics. This evaluation dataset contains solely global and local topics and
+was created as follows. To learn topics across datasets, we ﬁrst translated the
+datasets into English and encoded them with a sentence transformer [26]. Second,
+we learned a topic modeling on the training datasets in the WLs by using
+BERTopic [10] to assign topics to test samples in all languages. Test samples with
+topics present in all WL languages were added as presumably global topics to the
+evaluation set. BERTopic labeled topics that are unrelated to the learnt topics
+with -1. To select samples with local topics, we chose the samples labeled with -1
+from the evaluation and applied a new topic modeling on them. Test samples
+with topics that were not present in the test dataset of any other language (i.e.,
+local topics) were added to the evaluation set for local topics. The statistics of
+the local and global evaluation sets are presented in Table 3.
+4
+Methodology
+4.1
+World Language Adapter Fusion
+This section describes the WL+AF models. The WL+AF models are transformers
+containing additional modules called adapters. During training, only the adapters
+are trained and the weights of pre-trained model are frozen. Therefore, it is a
+parameter-eﬃcient approach. We experiment with two types of WL+AF models.
+WL+AF is a standard setup for combining WL task adapters. WL+AF+LA has
+additional language adapters (LAs) [24] by stacking task adapters. We illustrate
+the architecture of the models in Figure 1. The input of the architecture is a text
+while the output is a probability score describing the check-worthiness of the
+input.
+
+6
+Schlicht et al.
+Transformer Encoder. To provide cross-lingual representations, we use mul-
+tilingual BERT (mBERT) [4] and XLM-Roberta (XLM-R) [3]6. Because the
+transformers were previously used by the related studies [34,1]. Furthermore,
+there are publicly available LAs for the transformers. Before encoding text with
+transformers, we ﬁrst clean it from URLs, mentions and retweets, then truncate
+or pad it to 128 tokens.
+Task Adapter. The annotations might be aﬀected by the diﬀerent cultural
+backgrounds and events across the countries, like the CW claims. Additionally,
+some may have been created from journalists following manual fact-checking
+procedures while others stem from crowd-sourcing [21,18] For these reasons, we
+treat each WL dataset as a separate task. Then, we obtain TAs by optimizing
+on their corresponding WL dataset. TAs consist of one down projection layer
+followed by a ReLU activation and one up projection layer [23]. The TA of each
+WL is ﬁne-tuned on its corresponding dataset.
+Adapter Fusion. To share knowledge from the diﬀerent TAs for predicting
+samples in an unseen language or new topics, we need to combine them eﬀectively.
+AF is a method for combining multiple TAs, and mitigating the common issues of
+multi-task learning, such as catastrophic forgetting and complete model retraining
+for supporting new tasks [22]. AF consists of an attention module which learns
+how to combine knowledge from the TAs dynamically. By analyzing the attention
+weights of the AF, we could learn which source task adapter contributes more to
+test predictions. We combine the TAs trained on the WLs with an AF. Then, the
+AF is ﬁne-tuned on mixed datasets of the WLs to use for the target languages.
+Language Adapter. To learn CW claim detection from various cross-lingual
+sources, we should ensure that the model does not learn a language classiﬁcation
+task but learns how to identify CW claims. Therefore, we need to separate
+language-speciﬁc knowledge from task-speciﬁc knowledge. A recent study [24]
+demonstrated that LAs achieved better results when transferring the knowledge
+of a task performed in one source language into another language. To encode
+language-speciﬁc information into the transformer model and to see the LAs
+impact on the performance of the AF models, we use the LAs from Adapter
+Hub [23]. The architecture of the LAs is analog to those of the TAs. However,
+these LAs were pre-trained on the unlabeled Wikipedia [24] by using a masked
+language model objective. While learning task-speciﬁc transformations with TAs,
+each world LA is stacked on its corresponding TA. The weights of the LAs are
+kept frozen, so they are not learned again. During inference of the target task,
+the source LA is replaced with the target LA.
+4.2
+Implementation Details
+We download the pre-trained transformers from Huggingface [36]. We ﬁne-tune
+the TAs on English, Arabic, and Spanish training samples (WLs), and evaluate
+the models for their capability of zero-shot learning by testing on the other
+6 We use the base version of the model, which consists of 12 layers.
+
+Multilingual Detection of Check-Worthy Claims using WL+AF
+7
+languages. As LAs for Arabic, English, Spanish and Turkish samples in the
+dataset [24], we download the pre-trained LAs from Adapter Hub [23] for both
+transformers. However, a LA for Bulgarian and Dutch is not available in Adapter
+Hub, therefore, we use the English LA.
+We use the trainers of AdapterHub [23] for both full ﬁne-tuning and adapter
+tuning. We set the number of epochs as 10 and train the models with a learning
+rate of 1e-4 for CT21 and 2e-5 for CT227, and batch size of 16. We use the best
+models on the development set according to the dataset metrics. We repeat the
+experiments ten times using diﬀerent random seeds using an NVIDIA GeForce
+RTX 2080.
+5
+Baselines
+We compare the performance of the WL AF models against various baselines:
+– Top performing systems: We chose the top-performing systems on CT21
+and CT22 which used a single model for the multilingual CW detection instead
+of containing language-speciﬁc models. Schlicht et al. [28] is a runner-up 8
+system on CT21. The original implementation uses a sentence transformer and
+the model was ﬁne-tuned on all the language datasets. For a fair comparison,
+we set the language identiﬁcation task to WLs and replaced the sentence
+transformer with mBERT and XLM-R. The state-of-the-art model on CT22 is
+based on mT5-xlarge [5], a multi-task text-to-text transformer. Like Schlicht
+et al., the model is ﬁne-tuned on all of the corpora by using multi-task
+learning. Due to the limited computing resources, we couldn’t ﬁne-tune this
+model on WLs alone. We report the results from [5].
+– Fully ﬁne tuned (FFT) Transformers (on Single Language): We ﬁne-
+tune the datasets on a single language of the WLs to evaluate the eﬃciency
+of cross-lingual learning: AR+FFT, EN+FFT, and ES+FFT. We also add
+BG+FFT, ES+FFT, and NL+FFT as the baseline for zero-shot learning.
+– Task Adapters (on Single Language): These baselines contain a task
+adapter followed by a LA, a widely used setup for cross-lingual transfer learn-
+ing with adapters [24]: AR+TA+LA, EN+TA+LA, ES+TA+LA. Comparing
+our model to these baselines can help understand whether cross-training with
+WLs is eﬃcient.
+– Other WL Models: We evaluate the AF models against a model containing
+a task adapter trained on WLs (WL+TA). In addition to this baseline, to see
+if we need a complex fusion method, we use WL+TA+LA+Mean, which takes
+the average of the predictions by AR+TA, EN+TA and ES+TA. Finally, we
+analyze the adapter tuning on multiple WLs against the fully ﬁne tuning of
+mBERT: WL+FFT.
+7 2e-5 gives better results on the development set of CT22
+8 BigIR is the state of art approach, but there is no associated paper/code describing
+the system.
+
+8
+Schlicht et al.
+Table 4: MAP scores for CT21 and F1 scores for CT22 of the CW detection in WLs.
+The bold indicates the best score and underline indicates the second best score. Overall
+the AF models performed well on multiple languages while the performance of other
+models are sensitive to the characteristics of the training set.
+CT21
+CT22
+ar
+es
+en
+ar
+es
+en
+avg
+Du et al.[5]
+-
+-
+-
+62.8 57.1
+51.9 -
+mBERT
+AR+FFT
+50.17 15.78 6.03
+55.52 17.85 42.92 31.38
+ES+FFT
+41.22 20.30 6.80
+37.30 54.05 45.28 34.16
+EN+FFT
+51.63 15.90 10.80 40.97 22.49 44.29 31.01
+AR+TA+LA
+58.20 19.97 8.62
+18.13 17.61 45.73 28.04
+ES+TA+LA
+48.07 18.93 11.06 37.30 54.05 45.73 35.86
+EN+TA+LA
+50.81 40.81 21.21 56.39 24.63 12.93 34.46
+WL+FFT
+47.93 51.50 13.85 51.50 63.20 39.94 44.65
+Schlicht et al.[28]
+51.51 31.04 7.87
+45.93 66.48 34.18 39.50
+WL+TA
+53.77 46.58 14.44 39.54 62.69 37.19 42.37
+WL+TA+LA+Mean 54.89 35.72 12.96 0.00
+33.21 51.03 31.30
+WL+AF
+55.13 46.29 16.05 36.45 64.32 39.73 42.96
+WL+AF+LA
+55.32 46.58 15.66 39.87 64.64 37.27 43.22
+XLM-R
+AR+FFT
+43.55 12.80 5.88
+38.72 6.83
+41.29 24.85
+ES+FFT
+41.22 15.90 6.80
+40.25 21.69 43.51 28.23
+EN+FFT
+43.64 10.49 5.64
+31.46 64.66 45.69 33.60
+AR+TA+LA
+58.16 25.87 7.64
+6.93
+0.06
+1.40
+16.68
+ES+TA+LA
+50.27 52.51 11.53 41.24 65.45 38.79 43.30
+EN+TA+LA
+56.39 24.63 12.93 12.82 0.06
+28.74 22.60
+WL+FFT
+47.93 13.85 6.37
+44.53 64.75 50.93 38.06
+Schlicht et al.[28]
+51.56 21.61 7.32
+42.59 67.13 36.40 37.77
+WL+TA
+58.02 50.76 11.53 42.91 63.36 31.69 43.05
+WL+TA+LA+Mean 59.32 46.11 10.49 25.32 35.55 35.28 35.35
+WL+AF
+58.39 49.42 13.29 39.84 65.66 46.96 45.59
+WL+AF+LA
+58.83 47.26 16.06 35.17 65.80 43.46 44.43
+6
+Results and Discussion
+In this section, we present and analyze the results of the WL AF(+LA) models.
+We compare the models performance at CW detection for (1) WLs, (2) zero-shot
+languages and (3) local and global topics. Lastly, we compare the performance
+of WL+AF and WL+AF+LA to investigate whether LA is eﬀective in model
+performance.
+As seen in Table 4, the models trained on single languages are able to perform
+well for other WLs if only provided with training sets of considerable size, or
+language of the training and test sets are same. Additionally, Schlicht et al.[28]
+and WL+FFT were performing well only on CT22, overall, the AF models,
+perform well for various languages. Du et al. [5] outperformed the AF models
+for Arabic and English samples of CT22, but it underperformed for the Spanish
+samples.
+As shown in Table 5, the AF models achieve good results on target sets in
+zero-shot languages. It shows that the fusion of multiple sources with adapters
+
+Multilingual Detection of Check-Worthy Claims using WL+AF
+9
+Table 5: MAP for CT21 and F1 for CT22 of the CW detection in zero-shot languages.
+The bold indicates the best score and underline indicates the second best score. The
+AF models performed well, even outperformed WL+FFT and Schlicht et al. [28] and
+some of the monolingual approaches in terms of average score.
+CT21
+CT22
+tr
+bg
+tr
+bg
+nl
+avg
+Du et al.[5]
+-
+-
+17.3
+61.7
+64.2 -
+mBERT
+BG+FFT
+-
+35.64 -
+57.16 -
+-
+TR+FFT
+28.47 -
+14.66 -
+-
+-
+NL+FFT
+-
+-
+-
+-
+49.80 -
+AR+FFT
+30.14 22.12 10.71 54.84 45.55 32.67
+ES+FFT
+23.17 24.15 8.19
+47.67 33.82 27.4
+EN+FFT
+42.80 33.20 13.57 54.58 54.32 39.69
+AR+TA+LA
+58.08 26.76 8.04
+57.43 58.99 41.86
+ES+TA+LA
+49.09 28.09 8.58
+47.67 42.16 35.12
+EN+TA+LA
+54.16 44.98 8.19
+33.92 33.82 35.01
+WL+FFT
+27.61 24.29 10.90 58.53 29.03 30.07
+Schlicht et al.[28]
+27.81 24.41 7.86
+51.94 29.33 28.27
+WL+TA
+54.11 37.04 9.73
+48.02 36.95 37.17
+WL+TA+LA+Mean 62.32 34.52 12.02 47.17 39.91 39.19
+WL+AF
+50.46 39.80 9.63
+53.55 38.76 38.44
+WL+AF+LA
+50.94 40.27 9.73
+52.75 43.07 39.35
+XLM-R
+BG+FFT
+-
+24.68 -
+43.47 -
+-
+TR+FFT
+24.57 -
+18.90 -
+-
+-
+NL+FFT
+-
+-
+-
+-
+58.61 -
+AR+FFT
+23.40 21.86 11.62 45.10 38.73 28.14
+ES+FFT
+23.17 24.15 9.07
+62.72 31.24 30.07
+EN+FFT
+22.63 21.76 18.43 49.25 45.62 31.54
+AR+TA+LA
+56.19 21.37 0.48
+9.75
+5.22
+18.60
+ES+TA+LA
+44.98 23.86 8.04
+46.72 30.52 30.82
+EN+TA+LA
+58.38 41.61 15.19 8.42
+25.83 29.89
+WL+FFT
+27.61 24.29 14.02 63.79 36.34 33.21
+Schlicht et al.[28]
+25.86 22.19 9.55
+53.75 24.44 27.16
+WL+TA
+59.37 39.72 15.60 66.14 35.98 43.36
+WL+TA+LA+Mean 63.65 32.28 9.90
+31.27 19.91 31.40
+WL+AF
+57.46 46.86 12.73 59.12 40.83 43.4
+WL+AF+LA
+61.74 41.78 17.77 63.88 37.59 44.55
+could be beneﬁcial in knowledge transfer and is better than the other fusion
+method WL+TA+LA+Mean. It is noteworthy that Du et al [5] was trained on
+all samples of the training datasets and hence has no zero-shot learning capacity.
+Although Du et al. achieved a better performance on the Dutch samples, the
+AF models could obtain similar results in other languages. In terms of resource
+eﬃciency, the AF models required less space than WL+FFT and mT5 for storing
+new weights, as shown in Table 8, which make them more suitable than updating
+mT5 for newsrooms with a limited budget.
+We compare the performance of models trained on multiple WLs for identifying
+CW claims about global or local topics. We tested this experiment with the
+evaluation set described in Section 3.2 in terms of F1 score. We take the average
+
+10
+Schlicht et al.
+Table 6: F1 scores of the models on global topics for each dataset. Adapter training is
+more eﬀective than fully ﬁne-tuning. Although WL+TA outperformed the AF models
+in particular languages, at average the AF models performed better.
+CT21
+CT22
+tr
+es
+ar
+en
+bg
+es
+ar
+en
+bg
+nl
+avg
+WL+FFT
+0.00
+0.00
+2.60
+0.59
+0.10
+77.59 52.13 52.05 48.52 38.53 27.21
+Schlicht et al.[28] 18.15 17.92 58.84 7.18
+19.75 81.81 48.12 28.33 36.55 30.34 34.70
+WL+TA+LA
+52.37 38.09 61.01 13.58 38.44 77.28 45.47 22.57 41.31 45.09 38.52
+WL+AF
+45.02 41.57 61.51 13.36 36.23 79.14 44.61 50.96 40.58 43.19 45.62
+WL+AF+LA
+48.52 37.44 61.79 13.38 28.72 77.95 42.84 44.23 41.09 43.99 44.00
+Table 7: F1 scores of the models on local topics for each dataset. The AF models show
+similar results to WL+TA and outperformed WL+FFT.
+CT21 CT21
+ar
+es
+nl
+avg
+WL+FFT
+0.93
+60.64 31.11 30.89
+Schlicht et al.[28] 46.80
+64.65 14.44 41.96
+WL+TA+LA
+50.88 61.65 38.47 50.33
+WL+AF
+48.15
+62.01 34.38 48.18
+WL+AF+LA
+46.41
+63.07 41.16 50.21
+Table 8: Number of training parameters and ﬁle size comparisons for the models. mT5
+is larger than mBERT and XLM-R.
+Model
+Base Model Parameters Model Size
+WL+FFT
+mBERT
+178 M
+711.5 MB
+XLM-R
+278 M
+1.1 GB
+Schlicht et al.[28]
+mBERT
+179 M
+716.3 MB
+XLM-R
+279 M
+1.1 GB
+TA & WL+TA+LA mBERT
+1.5 M
+6 MB
+XLM-R
+1.5 M
+6 MB
+AF
+mBERT
+22 M
+87.4 MB
+XLM-R
+22 M
+87.4 MB
+LA
+mBERT
+-
+147.78 MB
+XLM-R
+-
+147.78 MB
+mT5
+3.7 B
+15 GB
+of the scores of the models coded with mBERT and XLM-R and present them in
+Tables 6 and 7, respectively, for global and local topics. Overall, the AF models
+performed better than WL+FFT and Schlicht et al.[28] for both types. However,
+WL+TA performed similarly to WL+AF+LA in predicting local statements in
+Arabic samples in CT21.
+Last, we compare the performance of WL+AF and WL+AF+LA to investigate
+whether LA is eﬀective in model performance. We computed the Fleiss Kappa
+scores of the AF models for each experiment and language. The overall score is
+
+Multilingual Detection of Check-Worthy Claims using WL+AF
+11
+(a) CT21
+TR
+BG
+AR
+ES
+EN
+AR
+EN
+ES
+0.35 0.23 0.91 0.0350.098
+0.24
+0.2 0.0290.028 0.74
+0.4
+0.57 0.061 0.94 0.16
+(b) mBERT
+TR
+BG
+AR
+ES
+EN
+AR
+EN
+ES
+0.4
+0.43 0.67 0.33 0.39
+0.18 0.16 0.11 0.12 0.27
+0.42 0.42 0.22 0.55 0.35
+(c) XLM-R
+(d) CT22
+TR
+BG
+AR
+ES
+EN
+NL
+AR
+EN
+ES
+0.14 0.15 0.270.0430.12 0.13
+0.33 0.31 0.440.092 0.6 0.33
+0.53 0.54 0.29 0.87 0.28 0.54
+(e) mBERT
+TR
+BG
+AR
+ES
+EN
+NL
+AR
+EN
+ES
+0.16 0.14 0.19 0.13 0.14 0.15
+0.35 0.29 0.35 0.19 0.43 0.32
+0.49 0.57 0.45 0.68 0.43 0.52
+(f) XLM-R
+Fig. 2: The left images are topical relation graphs of CT21 (top left) and CT22 (bottom
+left). In the graphs, the size of the nodes varies by the number of samples, and the edge
+thickness depends on the overlapping topics. x-axis of heatmaps shows task adapters,
+y-axis shows the test samples in the diﬀerent languages. (b), (c) attention heatmaps of
+mBERT, (e), (f) attention heatmaps of XLM-R. Topical distribution, and the sample
+sizes of the training datasets impact the task adapters’ activations. Especially XLM-R
+TAs are more sensitive than mBERT.
+0.63, which is a moderate agreement. We further investigate the disagreements
+where the kappa is below 0.5. The conﬂicts mainly occurred in the zero shot
+languages and English, with the lowest CW samples on both datasets. Since
+sometimes WL+AF+LA is better than WL+AF and vice versa, we conclude
+that LA is not eﬀective in our experiments. The pre-trained LAs were trained on
+the Wikipedia texts [24]. Thus, they might miss the properties of social texts,
+which are mostly noisy.
+7
+Further Analysis
+In this section, we present further analysis of the AF models. We investigate AF
+attentions and then apply an error analysis on the models’ predictions.
+Interpretation of the Fusion Attentions. The AF models can provide an
+interpretation of which source task adapter might be useful when transferring the
+knowledge into the target dataset. This kind of analysis would help a data scientist
+at a newsroom on a decision on which WL should be collected for updating model
+and managing new resources. To check the AF behavior on WL+TA+LA+AF,
+we took the average of the softmax probabilities of the layer of each task adapter
+in the fusion layer. The higher probability means the more useful the task for
+determining the label [22]. In addition, to correlate the attention with the source
+datasets, we created a graph displaying the topical relationship between source
+
+es test
+tr test
+en test
+ar test
+bg test
+ar train
+es train
+en traines test
+en test
+tr test
+nl test
+ar test
+bg_test
+ar train
+es train
+en train12
+Schlicht et al.
+Table 9: The CW claims predicted correctly by the WL+TA+AF, the examples are in
+Spanish and Bulgarian. The order of the texts for each example: 1) Visualizations on
+mBERT, 2) Visualizations on XLM-R 3) the red text is the translation. The models
+focus more on GPE (e.g. country names) than the other entity types. We colorized the
+claims based on their integrated gradients [32].
+▁España ▁es ▁el ▁2. o ▁país ▁de ▁la ▁UE ▁que ▁más ▁empleo ▁ha ▁creado ▁entre ▁las ▁mujeres . ▁Un ▁buen
+▁dato ▁sobre ▁el ▁que ▁seguire mos ▁trabajando . ▁Hay ▁que ▁combat ir ▁la ▁fem in ización ▁de ▁la ▁precari edad
+, ▁reducir ▁el ▁paro ▁fem en ino ▁y ▁la ▁bre cha ▁salarial .
+España es el 2 . º país de la UE que más empleo ha creado entre las mujeres . Un buen dato sobre el que seguiremos
+trabajando . Hay que combatir la feminización de la precariedad , reducir el paro femenino y la brecha salarial .
+Spain is the 2nd. or EU country that has created the most employment among women . A good data on which I will
+continue mos working . The feminization of precarious age must be combated , female unemployment and the wage
+gap must be reduced .
+▁Швеция ▁при ну ж дава ▁родителите ▁да ▁изпраща т ▁децата ▁си ▁на ▁училище . ▁Някои ▁се ▁страх уват
+▁децата ▁им ▁в ▁крайна ▁сметка ▁да ▁бъдат ▁от нети , ▁ако ▁от кажа т .
+Швеция принуждава родителите да изпращат децата си на училище . Някои се страхуват децата им в крайна
+сметка да бъдат отнети , ако откажат .
+Sweden forces parents to send their children to school. Some fear their children will eventually be taken away if they
+refuse.
+Table 10: The performance of the AF model at predicting entity types in terms of
+average F1 and the standard deviation. The models could predict GPE more accurately
+than the others.
+Geo-political Entity Organization Number
+People
+F1 46.83 ± 17.37
+40.44 ± 18.62
+40.99 ± 22.52 37.88 ± 18.83
+and target sets. In the graph, the nodes are the monolingual datasets; the edges
+are the overlapped topics between the source and target dataset, weighted by
+the percentage of the samples about the overlapped topic. The size of nodes are
+scaled according to sample size. Figure 2 shows the graph for both datasets and
+the attention weights of mBERT and XLM-R task adapters. Topical distributions
+and source datasets’ size aﬀect which task adapter activates. XLM-R TAs are
+more sensitive to the source data size and topical relationship. For instance, the
+Spanish tests in CT22 are weakly connected with the Arabic and English source
+datasets, and the Spanish TA of XLM-R has less activation than the mBERT
+TA.
+Error analysis. Last, we analyze the misclassiﬁed/correctly classiﬁed samples
+by both AF models. As shown in Table 9, we noted that the AF model focuses
+on geo-political entities (GPE). The models could categorize the claims with
+GPE better than claims containing other type of entities as shown in Table 10.
+The importance of the GPE could be learned from the WL corpus whose CW
+samples have no negligible amount of these entities (e.g. %76 of CT21 and %77 of
+CT22 Arabic source datasets are GPE). However, the models cannot predict the
+claims requiring local context, especially in the zero-shot languages. Moreover,
+the models cannot identify the claims whose veracity can be changed to not CW
+by time. Some examples are shown in Table 11.
+Training eﬃciency. We measured the models’ training time for one epoch on
+the datasets. The TA training is on average 4 minutes less than the fully ﬁne
+
+Multilingual Detection of Check-Worthy Claims using WL+AF
+13
+Table 11: The CW claims that are misclassiﬁed by the AF models. The black texts
+show claims in Turkish. The red texts are the translations, and the blue ones are the
+explanation of the claims.
+Bunu hep yazdım yine yazaca˘gım , Bakanların aileleri , annesi - babası tam kapsamlı sa˘glık tedavileri buna ( Estetik
+dahil ) devlet b¨utcesinden kar¸sılanıyor da , SMA hastası ¸cocukların tedavisi i¸cin niye bir b¨ut¸ce olu¸sturulmuyor
+[UNK] [UNK] # DevletSMAyıYa¸satsın
+I’ve always written this and I will write it again. The families of the ministers, their mother-father full health
+treatments (including Aesthetics) are covered by the state budget, but why isn’t a budget created for the treatment
+of children with SMA [UNK] [UNK] # Let The State Live
+Example of a CW claim that requires local context. SMA is a disease that aﬀects children, and the treatment of
+SMA is a controversial issue in Turkey.
+Koronavir¨us salgınında vaka sayısı 30 bin 021 [UNK] e ula¸stı # Corona # COVID # coronavirus
+The number of cases in the coronavirus epidemic reached 30 thousand 021 [UNK] # Corona # COVID #
+coronavirus
+An example of a CW claim whose veracity could be changed by time.
+tuning. However, the AF training without LAs lasts 3 minutes more, and the
+training with LAs 9 minutes more than the training time of WL+FFT which
+was approx. 22 minutes. The methods such as AdapterDrop [27] could speed up
+the AF training.
+8
+Conclusion and Future Work
+In this paper, we investigated the cost eﬃcient cross-training of adapter fusion
+models on world languages to detect check-worthiness in multiple languages.
+The proposed solution performs well on multiple languages, even on zero-shot
+learning. Thanks to adapter fusion, the eﬀectiveness of the adapters on particular
+languages was possible.
+The attention of some task adapters seems to depend on the topic and
+sample distribution in the source dataset. Ensuring a topical balance across world
+languages appears to be important. Our error analysis results indicate that local
+context is required to detect local claims. We recommend the usage of background
+knowledge injection to detect local claims.
+In the future, we would like to investigate the injection of background knowl-
+edge in adapters and verify our results in additional domains (e.g. war), employing
+more languages such as German and focusing on zero-shot learning.
+Acknowledgements We would like to thank the anonymous reviewers, Joan
+Plepi, Flora Sakketou, Akbar Karimi and Nico Para for their constructive feedback.
+The work of Ipek Schlicht was part of the KID2 project (led by DW Innovation
+and co-funded by BKM). The work of Lucie Flek was part of the BMBF projects
+DeFaktS and DynSoDA. The work of Paolo Rosso was carried out in the frame-
+work of IBERIFIER (INEA/CEF/ICT/A202072381931 n.2020-EU-IA-0252), XAI
+Disinfodemics (PLEC2021-007681) and MARTINI (PCI2022-134990-2).
+
+14
+Schlicht et al.
+References
+1. Alam, F., Shaar, S., Dalvi, F., Sajjad, H., Nikolov, A., Mubarak, H., Da San Martino,
+G., Abdelali, A., Durrani, N., Darwish, K., et al.: Fighting the covid-19 infodemic:
+Modeling the perspective of journalists, fact-checkers, social media platforms,
+policy makers, and the society. In: Findings of the Association for Computational
+Linguistics: EMNLP 2021. pp. 611–649 (2021)
+2. Barr´on-Cede˜no, A., Elsayed, T., Nakov, P., Martino, G.D.S., Hasanain, M., Suwaileh,
+R., Haouari, F., Babulkov, N., Hamdan, B., Nikolov, A., Shaar, S., Ali, Z.S.:
+Overview of checkthat! 2020: Automatic identiﬁcation and veriﬁcation of claims
+in social media. In: CLEF. Lecture Notes in Computer Science, vol. 12260, pp.
+215–236. Springer (2020)
+3. Conneau, A., Khandelwal, K., Goyal, N., Chaudhary, V., Wenzek, G., Guzm´an,
+F., Grave, ´E., Ott, M., Zettlemoyer, L., Stoyanov, V.: Unsupervised cross-lingual
+representation learning at scale. In: Proceedings of the 58th Annual Meeting of the
+Association for Computational Linguistics. pp. 8440–8451 (2020)
+4. Devlin, J., Chang, M., Lee, K., Toutanova, K.: BERT: pre-training of deep bidirec-
+tional transformers for language understanding. In: Burstein, J., Doran, C., Solorio,
+T. (eds.) Proceedings of the 2019 Conference of the North American Chapter of
+the Association for Computational Linguistics: Human Language Technologies,
+NAACL-HLT 2019, Minneapolis, MN, USA, June 2-7, 2019, Volume 1 (Long and
+Short Papers). pp. 4171–4186. Association for Computational Linguistics (2019).
+https://doi.org/10.18653/v1/n19-1423, https://doi.org/10.18653/v1/n19-1423
+5. Du, S.M., Gollapalli, S.D., Ng, S.K.: Nus-ids at checkthat! 2022: Identifying check-
+worthiness of tweets using checkthat5. Working Notes of CLEF (2022)
+6. Fuhr, N., Giachanou, A., Grefenstette, G., Gurevych, I., Hanselowski, A., J¨arvelin,
+K., Jones, R., Liu, Y., Mothe, J., Nejdl, W., Peters, I., Stein, B.: An in-
+formation nutritional label for online documents. SIGIR Forum 51(3), 46–
+66 (2017). https://doi.org/10.1145/3190580.3190588, https://doi.org/10.1145/
+3190580.3190588
+7. Gencheva, P., Nakov, P., M`arquez, L., Barr´on-Cede˜no, A., Koychev, I.: A context-
+aware approach for detecting worth-checking claims in political debates. In: Mitkov,
+R., Angelova, G. (eds.) Proceedings of the International Conference Recent Advances
+in Natural Language Processing, RANLP 2017, Varna, Bulgaria, September 2 - 8,
+2017. pp. 267–276. INCOMA Ltd. (2017). https://doi.org/10.26615/978-954-452-
+049-6 037, https://doi.org/10.26615/978-954-452-049-6_037
+8. Ginsborg, L., Gori, P.: Report on a survey for fact checkers on covid-19 vaccines and
+disinformation. Tech. rep., European Digital Media Observatory (EDMO) (2021),
+https://cadmus.eui.eu/handle/1814/70917
+9. Graves, L.: Understanding the promise and limits of automated fact-checking (2018)
+10. Grootendorst, M.: Bertopic: Neural topic modeling with a class-based tf-idf proce-
+dure. arXiv preprint arXiv:2203.05794 (2022)
+11. Hassan, N., Adair, B., Hamilton, J.T., Li, C., Tremayne, M., Yang, J., Yu, C.:
+The quest to automate fact-checking. In: Proceedings of the 2015 Computation
+Journalism Symposium (2015)
+12. Hassan, N., Arslan, F., Li, C., Tremayne, M.: Toward automated fact-checking:
+Detecting check-worthy factual claims by claimbuster. In: Proceedings of the
+23rd ACM SIGKDD International Conference on Knowledge Discovery and
+Data Mining, Halifax, NS, Canada, August 13 - 17, 2017. pp. 1803–1812.
+ACM (2017). https://doi.org/10.1145/3097983.3098131, https://doi.org/10.
+1145/3097983.3098131
+
+Multilingual Detection of Check-Worthy Claims using WL+AF
+15
+13. Hassan, N., Li, C., Tremayne, M.: Detecting check-worthy factual claims in pres-
+idential debates. In: Bailey, J., Moﬀat, A., Aggarwal, C.C., de Rijke, M., Ku-
+mar, R., Murdock, V., Sellis, T.K., Yu, J.X. (eds.) Proceedings of the 24th
+ACM International Conference on Information and Knowledge Management,
+CIKM 2015, Melbourne, VIC, Australia, October 19 - 23, 2015. pp. 1835–
+1838. ACM (2015). https://doi.org/10.1145/2806416.2806652, https://doi.org/
+10.1145/2806416.2806652
+14. Houlsby, N., Giurgiu, A., Jastrzebski, S., Morrone, B., de Laroussilhe, Q., Gesmundo,
+A., Attariyan, M., Gelly, S.: Parameter-eﬃcient transfer learning for NLP. In: ICML.
+Proceedings of Machine Learning Research, vol. 97, pp. 2790–2799. PMLR (2019)
+15. Jaradat, I., Gencheva, P., Barr´on-Cede˜no, A., M`arquez, L., Nakov, P.: ClaimRank:
+Detecting check-worthy claims in Arabic and English. In: Proceedings of the 2018
+Conference of the North American Chapter of the Association for Computational
+Linguistics: Demonstrations. pp. 26–30. Association for Computational Linguistics,
+New Orleans, Louisiana (Jun 2018). https://doi.org/10.18653/v1/N18-5006, https:
+//aclanthology.org/N18-5006
+16. Kartal, Y.S., Kutlu, M.: Re-think before you share: A comprehensive study on
+prioritizing check-worthy claims. IEEE Transactions on Computational Social
+Systems (2022)
+17. Lespagnol, C., Mothe, J., Ullah, M.Z.: Information nutritional label and word
+embedding to estimate information check-worthiness. In: Proceedings of the 42nd
+International ACM SIGIR Conference on Research and Development in Information
+Retrieval. p. 941–944. SIGIR’19, Association for Computing Machinery, New York,
+NY, USA (2019). https://doi.org/10.1145/3331184.3331298, https://doi.org/10.
+1145/3331184.3331298
+18. Nakov, P., Barr´on-Cede˜no, A., Martino, G.D.S., Alam, F., Struß, J.M., Mandl, T.,
+M´ıguez, R., Caselli, T., Kutlu, M., Zaghouani, W., Li, C., Shaar, S., Shahi, G.K.,
+Mubarak, H., Nikolov, A., Babulkov, N., Kartal, Y.S., Beltr´an, J.: The clef-2022
+checkthat! lab on ﬁghting the covid-19 infodemic and fake news detection. In:
+European Conference on Information Retrieval (2022)
+19. Nakov, P., Corney, D.P.A., Hasanain, M., Alam, F., Elsayed, T., Barr´on-Cede˜no,
+A., Papotti, P., Shaar, S., Martino, G.D.S.: Automated fact-checking for assisting
+human fact-checkers. In: IJCAI. pp. 4551–4558. ijcai.org (2021)
+20. Nakov, P., Da San Martino, G., Elsayed, T., Barr´on-Cedeno, A., M´ıguez, R.,
+Shaar, S., Alam, F., Haouari, F., Hasanain, M., Babulkov, N., et al.: The clef-2021
+checkthat! lab on detecting check-worthy claims, previously fact-checked claims,
+and fake news. In: European Conference on Information Retrieval. pp. 639–649.
+Springer (2021)
+21. Nakov, P., Da San Martino, G., Elsayed, T., Barr´on-Cede˜no, A., M´ıguez, R.,
+Shaar, S., Alam, F., Haouari, F., Hasanain, M., Mansour, W., et al.: Overview
+of the clef–2021 checkthat! lab on detecting check-worthy claims, previously fact-
+checked claims, and fake news. In: International Conference of the Cross-Language
+Evaluation Forum for European Languages. pp. 264–291. Springer (2021)
+22. Pfeiﬀer, J., Kamath, A., R¨uckl´e, A., Cho, K., Gurevych, I.: Adapterfusion: Non-
+destructive task composition for transfer learning. In: Merlo, P., Tiedemann, J.,
+Tsarfaty, R. (eds.) Proceedings of the 16th Conference of the European Chapter of
+the Association for Computational Linguistics: Main Volume, EACL 2021, Online,
+April 19 - 23, 2021. pp. 487–503. Association for Computational Linguistics (2021).
+https://doi.org/10.18653/v1/2021.eacl-main.39, https://doi.org/10.18653/v1/
+2021.eacl-main.39
+
+16
+Schlicht et al.
+23. Pfeiﬀer, J., R¨uckl´e, A., Poth, C., Kamath, A., Vuli´c, I., Ruder, S., Cho, K., Gurevych,
+I.: AdapterHub: A framework for adapting transformers. In: Proceedings of the
+2020 Conference on Empirical Methods in Natural Language Processing: System
+Demonstrations. pp. 46–54. Association for Computational Linguistics, Online (Oct
+2020). https://doi.org/10.18653/v1/2020.emnlp-demos.7, https://aclanthology.
+org/2020.emnlp-demos.7
+24. Pfeiﬀer, J., Vuli´c, I., Gurevych, I., Ruder, S.: MAD-X: An Adapter-Based
+Framework for Multi-Task Cross-Lingual Transfer. In: Proceedings of the 2020
+Conference on Empirical Methods in Natural Language Processing (EMNLP).
+pp. 7654–7673. Association for Computational Linguistics, Online (Nov 2020).
+https://doi.org/10.18653/v1/2020.emnlp-main.617, https://aclanthology.org/
+2020.emnlp-main.617
+25. Pfeiﬀer, J., Vuli´c, I., Gurevych, I., Ruder, S.: UNKs everywhere: Adapting mul-
+tilingual language models to new scripts. In: Proceedings of the 2021 Confer-
+ence on Empirical Methods in Natural Language Processing. pp. 10186–10203.
+Association for Computational Linguistics, Online and Punta Cana, Dominican
+Republic (Nov 2021). https://doi.org/10.18653/v1/2021.emnlp-main.800, https:
+//aclanthology.org/2021.emnlp-main.800
+26. Reimers, N., Gurevych, I.: Sentence-bert: Sentence embeddings using siamese
+bert-networks. In: Proceedings of the 2019 Conference on Empirical Methods in
+Natural Language Processing and the 9th International Joint Conference on Natural
+Language Processing (EMNLP-IJCNLP). pp. 3982–3992 (2019)
+27. R¨uckl´e, A., Geigle, G., Glockner, M., Beck, T., Pfeiﬀer, J., Reimers, N., Gurevych,
+I.: AdapterDrop: On the eﬃciency of adapters in transformers. In: Proceedings of
+the 2021 Conference on Empirical Methods in Natural Language Processing. pp.
+7930–7946. Association for Computational Linguistics, Online and Punta Cana, Do-
+minican Republic (Nov 2021). https://doi.org/10.18653/v1/2021.emnlp-main.626,
+https://aclanthology.org/2021.emnlp-main.626
+28. Schlicht, I.B., de Paula, A.F.M., Rosso, P.: UPV at checkthat! 2021: Mitigating
+cultural diﬀerences for identifying multilingual check-worthy claims. In: CLEF
+(Working Notes). CEUR Workshop Proceedings, vol. 2936, pp. 465–475. CEUR-
+WS.org (2021)
+29. Shaar, S., Hasanain, M., Hamdan, B., Ali, Z.S., Haouari, F., Nikolov, A., Kutlu, M.,
+Kartal, Y.S., Alam, F., Martino, G.D.S., Barr´on-Cede˜no, A., M´ıguez, R., Beltr´an,
+J., Elsayed, T., Nakov, P.: Overview of the CLEF-2021 checkthat! lab task 1 on
+check-worthiness estimation in tweets and political debates. In: CLEF (Working
+Notes). CEUR Workshop Proceedings, vol. 2936, pp. 369–392. CEUR-WS.org (2021)
+30. Singh, K., Lima, G., Cha, M., Cha, C., Kulshrestha, J., Ahn, Y.Y., Varol, O.:
+Misinformation, believability, and vaccine acceptance over 40 countries: Takeaways
+from the initial phase of the covid-19 infodemic. Plos one 17(2), e0263381 (2022)
+31. Stickland, A.C., Murray, I.: BERT and pals: Projected attention layers for eﬃcient
+adaptation in multi-task learning. In: ICML. Proceedings of Machine Learning
+Research, vol. 97, pp. 5986–5995. PMLR (2019)
+32. Sundararajan, M., Taly, A., Yan, Q.: Axiomatic attribution for deep networks. In:
+ICML. Proceedings of Machine Learning Research, vol. 70, pp. 3319–3328. PMLR
+(2017)
+33. ¨Ust¨un, A., Bisazza, A., Bouma, G., van Noord, G.: UDapter: Language adaptation
+for truly Universal Dependency parsing. In: Proceedings of the 2020 Conference on
+Empirical Methods in Natural Language Processing (Empirical Methods in Natural
+
+Multilingual Detection of Check-Worthy Claims using WL+AF
+17
+Language Processing). pp. 2302–2315. Association for Computational Linguistics,
+Online (Nov 2020), https://www.aclweb.org/anthology/2020.emnlp-main.180
+34. Uyangodage, L., Ranasinghe, T., Hettiarachchi, H.: Can multilingual transformers
+ﬁght the COVID-19 infodemic? In: Proceedings of the International Conference
+on Recent Advances in Natural Language Processing (RANLP 2021). pp. 1432–
+1437. INCOMA Ltd., Held Online (Sep 2021), https://aclanthology.org/2021.
+ranlp-1.160
+35. Vasileva, S., Atanasova, P., M`arquez, L., Barr´on-Cede˜no, A., Nakov, P.: It takes nine
+to smell a rat: Neural multi-task learning for check-worthiness prediction. In: Mitkov,
+R., Angelova, G. (eds.) Proceedings of the International Conference on Recent Ad-
+vances in Natural Language Processing, RANLP 2019, Varna, Bulgaria, September
+2-4, 2019. pp. 1229–1239. INCOMA Ltd. (2019). https://doi.org/10.26615/978-954-
+452-056-4 141, https://doi.org/10.26615/978-954-452-056-4_141
+36. Wolf, T., Debut, L., Sanh, V., Chaumond, J., Delangue, C., Moi, A., Cistac, P.,
+Rault, T., Louf, R., Funtowicz, M., Davison, J., Shleifer, S., von Platen, P., Ma, C.,
+Jernite, Y., Plu, J., Xu, C., Le Scao, T., Gugger, S., Drame, M., Lhoest, Q., Rush,
+A.: Transformers: State-of-the-art natural language processing. In: Proceedings of
+the 2020 Conference on Empirical Methods in Natural Language Processing: System
+Demonstrations. pp. 38–45. Association for Computational Linguistics, Online (Oct
+2020). https://doi.org/10.18653/v1/2020.emnlp-demos.6, https://aclanthology.
+org/2020.emnlp-demos.6
+37. Xue, L., Constant, N., Roberts, A., Kale, M., Al-Rfou, R., Siddhant, A., Barua,
+A., Raﬀel, C.: mt5: A massively multilingual pre-trained text-to-text transformer.
+In: Proceedings of the 2021 Conference of the North American Chapter of the
+Association for Computational Linguistics: Human Language Technologies. pp.
+483–498 (2021)
+
diff --git a/ztE5T4oBgHgl3EQfOA6e/content/tmp_files/load_file.txt b/ztE5T4oBgHgl3EQfOA6e/content/tmp_files/load_file.txt
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+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf,len=1436
+page_content='Multilingual Detection of Check-Worthy Claims  using World Languages and Adapter Fusion⋆  Ipek Baris Schlicht1,2 , Lucie Flek3 , and Paolo Rosso1  1 PRHLT Research Center, Universitat Polit`ecnica de Val`encia, Spain  2 DW Innovation, Germany  3 CAISA Lab, University of Marburg, Germany  {ibarsch@doctor,prosso@dsic}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='upv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='es, lucie.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='flek@uni-marburg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='de  Abstract.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' Check-worthiness detection is the task of identifying claims,  worthy to be investigated by fact-checkers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' Resource scarcity for non-  world languages and model learning costs remain major challenges for the  creation of models supporting multilingual check-worthiness detection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='  This paper proposes cross-training adapters on a subset of world languages,  combined by adapter fusion, to detect claims emerging globally in multiple  languages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' (1) With a vast number of annotators available for world  languages and the storage-eﬃcient adapter models, this approach is more  cost eﬃcient.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' Models can be updated more frequently and thus stay up-  to-date.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' (2) Adapter fusion provides insights and allows for interpretation  regarding the inﬂuence of each adapter model on a particular language.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='  The proposed solution often outperformed the top multilingual approaches  in our benchmark tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='  Keywords: Fact-checking · Checkworthiness Detection · Mutilingual ·  Adapters .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='  1  Introduction  There is an increasing demand for automated tools that support fact-checkers  and investigative journalists, especially in the event of breaking or controversial  news [11,19].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' Identifying and prioritizing claims for fact-checking, aka.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' check-  worthy (CW) claim detection, is the ﬁrst task of such automated systems [9].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='  This task helps guiding fact-checkers to potentially harmful claims for further  investigation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' CW claims, as shown in Table 1, are veriﬁable, of public interest  and may invoke emotional responses [20].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' Most studies in this area focus on  monolingual approaches, predominantly using English datasets for learning the  model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' Support for multilingualism has become an essential feature for fact-  checkers who investigate non-English resources [8].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='  Although transformers achieved competitive results on several multilingual ap-  plications [4,3] including CW detection [21,18], there are still two main challenges  in the CW task: (1) Because of the task complexity, there are a few publicly  ⋆ This paper is accepted at ECIR 2023.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='05494v1  [cs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='CL]  13 Jan 2023  2  Schlicht et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='  Table 1: An example of a check-worthy claim from CT21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='  Those who falsely claim Vaccines are 100% safe and who laugh at anti-vaxxers will be dependent on  those who refuse to tell the oﬃcial lies to say that wide-spread vaccination *is* critical.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' 23 die in  Norway after receiving COVID-19 vaccine: [URL] via [MENTION]  available datasets in multiple languages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' Updating a multilingual model to detect  even recently emerged claims requires data annotation and timely retraining.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='  Finding fact-checking experts to annotate samples would be hard, especially in  low-resourced languages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' (2) Storing standalone copies of each ﬁne-tuned model  for every supported language requires vast storage capacities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' Because of the  limited budgets of non-proﬁt organizations and media institutes, it would be  infeasible to update the models frequently.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='  World Languages (WLs) are languages spoken in multiple countries, while  non-native speakers can still communicate with each other using the WL as a  foreign language.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' English, Arabic and Spanish are examples of WLs 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' It would  appear that ﬁnding expert annotators for collecting samples in a WL is easier  than ﬁnding expert annotators for low-resourced languages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='  As a resource-eﬃcient alternative to fully ﬁne-tuning transformer models,  adapters [14,31] have been recently proposed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' Adapters are lightweight and  modular neural networks, learning tasks with fewer parameters and transferring  knowledge across tasks [14,31,22] as well as languages [24].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' Fine-tuned adapters  require less storage than fully ﬁne-tuned pre-trained models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='  In this paper, we propose cross-lingual training of datasets in WLs with  adapters to mitigate resource scarcity and provide a cost-eﬃcient solution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' We  ﬁrst train Task Adapters (TAs) [23] for each WL and incorporate an interpretable  Adapter Fusion (AF) [22] to combine WL TAs for an eﬀective knowledge transfer  among the heterogeneous sources.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='  Our contributions for this paper are summarized as follows 5:  – We extensively analyze the WL AF models on the multilingual CW claim  detection task and evaluate the models on zero-shot learning (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', the target  languages were unseen during training).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' We show that the models could  perform better than monolingual TAs and fully ﬁne-tuned models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' They also  outperformed the related best performing methods in some languages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' In  addition, zero-shot learning is possible with the WL AF models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='  – We construct an evaluation to quantify the performance of the models on  claims about global/local topics across the languages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' Our approach for  curating the evaluation set could be reused for the assessment of other  multilingual, social tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='  – We present a detailed ablation study for understanding the limitations of AF  models and their behavior on the CW task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='  4 https://bit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='ly/3eMIZ9q  5 We share our source code at https://bit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='ly/3rH6yXu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='  Multilingual Detection of Check-Worthy Claims using WL+AF  3  2  Related Work  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='1  Identifying Check-Worthy Claims  Early studies applied feature engineering to machine learning models and neural  network models to identify CW claims in political debates and speeches.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' Claim-  Buster [13,12] was one of the ﬁrst approaches using a Support Vector Machine  (SVM) classiﬁer trained on lexical, aﬀective feature sets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' Gencheva et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' [7]  combined sentence-level and contextual information from political debates for  training neural network architectures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' Lespagnol et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' [17] employed information  nutritional labels [6] and word embeddings as features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' Vasileva et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' [35] applied  multitask learning from diﬀerent fact-checking organizations to decide whether a  statement is CW.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' Jaradat et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' [15] used MUSE word embeddings to support  the CW detection task in English and Arabic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='  CheckThat!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' (CT) organized multilingual CW detection tasks since 2020 [2,21,18].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='  They support more languages every year and an increasing number of multilingual  systems have been submitted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' Schlicht et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' [28] proposed a model supporting  all languages in the dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' They used a multilingual sentence transformer [26]  and then ﬁne-tuned the model jointly on a language identiﬁcation task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' Similarly,  Uyangodage et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' [34] ﬁne-tuned mBERT on a dataset containing balanced  samples for each language.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' Recently, Du et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' [5] ﬁne-tuned mT5 [37] on the CW  detection task, jointly with multiple related tasks and languages by inserting  prompts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' All of the listed methods were limited to the languages they were  trained on.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='  Kartal and Kutlu [16] evaluated mBERT for zero-shot learning in English,  Arabic and Turkish, and observed the performance drop in cross-training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' A  more eﬀective method would be required for cross-lingual training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' Furthermore,  none of the approaches tackled the resource eﬃciency issue.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' In this paper, we use  adapters and train them only on WLs for resource eﬃciency and evaluate unseen  languages, leveraging AF to understand which target language in the dataset  beneﬁts from transferring knowledge from WLs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='2  Adapters  Adapters have been successfully applied to pre-trained models for eﬃcient ﬁne-  tuning to various applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' Early studies [14,22] used adapters for task  adaptation in English.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' Pfeiﬀer et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' [22] propose an AF module for learning to  combine TAs as an alternative to multi-task learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' Some researchers [33,24,25]  exploit language-speciﬁc adapters for cross-lingual transfer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' This paper builds  upon the works of [22,25].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' We exploit a cross-lingual training set to learn TAs  and then use AF to combine them eﬀectively and provide interpretability on  which source TAs are eﬃcient on the target language.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='  4  Schlicht et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='  Table 2: Statistics of CT21 and CT22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='  CT21  CT22  Split Total %CW Total %CW  ar  Train 3444  22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='15  2513  38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='28  Dev  661  40.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='09  235  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='55  Test  600  40.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='33  682  35.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='28  es  Train 2495  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='02  4990  38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='14  Dev  1247  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='74  2500  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='20  Test  1248  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='62  4998  14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='09  en  Train 822  35.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='28  2122  21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='07  Dev  140  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='86  195  22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='56  Test  350  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='43  149  26.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='17  tr Test  1013  18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='07  303  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='62  bg Test  357  21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='29  130  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='85  nl Test 666  47.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='45  Table 3: Statistics of Global and Local Top-  ics  CT21  CT22  Split  Total %CW Total %CW  ar Global 269  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='12  116  46.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='55  Local  40  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='5 es Global 1208  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='93  148  22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='97  Local 917  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='43  nl Global - 103  56.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='31  Local 15  46.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='67  en Global 349  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='44  14  28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='57  tr Global 887  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='91 bg Global 356  21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='35  25  32  3  Datasets  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='1  Task Datasets  We looked for multilingual datasets in WLs and other languages for the exper-  iments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' CT21 [29] and CT22 [18] are the only publicly available datasets that  meet this requirement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' CT21 includes English, Arabic, Turkish, Spanish, and  Bulgarian samples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' It deals mainly with Covid-19 events, except for the Spanish  samples, which focus only on politics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' Compared with CT21, CT22 also includes  samples in Dutch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' The English, Arabic, Bulgarian, and Dutch samples in the  dataset build on the corpora on Covid-19 [1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' The researchers collected new  samples in Turkish and Spanish.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' The Spanish samples were augmented with  CT21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='  The statistics of the datasets are shown in Table 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' English, Spanish and  Arabic are the WLs contained in the datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' Both datasets are imbalanced,  i,e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' CW samples are under-represented across the languages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' Although English  is considered a high-resource language, there are considerably fewer English  samples than samples in other languages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' Since some samples of the datasets  could overlap, we conducted our research experiments per dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='2  Topical Evaluation Dataset  Some countries are culturally dissimilar or might have diﬀerent political agendas,  thus CW topics might diﬀer among countries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' For example, while vaccination  was a globally CW topic throughout the COVID-19 pandemic, some COVID-19  myths were believed only by a few communities [30].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' An ideal multilingual system  should perform well on global as well as local topics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='  Global topics are the topics present in all languages in all datasets, while local  topics are present in only one language.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' We created dedicated datasets to evaluate  the performance of the WL models for identifying CW claims across global and  Multilingual Detection of Check-Worthy Claims using WL+AF  5  Adapter Fusion  WL1 Task Adapter  Multi-Head Attention  WL1 Language Adapter .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='  Target Language Adapter  Add & Norm  Add & Norm  WLn Task Adapter  Add & Norm  Feed Forward  WLn Language Adapter  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' 1: The architecture of the WL+AF models within a transformer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' WL+AF+LA  is the setup when the LAs (blocks with the dashed lines) are stacked into the task  adapters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='  local topics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' This evaluation dataset contains solely global and local topics and  was created as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' To learn topics across datasets, we ﬁrst translated the  datasets into English and encoded them with a sentence transformer [26].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' Second,  we learned a topic modeling on the training datasets in the WLs by using  BERTopic [10] to assign topics to test samples in all languages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' Test samples with  topics present in all WL languages were added as presumably global topics to the  evaluation set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' BERTopic labeled topics that are unrelated to the learnt topics  with -1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' To select samples with local topics, we chose the samples labeled with -1  from the evaluation and applied a new topic modeling on them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' Test samples  with topics that were not present in the test dataset of any other language (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=',  local topics) were added to the evaluation set for local topics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' The statistics of  the local and global evaluation sets are presented in Table 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='  4  Methodology  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='1  World Language Adapter Fusion  This section describes the WL+AF models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' The WL+AF models are transformers  containing additional modules called adapters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' During training, only the adapters  are trained and the weights of pre-trained model are frozen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' Therefore, it is a  parameter-eﬃcient approach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' We experiment with two types of WL+AF models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='  WL+AF is a standard setup for combining WL task adapters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' WL+AF+LA has  additional language adapters (LAs) [24] by stacking task adapters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' We illustrate  the architecture of the models in Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' The input of the architecture is a text  while the output is a probability score describing the check-worthiness of the  input.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='  6  Schlicht et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='  Transformer Encoder.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' To provide cross-lingual representations, we use mul-  tilingual BERT (mBERT) [4] and XLM-Roberta (XLM-R) [3]6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' Because the  transformers were previously used by the related studies [34,1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' Furthermore,  there are publicly available LAs for the transformers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' Before encoding text with  transformers, we ﬁrst clean it from URLs, mentions and retweets, then truncate  or pad it to 128 tokens.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='  Task Adapter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' The annotations might be aﬀected by the diﬀerent cultural  backgrounds and events across the countries, like the CW claims.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' Additionally,  some may have been created from journalists following manual fact-checking  procedures while others stem from crowd-sourcing [21,18] For these reasons, we  treat each WL dataset as a separate task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' Then, we obtain TAs by optimizing  on their corresponding WL dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' TAs consist of one down projection layer  followed by a ReLU activation and one up projection layer [23].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' The TA of each  WL is ﬁne-tuned on its corresponding dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='  Adapter Fusion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' To share knowledge from the diﬀerent TAs for predicting  samples in an unseen language or new topics, we need to combine them eﬀectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='  AF is a method for combining multiple TAs, and mitigating the common issues of  multi-task learning, such as catastrophic forgetting and complete model retraining  for supporting new tasks [22].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' AF consists of an attention module which learns  how to combine knowledge from the TAs dynamically.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' By analyzing the attention  weights of the AF, we could learn which source task adapter contributes more to  test predictions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' We combine the TAs trained on the WLs with an AF.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' Then, the  AF is ﬁne-tuned on mixed datasets of the WLs to use for the target languages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='  Language Adapter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' To learn CW claim detection from various cross-lingual  sources, we should ensure that the model does not learn a language classiﬁcation  task but learns how to identify CW claims.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' Therefore, we need to separate  language-speciﬁc knowledge from task-speciﬁc knowledge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' A recent study [24]  demonstrated that LAs achieved better results when transferring the knowledge  of a task performed in one source language into another language.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' To encode  language-speciﬁc information into the transformer model and to see the LAs  impact on the performance of the AF models, we use the LAs from Adapter  Hub [23].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' The architecture of the LAs is analog to those of the TAs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' However,  these LAs were pre-trained on the unlabeled Wikipedia [24] by using a masked  language model objective.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' While learning task-speciﬁc transformations with TAs,  each world LA is stacked on its corresponding TA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' The weights of the LAs are  kept frozen, so they are not learned again.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' During inference of the target task,  the source LA is replaced with the target LA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='2  Implementation Details  We download the pre-trained transformers from Huggingface [36].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' We ﬁne-tune  the TAs on English, Arabic, and Spanish training samples (WLs), and evaluate  the models for their capability of zero-shot learning by testing on the other  6 We use the base version of the model, which consists of 12 layers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='  Multilingual Detection of Check-Worthy Claims using WL+AF  7  languages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' As LAs for Arabic, English, Spanish and Turkish samples in the  dataset [24], we download the pre-trained LAs from Adapter Hub [23] for both  transformers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' However, a LA for Bulgarian and Dutch is not available in Adapter  Hub, therefore, we use the English LA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='  We use the trainers of AdapterHub [23] for both full ﬁne-tuning and adapter  tuning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' We set the number of epochs as 10 and train the models with a learning  rate of 1e-4 for CT21 and 2e-5 for CT227, and batch size of 16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' We use the best  models on the development set according to the dataset metrics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' We repeat the  experiments ten times using diﬀerent random seeds using an NVIDIA GeForce  RTX 2080.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='  5  Baselines  We compare the performance of the WL AF models against various baselines:  – Top performing systems: We chose the top-performing systems on CT21  and CT22 which used a single model for the multilingual CW detection instead  of containing language-speciﬁc models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' Schlicht et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' [28] is a runner-up 8  system on CT21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' The original implementation uses a sentence transformer and  the model was ﬁne-tuned on all the language datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' For a fair comparison,  we set the language identiﬁcation task to WLs and replaced the sentence  transformer with mBERT and XLM-R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' The state-of-the-art model on CT22 is  based on mT5-xlarge [5], a multi-task text-to-text transformer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' Like Schlicht  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', the model is ﬁne-tuned on all of the corpora by using multi-task  learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' Due to the limited computing resources, we couldn’t ﬁne-tune this  model on WLs alone.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' We report the results from [5].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='  – Fully ﬁne tuned (FFT) Transformers (on Single Language): We ﬁne-  tune the datasets on a single language of the WLs to evaluate the eﬃciency  of cross-lingual learning: AR+FFT, EN+FFT, and ES+FFT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' We also add  BG+FFT, ES+FFT, and NL+FFT as the baseline for zero-shot learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='  – Task Adapters (on Single Language): These baselines contain a task  adapter followed by a LA, a widely used setup for cross-lingual transfer learn-  ing with adapters [24]: AR+TA+LA, EN+TA+LA, ES+TA+LA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' Comparing  our model to these baselines can help understand whether cross-training with  WLs is eﬃcient.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='  – Other WL Models: We evaluate the AF models against a model containing  a task adapter trained on WLs (WL+TA).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' In addition to this baseline, to see  if we need a complex fusion method, we use WL+TA+LA+Mean, which takes  the average of the predictions by AR+TA, EN+TA and ES+TA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' Finally, we  analyze the adapter tuning on multiple WLs against the fully ﬁne tuning of  mBERT: WL+FFT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='  7 2e-5 gives better results on the development set of CT22  8 BigIR is the state of art approach, but there is no associated paper/code describing  the system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='  8  Schlicht et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='  Table 4: MAP scores for CT21 and F1 scores for CT22 of the CW detection in WLs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='  The bold indicates the best score and underline indicates the second best score.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' Overall  the AF models performed well on multiple languages while the performance of other  models are sensitive to the characteristics of the training set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='  CT21  CT22  ar  es  en  ar  es  en  avg  Du et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' [5] 62.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='8 57.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='1  51.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='9 -  mBERT  AR+FFT  50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='17 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
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+page_content='38  ES+FFT  41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='22 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
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+page_content='16  EN+FFT  51.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='63 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
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+page_content='01  AR+TA+LA  58.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='20 19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
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+page_content='04  ES+TA+LA  48.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='07 18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
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+page_content='86  EN+TA+LA  50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='81 40.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='81 21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='21 56.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='39 24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
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+page_content='46  WL+FFT  47.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='93 51.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='50 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
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+page_content='65  Schlicht et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' [28]  51.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='51 31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
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+page_content='50  WL+TA  53.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
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+page_content='37  WL+TA+LA+Mean 54.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
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+page_content='05  WL+TA+LA+Mean 59.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
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+page_content='59  WL+AF+LA  58.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
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+page_content='43  6  Results and Discussion  In this section, we present and analyze the results of the WL AF(+LA) models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='  We compare the models performance at CW detection for (1) WLs, (2) zero-shot  languages and (3) local and global topics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' Lastly, we compare the performance  of WL+AF and WL+AF+LA to investigate whether LA is eﬀective in model  performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='  As seen in Table 4, the models trained on single languages are able to perform  well for other WLs if only provided with training sets of considerable size, or  language of the training and test sets are same.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' Additionally, Schlicht et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' [28]  and WL+FFT were performing well only on CT22, overall, the AF models,  perform well for various languages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' Du et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' [5] outperformed the AF models  for Arabic and English samples of CT22, but it underperformed for the Spanish  samples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='  As shown in Table 5, the AF models achieve good results on target sets in  zero-shot languages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' It shows that the fusion of multiple sources with adapters  Multilingual Detection of Check-Worthy Claims using WL+AF  9  Table 5: MAP for CT21 and F1 for CT22 of the CW detection in zero-shot languages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='  The bold indicates the best score and underline indicates the second best score.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' The  AF models performed well, even outperformed WL+FFT and Schlicht et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' [28] and  some of the monolingual approaches in terms of average score.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='  CT21  CT22  tr  bg  tr  bg  nl  avg  Du et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' [5] 17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='3  61.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
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+page_content='21  Schlicht et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' [28]  25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='86 22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
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+page_content='55  53.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='75 24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='44 27.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='16  WL+TA  59.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='37 39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='72 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='60 66.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='14 35.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='98 43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='36  WL+TA+LA+Mean 63.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='65 32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='28 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='90  31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='27 19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='91 31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='40  WL+AF  57.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='46 46.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='86 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='73 59.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='12 40.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='83 43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='4  WL+AF+LA  61.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='74 41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='78 17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='77 63.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='88 37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='59 44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='55  could be beneﬁcial in knowledge transfer and is better than the other fusion  method WL+TA+LA+Mean.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' It is noteworthy that Du et al [5] was trained on  all samples of the training datasets and hence has no zero-shot learning capacity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='  Although Du et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' achieved a better performance on the Dutch samples, the  AF models could obtain similar results in other languages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' In terms of resource  eﬃciency, the AF models required less space than WL+FFT and mT5 for storing  new weights, as shown in Table 8, which make them more suitable than updating  mT5 for newsrooms with a limited budget.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='  We compare the performance of models trained on multiple WLs for identifying  CW claims about global or local topics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' We tested this experiment with the  evaluation set described in Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='2 in terms of F1 score.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' We take the average  10  Schlicht et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='  Table 6: F1 scores of the models on global topics for each dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' Adapter training is  more eﬀective than fully ﬁne-tuning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' Although WL+TA outperformed the AF models  in particular languages, at average the AF models performed better.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='  CT21  CT22  tr  es  ar  en  bg  es  ar  en  bg  nl  avg  WL+FFT  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
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+page_content='59  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='10  77.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='59 52.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
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+page_content='21  Schlicht et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' [28] 18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='15 17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='92 58.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='84 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='18  19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='75 81.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='81 48.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='12 28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='33 36.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='55 30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='34 34.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='70  WL+TA+LA  52.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='37 38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='09 61.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='01 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='58 38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='44 77.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='28 45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='47 22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='57 41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='31 45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='09 38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='52  WL+AF  45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='02 41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='57 61.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='51 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='36 36.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='23 79.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='14 44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='61 50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='96 40.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='58 43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='19 45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='62  WL+AF+LA  48.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='52 37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='44 61.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='79 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='38 28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='72 77.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='95 42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='84 44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='23 41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='09 43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='99 44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='00  Table 7: F1 scores of the models on local topics for each dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' The AF models show  similar results to WL+TA and outperformed WL+FFT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='  CT21 CT21  ar  es  nl  avg  WL+FFT  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='93  60.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='64 31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='11 30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='89  Schlicht et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' [28] 46.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='80  64.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='65 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='44 41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='96  WL+TA+LA  50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='88 61.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='65 38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='47 50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='33  WL+AF  48.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='15  62.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='01 34.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='38 48.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='18  WL+AF+LA  46.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='41  63.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='07 41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
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+page_content='21  Table 8: Number of training parameters and ﬁle size comparisons for the models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' mT5  is larger than mBERT and XLM-R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='  Model  Base Model Parameters Model Size  WL+FFT  mBERT  178 M  711.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='5 MB  XLM-R  278 M  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='1 GB  Schlicht et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' [28]  mBERT  179 M  716.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='3 MB  XLM-R  279 M  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='1 GB  TA & WL+TA+LA mBERT  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='5 M  6 MB  XLM-R  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='5 M  6 MB  AF  mBERT  22 M  87.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='4 MB  XLM-R  22 M  87.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='4 MB  LA  mBERT 147.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='78 MB  XLM-R 147.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='78 MB  mT5  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='7 B  15 GB  of the scores of the models coded with mBERT and XLM-R and present them in  Tables 6 and 7, respectively, for global and local topics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' Overall, the AF models  performed better than WL+FFT and Schlicht et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' [28] for both types.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' However,  WL+TA performed similarly to WL+AF+LA in predicting local statements in  Arabic samples in CT21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='  Last, we compare the performance of WL+AF and WL+AF+LA to investigate  whether LA is eﬀective in model performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' We computed the Fleiss Kappa  scores of the AF models for each experiment and language.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
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+page_content='52  (f) XLM-R  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' 2: The left images are topical relation graphs of CT21 (top left) and CT22 (bottom  left).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' In the graphs, the size of the nodes varies by the number of samples, and the edge  thickness depends on the overlapping topics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' x-axis of heatmaps shows task adapters,  y-axis shows the test samples in the diﬀerent languages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' (b), (c) attention heatmaps of  mBERT, (e), (f) attention heatmaps of XLM-R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' Topical distribution, and the sample  sizes of the training datasets impact the task adapters’ activations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' Especially XLM-R  TAs are more sensitive than mBERT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='63, which is a moderate agreement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' We further investigate the disagreements  where the kappa is below 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' The conﬂicts mainly occurred in the zero shot  languages and English, with the lowest CW samples on both datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' Since  sometimes WL+AF+LA is better than WL+AF and vice versa, we conclude  that LA is not eﬀective in our experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' The pre-trained LAs were trained on  the Wikipedia texts [24].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' Thus, they might miss the properties of social texts,  which are mostly noisy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='  7  Further Analysis  In this section, we present further analysis of the AF models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' We investigate AF  attentions and then apply an error analysis on the models’ predictions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='  Interpretation of the Fusion Attentions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' The AF models can provide an  interpretation of which source task adapter might be useful when transferring the  knowledge into the target dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' This kind of analysis would help a data scientist  at a newsroom on a decision on which WL should be collected for updating model  and managing new resources.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' To check the AF behavior on WL+TA+LA+AF,  we took the average of the softmax probabilities of the layer of each task adapter  in the fusion layer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' The higher probability means the more useful the task for  determining the label [22].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' In addition, to correlate the attention with the source  datasets, we created a graph displaying the topical relationship between source  es test  tr test  en test  ar test  bg test  ar train  es train  en traines test  en test  tr test  nl test  ar test  bg_test  ar train  es train  en train12  Schlicht et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='  Table 9: The CW claims predicted correctly by the WL+TA+AF, the examples are in  Spanish and Bulgarian.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' The order of the texts for each example: 1) Visualizations on  mBERT, 2) Visualizations on XLM-R 3) the red text is the translation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' The models  focus more on GPE (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' country names) than the other entity types.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' We colorized the  claims based on their integrated gradients [32].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='  ▁España ▁es ▁el ▁2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' o ▁país ▁de ▁la ▁UE ▁que ▁más ▁empleo ▁ha ▁creado ▁entre ▁las ▁mujeres .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' ▁Un ▁buen  ▁dato ▁sobre ▁el ▁que ▁seguire mos ▁trabajando .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' ▁Hay ▁que ▁combat ir ▁la ▁fem in ización ▁de ▁la ▁precari edad  , ▁reducir ▁el ▁paro ▁fem en ino ▁y ▁la ▁bre cha ▁salarial .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='  España es el 2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' º país de la UE que más empleo ha creado entre las mujeres .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' Un buen dato sobre el que seguiremos  trabajando .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' Hay que combatir la feminización de la precariedad , reducir el paro femenino y la brecha salarial .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='  Spain is the 2nd.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' or EU country that has created the most employment among women .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' A good data on which I will  continue mos working .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' The feminization of precarious age must be combated , female unemployment and the wage  gap must be reduced .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='  ▁Швеция ▁при ну ж дава ▁родителите ▁да ▁изпраща т ▁децата ▁си ▁на ▁училище .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' ▁Някои ▁се ▁страх уват  ▁децата ▁им ▁в ▁крайна ▁сметка ▁да ▁бъдат ▁от нети , ▁ако ▁от кажа т .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='  Швеция принуждава родителите да изпращат децата си на училище .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' Някои се страхуват децата им в крайна  сметка да бъдат отнети , ако откажат .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='  Sweden forces parents to send their children to school.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' Some fear their children will eventually be taken away if they  refuse.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='  Table 10: The performance of the AF model at predicting entity types in terms of  average F1 and the standard deviation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' The models could predict GPE more accurately  than the others.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='  Geo-political Entity Organization Number  People  F1 46.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='83 ± 17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='37  40.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='44 ± 18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='62  40.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='99 ± 22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='52 37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='88 ± 18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='83  and target sets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' In the graph, the nodes are the monolingual datasets;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' the edges  are the overlapped topics between the source and target dataset, weighted by  the percentage of the samples about the overlapped topic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' The size of nodes are  scaled according to sample size.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' Figure 2 shows the graph for both datasets and  the attention weights of mBERT and XLM-R task adapters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' Topical distributions  and source datasets’ size aﬀect which task adapter activates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' XLM-R TAs are  more sensitive to the source data size and topical relationship.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' For instance, the  Spanish tests in CT22 are weakly connected with the Arabic and English source  datasets, and the Spanish TA of XLM-R has less activation than the mBERT  TA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='  Error analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' Last, we analyze the misclassiﬁed/correctly classiﬁed samples  by both AF models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' As shown in Table 9, we noted that the AF model focuses  on geo-political entities (GPE).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' The models could categorize the claims with  GPE better than claims containing other type of entities as shown in Table 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='  The importance of the GPE could be learned from the WL corpus whose CW  samples have no negligible amount of these entities (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' %76 of CT21 and %77 of  CT22 Arabic source datasets are GPE).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' However, the models cannot predict the  claims requiring local context, especially in the zero-shot languages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' Moreover,  the models cannot identify the claims whose veracity can be changed to not CW  by time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' Some examples are shown in Table 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='  Training eﬃciency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' We measured the models’ training time for one epoch on  the datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' The TA training is on average 4 minutes less than the fully ﬁne  Multilingual Detection of Check-Worthy Claims using WL+AF  13  Table 11: The CW claims that are misclassiﬁed by the AF models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' The black texts  show claims in Turkish.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' The red texts are the translations, and the blue ones are the  explanation of the claims.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='  Bunu hep yazdım yine yazaca˘gım , Bakanların aileleri , annesi - babası tam kapsamlı sa˘glık tedavileri buna ( Estetik  dahil ) devlet b¨utcesinden kar¸sılanıyor da , SMA hastası ¸cocukların tedavisi i¸cin niye bir b¨ut¸ce olu¸sturulmuyor  [UNK] [UNK] # DevletSMAyıYa¸satsın  I’ve always written this and I will write it again.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' The families of the ministers, their mother-father full health  treatments (including Aesthetics) are covered by the state budget, but why isn’t a budget created for the treatment  of children with SMA [UNK] [UNK] # Let The State Live  Example of a CW claim that requires local context.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' SMA is a disease that aﬀects children, and the treatment of  SMA is a controversial issue in Turkey.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='  Koronavir¨us salgınında vaka sayısı 30 bin 021 [UNK] e ula¸stı # Corona # COVID # coronavirus  The number of cases in the coronavirus epidemic reached 30 thousand 021 [UNK] # Corona # COVID #  coronavirus  An example of a CW claim whose veracity could be changed by time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='  tuning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' However, the AF training without LAs lasts 3 minutes more, and the  training with LAs 9 minutes more than the training time of WL+FFT which  was approx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' 22 minutes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' The methods such as AdapterDrop [27] could speed up  the AF training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='  8  Conclusion and Future Work  In this paper, we investigated the cost eﬃcient cross-training of adapter fusion  models on world languages to detect check-worthiness in multiple languages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='  The proposed solution performs well on multiple languages, even on zero-shot  learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' Thanks to adapter fusion, the eﬀectiveness of the adapters on particular  languages was possible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='  The attention of some task adapters seems to depend on the topic and  sample distribution in the source dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' Ensuring a topical balance across world  languages appears to be important.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' Our error analysis results indicate that local  context is required to detect local claims.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' We recommend the usage of background  knowledge injection to detect local claims.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='  In the future, we would like to investigate the injection of background knowl-  edge in adapters and verify our results in additional domains (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' war), employing  more languages such as German and focusing on zero-shot learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='  Acknowledgements We would like to thank the anonymous reviewers, Joan  Plepi, Flora Sakketou, Akbar Karimi and Nico Para for their constructive feedback.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='  The work of Ipek Schlicht was part of the KID2 project (led by DW Innovation  and co-funded by BKM).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' The work of Lucie Flek was part of the BMBF projects  DeFaktS and DynSoDA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' The work of Paolo Rosso was carried out in the frame-  work of IBERIFIER (INEA/CEF/ICT/A202072381931 n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='2020-EU-IA-0252), XAI  Disinfodemics (PLEC2021-007681) and MARTINI (PCI2022-134990-2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='  14  Schlicht et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='  References  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' Alam, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Shaar, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Dalvi, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Sajjad, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Nikolov, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Mubarak, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Da San Martino,  G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Abdelali, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Durrani, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Darwish, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' : Fighting the covid-19 infodemic:  Modeling the perspective of journalists, fact-checkers, social media platforms,  policy makers, and the society.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' In: Findings of the Association for Computational  Linguistics: EMNLP 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' 611–649 (2021)  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' Barr´on-Cede˜no, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Elsayed, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Nakov, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Martino, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
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+page_content=', Hasanain, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
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+page_content=', Hamdan, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
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+page_content=', Shaar, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Ali, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' :  Overview of checkthat!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' 2020: Automatic identiﬁcation and veriﬁcation of claims  in social media.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
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+page_content=' Lecture Notes in Computer Science, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' 12260, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='  215–236.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
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+page_content=' Conneau, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Khandelwal, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Goyal, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Chaudhary, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Wenzek, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Guzm´an,  F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Grave, ´E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Ott, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Zettlemoyer, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Stoyanov, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
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+page_content=' In: Proceedings of the 58th Annual Meeting of the  Association for Computational Linguistics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
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+page_content=' 8440–8451 (2020)  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
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+page_content=', Chang, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
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+page_content=', Doran, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
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+page_content=') Proceedings of the 2019 Conference of the North American Chapter of  the Association for Computational Linguistics: Human Language Technologies,  NAACL-HLT 2019, Minneapolis, MN, USA, June 2-7, 2019, Volume 1 (Long and  Short Papers).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
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+page_content=' 4171–4186.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' Association for Computational Linguistics (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='  https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
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+page_content=' Du, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Gollapalli, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Ng, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' : Nus-ids at checkthat!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
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+page_content=' Working Notes of CLEF (2022)  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' Fuhr, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Giachanou, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Grefenstette, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Gurevych, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Hanselowski, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', J¨arvelin,  K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Jones, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Liu, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Mothe, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Nejdl, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Peters, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Stein, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
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+page_content=' SIGIR Forum 51(3), 46–  66 (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
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+page_content='3190588, https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
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+page_content=' Gencheva, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Nakov, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', M`arquez, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Barr´on-Cede˜no, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Koychev, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
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+page_content=', Angelova, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' (eds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=') Proceedings of the International Conference Recent Advances  in Natural Language Processing, RANLP 2017, Varna, Bulgaria, September 2 - 8,  2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' 267–276.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' INCOMA Ltd.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
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+page_content='26615/978-954-452-  049-6 037, https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='26615/978-954-452-049-6_037  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' Ginsborg, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Gori, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=': Report on a survey for fact checkers on covid-19 vaccines and  disinformation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
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+page_content=' rep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', European Digital Media Observatory (EDMO) (2021),  https://cadmus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
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+page_content=' Graves, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=': Understanding the promise and limits of automated fact-checking (2018)  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' Grootendorst, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=': Bertopic: Neural topic modeling with a class-based tf-idf proce-  dure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' arXiv preprint arXiv:2203.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='05794 (2022)  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' Hassan, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Adair, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Hamilton, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Li, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Tremayne, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Yang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Yu, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
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+page_content=', Arslan, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Li, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
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+page_content=' In: Proceedings of the  23rd ACM SIGKDD International Conference on Knowledge Discovery and  Data Mining, Halifax, NS, Canada, August 13 - 17, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
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+page_content=' 1803–1812.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
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+page_content='3098131  Multilingual Detection of Check-Worthy Claims using WL+AF  15  13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' Hassan, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Li, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Tremayne, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
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+page_content=' In: Bailey, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Moﬀat, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Aggarwal, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', de Rijke, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Ku-  mar, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Murdock, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Sellis, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Yu, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' (eds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=') Proceedings of the 24th  ACM International Conference on Information and Knowledge Management,  CIKM 2015, Melbourne, VIC, Australia, October 19 - 23, 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
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+page_content=' 1835–  1838.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' ACM (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
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+page_content='2806652, https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
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+page_content=' Houlsby, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Giurgiu, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Jastrzebski, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Morrone, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', de Laroussilhe, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Gesmundo,  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Attariyan, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Gelly, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=': Parameter-eﬃcient transfer learning for NLP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' In: ICML.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='  Proceedings of Machine Learning Research, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' 97, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' 2790–2799.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' PMLR (2019)  15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' Jaradat, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Gencheva, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Barr´on-Cede˜no, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', M`arquez, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Nakov, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=': ClaimRank:  Detecting check-worthy claims in Arabic and English.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' In: Proceedings of the 2018  Conference of the North American Chapter of the Association for Computational  Linguistics: Demonstrations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' 26–30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' Association for Computational Linguistics,  New Orleans, Louisiana (Jun 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='18653/v1/N18-5006, https:  //aclanthology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='org/N18-5006  16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' Kartal, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Kutlu, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=': Re-think before you share: A comprehensive study on  prioritizing check-worthy claims.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' IEEE Transactions on Computational Social  Systems (2022)  17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' Lespagnol, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Mothe, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Ullah, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' : Information nutritional label and word  embedding to estimate information check-worthiness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' In: Proceedings of the 42nd  International ACM SIGIR Conference on Research and Development in Information  Retrieval.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' 941–944.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' SIGIR’19, Association for Computing Machinery, New York,  NY, USA (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='1145/3331184.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='3331298, https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='  1145/3331184.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='3331298  18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' Nakov, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Barr´on-Cede˜no, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Martino, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Alam, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Struß, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Mandl, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=',  M´ıguez, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Caselli, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Kutlu, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Zaghouani, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Li, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Shaar, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Shahi, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=',  Mubarak, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Nikolov, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Babulkov, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Kartal, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Beltr´an, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
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+page_content=' lab on ﬁghting the covid-19 infodemic and fake news detection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
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+page_content=', Corney, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Hasanain, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Alam, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Elsayed, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Barr´on-Cede˜no,  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Papotti, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Shaar, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Martino, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
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+page_content=' pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' 4551–4558.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' ijcai.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='org (2021)  20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
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+page_content=', Da San Martino, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Elsayed, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Barr´on-Cedeno, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', M´ıguez, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=',  Shaar, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Alam, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Haouari, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Hasanain, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Babulkov, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' : The clef-2021  checkthat!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' lab on detecting check-worthy claims, previously fact-checked claims,  and fake news.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' In: European Conference on Information Retrieval.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' 639–649.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='  Springer (2021)  21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' Nakov, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Da San Martino, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
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+page_content=', Barr´on-Cede˜no, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', M´ıguez, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=',  Shaar, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Alam, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Haouari, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Hasanain, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Mansour, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' : Overview  of the clef–2021 checkthat!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
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+page_content=' pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' 264–291.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' Springer (2021)  22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' Pfeiﬀer, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Kamath, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', R¨uckl´e, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Cho, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Gurevych, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
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+page_content=' In: Merlo, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Tiedemann, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=',  Tsarfaty, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' (eds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=') Proceedings of the 16th Conference of the European Chapter of  the Association for Computational Linguistics: Main Volume, EACL 2021, Online,  April 19 - 23, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
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+page_content=' 487–503.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' Association for Computational Linguistics (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='  https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='18653/v1/2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='eacl-main.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='39, https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='18653/v1/  2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='eacl-main.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='39  16  Schlicht et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='  23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' Pfeiﬀer, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', R¨uckl´e, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Poth, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Kamath, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Vuli´c, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Ruder, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Cho, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Gurevych,  I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=': AdapterHub: A framework for adapting transformers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' In: Proceedings of the  2020 Conference on Empirical Methods in Natural Language Processing: System  Demonstrations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' 46–54.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' Association for Computational Linguistics, Online (Oct  2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='18653/v1/2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='emnlp-demos.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='7, https://aclanthology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='  org/2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='emnlp-demos.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='7  24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' Pfeiﬀer, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Vuli´c, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Gurevych, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Ruder, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=': MAD-X: An Adapter-Based  Framework for Multi-Task Cross-Lingual Transfer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' In: Proceedings of the 2020  Conference on Empirical Methods in Natural Language Processing (EMNLP).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='  pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' 7654–7673.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' Association for Computational Linguistics, Online (Nov 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='  https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='18653/v1/2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='emnlp-main.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='617, https://aclanthology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='org/  2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
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+page_content=', Vuli´c, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
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+page_content=' Reimers, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Gurevych, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
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+page_content=' In: Proceedings of the 2019 Conference on Empirical Methods in  Natural Language Processing and the 9th International Joint Conference on Natural  Language Processing (EMNLP-IJCNLP).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
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+page_content=' 3982–3992 (2019)  27.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' R¨uckl´e, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Geigle, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Glockner, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Beck, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Pfeiﬀer, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Reimers, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
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+page_content='  7930–7946.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' Association for Computational Linguistics, Online and Punta Cana, Do-  minican Republic (Nov 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
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+page_content=' Schlicht, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', de Paula, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Rosso, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=': UPV at checkthat!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
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+page_content=' In: CLEF  (Working Notes).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' CEUR Workshop Proceedings, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' 2936, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' 465–475.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
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+page_content='org (2021)  29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' Shaar, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Hasanain, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Hamdan, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Ali, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Haouari, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Nikolov, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Kutlu, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=',  Kartal, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Alam, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Martino, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Barr´on-Cede˜no, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', M´ıguez, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Beltr´an,  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Elsayed, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Nakov, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
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+page_content=' 369–392.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
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+page_content='org (2021)  30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' Singh, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Lima, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Cha, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Cha, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Kulshrestha, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Ahn, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Varol, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
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+page_content=' Stickland, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Murray, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=': BERT and pals: Projected attention layers for eﬃcient  adaptation in multi-task learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' In: ICML.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' Proceedings of Machine Learning  Research, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' 97, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' 5986–5995.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' PMLR (2019)  32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' Sundararajan, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Taly, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Yan, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=': Axiomatic attribution for deep networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' In:  ICML.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' Proceedings of Machine Learning Research, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' 70, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' 3319–3328.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' PMLR  (2017)  33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' ¨Ust¨un, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Bisazza, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Bouma, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', van Noord, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=': UDapter: Language adaptation  for truly Universal Dependency parsing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' In: Proceedings of the 2020 Conference on  Empirical Methods in Natural Language Processing (Empirical Methods in Natural  Multilingual Detection of Check-Worthy Claims using WL+AF  17  Language Processing).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
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+page_content=' 2302–2315.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
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+page_content=' Uyangodage, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Ranasinghe, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Hettiarachchi, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
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+page_content=' 1432–  1437.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
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+page_content=', Held Online (Sep 2021), https://aclanthology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
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+page_content='160  35.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' Vasileva, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Atanasova, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', M`arquez, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Barr´on-Cede˜no, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Nakov, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
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+page_content=' In: Mitkov,  R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Angelova, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' (eds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=') Proceedings of the International Conference on Recent Ad-  vances in Natural Language Processing, RANLP 2019, Varna, Bulgaria, September  2-4, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
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+page_content=' 1229–1239.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
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+page_content=' (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='26615/978-954-  452-056-4 141, https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='26615/978-954-452-056-4_141  36.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' Wolf, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Debut, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Sanh, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Chaumond, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Delangue, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Moi, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Cistac, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=',  Rault, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Louf, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Funtowicz, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Davison, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Shleifer, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', von Platen, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Ma, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=',  Jernite, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Plu, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Xu, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Le Scao, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Gugger, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Drame, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Lhoest, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Rush,  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=': Transformers: State-of-the-art natural language processing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' In: Proceedings of  the 2020 Conference on Empirical Methods in Natural Language Processing: System  Demonstrations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' 38–45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' Association for Computational Linguistics, Online (Oct  2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='18653/v1/2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='emnlp-demos.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='6, https://aclanthology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='  org/2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='emnlp-demos.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='6  37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' Xue, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Constant, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Roberts, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Kale, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Al-Rfou, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Siddhant, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Barua,  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=', Raﬀel, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=': mt5: A massively multilingual pre-trained text-to-text transformer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='  In: Proceedings of the 2021 Conference of the North American Chapter of the  Association for Computational Linguistics: Human Language Technologies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content=' pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}
+page_content='  483–498 (2021)' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE5T4oBgHgl3EQfOA6e/content/2301.05494v1.pdf'}